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Microwave effects on snail neuron activity: A statistical analysis

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Microwave effects on snail neuron activity: A statistical analysis
Ginsburg, Kenneth Stacey, Ph.D.
University of Illinois at Chicago, 1987
UMI
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MICROWAVE EFFECTS ON SNAIL NEURON ACTIVITY:
A STATISTICAL ANALYSIS
BY
KENNETH STACEY GINSBURG
B.A., University of Chicago
M.S., University of Illinois at Chicago
THESIS
Submitted in partial fulfillment of the requirements
for the degree of Doctor of Philosophy in Bioengineering
in the Graduate College of the
University of Illinois at Chicago, 1987
Chicago, Illinois
THE UNIVERSITY OF ILLINOIS AT CHICAGO
The Graduate College
OCTOBER 15, 1987
I hereby recommend that the thesis prepared under my supervision by
KENNETH STACEY GINSBURG
entitled
MICROWAVE EFFECTS ON SNAIL NEURON ACTIVITY:
A STATISTICAL
ANALYSIS
be accepted in partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
In Charge of Thesis
Recommendation concurred in
Committee
Final Examination
UNIVERSITY
ILLINOIS
AT
CHICAGO
0617 fln. 1/87
DEDICATION
To Spike, whatever he may become.
And to Spike's mother.
And to all who hold that every person has dignity, beauty, and worth.
ACKNOWLEDGMENT
This work was directed by Drs. James C. Lin and William D. O'Neill.
I thank them for their many contributions, but especially the following:
Dr. Lin provided all equipment and materials that I needed, and
also arranged my financial support.
He guided me carefully into the
problems of microwave biological effects.
To whatever extent my treat­
ment of the literature is reasoned and balanced, credit should redound
to Dr. Lin.
Finally, every graduate student needs a manager to help
him/her to organize their effort, and to keep the overall meaning of the
work in clear view.
In this regard, Dr. Lin was superb.
Dr. O'Neill introduced me to this project, but his influence has a
longer history.
ground I needed.
He gave me essentially all of the statistical back­
With his direction, I was able to turn what seemed at
first to be esoterica into things that I could observe and test.
But at
least as valuable as this have been the consistency of his time commit­
ment and personal support.
I am grateful to the other members of my committee, Dr. Christopher
Comer, Dr. Gyan Agarwal, and Dr. Emmanuel Pollack, not only for their
careful reading of my work, but for asking questions that I will contin­
ue to think about.
Ms. Julie Furlong designed the data acquisition and reduction soft­
ware, and conducted several pilot analyses.
V
Mr. Aaron Field built new recording and playback preamplifiers for
this project.
microwave.
He has done a study similar to this one, but using pulsed
In doing this by his own hand, he provided essential confir­
mation that the preparation, recording, and analysis techniques were
stable and free of artifacts or idiosyncrasies.
Previous to starting this project, I worked in the laboratory of
Dr. Michael Levine, where I did my MS thesis.
Although Dr. Levine was
not involved in my PhD project, his beneficial
influence on my develop­
ment remains significant and will be remembered.
KSG
vi
SUMMARY
Weak microwave (MW) fields have been reported to affect nervous
system activity.
Effects due to increased thermal energy have been
observed .frequently, but the question persists as to whether there are
also nonthermal effects.
Nonthermal MW effects can be sought isolated
from thermal effects if a suitable physiological variable is studied,
and if temperature is held strictly constant during irradiation.
In
addition, the experiments and the statistical analysis have to be
designed to ensure a reliable demonstration.
This is a statistical study of whether CW (continuous wave) MW
energy at 2*»50MHz affects ongoing activity of neurons in the snail H.
Aspersa at constant temperature.
Action potentials (APs) of spontane­
ously active neurons were recorded continuously over periods of two to
three hours, with MW applied during the middle one-third of each period.
Experiments done with specific absorption rates (SAR) of 12.5mW/g
(typical
in previous work) and 125mW/g were compared with control exper­
iments which were identical except that no MW was given.
For the pur­
pose of statistical analysis, eleven MW experiments and six control
experiments were completed on identified neurons of types F1 and E6.
Four MW and two control experiments were done on additional neurons
which were not identified positively.
Also, five experiments in which
the temperature was deliberately changed were done, two on E6 neurons,
two on Fl, and one on an unidentified cell.
vi i
At intervals during each experiment, the transmembrane input resis­
tance and time constant were measured.
Input resistances were measured
on additional neurons besides the above, both identified and unidentifed, whose AP patterns were not studied.
Resistances measured before,
during, and after MW irradiation were expressed as fractional changes,
and compared with changes measured after comparable times in control
experiments.
The resistance of MW irradiated cells tended to increase,
while the resistance of untreated cells tended to decrease.
The differ­
ence grew gradually, not becoming significant (by two sample t and MannWhitney tests) until after the period of MW exposure.
The effect was
not significant for a group consisting only of neurons exposed to
125mW/g.
Similar tests on the time constant revealed no significant MW
effect.
Neuron activity has a dual nature.
described as a stochastic point process.
On the one hand, it can be
In this view, all the informa­
tion is contained in the interspike intervals (IS1).
On the other hand,
neuron activity evolves in time.
The descriptive statistics of the ISIs were studied first, using
the histogram and the serial correlogram.
Changes in the interval his­
togram were tracked by comparing histograms of data recorded during and
after MW irradiation against against histograms from pre-exposure con­
trol data, using a x 2 goodness of fit test.
In control experiments,
histograms were compared for data recorded for periods and at times cor­
responding with MW exposure.
The interval histogram of all cells,
whether or not exposed to MW, underwent severe variations which could
not be described properly with the x 2 statistic.
Thus the histogram
analysis could not demonstrate whether a MW effect occurred.
vi i i
The serial correlogram of intervals was calculated from continuous
data segments which matched as closely as possible the segments used in
the histogram analysis.
Each correlogram was characterized using a x J
statistic which measured the deviation of its frequency spectrum from a
flat spectrum, which would represent a point process with uncorrelated
intervals.
During the course of an experiment, the character of the
correlogram described by this statistic changed to a greater or lesser
degree.
Two criteria were devised to determine whether the change was
significant.
Each experiment was considered a binomial trial
changes could succeed or fail to meet a criterion.
in which
The serial correlo­
gram was more likely to change in MW experiments than in control experi­
ments, but the effect was of marginal significance.
Time dependencies were described using six features extracted from
the AP data.
The first two features were the means and standard devia­
tions of intervals.
To get the remaining four features, a pure integra­
tor model, as previously proposed in our laboratory, was used to esti­
mate a synaptic or leak induced input current.
The input current
parameter of the model compactly describes AP generation.
It is a ran­
dom process with a mean greater than zero, which pushes the intracellu­
lar voltage from minimum to threshold, at which time an AP is fired.
To
estimate the input current, the minimum of the previous AP, the thresh­
old of the current AP, and the interval from previous to current AP
(ISI) were extracted from the intracellular voltage record and treated
as random variables.
The advantage of postulating the input current parameter is that it
exists continuously in time.
It was estimated recursively as an explic­
ix
it function of time, and thereafter treated as an experimental variable.
The four features taken from the input current were its mean, standard
deviation, and correlation properties.
The correlation property was
expressed in two autoregressive (AR) parameters.
The six time-dependent AP features (mean and SD of ISIs, mean, SD,
and two AR parameters of input current) were studied independently, each
in two ways.
First, each feature was estimated from data recorded
before, during, and after MW irradiation (the same data segments used in
the histogram analysis), assuming a steady state in each condition.
Fractional changes that occurred during corresponding conditions in MW
and control experiments were compared using two sample tests, just as
was done for the input resistance data.
In this analysis, no feature
was significantly affected by MW.
Secondly, each feature was estimated as an explicit function of
time using a window which moved through an experimental record.
For
each experiment, each feature was regressed on an indicator variable
representing the condition (on or off) of MW exposure, actual or sham.
An F-ratio test was applied to show whether the indicator influenced a
feature significantly.
As with the serial correlograms, the signifi­
cance judgments in different experiments were treated as outcomes in
binomial trials.
Features of AP intervals and the input current changed
in a greater proportion of exposed neurons, than of control only neu­
rons.
These effects were significant only for the mean interval and the
ARi parameter of the input current.
Even in these cases, the signifi­
cance depended on the particular model tested, and the direction of
effect was not consistent across cells.
Models proposed in the literature for MW effects due to nondissipa
tive mechanisms involve coherent resonant excitation of molecules.
Through nonlinearity, amplification, or cooperativity, excited states
could conspire to exert physiological effects, such as transfers of gat
ing charges, which could cause conformational changes in membrane macro
molecules (ion channels).
These could in turn trigger or change the
probabilities of APs.
The results of the present study do not demonstrate a specific
reliable and repeatable MW effect.
To evoke a nondissipative effect
would require careful choice of the irradiation regime to match and
couple into the particular mechanism.
Although it is possible that the
conditions set in this study were simply incorrect, they were chosen
with careful attention to previous studies which reported effects.
Assuming a good choice of conditions, a nondissipative mechanism
should be expected to operate coherently, and repeated consistent demon
strations of an effect should be possible.
This study provides no such
specific support for the existence of nondissipative mechanisms.
The diverse effects of MW on input resistance, time constant,
interval correlograms, and time-dependent AP properties which were seen
need to be explained.
These seem most likely to reflect an overall
degeneration or disruption of the health of exposed preparations.
Espe
cially likely is a degeneration of transmembrane ion channel proteins.
This explanation is plausible partly because the observed effects were
not reversible.
Instabilities could have been induced by highly local­
ized heating, particularly of membrane or protein associated water.
This may have occurred despite careful and successful control of the
grossly sensed temperature.
Changes in input resistance and time constant of neurons recorded
while temperature was changed, without MW exposure, provided assurance
that the system temperature was controlled adequately.
It was shown
that temperature control within ±0.3°C was sufficient to prevent contam­
ination of data from MW experiments by gross temperature changes.
If the system temperature had changed, rapid, reversible thermal
effects could have occurred, as heat dissipated at the sites of interac­
tion would have been insufficiently absorbed in the surroundings.
Indeed, when temperature was changed purposely by a sufficient amount,
reversible effects were readily evident in the interval histograms,
despite severe overall nonstationarities.
Also, the time dependent AP
features were reliably and significantly influenced by temperature.
However, no systematic effect on the serial correlograms was discerned.
To find no evidence for coherent nondissipative MW effects, and to
attribute the effects actually seen to degeneration contingent on highly
localized heating is not to dismiss MW interactions as artifact or
error.
Appropriately induced and controlled, MW effects may yet be dem­
onstrated which have the coherency and repeatability necessary to make
MW a useful biophysical tool.
xi i
CONTENTS
DEDICATION
iii
ACKNOWLEDGMENT
iv
SUMMARY
vi
CHAPTER
PAGE
I.
INTRODUCTION
Microwave Biological Effects
Microwave Absorption by Tissues and its Consequences ....
Specificity of Microwave Effects
Neurophysiological and Allied Microwave Phenomena
Mechanisms for Nondisspative Microwave Interaction
Biophysical Considerations
Electromagnetic Fields and Cellular Calcium
Temperature Dependencies
Analysis of Neuron Activity
Descriptive Statistics of Intervals
Modeling of Action Potential Generation
Relationship of Interval and Temporal Statistics ....
Design of the Present Study
Choice of Experimental Subject
Choice of Experimental Variables
Temperature Control
Exposure Regime
Testing the Hypothesis that Microwave Does not Affect
Neuron Activity
1
1
2
5
7
14
15
17
19
20
21
22
25
26
26
27
27
29
II.
METHODS
Experimental
Preparation and Recording
Microwave Irradiation
Experimental Procedure
Temperature control
Statistical
Selection and Editing of Data
Data Reduction
31
31
31
39
39
A1
47
47
48
III.
MICROWAVE EFFECTS ON INPUT RESISTANCE AND TIME CONSTANT .... 51
IV.
MICROWAVE EFFECTS ON NEURON ACTIVITY
Evident Features of the Data
Features of the Action Potential Records
30
64
64
64
Features of Reset, Threshold and Interspike Interval . . 73
Descriptive Statistics of Interspike Intervals
80
Interspike Interval Histograms
80
Serial correlograms of Interspike Intervals
97
Effects on Time-dependent Action Potential Properties . . 115
Effects on the Mean and Standard Deviation of
Intervals
116
Steady State Case
116
Time Dependent Case
118
Effects on the Properties of the Input Current .... 130
Steady State Case
13**
Time Dependent Case
136
Overall tests for Microwave Effects on Time-Dependent
Properties
150
V.
VI.
TEMPERATURE EFFECTS; COMPARISON WITH MICROWAVE EFFECTS ...
Evident Features of the Data
Resistance and Time Constant
Descriptive Statistics of Intervals
Interval Histogram
Serial Correlogram
Effects on Time-dependent Action Potential Properties . .
Effects on the Mean and Standard Deviation of
Intervals
.
Effects on the Properties of the Input Current ....
170
17^
CONCLUSIONS
180
APPENDIX
A.
USE OF ONE MOLAR POTASSIUM CHLORIDE FILLED ELECTRODES
Introduction
Passive properties of Electrodes
Results
Discussion
Recording quality
156
157
161
l6i»
16A
167
170
PAGE
186
186
187
187
192
192
B.
EMPIRICAL THRESHOLD ESTIMATION
19^
C.
CALCULATIONS AND TESTS FOR INTERVAL STATISTICS
197
Interval histograms; comparison using a Chi-squared test . .
Tests on the Serial Correlogram of Intervals
D.
ESTIMATION AND VERIFICATION OF THE INTEGRATOR MODEL
Weighted Least Squares Estimation
197
199
205
205
xiv
Forgetful Recursive Weighted Least Squares Estimation
E.
...
TESTING TIME-DEPENDENT ACTION POTENTIAL PROPERTIES FOR EFFECTS
Time Dependent Measure of Mean and Variance of Intervals . .
Properties of the Input Current
Interpolation and Uniform Resampling
Characterization of the Input Current
Testing the Time-dependent Signals for Microwave Effects . .
F.
MICROWAVE DOSIMETRY
208
21 i+
21A
216
216
220
222
227
REFERENCES
230
VITA
237
XV
LIST OF TABLES
TABLE
PAGE
1.
LIST OF EXPERIMENTS
. . . 48
2.
MW EFFECT ON FRACTIONAL CHANGE OF INPUT RESISTANCE:
3.
MW EFFECT ON INPUT RESISTANCE:
T-TESTS . . 55
MANN-WHITNEY TESTS
MW EFFECT ON FRACTIONAL CHANGE IN TIME CONSTANT:
57
T-TESTS
. . . 6l
5.
MW EFFECT ON TIME CONSTANT:
MANN-WHITNEY TESTS
62
6.
HISTOGRAM x 2 VALUES, MW AND CONTROL EXPERIMENTS
89
7.
x 2 VALUES, RAW AND ADJUSTED, IDENTIFIED NEURONS
95
8.
x 2 VALUES, RAW AND ADJUSTED, UNIDENTIFIED NEURONS
96
9.
TESTS O c HO:
INTERVALS ARE NOT SERIALLY CORRELATED (MW) . . .
10.
TESTS OF HO:
(CONTROL)
INTERVALS ARE NOT SERIALLY CORRELATED
107
108
11.
MW EFFECT ON THE SIGNIFICANCE OF CORRELOGRAM x 2 STATISTIC H
12.
CHANGES IN THE VALUE OF CORRELOGRAM x 2 STATISTIC H
112
13-
MW EFFECT ON THE VALUE OF CORRELOGRAM x 2 STATISTIC H
113
ll».
MW EFFECT ON MEAN INTERSPIKE INTERVAL (STEADY STATE) . . . . .
117
15.
MW EFFECT ON SD OF INTERSPIKE INTERVALS (STEADY STATE) . . . .
118
16.
ANALYSIS OF TIME DEPENDENT MODELS FOR MEAN AP INTERVAL . . . .
128
17.
ANALYSIS OF TIME DEPENDENT MODELS FOR SD OF AP INTERVAL
129
18.
MW EFFECT ON MEAN OF INPUT CURRENT . (STEADY STATE)
19.
MW EFFECT ON SD OF INPUT CURRENT (STEADY STATE)
20.
MW EFFECT ON AR1 COEFFICIENT OF INPUT CURRENT (STEADY STATE) .
135
21.
MW EFFECT ON AR2 COEFFICIENT OF INPUT CURRENT (STEADY STATE) .
136
.
...
110
Mk
. .'
135
x vi
22.
ANALYSIS OF TIME DEPENDENT MODELS FOR MEAN INPUT CURRENT ...
U6
23.
ANALYSIS OF TIME DEPENDENT MODELS FOR SD OF INPUT CURRENT
..
ll»7
2k.
ANALYSIS OF TIME DEPENDENT MODELS FOR AR1 OF INPUT CURRENT . .
148
25.
ANALYSIS OF TIME DEPENDENT MODELS FOR AR2 OF INPUT CURRENT . .
T»9
26.
TESTS of HO: MW DID NOT AFFECT ISI OR CURRENT (STATIC MODEL) .
I52
27.
TESTS of HO: MW DID NOT AFFECT ISI OR CURRENT (DYNAMIC
MODEL)
153
HISTOGRAM x 2 VALUES, TEMPERATURE STUDIES
168
*28.
29.
TEMPERATURE EFFECTS ON AP INTERVALS AND INPUT CURRENT
....
179
xv i i
LIST OF FIGURES
FIGURE
PAGE
1.
Recording chamber and waveguide arrangement
2.
Schematic of data recording system
38
3.
Performance of the temperature control system
^2
I*.
Continuous temperature records from representative
experiments
J»6
Input resistance and time constant responses of example
neurons
52
6.
Time course of input resistance; tests for MW effect
58
7.
Time course of time constant; tests for MW effect
63
8.
Segments of raw AP data; experiment A0219&, neuron E6,
12.5mW/g
65
Segments of raw AP data; experiment A02157. neuron Fl,
12.5mW/g
67
10.
Segments of raw AP data; experiment A09106, 125mW/g
68
11.
Experiment with an apparently reversible MW effect (I)
70
12.
Data which appeared to show a reversible MW effect (II)
13.
MW exposure at 12.5mW/g; experiment A03286, neuron Fl
7k
H.
MW exposure at 12.5mW/g; experiment A02056, neuron E6
75
15.
MW exposure at 12.5mW/g; experiment A02157. neuron Fl
77
16.
MW exposure at 12.5mW/g; experiment A02196, neuron E6
78
17.
MW exposure at 125mW/g; experiment A03177• neuron E6
79
18.
Interspike interval histograms, A03286(F1), 12.5mW/g
82
19-
Interspike interval histograms, A02056(E6), 12.5mW/g
8^
20.
Interspike interval histograms, A02157(F1), 12.5mW/g
85
5.
9.
.... 71
xv i i i
21.
Interspike interval histograms, A02196(E6), 12.5mW/g
86
22.
Interspike interval histograms, A03177(E6), 125mW/g
87
23.
Interspike interval histograms, A03117(E6), control only .... 88
24.
Histograms, A02196(E6), means and variances standardized .... 93
25.
Histograms, A03117(E6), means and variances standardized . ... 94
26.
Serial correlogram of interspike intervals, A03286(F1),
12.5mW/g
99
Serial correlogram of interspike intervals, A02056(E6),
12.5mW/g
100
Serial correlogram of interspike intervals, A02157(F1),
12.5mW/g
102
Serial correlogram of interspike intervals, A02196(E6),
12.5mW/g
10;
Serial correlogram of interspike intervals, A03177 (E6),
125mW/g
105
31.
MW effects on mean and SD of ISI
121
32.
MW effects on mean and SD of ISI (static model; II)
122
33*
MW effects on mean and SD of ISI (dynamic model; I)
12^+
3*4.
MW effects on mean and SD of ISI (dynamic model; II)
125
35.
Estimation of input current model, A02056(E6), 12.5mW/g
. . .
131
36.
Estimation of input current model, A02157(F1), 12.5mW/g
. . .
132
37.
Predicted instantaneous effects on input current, A03286(F1) .
138
38.
Predicted instantaneous effects on input current, A02196(E6) .
139
39*
Predicted instantaneous effects on input current, AO91O6(N0
ID)
140
40.
Predicted instantaneous effects on input current, B02196(E6) .
141
41.
Predicted effects on dynamics of input current, A03286 (F1) . .
142
42.
Predicted effects on dynamics of input current, A02196(E6) . .
143
43.
Predicted effects on dynamics of input current, A09106(N0
ID)
144
Predicted effects on dynamics of input current, B02196(E6) . .
145
27.
28.
29.
30.
44.
(static model; I)
xix
45.
Rapid reversible response to +2.0°C steps, A03l66(E6)
46.
Contrast between temperature and MW effects, neuron
A05206(F1)
....
158
160
47.
Temperature effects on input resistance and time constant
48.
Interval histograms, A02117(F1), +0.5 9 C steps
165
49.
Histograms, A03126(F1), -2.0°C then -4.5°C step
166
50.
Interval histograms, A03166(E6) +2.0°C steps
169
51.
Effects on mean and SD of ISI, A03126(F1), +2.0°C steps
52.
Effects on mean and SD of ISI, A09106(NC) ID), -3-4°C step
. .
173
53.
Effects on input current, A03126 (F1), +2.0°C step (static) . .
175
54.
Effects on input current, A03126 (F1), +2.0°C step (dynamic)
.
176
55«
Effects on input current, A09106(N0 ID), -3.4°C (static) . . .
177
56.
Effects on input current, AO91O6(N0 ID), -3.4°C (dynamic)
. .
178
57.
Transient responses of 1.0M and 2.5M KC1 filled electrodes . .
188
58.
Low frequency responses of 1.0M and 2.5M KC1 electrodes
. ..
190
59-
Deviation of electrodes from linear resistance behavior
. . .
191
60.
Recording quality of 1.0M and 2.5M KC1 filled electrodes . . .
193
61.
Detection of action potential threshold and reset
195
62.
Operation of the test for a renewal process of intervals (I) .
202
63.
Operation of the test for a renewal process of intervals
(II)
203
Demonstration of forgetful weighted least squares estimation .
212
64.
..
. . .
162
172
1
Chapter I
INTRODUCTION
1.1
MICROWAVE BIOLOGICAL EFFECTS
Microwave (MW) biological effects have been observed at levels from
microscopic anatomy through ecology and behavior.
The range of observa­
tions has been reviewed comprehensively by Adey (1981).
Microwave bioeffects will be subtle compared with effects of ioniz­
ing radiations.
From a microscopic viewpoint, gross disruptions of
physical structure are out of the question:
a photon of MW radiation
does not have enough energy (h^ = 1.62 x 10~ J4 joule at 2.^5 GHz) sub­
stantially to perturb a particle, which has a thermal energy ( 3 /2kT;
three degrees of freedom) of 6.21 x 10~ 21 joule at 27°C (Adey, 1981).
Nonetheless, energy absorbed from a MW source will
internal energy of a system.
increase the
Some of this energy will be dissipated as
heat, and heating is the basis for a number of observed MW effects.
However, biological systems could also be susceptible to MW through
nondissipative interaction mechanisms.
This follows from the fact that
biological systems are organized to support highly directed transfers of
small amounts of energy.
Examples at the cellular level
include sensory
transduction, action potential propagation, and induction of enzyme cas­
cades.
Also included are changes in membrane fluidity and organization,
such as occur in cell fusion, endocytosis, and secretion.
Mobilization
and channeling of small amounts of absorbed MW energy through processes
similar to these could lead to detectable effects (Frohlich, 1980).
Biological energy transduction processes operate with very high
signal to noise ratios, and discriminate rigorously between appropriate
and inappropriate stimuli.
In contrast, if thermal effects are exclud­
ed, many MW responses seem to be buried in noise, and fine discriminato­
ry abilities are not apparent.
Microwave seems therefore not likely to
act agonistically to, say, a sensory stimulus.
Possibly MW responses which have so far been subtle would become
robust and unmistakeable, if particularly effective combinations of
irradiation frequency, intensity, and modulation, not yet discovered,
were tried.
It seems more reasonable, though, to expect MW mainly indi­
rectly to perturb the function of ongoing processes.
Since the above named and similar processes are highly nonlinear or
are held far from equilibrium with respect to particular steps, they
could be susceptible to perturbation by MW energy.
Viewed formally, MW
might reset a parameter, or change the probability of a key step in a
process, thereby affecting noticeably the overall transfer properties
(Frohlich, 1980).
1.2
MICROWAVE ABSORPTION BY TISSUES AND ITS CONSEQUENCES
Any MW phenomenon depends on absorption of MW.
Some basic features
of MW interactions with tissues are as follows (Burdette et al., 1982;
Adey, 1981; McLees and Finch, 1973; Schwan, 1975; Michaelson and Lin,
1987).
First, biologically relevant magnetic dipoles exist or can be
induced in organisms, as is known from species that navigate geomagneti­
cal ly, from magnetotaxic bacteria, and from magnetoencephalography.
However, tissues are hardly susceptible at all to magnetic fields which
oscillate at MW frequencies.
Thus the electric rather than the magnetic
component of a MW field will affect biological molecules.
An electromagnetic (EM) field will induce polarization in an indi­
vidual molecule periodically at the field frequency, with intervening
relaxations.
Macroscopic EM properties of materials are described by
the relative dielectric permittivity e r and the conductivity cr.
For
tissues with substantial water and ion content, e r is highest at DC.
In
the low frequency region, dielectric polarization and relaxation follow
the electric field oscillations closely.
As frequency increases toward
100 MHz or so, « r decreases greatly, and the intrinsic relaxation time
becomes significant, so that resonant interactions can take place.
The
conductivity tends to increase gradually as frequency increases from DC,
but increases very steeply above about 6 GHz.
At frequencies where con­
ductivity is very high, an EM field hardly penetrates into tissues.
The
frequency range of interest for MW effects studies is therefore interme­
diate between 100 MHz and 6 GHz at the extremes.
Relaxation times are intrinsic properties of molecules, but are
distributed, owing to prior states of motion and thermodynamic condi­
tions.
The distributed nature of relaxation times causes the polariza­
tion response of a pure substance to periodic excitation to be broadly
frequency selective (dispersive).
In addition, the interactions of mol­
ecules with their neighbors cause the resonance to be heavily damped.
In a tissue, the relaxation spectra of the various molecular spec­
ies will also depend on how they interact with their neighbors.
Gross
samples of tissues will therefore have multiply peaked MW absorption
k
spectra.
For instance, pure water relaxes in the 20GHz range, while
water associated with membrane proteins will relax in the MW range,
1GHz.
Relaxation times may lengthen when water forms hydrogen bonds
with other species, rather than only with other water molecules.
In muscle and nerve, absorption by water and ions will mainly
determine the relaxation spectrum in the MW frequency range.
Cell mem­
branes, organelles, proteins, and other macromolecules will have only a
minimal role, as they absorb mainly at much lower frequencies.
For
instance, direct MW effects on transmembrane potentials of cells can be
excluded.
A resting cell membrane supports a huge electric potential
gradient (10* V/m for 90 mV across 90 nm) at DC, where the transmembrane
impedance is at least a few MO.
A MW induced gradient will not mainly
appear across a membrane, however.
At 3GHz, the impedance of a membrane
is in the
In any case, a field that measures
range (Schwan, 1975)*
10mW/cm 2 in air (a typical field strength for nonthermal effects stud­
ies) will
induce a gradient only of the order of 2V/cm in a tissue
(Stuchly, 1981).
As indicated in sec. 1.1, MW effects should be expected to depend
on properties of the organization of a biological system, rather than of
the initial
interaction of MW with individual molecules.
Therefore,
although absorption has to have occurred if a MW effect is observed,
more overall absorption needs not cause a more evident MW response, or
indeed any response.
For instance, free water may absorb most of the
energy during an exposure, but may produce no physiological consequences
if temperature is constant.
Nor should it be concluded that the fre­
quency selectivity of absorption is the same as the frequency selectivi­
ty of a response.
A final basis for distinguishing MW absorption fron MW phenomena i
that MW dielectric properties of substances, which describe absorption
quite closely, tend to be constant, regardless of field strength, up to
the order of KV/cm (Schwan, 1975). indicating a linear interaction.
On the other hand, an MW effect can be manifest to us only after
the MW signal has been rectified or demodulated by a nonlinearity.
In
certain phenomena evoked by modulated fields in the MW and other fre­
quency ranges, this is obvious: in MW auditory effects (Lin, 1978), as
well as EEG or ECoG synchroni2ation effects (Servantie et al., 1975) >
the modulating frequency is evident (see sec. 1.5-2).
1.3
SPECIFICITY OF MICROWAVE EFFECTS
As stated in sec. 1.1, any energy absorbed from a MW field will
increase the internal energy of a system.
When energy is absorbed, ter
tiary phenomena of molecular structures, movements, and constraints
(bond angles, hydrophobic or hydrophilic interactions, and so on) will
change, and charges will be displaced or rearranged.
These changes in
general reflect increases in both free energy and thermal energy.
A
fundamental theoretical and experimental question is whether these can
be distinguished.
McLees and Finch (1973). Adey (1981) , Frohlich
(1980), and other authors have addressed this question.
In systems of homogeneous composition, the energy relations (macro
scopic) might usefully be connected with probabilistic properties of
molecular movements (microscopic).
The contribution of a free energy
change to molecular responses could be identified formally at least if
temperature were held constant.
For a biological system making this connection would be formidably
difficult.
Fortunately, though, if it is accepted that MW phenomena are
multimolecular, then it can also be accepted that thermal and free ener­
gy effects can be distinguished sufficiently well at the macroscopic
level.
An empirical definition of specific MW effects, which requires no
assumptions about molecular effects, can be made as follows:
first, a
temperature threshold for effects due only to temperature changes, with
no exposure, is found.
Any MW effects that occur while the temperature
change remains below threshold can be considered specific.
This study is intended to discover if there are effects which are
specific in this sense.
1.8.3.
This definition is discussed further in sec.
Technical aspects and criteria for adequate temperature control
are discussed in Chapter II.
Specific MW effects could occur simultaneously with thermal effects
(Frohlich, 1980).
Some authors have attempted experimentally to isolate
specific from thermal MW effects by comparing effects due to a particu­
lar temperature change when induced by MW and by another heat source
(infrared).
For instance, Wachtel et al. (1975) found that MW and
infrared irradiations which caused the same gross temperature change did
not always affect individual neurons in Aplys i a the same way.
Kamenskiy
(196^) found the same was true for a prepared frog sciatic nerve (see
sec. 1.1»).
Experiments of this design should be viewed cautiously, as
the penetrations and consequently the heating patterns of MW and other
sources could be very different (Arber, 1979)-
7
Microwave irradiations with and without compensatory cooling have
also been compared (McAfee, 1961; Taylor and Ashleman, 1975)-
Data
obtained with the compensation are useful, but the comparison with
uncompensated exposures is of value only if it can be assumed that spe­
cific and thermal effects take place independently.
1.14
NEUROPHYS IOLOG I CAL AND ALLIED MICROWAVE PHENOMENA
In this section, MW phenomena relevant to cellular physiology are
reviewed.
The emphasis is on studies done at constant temperature (see
sec. 1.3)• at or near 2.kS GHz (see sec. 1.2), and, for reasons that
will be given in sec. 1.8.3, with unmodulated fields.
Some results
obtained with modulated or pulsed fields, at other frequencies, or with
temperature changes, are included where they offer added insight.
It is useful to classify MW experiments in the literature by the
type of effect found.
Broadly, MW phenomena at the cellular level have
been either rapid (less than one minute) and reversible or slow (tens of
minutes) and possibly irreversible.
The rapid reversible effects seem
most likely to be thermal while the slow effects may be specific.
Seaman and Wachtel (1978; see also Wachtel et al., 1975) found
obvious rapid reversible MW effects on neurons in Aplysia.
interspike interval
The average
(ISI) of regularly firing neurons usually decreased,
but a given neuron did not always behave repeatably.
The average inter-
burst interval (IBI) of regularly bursting neurons also changed; this
change also was not always repeatable in a given cell.
Although Seaman and Wachtel (1978) acknowledge that they observed
mainly thermal effects, they thought some effects they saw were nonther-
mal.
This seems unlikely.
On irradiation the temperature changed by a
large fraction of a degree or more.
This change is large enough (see
sec. 1.6) to cause effects by itself, and the thermal time constant of
the experimental system (one minute) matched the time constant of most
responses.
A minority of neurons were oppositely affected by MW and by
non-MW temperature elevations.
This could be explained by differences
in the detailed distribution of heating between MW and non-MW sources
(see sec. 1.3; Arber, 1979)*
The authors also claimed that very rapid
transient responses (evident within one or two AP intervals) they saw in
some neurons were not thermal, but steep temperature steps often do
cause rapid transients (see sees. 1.6 and 5-1)•
radiations showed little difference in effect.
Finally, pulsed and CW
This is not what would
be predicted under a constant temperature condition (see sec. 1.8.3).
Seaman and Wachtel (1978) established specific absorption rates
(SAR; see Appendix F) at the threshold of observable effects:
the medi­
an neuron in their sample was noticeably affected at 1^.5mW/g.
As will
be seen, this SAR compares with SARs used in several studies, including
the present one.
Courtney et al. (1975; see also Lin et al., 197^) found no change
in distribution of transmission latencies through the rabbit. superior
cervical ganglion on MW exposure (isolated preparation).
In this work
the temperature was kept within fractional degree tolerance even at
large SARs up to lW/g.
The conclusion was based on comparison of data
from exposed ganglia with data from unexposed controls recorded for the
same length of time, and would therefore seem quite robust.
tion on this study comes from the exposure regime.
One limita­
Some workers have
predicted MW effects which evolve slowly, over tens of minutes (see
below and sec. 1.8.3).
To prevent artifacts, Courtney et al. (1975)
interrupted the MW to make measurements (1 min on/1 min off), possibly
harming the chance of inducing slowly evolving effects.
Taylor and Ashleman (1975) recorded in intact cat from spinal cord
ventral root (lumbar-sacral).
They stimulated the gastrocnemius elec­
trical ly, while recording the gross extracellular ventral root poten­
tial.
Microwave applied directly on the cord attenuated the dominant
component, a monosynaptic efferent potential.
McAfee (1961)» also using
cats, observed a nocioceptive blood pressure increase when MW was
directed to the sciatic nerve.
In both studies the effects seemed
directly related to local temperature changes, in that they were prompt­
ly reversed on simultaneous cooling.
These experiments appear to have
shown that nulling of a large (several degrees) temperature change also
nulled a large MW effect, but the null temperature condition was not
established accurately.
Therefore it could not be determined whether a
small nonthermal effect may have occurred.
Microwave irradiation lasting some 60 min hyperpolarized the mem­
brane potential (Arber, 1976; Helix Pomatia). lowered the input resis­
tance and shortened the time constant of neurons in snails (Arber, 1981;
Helix Lucorum).
These changes were monotonic and irreversible.
Each
variable changed significantly (the fractional change was about ten per
cent).
At least in the 1981 study the temperature was held within ±
0.1°C.
Apparently in these studies no comparison was made with separate
unirradiated control experiments.
For control purposes in the 1981
study, some cells were treated with EDTA in addition to irradiation.
Using EDTA abolished the MW induced lowering of input resistance.
(This
result indicates that cellular Ca ++ is involved in MW interactions; see
section 1.5.2.)
Lowering of membrane resistance by MW depended on the working temp­
erature.
No effects occurred at 28°C (Arber and Lin, 1983. 1985b), but
only at 21°C and 8°C.
28° is outside the normal range of adaptation for
Helix; at this starting temperature, membrane properties may already
have undergone changes which could obscure MW effects.
Possible reasons
to expect MW effects to depend on the working temperature are given in
section 1.5 -1 The neurons used in Arber (1976 and 1981) were apparently silent.
In active neurons of Helix Aspersa. MW irradiation (SAR 15mW/g) lasting
tens of minutes gradually inhibited ongoing firing (Arber and Lin,
1983,1985b).
This effect was occasionally reversible.
Although hyper-
polarization and lower resistance could come from a temperature
increase, inhibition of ongoing activity would not be expected (see sec.
1 .6) .
Another case of effects evolving over tens of minutes is from tur­
tle heart.
MW radiant flux estimated to have raised the temperature by
0.5°C or more caused tachycardia, as expected, but weaker fluxes caused
bradycardia, which was unexpected (Lords et al., 1973)-
Lords et al.
(1973) thought that MW fluxes too weak to raise the temperature may have
directly stimulated synaptic terminals which remained with the heart,
preferentially affecting those of the parasympathetic system.
Unfortunately in these experiments the SAR could not be measured.
11
Relatively long term but transient effects occurred in frog neuro­
muscular junctions (Portela et al., 1975)*
Pulsed MW at 10 GHz
increased the local propagation velocity, lowered membrane resistances,
and sped up the rising phase of the AP.
Comparisons were against unir­
radiated but otherwise identically treated controls.
Possible roles of temperature are not clear in this study.
The
average power density of irradiation, 10 mW/cm 2 , was comparable to power
densities in other low-power or "nonthermal" studies.
The perfusate and
a coolant were recirculated at a controlled temperature; the temperature
can be presumed to have been constant if the thermal coupling between
tissue and perfusate was good.
was presumably required.
The exposure duration was 120 min; this
All effects (which were measured starting
immediately at MW offset) persisted for several tens of minutes.
These
long time constants would occur only in the most massive thermal control
systems, and may be characteristic of nonthermal mechanisms (see sec.
1.5.1) •
On the other hand, all the effects were in the direction expected
for a temperature increase and were systematically reversible.
Also, as
will be indicated in sec. 1.8.3. pulsed sources can cause distinct ther­
mal phenomena not seen with CW sources.
Using comparable field intensities (no SAR was available),
Kamenskiy (196^) found that CW MW shortened refractory periods and
increased conduction velocities in a prepared frog sciatic nerve.
Here
too the effects were perhaps greater than expected for the reported
temperature changes, but the time required for them to develop was the
same as the time for the temperature changes.
RF and MW irradiation responses of two species of algae, Chara
braun i i and Ni tella f1 ex i1 is. have been studied by Pickard and his
coworkers (Barsoum and Pickard, 1982; Gokhale, Brunkard, and Pickard,
198^).
These cells are large and elongate; one end of a cell can be
exposed while the other is recorded, without risk of artifact.
Over the
range of 200 to 8200 MHz, and at a power density of 10mW/cm 2 (the SAR
was 6.7J»mW/g at 2^50 MHz), irradiation had no effect on membrane poten­
tial.
However, at 2^50 MHz, and 15.5mW/g, conditions which specifically
match those in Arber (1981), transmembrane resistances fell by some
eighteen percent after 60 min of irradiation (Barsoum and Pickard,
1982).
Although no minimum criterion on irradiation time was reported,
and no statement was made as to the temperature control, this result
appears to confirm that in Arber (1981).
At much higher power density,
1 .1*5 x 10 5 mW/cm 2 , the cells hyperpol ar i zed (Gokhale et al., ^B^).
As
this hyperpolarization was rapid and as it increased at higher frequen­
cies, along with tissue conductivity, it was most likely thermal.
The height of the compound action potential (CAP) of isolated frog
sciatic nerves decreases over time.
McRee and Wachtel 0980) elicited
CAPs in these nerves with repeated paired stimuli, spaced 5 msec.
Loss
of height of the first CAP would indicate loss of overall function, and
additional loss in the second CAP would indicate longer refractoriness..
In MW irradiated nerves, the height of both CAPs decreased more rapidly
than in otherwise identical controls.
Twenty to thirty minutes of expo­
sure were required.
The role of temperature in this study is difficult to interpret.
In experiments with SARs of 100,50, and 20 mW/g, both control and
13
exposed nerves experienced temperature increases, with exposed nerves
being warmed more.
Temperature increased fastest in the first 20 to 30
minutes, during which MW effects were becoming apparent.
However, in
later experiments at 20,10, and 5 mW/g, temperature was held constant
and matched for both nerves, and an unmistakeable loss in the CAPs was
apparent at 10 mW/g.
McRee and Wachtel (1980) concluded that MW may have disrupted long
term regulatory mechanisms, but did not exclude the possibility that the
specificity of the MW action lay in its heating pattern.
An alternative measure of the vitality of a nerve prepration (crab
leg nerve) was offered by Brown and Larsen (1980).
As a CAP is propa­
gated, membrane proteins will change conformation, causing a change in
the optical rotation properties of a nerve.
Transmitted polarized light
records of the CAP are less temperature sensitive than electrical
records, and do not interact with the MW field.
Using nerves from a
single crab in each experiment, Brown and Larsen (1980) compared control
nerves with nerves treated using pulsed MW, CW MW (123mW/g average SAR
in both cases) or heating by 3°C (this is the temperature rise that was
observed with MW at 123mW/g).
Only pulsed MW significantly changed the
amplitude of the birefringence signal, generally causing it to decrease.
Chou and Guy (1978) sought effects of 2^50MHz MW, CW and pulsed, on
nerve conduction velocities (rabbit superior cervical ganglion and
vagus; frog sciatic; cat saphenous) and on muscle tension (rat dia­
phragm).
Their study was comparable to Courtney et al. (1975). except
that stimuli were coupled to each preparation from outside the exposure
chamber.
Therefore MW could be applied continuously during recording.
14
For CW MW up to 1-5W/g and pulsed MW up to 220mW/g (average), applied
for up to 15 min, only slight effects occurred in any preparation, and
only at the highest powers.
These effects were thermal, as they were
reproduced by equivalent heating of the cooling bath (in any case no
more than 1°C).
Chou and Guy (1978) designed their study to overcome possible
objections to the other studies reviewed above.
Of particular note are
the superior thermal control (compare Seaman and Wachtel, 1978; Portela
et al., 197^; Kamenskiy, 1964) and longer time of irradiaton (compare
Courtney et al., 1975; Taylor and Ashleman, 1975)*
Chou and Guy also
concluded that the lack of results with high powers contradicted the
possibility of direct field stimulation suggested in Lords et al.
(1973) •
In summary of reported MW phenomena, the most robust results seem
to be the lowering of membrane resistances (Arber, 1981; Barsoum and
Pickard, 1982) and the tendency of preparations more quickly to lose
their viability (McRee and Wachtel, I98O; Brown and Larsen, 1 9 8 0 ) .
Insofar as these effects occurred without gross temperature elevations,
they meet the criterion for nonthermal effects given in sec 1.3-
1.5
MECHANISMS FOR NONDISSPATIVE MICROWAVE INTERACTION
A number of authors, including Arber (1979). Frohlich (1980), Adey
(1981), Barnes and Hu (1977) » and others, have elaborated on possibili­
ties for nondissipative MW interactions, which, as suggested in section
1.1, could lead to electrophysiological effects.
Unfortunately, with
the exception of Arber, none of the originators of the phenomenological
15
studies of the previous section have offered mechanistic interpretations
(however, see section 1.5-1)•
In this section, some general features to
be expected in nondissipative interactions are first pointed out.
Next,
some ideas at the level of cellular physiology are reviewed, referring
espec i a 11y to Ca* *.
1.5.1
Biophysical Considerations
Frohlich (1980) has offered a model to explain effects in the mil­
limeter w'ave region; among experiments which have sought millimeter wave
effects is Grundler and Keilmann (1978).
Of more importance, though,
Frohlich has suggested fundamental features to be expected generally of
nonthermal MW interaction mechanisms.
A comprehensive discussion of the
biophysics of MW and other EM fields at low intensities as they interact
with brain tissue is in Adey and Bawin (1977).
It was already pointed out in sec. 1.2 that knowledge of absorption
properties is not sufficient to predict whether MW responses will occur.
Even knowledge of microscopic (molecular) properties of particular chem­
ical species is not helpful, as MW responses depend on system properties
of tissues, whose composition is heterogeneous.
Since perturbations taken individually would be buried in thermal
noise (see sec. 1.1), a MW interaction must become coherent over many
molecules.
A marginal ratio of coherent signal to thermal noise could
explain why the lowering of membrane resistance found by Arber and Lin
(1983.1985b) depended strongly on the working temperature.
Coherency over space would give a specific MW interaction high
gain.
One feature which could result in high gains for MW effects is
mobilization of metabolic energy.
High gain would also result when MW affected a process which was
not near equilibrium.
As an example, physical studies of cell and arti­
ficial membranes indicate that cell membranes undergo isothermal phase
transitions and rearrangements when performing secretion, endocytosis,
division and other functions (for review see Cull is et al., 1983)*
Microwave could influence the probabilities of these events, while con­
ditions remained isothermal (Bond and Wyeth, 1986).
In fact, Liburdy
and Vanek (1985) have found that MW (100mW/cm 2 ) at 2.^5GHz reversibly
increased Na* influx into rabbit erythrocytes, provided the experiment
was done at a critical phase transition temperature.
Owing to the nonlinearity of MW interactions which lead to effects
(see section 1.2), it is reasonable to expect the strength of an effect
to saturate or decline as irradiation intensity increases.
would not be expected in a purely thermal
This feature
interaction, at least for
temperature changes within the physiological range.
Another possible
consequence of nonlinear interactions is indirect transmembrane effects.
Changes in potential and conductance, manifest at DC or low frequency,
could occur secondarily to MW induced structural changes, even though
direct MW perturbation of membrane potential can be excluded (section
1.2).
A question of interest is whether to expect sharp frequency selec­
tivity.
Again this would not probably be a feature of a thermal effect.
If the basis of the effective interaction were coherent resonance of an
extensive array of molecules, then sharp selectivity for the irradiating
frequency might be expected.
This selectivity, operating before any
nonlinear interaction, appears in reported millimeter wave effects
(Grundler and Keilmann, 1978).
operate after the nonlinearity.
On the other hand, selectivity could
Certain modulated field effects, dis­
cussed in the next section, depend on the modulating rather than the
irradiating frequency (see also section 1.2).
One possible consequence of conformation changes that are coopera­
tive among many macromolecules is quite long time constants.
These were
seen, for instance, by Arber and Lin (1983). who reported resistance
changes only after approximately 25 minutes; see also Arber (1979)Suppose MW forced conformational changes in a critical substance, but
that an effect became evident only after a criterion concentration of
molecules had been changed.
If the probability of a change per unit
time per molecule were fixed, and the probability of reverting were just
slightly lower, then a long time constant could result.
1.5.2
Electromaqnetic F ields and Cellular Ca1cium
Injecting the oxidative metabolism inhibitor 2,^-DNP produced
changes similar to MW effects (Arber, 1981).
Microwave and 2,^-DNP
might both deteriorate a cell by disrupting basic metabolism, especially
in long experiments.
This possibility is supported by McRee and Wachtel
(1980) and by Brown and Larsen (1980) ; see section l.l».
On the other
hand, Arber has related MW phenomena with movements of calcium ions that
occur in healthy cells.
Ca** has roles in controlling sensory transduction, neurotransmit­
ter release, muscular contraction, and AP generation.
Inside excitable
cells at rest, the Ca** concentration is held far below equilibrium,
indicating low permeability for this ion.
With depolarization or
injected Ca**, the permeability increases steeply (Hi lie, 198^).
18
Microwave hyperpolarization and lowering of resistance could be due
to increased K* conductance and/or electrogenic Na* pumping (Arber,
1976)-
An increase in Ca* + inside the cell is implicated, as a cell's
K* conductance is partly gated by Ca 4 * (Hi lie, 198^).
This suggestion
seems strong, since diffusing the Ca* + chelator EDTA into a cell pre­
vented MW effects (Arber, 1981).
Extra Ca + * set free within a cell by MW seems to come from intra­
cellular stores, rather than through the cell membrane (Arber and Lin,
1984, 1985a).
An explanation in terms of mobilized intracellular Ca ++ unfortu­
nately does not provide much insight about nonthermal effects, because
cellular Ca + < control mechanisms are quite sensitive to temperature (for
references, see Narahashi, Tsunoo, and Yoshii, 1987).
Although conser­
vative temperature control methods were used by Arber, the effects seen
were in the direction expected for a temperature increase (see next sec­
tion).
Other workers have both supported and questioned the idea that an
effect on Ca* + may be an endpoint in EM field interactions with cells.
Adey and coworkers (see Bawin, Adey, and Sabbot, 1978) have elicited
increased efflux of Ca** from chick forebrain slices using very weak
(<lmW/cmJ) radio frequency fields (147MHz).
With this low intensity,
heating would not have been a significant factor in this work.
The
fields had to be modulated in the EEG frequency range to be effective,
and the selectivity for modulating frequency was definite, with a peak
at 16Hz.
The nonlinear character of the effect is indicated by the fact
that its dose-response relation was windowed.
It may be speculated from
19
the lack of selectivity for the irradiating frequency (A50MHz was also
effective) that a modulated MW field could elicit similar phenomena.
A
critical review of this and some similar studies has been offered by
Myers and Ross (1981).
1.6
TEMPERATURE DEPENDENCIES
Neuron and neuromuscular junction properties show various tempera­
ture sensitivities, sometimes severe, within the physiological range.
In squid axon the resting potential and AP height hardly changed
but the rising and falling rates were drastically shortened with higher
temperature (Q10 of 2.0 and 3-2, respectively; Hodgkin and Katz, 19^9).
In frog neuromuscular junction, synaptic "unit delay" had a Q10 ot 3>1^
while conduction velocity at the neuron terminals had Q10=1 .5 to 2.0
(Katz and Miledi, 19&5)•
In Heli x Aspersa. Kerkut and Ridge (1962) found the resting poten­
tial either did not change or hyperpolarized as temperature increased
(Q10 from 1.0 to 2.0).
Murray (1966), in Aplysia. found that rest
potentials usually hyperpolarized on warming but in some neurons depo­
larized or were nonmonotonic.
The membrane resistance tended to covary
with the rest potential, decreasing with hyperpolarization.
Occasionally the slopes for small changes represented Q 1 0 as great as
1.5 (rest potential) and 6 (resistance).
Murray thought these types of
temperature responses to be analogous with temperature transduction in
vertebrate thermoreceptors.
AP interval patterns of neurons vary widely in their sensitivities
to temperature.
In Helix (Kerkut and Ridge, 1962), AP rates of sponta­
neously active cells increased with temperature or did not change, while
silent cells either became active with lowered temperature or did not
respond.
Some active cells showed a transient rate change which was
opposite to the ultimate change.
In Aplys ia. Murray (7 966) found the
same variety of AP rate responses in active cells as for membrane resis­
tance responses.
One common feature of these responses is that all were evident and
some were complete within seconds.
Another feature is that at least resistances and rest potentials
change more severely with temperature than predicted by the factor RT in
the Nernst equation and the Goldmann model of passive membrane proper­
ties.
This can be explained if in the Goldmann equation the ionic
permeabilities acquire temperature dependence.
Lower resistance and
hyperpolarization at higher temperature can indicate increased K* con­
ductance (Murray, 1966), or a decrease in the permeability ratio of Na 4
to K* (Fischbarg, 1972; barnacle muscle fibers).
In a molluscan neuron,
Gorman and Marmor (1970) attributed depolarization at higher temperature
to an increase in this same ratio.
1.7
ANALYSIS OF NEURON ACTIVITY
A random process is characterized fundamentally by the probability
density function (PDF) or probability distribution of its amplitude.
The PDF has to account in some way for the dependence of the process on
its past.
Neuron activity has a dual nature.
On the one hand, spiking is a
stochastic point process, for which only the intervals between APs is of
21
interest.
On the other hand, spiking results from underlying processes
which evolve continuously in time.
These dual properties have to be
described by two sets of measures which are discussed in turn in the
next two sections.
in sec. 1.7•3-
The relationship between them is considered briefly
Basic problems in AP analysis are considered by Moore,
Perkel, and Segundo (1966).
1.7.1
Descr i pt i ve Stat i st i cs of Intervals
Action potential sequences are characterized in the most generality
by a set of joint PDFs of all orders for the lengths of intervals.
In
practice, the PDF (first order) and autocorrelation (second order) form
a useful description, and estimates of these are used in this study.
Correlation of the length T of interval j with the length of the
nth previous interval
is expressed in the autocorrelation of intervals:
R-rrU.n) - E ( Tj - E (Tj) ) ( T j+n - E(T j+n ) ),
1.7-1
in which E stands for expected value.
To estimate the PDF and the autocorrelation, the sequence is
assumed stationary.
The PDF is estimated by a binned histogram, while
the autocorrelation is estimated by the serial correlogram.
In the
serial correlogram the expectations in Eq. 1.7~1 become time averages:
N-n
RTT(n) - (1/(N-n)) 2 (Tj - T,) (Tj+n - Tn+1),
J-l
in which
1.7-2
22
N
N-n
T! - (1/(N-n)) 2 T k
and
T n+1 = (1/(N-n)) 2 T k .
k=l
k=n+l
Ordinarily the function is normalized to a maximum value (at n=0) of
one.
Estimation and validation of the serial correlogram are covered
extensively in Cox and Lewis (1966).
Their arguments are reviewed, and
considerations for estimating interval histograms are given, in Appendix
C.
An application of the serial correlogram in neuron modeling appears
in Ekholm and Hyvarinen (1970).
An alternative interval analysis, which
takes into account dependencies higher than second order, has been used
extensively by Brudno and Marczynski (1977)-
1.7.2
Modeling of Action Potential Generation
A measure of dependency of AP generation on time is the renewal
density (also called intensity function):
h (t) = lim ( Pr { AP in [t,t+At)|AP at 0 } / At )
At+0
1.7-3
The renewal density is similar to a temporal autocorrelation, but it can
also serve as a cross correlation measure, if the conditioning event "AP
at time=0" is replaced by a different event, such as "AP at time=0 in a
different neuron", or the onset of a stimulus.
In estimating the renew­
al density, the probability is measured by relative frequency and At is
made finite.
Further analyses of AP sequences postulate that the AP is related
to a continuous-time signal.
A variety of models exist in which the
continuous signal is the input to a process which generates APs (Moore
et al., 1966; Holden, 1976).
Implicit models exist in which a continu­
ous measure of the AP rate is calculated by filtering the spike train,
then resampling at uniform intervals (French and Holden, 1971). or by
generating a signal inversely proportional to each interval (Shapley,
1971S Ginsburg, 1983) •
Among the multitude of explicit models, the "integrate-and-fire"
model has attractive properties (see Stein, French, and Holden, 1972;
Knight, 1972; O'Neill and Lin, 198^)r
V (t) = V(t 0 ) + (1/C) /iWdr.
to
In this model, as the net synaptic input current i
1.7-Jt
is integrated, the
intracellular voltage V (t) moves from the reset value V(to), just after
the previous AP was fired, up to the threshold value, when a new AP is
f i red.
In a neuron model, randomness is conferred on AP intervals either
by randomness in the inputs or random properties of generation or both.
The threshold value of V (t), the reset value V(to), and the synaptic
input current i (t) , of the integrator model, have all been cast as ran­
dom variables by O'Neill, Lin, and Ma (1986).
The input signals may be exogenous (stimuli under our control) or
endogenous, in which case their properties have to be inferred.
study, only spontaneously active neurons were used.
In this
Although many
active neurons in Helix respond to stimulation of one or more major
nerve trunks (Kerkut et al., 1975; Loker et al., 1975) the synaptic
2k
pathways and coverages have not been described.
to deliver electrical stimuli
artifacts.
Also, it is difficult
in the presence of MW without danger of
For these reasons, all neuron activity was considered to be
endogenous.
It is true that the integrator and other neuron models are mainly
phenomenological.
Even so, the model is simplifying in that it captures
the effects of changes in the inputs as well as in the AP generating
properties, (i.e., the integration of inputs; Arber, 1981), in a single
parameter.
In discrete time the model is:
t 0 +(n-1)At
z(t) = V(t 0 +nAt) - V(t 0 ) = (/uAt/C) T.+ (/uAt/C) 2 e(T)
T=t
1 .7~5
0
in which:
z(t) is the voltage increase from reset V(to) of previous AP to
threshold of current AP,
At is the sampling interval,
T • nAt is the current ISI,
M is the mean synaptic input current density,
C is a specific capacitance, and
e(T) are random components of the input current density.
This model relates reset, threshold and ISI for a particular AP,
with only minimal restrictive assumptions.
Reset and threshold voltages
may have any variations including dependence on previous spiking.
change z(t) in membrane potential during an ISI
synaptic current
The
is the result of mean
charging C for integration time T which is the length
of the particular ISI.
(The duration of the AP itself is neglected.)
The noise e(r) which corrupts the input current has zero mean and
is unautocorrelated, so that successive samples at intervals At are
independent.
For this reason the variance of the noise for each ISI
proportional to that ISI.
is
Then for analysis purposes the model can be
written as:
Zj = (/uAt/C) T j + v j
1.7-6
in which subscript j refers to interval j, and
tQ+(n-1) At
v.- = (At/C) 2 e(r).
r=t0
*
The parameter of the equation is expressed as yuAt/C because C and
i (t) can not be measured or separated.
Because the variance of each
sample vj of the summed input noise is proportional
to the ISI T j , (het-
eroscedast i c i ty; Johnston, 198*4), /uAt/C can be estimated by a weighted
least squares linear regression.
Details of the estimation are in
Appendix 0.
I.7.3
Relat ionsh i p of Interval and Temporal Stati st i cs
In this study, interval analysis and analysis of time dependencies
are considered as two independent bases for tests on the hypothesis that
MW affects neuron activity.
Some important properties of neuron activi­
ty, not apparent in either set of measures alone, have been revealed in
studies on their interrelationship.
In certain systems, where the main­
tained neuron activity has little or no serial correlation among inter­
vals, the variance of the spike frequency is lower than expected.
This
has been attributed to refractoriness in spike generation (Teich, Matin,
and Cantor, 1978), or to processes of long term regulation (Levine,
1980).
1.8
1.8.1
DESIGN OF THE PRESENT STUDY
Choi ce of Exper imental Sub iect
Microwave nervous system effects might be observed in intact ani­
mals through EEG or behavior, or in a suitable preparation through cel­
lular events.
In designing a MW exposure experiment the likely interac­
tions among the various physiological subsystems are naturally of
concern.
Also, as MW encounters tissue layers of various types it will
be absorbed inhomogeneous1y, so that dosimetry and prediction of temper­
ature rises in the region of interest can be major problems.
These problems can be most vexing with intact animals.
aimed at gaining biophysical
For studies
insight, dissected brains of invertebrates
such as Aplys ia or Helix Aspersa are probably the most tractable.
Because of their small mass and volume these brains can be kept easily
at the desired temperature.
The brain is also not too large compared
with the length constant for MW attenuation in watery tissues, so that
dosimetry requires only a simple model (see appendix F).
Referring particularly to Helix Aspersa. a number of neurons has
been identified as to location, connections with major nerve trunks, and
pharmacology (Kerkut et a)., 1975; Loker et al., 1975)-
There is also
background on ionic mechanisms (Eckert and Lux, 1976; Brown et al.,
1980) and on ecological influences on neuron activity (Gainer, )972a,b).
27
1.8.2
Choice of Experiment'al Variables •
In nerve preparations, it has been typical to search for MW effects
through disturbances in conduction velocity, or in the shape of propa­
gated compound action potentials (see section 1.it) .
One possible limi­
tation on these measures (indeed on the use of whole nerve or ganglion
preparations) is that the nerve axon may be relatively insensitive to
perturbations, robust transmission being its adaptive purpose.
In this study, transmembrane (input) resistances and action poten­
tial time and interval statistics were measured.
Resistance data pro­
vide a summary measure of the state of ionic conductances, and AP sta­
tistics reflect directly the operation of the mechanism of spike
generation.
Both offer the advantage of reflecting the condition of the
somatic membrane, which has a richer variety of ionic channels and much
of the specialization needed for integration of information, as con­
trasted with the relative simplicity of the axonal membrane.
Particularly to be noted is conductance of Ca* + , whose possible role in
MW and other EM effects was discussed in section 1.5.2.
Ca + * also pro­
foundly affects spiking statistics; the interaction among Ca 4+ ,
Ca 4 '-dependent K" conductance, and membrane potential governs bursting
behavior (Hi lie, 198i+) .
1.8.3
Temperature Control
To us, heat dissipation will be manifest only macroscopical1y, as a
temperature change and/or as thermal physiological effects.
In this
work, it was assumed that holding the experimental system at a constant
temperature was sufficient to prevent all effects due to heat dissipa­
tion.
How well does the temperature as measured at one point reflect in
tiiAe and space the microscopic heat dissipation when MW is applied?
With respect to time, if MW is applied suddenly, or is pulsed, the
temperature in a local absorbing area will undergo transient
increase(s).
This follows from the Fourier law, which indicates that
heat propagates into neighboring areas of the medium at a rate propor­
tional to the spatial temperature gradient.
When MW is applied with a
steep wavefront, many materials respond with a thermoelastic expansion.
Thermoelasticity is the basis of definite and distinct MW phenomena,
such as the MW hearing effect (Lin, 1978)*
It can occur with minimal or
no grossly sensible change in the average temperature.
Thermoelasticity
probably explains why pulsed MW caused more cataractous damage to rat
lenses than CW MW at the same average SAR and constant temperature
(Stewart-DeHaan et al., 1983)-
Thermoelasticity may also be involved in
pulsed MW effects on membrane birefringence (Brown and Larsen, 1980).
To minimize time transients in temperature, and to avoid possible ther­
moel asticity, only CW (unmodulated) MW was used in this study, and it
was applied and removed over a few seconds.
Electromagnetic theory indicates that charges can accumulate and
currents can flow along boundaries between different media.
will cause hot spots in regions where they flow.
Currents
Care was taken to
avoid introducing excessively lossy materials into the exposure system
(see Appendix A).
space.
Biological tissues are of course inhomogeneous over
However it was assumed for this study that the absorption prop­
erties of the neural tissue were essentially those of water.
Even in homogeneous media, temperature will not remain truly con­
stant, if energy is being introduced into only one part of the system.
Heat will not flow from absorbing regions without a temperature gradi­
ent.
It was assumed that the entire upper part of the exposure wave­
guide, consisting of ganglion, inner chamber, Ringer solution, elec­
trodes with electrolytes, and cooling water, was homogeneous.
Since the
volume of the ganglion was small compared to the whole, it was unlikely
that any substantial gradient could exist across the ganglion.
1 . 8 .J»
Exposure Regime
In sec. 1.1» it was pointed out that a number of MW phenomena took
some tens of minutes to evolve, under continuous irradiation.
It was
reasoned in sec. 1.5.1 that mechanisms requiring extensive cooperativity
might be the basis of this slow evolution of effects.
Finally, in the
previous section, it was suggested that care was needed to eliminate
effects of temperature transients.
For these reasons it was decided
that preparations should be irradiated continuously for periods of tens
of minutes.
From the viewpoint of statistical analysis, this exposure regime is
not as rich as one of repeated short.trials (which would permit response
averaging) or stimulation with pseudorandom modulation (which would sup­
port cross-correlation analysis).
While these designs would be superior
for, say, study of sensory system responses, it was decided that the
physical requirements, particularly for avoiding repeated temperature
transients, should take precedence.
30
1.8.5
Testing the Hypothesis that MW Does not Affect Neuron Activity
Two major classes of hypotheses were tested to determine whether MW
affected neuron activity under the conditions of the present study.
First, the quantity being tested was assumed to attain steady states
before, during, and after MW irradiation, and so was measured once,
independently for each condition.
Second, the quantity was measured as
an explicit function of time over an entire experiment, so that all var­
iations could be tracked, whether or not related to experimental condi­
tions.
The first treatment was applied to the input resistance data, as
only one or sometimes two point estimates were available for each exper­
imental condition.
It was also applied to the interval histograms and
the serial correlograms, as these could not be estimated or validated
without substantially long records of data.
An assumption of steady states in each condition was also used in
tests on the mean and standard deviation of the intervals, and on fea­
tures of the input current parameter of the integrator model.
For these
functions, though, the data were also treated as explicitly dependent on
time.
A regression analysis was used to test the time dependent func­
tions for MW influences.
31
Chapter
I I
METHODS
2.1
EXPERIMENTAL
2.1.1
Preparation and Recordi nq
Snails ( Heli x Aspersa. College Biological Supply, Escondido, CA)
were maintained in hibernation (dry, dark, 10°C) in a household refrig­
erator.
Hibernation and estivation states of land snails, whose adap­
tive purpose is reducing water loss, are associated with profound chang­
es in spiking activity and membrane resistance of certain neurons
(Gainer, 1972a).
For this reason, snails were brought into a humidified
environment at room temperature with diurnal light cycling for at least
one week before use.
Only obviously active snails were selected for
exper iments.
Snail brains were prepared by a procedure similar to that in Walker
(1968).
As a snail began to forage and extended its body, the posterior
part of the body was removed with a single cut through the shell behind
the mantle.
The anterior part was immediately pinned on a dissecting
plate and the dorsal body wall was slit midsagitally, posterior to ante­
rior.
The flaps of body wall were pinned apart.
the esophagus passed through the ganglionic ring.
The gut was cut and
Then the nerve
trunks, eye stalks, and connectives were cut one by one until the brain
was free.
Every effort was made at this stage to avoid putting mechani­
cal tension on the ganglia.
Snail Ringer (NaCl 80mM, KC1 Wl, CaCl2 7mM, and MgCl2 5"iM; buff­
ered to pH 7.i* with Tris 5mM; see Kerkut et al., 1975) was flooded over
the ganglia at this point, and they remained covered through the rest of
each experiment.
The brain was pinned to a circular wax disk, by pass­
ing cactus needles through the connective tissue sheaths of the nerve
trunks and through the center of the circumesophagea1 ring.
Sufficient
of the thick outer connective tissue was snipped away to allow visualiz­
ing the ganglia and tentatively identifying neurons.
Many preparations
in which the contrast was poor, or the connective tissue was especially
stringy or tough, or the ganglia had an unusual conformation, were dis­
carded at this point.
A thin tough inner layer of connective tissue, which prevented
electrode penetrations, had to be removed.
This could seldom be done
without mechanically disrupting the organization of the ganglia.
Therefore, Sigma Pronase was applied on almost all preparations.
In
individual cases this aided in removing the inner layer or made removing
it unnecessary.
All but approximately one-half ml of Ringer solution
was dabbed away, then a few grains of Pronase were applied directly on
the brain and left for 8 to 10 minutes.
This procedure (Holden and
Ramadan, 1980) was chosen after Pronase in solution proved ineffective
at lmg/ml.
Treatment for 20 minutes, or treatment at lOmg/ml, were too
severe; they disrupted the entire ganglionic arrangement noticeably.
Pronase which reaches the interior of a cell will destroy its func­
tion.
To prevent residual Pronase from entering a cell as a microelec-
trode punctured it, each Pronase-treated brain was washed three to five
times in fresh Ringer solution, with agitation by hand.
Even on the
exterior, the enzyme can affect synaptic transmission markedly (Altrup
et al., 1980).
These effects were not of concern, though, as both con­
trol and MW exposed brains were treated with Pronase in the same way.
As shown in Figure 1, each prepared .brain was put in a thin walled
(approximately 1mm) styrene plastic recording chamber of volume approxi­
mately 1.2 cm 3 , which was centered transversely in the upper part of an
open waveguide.
Ringer solution flowed through the recording chamber at
0.l4ml/min, from a syringe pump.
rather withdrawn by a roller pump.
The solution was not recirculated, but
Surrounding the recording chamber
was water, temperature controlled at 20.9°C.
The inner chamber made
good thermal contact with but was electrically isolated from the cooling
water circuit.
Performance of the temperature control system is dis­
cussed in sec. 2.1.4.
The recording chamber and water filled the entire upper part of the
waveguide.
At the bottom of the waveguide, which was filled with air,
2^50 MHz radiation was introduced by a coaxial to waveguide transition.
An impedance transformation was made between the air and water filled
sections of the waveguide by a one-quarter wavelength dielectric plate.
The waveguide was dimensioned to have a cutoff frequency such that at
2450MHz, the only mode of propagation was TE10- (Paris and Hurd, 1969;
see Appendix F).
A comparable waveguide design was used by Chou and Guy
(1978).
Neurons were identified visually.
While cells were identified and
electrodes were positioned, Ringer solution continued to flow over the
brain, assuring that any lingering Pronase would be washed away.
3*»
FIGURE 2 '
Recording chamber and waveguide arrangement. Temperature was
sensed by a Vitek thermistor probe a t p o i n t T . The matching
device was a quarter-wave transformer.
35
The photographs, drawings, and nomenclature of Kerkut et al. (1975)
and Loker et al. (1975) were followed, for identification.
About half
the brains dissected were rejected because the desired neurons could not
be identified from the reference illustrations.
Emphasis will be put on
data from two neuron types which were identified reliably.
One, F1 (F designates neurons in the right parietal ganglion), usu­
ally fires AP bursts of irregular length, at irregular intervals.
At
certain times F1 fires more regularly; during a long recording (F1 neu­
rons were occasionally held for several hours), a transition from burst­
ing to regular firing or vice versa often occurred (see Gainer, 1972b).
During interburst intervals the neuron hyperpolarizes profoundly.
This bursting is due to an intrinsic property of the neuron, such as the
cycling of free intracellular Ca + * (Hi lie, 1981*, p.l05ff; Barker and
Gainer, 1975). but the neuron also has a rich variety of (mostly inhibi­
tory) inputs (Kerkut et al., 1975)•
Cell F1 was easy to identify as it
was clearly the largest in the right parietal ganglion, was not pigment­
ed, and responded to an injected hyperpolarizing current step with a
long time constant.
Presumably the long time constant is related to the
neuron's large size, assuming the specific capacitances of membranes to
be roughly constant.
The second neuron, E6 (E refers to cells in the visceral ganglion),
usually fires slowly (<0.5 AP/sec) and moderately irregularly, and has a
less rich variety of demonstrable inputs and pharmacological dependen­
cies.
Neuron E6 was often among the minority of neurons in the visceral
ganglion which were pigmented.
order of 30 to *»0 Mfl.
It had a membrane resistance of the
Its slow potential record often showed single
EPSPs and IPSPs but this feature did not appear reliably.
Cell E6 might
be confused with its near neighbors E5 and E2, which are similar in size
and firing pattern.
To minimize this possibility, E6 was recorded only
in preparations where both E6 and E5 could be seen clearly.
Additional
guidance was taken from the position of E6 relative to neurons F1 and E*»
(a large neuron in the visceral ganglion), and to the cleft between the
visceral and right parietal ganglia.
A few other neurons were recorded for which the identification was
not considered fully reliable.
Among these, neuron E7»
in the visceral
ganglion, is fast ( 1-3 AP/sec) and highly regular, with occasional
waves or bursts in the rate.
Although only slightly smaller than neuron
E6, it responded to injected current steps with a quite short time con­
stant.
Type E7 could not always be distinguished from a similar neigh­
bor, E9.
Neuron E7 and all others which were not definitely of type F1
or E6 were classed together as unidentified.
For recording, KC1 filled glass micropipette electrodes were used
(microfilament glass, type 6035» A-M Systems, Everett, WA).
To minimize
changes in the recording situation due to the presence of highly conduc­
tive media in the RF field, electrodes were filled with 1.0M KC1
of the usual 2.5 or 3.0M.
described in Appendix A.
instead
The properties of these electrodes are
Because the conductivity of this electrolyte
was low, the electrode tips were made large and stubby to lower the
impedance:
each pipette was elongated with a partial pull before it was
drawn to a tip.
Impedances of 5 to 20 megohms were usually measured.
Reference electrodes were made from pulled pipettes with broken
tips.
1.0M KC1 was heated with agar (0.02g/ml), injected into the ref­
erence pipette, and left to gelatinize.
Electrodes were made up to two weeks ahead of time and stored in
1,0M KC1.
Commercial microelectrode holders were used to ensure stabil­
ity.
Mechanical movements often caused degeneration of signal quality or
loss of cells.
To minimize these losses, the experimental system was
put on an air suspension table.
The recording setup is schematized in Figure 2.
The microe1ectrode
signal was conditioned with a unity gain high impedance amplifier (W-P
Instruments M707A) which included current injection and impedance bridge
circuitry.
Previously, 3*»0Hz had been found to be an adequate bandwidth
for recording from Helix (Ma, 1985) •
The amplifier bandwidth was 3 KHz,
and the capacitance compensation was adjusted for a flat or slightly
overdamped response to a current pulse.
An initial offset voltage
(before penetrating a cell) of approximately -2 to -5 mV (occasionally
it was as large as -15 mV) was bucked out.
An intermediate amplifier provided buffered outputs to an FM tape
recorder (HP 7^00 or Racal Store7DS; bandwidth 625Hz at -3 dB), and a
Gould 2200S oscillographic chart recorder.
The chart was run continu­
ously during all experiments, so that progress of the chart paper pro­
vided a time reference.
Owing to limited bandwidth, the chart recorder
registered APs at approximately 80% of their actual height.
(AP records
in Chapter 3 match closely their original heights, as these records were
made from tapes replayed at half-speed.)
38
Q£
UJ
in
o
on
h—
U
LU
FIGURE 2:
Schematic of data recording system.
are discussed i n Appendix A.
The electrode properties
39
2.1.2
Microwave Irradiation
Power entering the snail brain was quantified using the SAR (see
Appendix F).
In all MW experiments, the specific absorption rate (SAR)
was 12.5 or 125 mW/g; the power density at the surface of the brain was
10 or 100 mW/cm2 The frequency was always 2^50 MHz.
Continuous wave MW for the 12.5 mW/g exposures was generated with a
Hewlett-Packard 867O synthesizer and amplified with a HP i»91C TWT ampli­
fier.
Forward and reflected powers were observed on HP J»35B and HP ^31C
power meters, respectively.
Initially these meters were factory cali­
brated; thereafter they were occasionally checked against the internal
standard of the A35B meter.
A Narda directional coupler was used.
The
attenuation to either measuring port was 20dB.
For exposures at 125 mW/g, a Micro-Now 221 TWT amplifier was placed
in cascade after the HP i+91C amplifier.
A 10 dB attenuator was put in
series with each measuring port of the directional coupler.
Power levels were set by hand, but were observed almost continuous­
ly during all exposure periods.
Reflected power losses amounted to one-
quarter to one-third of the incident power.
As this amount of loss is
significant, dosimetry was based on the net transmitted power.
2.1.3
Exper imental Procedure
In conducting an experiment, a cell was penetrated and given time
to stabilize:
data recording in a session was begun only after tempera­
ture was stable and only when the neuron signal seemed free of excessive
variations, mechanical artifacts, or drifting (usually within fifteen
minutes).
The neuron transmembrane potential was recorded for at least
thirty minutes before MW irradiation to provide initial control data
(examples in Figures 15_19)•
MW irradiation was applied while data were
recorded for at least 50 minutes.
Finally additional data were recorded
after exposure to define the recovery period.
In three experiments the
recovery period was approximately 23 minutes, but in all others it was
at least 35 minutes.
To measure temperature responses, a period at a temperature differ­
ent from the control was substituted for the period of irradiation
(examples in Figures k0-k2).
For control-only (sham irradiation) exper­
iments, the design was also identical except that the MW source was not
started at the time this would normally have been done.
In a few exper­
iments more than one condition (MW or temperature change) was imposed,
always with an intervening control/recovery period.
Just before the
exposure condition or the temperature was changed, the inputs to the
recorders were blanked for approximately 30 sec, to provide a time ref­
erence marker.
Resistance measurements were made (at times marked by arrows in the
figures) near the end of recording in a given condition, so as to repre­
sent as nearly as possible a steady state.
Voltage responses to known
hyperpolarizing current passed through, the recording electrode were pho­
tographed from a storage oscilloscope.
These responses could not be
recorded on the FM tape without overload, as the AP signal level had
been adjusted to cover nearly all of the tape system's dynamic range.
I* 1
2.1 .It
Temperature control
-
Temperatures were sensed at point T in Figure 1, with a Vitek
noninteracting thermistor probe.
Temperature was recorded continuously
on paper throughout every experiment.
Cooled water was provided by a
Lauda K2R/D circulating bath, which was modified in two ways.
First,
the mercury thermosensor had been found to work erratically from time to
time, causing infrequent temperature excursions as large as several
degrees.
The mercury switch was replaced with a YSI thermistor and
appropriate signal conditioning to yield a reliable on/off temperature
signal.
Next, the float operated flow regulating valve was fixed in the
maximum flow rate position, as was the manual flow control.
This over­
came balkiness on starting and tendency to flooding after long opera­
tion.
Flow into the waveguide was thereafter regulated by a shunt.
Figure 3 shows important aspects of the temperature control per­
formance.
The temperature in the main reservoir of the Lauda cooler
normally oscillated approximately ±0.1°C about its set value, with a
period of approximately 10 sec (Figure 3.a)•
When water circulation was
started in the waveguide, the reservoir temperature was practically
undisturbed.
Sometimes the size of the variations was reduced, presum­
ably due to better mixing of the water.
essentially no additional effect.
Applying MW irradiation had
These observations indicate that the
waveguide system imposed an insignificant thermal load on the cooler.
When the set point temperature of the circulator was changed in a
step, the reservoir temperature responded at a constant rate, 1.^7cC/min
for increases and -0.i»7°C/min for decreases, until the new temperature
was reached.
Figure 3>a shows responses to steps of +0.25 and -0.5°C.
it 2
RESERVOIR
(A)
+0.25C STEP
•0.5C STEP
WAVEGUIDE
I
:
J _i i: I I •! i I; I !
l<-
1
i-! l.|:
'—4
i
!
'
i
M
i
j . i
j
i
i
i
,
\/\AAA>zi/\r>AA?y'iAA/,\AA/iAAA/\/\l \hf\f\f\I\j
^-4}:'1'1;1
MW ON
RECORDING CHAMBER
t -0.5C STEP
t
+0.5C STEP
RECORDING CHAMBER
(D)
|
NO MWi_i i r n^r i.
~="l.;Ul:.rrr=i .1 !.. T l
i
(E)
:
1
1
i..i
i
i ,
.
.
.
H
J^-LUkiiL.i-i -I 4-i-l'-;lv i;- ! L-".
CENTER
EDGE
EDGE
CTR
0.2C
5 min
FIGURE
Performance of the temperature control system.
( a ) . Temper­
ature v a r i a t i o n s and step responses i n main r e s e r v o i r .
(b).
Temperature i n w a t e r - f i l l e d p a r t of waveguide, with and w i t h ­
out MW a t average SAR 8lmW/g.
( c ) . Response of recording
chamber t o ±0.5°C steps i n temperature set p o i n t . Data from
actual experiment.
(d) Temperature a t center and near
periphery of recording chamber.
(e)
Same as ( d ) , but with
MW i r r a d i a t i o n a t average SAR 8lmW/g.
Temperature of the coolant in the waveguide followed the reservoir
temperature closely, but the peak height of the oscillations was smaller
(Figure 3. b).
20 sec.
In the step response (not shown), there was a delay of
Presumably transit time and mixing effects in the waveguide
loop caused both the attenuated variations and the response latency.
The temperature response in the recording chamber itself, when the
reservoir temperature set point was changed by a step, indicated that
the thermal resistance between the chamber and the surrounding water was
significant.
When the reservoir temperature set point was changed, the
temperature response at point T was similar to an exponential, contrast­
ing with the constant rate responses of the reservoir and waveguide coo­
lant.
The recording chamber response had a delay of up to 0.8 min and a
time constant between k and 6 min.
Figure 3»c shows responses to a
-0.5°C step followed by a +0.5°C step, recorded during a temperature
exper iment.
The quality of temperature regulation in the recording chamber
depended profoundly on the constancy of the volume and flow of Ringer
solution.
Gravity fed infusion proved particularly troublesome.
Infu­
sion at a steady rate was realized using a step motor driven syringe
pump, placed below the recording chamber.
The temperature distribution inside the recording chamber was
checked with the exposure system set up for recording, except that no
brain was in place.
O.l'tml/min.
Ringer solution circulated at its normal rate of
The Vitek probe was mounted concentrically in the tube
where the active recording electrode normally would be put.
Temperature
was measured at distances of 0 and U mm from the center of the recording
chamber along the electrode tube axis.
Zero corresponds closely to the
site of measurement during an experiment and would be within approxi- '
mately 2mm of a recorded neuron.
Temperature osci11 at ions from the circulator were weakly evident at
4mm, but not at Omm from the center (Figure 3. d).
at Omm was 0.05 to 0.1°C higher than at 4mm.
The mean temperature
This gradient disappeared
when the Ringer solution infusion was turned off.
When MW was turned on
the temperature gradient between the Omm and 4mm positions increased.
With a pulsed source of average SAR 81 mW/g, it was 0.15°C (Figure 3.
e).
In addition, with MW on, an oscillatory variation with a period of
approximately 2.5 min became evident in the recording chamber tempera­
ture.
At 12.5mW/g this variation was hardly detectable, but it was
clearly present with 8lmW/g (Figure 3. e) and was the dominant source of
variation at 125mW/g (see Figure 4).
Its peak height was at worst
±0.1°C (steady state, 125mW/g).
The origin of this oscillation was traced to variations in the
height of the Ringer solution.
stant rate.
Solution entered the chamber at a con­
When the chamber filling rose above the outlet hole, the
extraction pump created negative pressure in the outlet tube, then sud­
denly
withdrew about 0.1 to 0.2ml of solution.
tion formed a meniscus over the outlet hole.
Often the exiting solu­
When this meniscus broke
and the cycle restarted, the solution level had usually fallen below the
outlet hole.
The performance limitations on the temperature control were not
considered serious.
Much of the limitation is due to the use of a styr-
ene plastic for the recording chamber.
Unfortunately there is no alter­
45
native here to the use of this or a similar material with low-loss die­
lectric properties.
Low-loss materials have low thermal conductivities.
The oscillations seen in Figure 3. e« were suppressed when air was
bubbled into the recording chamber, but moving air sufficient for effec­
tive agitation would have threatened the mechanical stability of a prep­
aration.
An attempt was made to improve the temperature control by putting
the Vitek probe within the feedback loop of the Lauda controller.
It
was not possible to achieve stable control using this probe as a feed­
back element, owing to excessive loop phase shift caused by the transit
time of the water through the cooling circuit.
Complete temperature records from two MW experiments are in Figure
A.
Panel (a) shows that temperature variations in experiments at
12.5mW/g were very minimal.
experiment.
Panel (b) shows the record of a 125mW/g
In this experiment the temperature oscillations were among
the most severe observed.
In other 125mW/g experiments, the oscilla­
tions were smaller, but there was a larger shift in the average tempera­
ture during MW.
The Vitek probe was placed as near as possible to the recorded neu­
ron.
To realize the best possible temperature constancy, the set point
of the controller was adjusted to compensate for the temperature change
expected, just before MW was to be applied or removed (compare
Stewart-De Haan et al., 1983) lowered by about 0.5°C.
At 125 mW/g, the set temperature was
Early in an exposure period, the adjustment was
usually trimmed up once (arrow in Figure U, b).
U6
A022487Js 12.5mW/g
START REC
MW ON —
IZBlZi3EilEiI
MW O F F '
*'
-a\r
AO31787
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!5
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i • 11
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•••! :j; ; j... i:
--i'
^START REC-
=
H'MW ON ^CORRECT TEMP
: MW
FIGURE k :
OFF
5 min
Continuous temperature records from representative experi­
ments.
(a) . MW exposure, 12.5mW/g, A022<t87.
(b) . MW expo­
sure, 125mW/g, A031787 -
^7
Taking into account all sources of variations, the temperature at
the measuring point remained within ±0.03°C (12.5"iW/g) or ±0.3°C
(125mW/g) of the control value (20.8°C) throughout an experiment.
represents the worst transient deviation that was observed.
0.3°C
Normally
variations were held within less than ±0.1°C throughout each experiment
(Figure l»,b).
Temperature variations up to ±0.3°C did not evoke respon­
ses in neurons, as will be shown in sec. 3*3-
2.2
STATISTICAL
2.2.1
Selection and Edi ti nq of Data
Only experiments which met the following criteria for the entire
recording period of two to three hours were used: input transmembrane
resistance was cleanly measurable, offset voltage drift was free of sud­
den jumps and was no greater than 2 to 3 mV/hour, the temperature
remained within the limits named in sec. 2.1.3.
and the AP height
changed no more than ±10%.
Data which met these criteria were noticeably nonstationary in AP
rate.
F1 and E7 neurons were more stable than E6 neurons.
For E6
cells, the rate most often changed gradually, usually decreasing.
In a
number of preparations, particularly with E6 neurons, the AP rate
dropped precipitously or firing stopped altogether.
Stoppage of spiking
was not considered to be a possible MW effect, as it sometimes happened
in control-only experiments, and in MW experiments, occasionally hap­
pened before MW onset.
Loss of spiking may have been due to mechanical
disruption of synaptic inputs.
i»8
No specific criterion or test for stationarity was used.
Experi­
ments with precipitous drops in firing rate did not yield enough APs
under each condition for analysis, and so were not used.
Input resis­
tance data from these experiments were used, if they were cleanly reada­
ble.
Table 1 lists the numbers and types of experiments.
TABLE 1:
LIST OF EXPERIMENTS
Experiment type
Neuron ID
MW 12.5 mW/g
F1
9
E6
5
11
3
3
3
F1
2
2
E6
3
3
3
3
3
Others
7
k
6
F1
5
E6
9
Others
2
Others
MW 125 mW/g
Others
Control
F1
•
Temperature
a
E6
Input resistance
AP s
la
2
2
2
la
indicates MW exposure then temperature study on a single neuron.
2.2.2
Data Reduction
Input resistance data consisted of responses to hyperpolarizing
current steps (duration 2.5 sec), photographed from a storage oscillo­
scope.
Normally, the test current was -l.OnA, but if the resistance was
low, -2.5nA was used, or if it was high, -0.25 or -0.5nA was used.
All
voltage responses fell within the range of -10 to -65mV, and were most
frequently between -20 and -itOmV.
Voltage responses were assumed to.be single exponentials.
Their
magnitudes and time constants were measured by matching (by eye) the
photographic records to a series of templates made on transparencies.
The quality of fit to an exponential was quite variable, but every
attempt was made to avoid systematic over- or underestimation.
Because input resistances can depend on the type of cell, the sea­
son, and other factors, resistances were normalized.
The resistance
measured at the end of the initial control period was taken as a refer­
ence value (1.00), and resistances at all other times were expressed as
fractions (1 + AR/R) of this value (Arber, 1981).
Reset, threshold, and ISI values were extracted from the intracel­
lular voltage record as follows:
First, the data were sampled continu­
ously at 2.5KHz from the taped records, replayed at one-half speed
(equivalent real-time sampling rate 5KHz), filtered (second order,
fc«l*50Hz) , and put in a circular buffer.
When the buffer contained an
AP and data before and after the peak presumed sufficient to estimate
the threshold and reset, the contents were saved.
A fixed time was alloted following the detection of an AP, during
which no data were sampled.
During this time, the reset level was cal­
culated directly from the buffered data, as the minimum voltage in the
portion of data after the AP peak.
The time from the previous to the
current AP peak (the ISI) was also measured.
taining the threshold was saved in a file.
The portion of data con­
Every data set was checked
systematically to ensure that a new AP had not begun to form within the
processing time.
One otherwise useable data set from an F1 neuron was
rejected for this problem.
All subsequent stages in the data reduction and analysis were done
offline.
Data supposed to contain the threshold were retrieved from the
file, and the threshold was estimated as described in Appendix B (Ma,
1985).
Occasionally, the threshold algorithm failed for lack of suffi­
cient data.
If this happened, the data were reacquired from the tape
into a longer buffer.
Reset, maximum, threshold, and ISI of each AP were encoded as char­
acters and sent to the UIC Computer Center.
associated with each ISI, by cumulating ISIs.
A time of occurrence was
When the recording was
blanked for a resistance measurement, or to set a new condition, the
blanked time was added to all subsequent times of occurrence.
segment, time of occurrence had resolution of ±0.01 sec.
times between segments were resolved only within ±10 sec.
Within a
The offset
The time of
occurrence was not used directly in the statistical analysis, but only
to locate particular sections of an experimental record.
The first AP in any experimental segment was assigned an ISI of
zero and was not used.
For each experiment, reset, threshold, maximum, and ISI were plot­
ted against time.
This, along with the histogram and serial correlogram
analyses (Appendix C), and the recursive estimation of the integrator
model (Appendix D), were all programmed in Fortran, and run under the
control of the DISSPLA plotting package (Integrated Software Systems
Corp., I98M .
Some subroutines from the International Mathematica1 and
Statistical Library were incorporated in the Fortran programs.
For the analysis of the resistance data, for the fitting of the
time-dependent functions (Appendix E), and for a number of tests of the
Fortran software, MlNITAB (Ryan et al., 198O) was used.
51
Chapter I I I
MICROWAVE EFFECTS ON INPUT RESISTANCE AND TIME CONSTANT
The input resistance and time constant of each cell were measured
at the start of recording after the cell's AP rate had stabilized, then,
about 30 min later, at the end of the initial control period.
In MW
irradiated neurons, two measurements were made during the exposure.
few cells had only one.)
(A
A final measurement was made during the recov­
ery period, at least 25 and most often kO minutes or more after MW off­
set.
For some cells, a second value was obtained later during recovery.
For control-only (sham-exposed) cells, resistances and time constants
were measured at times corresponding to the times for MW exposed cells,
counting from the start of recording.
The resistance measured at the end of the initial control period
was taken as a reference for each cell and assigned the value 1.00 (see
also section 2.2.1).
Measurements at all other times on the same cell
were expressed as fractions (1 + AR/R) of this value (Arber, 1981).
The membrane conductance of a particular cell
is proportional
the total number of ion channels, among other factors.
to
Therefore the
absolute conductance depends on the size of the cell as well as the den­
sity of channels in the membrane.
Effects of MW on resistance were
expressed as fractional changes, in order to make them independent of
cell size and channel density.
Changes in
the fractional values meas­
ure the probability (relative frequency) of MW induced changes.
52
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Input resistance and time constant responses of example neu­
rons. Each row shows an Fl then an E6 neuron. Top row:
exposure to 12.5mW/g; middle row: exposure to 125mW/g; bot­
tom row: no exposure.
24 0
Figure
5 shows sequential input resistance and time constant devia­
tion measurements from representative neurons.
From top to bottom
appear examples of exposure to 12.5mW/g, to 125mW/g, and sham (control
only).
The left column shows F1 neurons; the right shows E6 neurons.
These examples are from neurons that were used in the statistical
study.
They show the range of variation of the resistance and time con­
stant data.
The resistance and time constant responses of all neurons,
whether or not used in the statistical study, were similar to these.
To enable comparison, data from MW and control cells were grouped
into samples.
Although the exact times of measurements varied from cell
to cell, logical groups were made easily.
An initial control group had
the measurements made at the start of experiments on all cells, whether
or not later exposed to MW.
During MW exposure, actual or sham, meas­
urements were made in the time ranges 30£t<40
m ' n ar| d
^05t<60 min.
This
division was intended to enable a check for slowly evolving effects (see
section 1.8.3)i but was abandoned to secure a larger sample size; all
measurements during MW were put into one group.
A separate group was
made for corresponding data from sham exposed (control only) cells.
Separate recovery groups (MW and sham) were also formed.
Both longitudinal and parallel comparisons of the grouped data were
made.
The longitudinal comparisons were:
initial control against MW,
initial control against recovery, and MW against recovery.
The parallel
comparisons were of MW against sham MW and recovery against sham recov­
ery.
Longitudinal comparisons can discern whether trends in the data,
like those that appear in Figure
5» are systematic. Parallel compari­
sons are robust against these trends, which may have affected all cells,
regardless of exposure.
The comparisons were made using a two-sample t-test for differences
of means (with possibly unequal variances; Walpole, 197^) • as well as
the Mann-Whitney test for equality of distributions (Johnson and Leone,
1977) •
When using tests to compare small (<30) samples of data, it is nec­
essary to consider discriminatory power, i.e., the ratio of probabili­
ties for type I and type II errors (Johnson and Leone, 1977)-
Although
the power of a test always increases with larger samples, it can not be
expressed as a single value.
It is a function of the size of difference
being sought, decreasing for small differences.
Fortunately, failure to
notice a difference (type II error) is seldom a serious mistake, when
the difference being sought is small (Blum and Rosenblatt, 1972), so
tests based on HO: mi = mo versus HI: mi * mo are universally accepted,
for "reasonable" sample sizes.
The t-test and the Mann-Whitney test differ in the way their dis­
criminatory power depends on factors other than the sample size.
t-test is more powerful
The
if the underlying distribution of the data is
normal, but is sometimes weaker otherwise (Hays, 1973)Table 2 lists all comparisons of mean normalized resistances in MW
and control cells, using t-tests.
Below the means are the t-values, the
p-values (Type I error), and the number of degrees of freedom.
Compari­
sons were done separately for cells exposed to 12.5mW/g, to 125mW/g, and
without regard to power.
TABLE 2:
MW EFFECT ON FRACTIONAL CHANGE OF INPUT RESISTANCE:
12.5mW/g
125mW/g
T-TESTS
12.5 and 125mW/g
MICROWAVE -vs- INITIAL CONTROL:
n«40 1.02810.120
n*45 0.991 ±0.126
t - 1.41 p=0.16 df=83
n«=i6 0 .94410.095
n=45 0.99110.126
t— 1.51* p=0.13 df=35
n=56 1.00410.119
n=i»5 0.99110.126
t = 0.55 P=0.59 df=92
RECOVERY -vs- INITIAL CONTROL:
n«32 1.08810.173
n«i»5 0.99110.126
*f= 2.71 p=0.009 df=54
n =l 1 0.99110.060
n=i»3 1 .06310.157
n=45 0.99H0.126
n=i»5 0.99110.126
t= 0.02 p=0.99 df=34 * t = 2.37 p=0.020 df=81
MICROWAVE -vs- SHAM EXPOSURE:
n»40 1 .02810.120
n=l6 0.94410.095
n=22 1.03010.130
n=22 1.03010.130
t—0.03 p=0.97 df=41 *t=-2.34 p=0.025 df=36
n=56 1.00410.119
n=22 I.03010.130
t—0.79 p=0.44 df=36
RECOVERY -vs- SHAM RECOVERY:
n=32 1.08810.173
n=19 0.94210. 149
*t= 3.19 p=0.003 df=43
n=l 1 0.99110.060
n=i»3 1.06310.157
n=19 0.94210.149
n=19 0.94210.149
t= 1.28 p=0.21 df=26 *t= 2.92 p=0.006 df=36
MICROWAVE -vs- RECOVERY:
n=40 1.02810.120
n=32 1.08810.173
t=-l.66 p=0.10 df=53
n=l6 0.94410.095
n=56 1.00410.119
n=l 1 0.99H0.060
n=43 1.06310.157
t=-1.58 p=0.13 df=25 *t=-2.05 p=0.044 df=76
* indicates significance at p£0.05.
Table 3 lists the same comparisons, done with the Mann-Whitney
test.
For each comparison, the median values of the data are listed.
Strictly, the Mann-Whitney test compares entire distributions, not
means.
However it is often assumed that the distributions under test
differ only in a "location parameter" such as the mean or median (John­
son and Leone, 1977)-
Below the medians appear the differences (E) in
this location parameter, with the test statistics W (some authors use S
or U), and the probabilities of type I errors.
Data from which Tables 2 and 3 were made appear in Figure 6.
Below
the plots are confidence intervals for the true differences of means
(t-tests) and of location (Mann-Whitney tests).
The significant t- and
W-values starred in Tables 2 and 3 have the confidence intervals in Fig­
ure 6 which do not include zero.
The two tests gave similar confidence
intervals, indicating that their powers were comparable.
Use of two
different tests overcomes a possible objection (Myers and Ross, 1981) to
the use of t-tests (which assume normality) on fractional change data
(whose actual distribution is unknown).
The input resistance of MW exposed cells increased, while the
resistance of control only cells decreased.
Arber (1981) and Arber and
Lin (1983. 1985b) had found in Helix neurons, and Barsoum and Pickard
(1982) had found in Chara algal cells that MW lowered the resistance.
As in Arber (1981, 1983» 1985b) and in Barsoum and Pickard (19 8 2 ) ,
the changes evolved slowly.
They did not become significant until after
the MW exposure period, that is, only when initial and recovery data
were compared (MW exposed cells), and when actual and sham recovery were
compared.
The .data in this study are more variable than the data of Arber
(1981).
study.
This is partly explained by the use active neurons for this
The input resistance of a neuron depends nonlinearly on the
TABLE 2.:
MW EFFECT ON INPUT RESISTANCE:
12.5mW/g
125mW/g
MANN-WHITNEY TESTS
12.5 and 125mW/g
MICROWAVE -vs- INITIAL CONTROL:
n«40 MED= 1.017
n«45 MED= 0.987
E«= 0.041 W= 1899
p-0.115
n=l6 MED= 0.955
n»45 MED= O.987
E—0.026 W= 437
P=0.338
n=5& MED= 1.000
n =lt5 MED= 0.987
E= 0.019 W=2976
p=0.i* 12
RECOVERY -vs- INITIAL CONTROL:
n«=32 MED= 1.041
n«45 MED= 0.987
E- 0.086 W=l497
*p=0.010
n=11 MED= 1.000
n=45 MED= O.987
E= 0.013 W= 3^0
P=0.585
n-43 MED= 1.028
n=45 MED= 0.987
E= 0.058 W=2190
*p=0.021
MICROWAVE -vs- SHAM EXPOSURE:
n=40 MED= 1.017
n-22 MED= 1.032
E—0.014 W=1225
p=0.612
n=l6 MED= 0.955
n=22 MED= 1.032
E=-0.091 W= 220
*p=0.007
n=56 MED= 1.000
n=22 MED= 1.032
E=-0.040 W=2085
p=0.160
RECOVERY -vs- SHAM RECOVERY:
n=32 MED= 1.041
n-19 MED= 0.947
E= 0.102 W= 975
*p>=0.005
n=l1 MED= 1.000
n=19 MED= 0.947
E= 0.032 W= 188
p=0.451
n=43 MED= 1.028
n=l9 MED= 0.947
E= 0.082 W=1516
Ap=0.0l4
n=l6 MED= 0.955
n=l1 MED= 1.000
E=-0.04l W= 194
p=0.146
n=56 MED= 1.000
n=43 MED88 1.028
E—0.039 W=2554
p^O.OSS
MICROWAVE -vs- RECOVERY:
n«40 MED= 1.017
n-32 MED« 1.041
E—0.038 W=1346
p-0.200
* indicates significance at p£0.05*
58
FRACTIONAL DEVIATION IN INPUT RESISTANCE
1.5-1
I
1.0-
0.5 J
i
H
I
I
1
r
CTL MW
1
i
REC
»
1
{
<:>
i
CTL MW
1
i
REC
ffl
1
l|
1
CTL MW
1
REC
T-TEST: 0.95 CONFIDENCE INTERVALS
MW-v»-CTRL
REC-v»-CTRL "
MW-vi-SHAM
REC-v»-SHAM
MW-vi-REC
-1
-0.5
0.0
l
0.5 -0.5
0.0
0.5 -0.5
0.0
MANN-WHITNEY TEST: 0.95 CONFIDENCE INTERVALS
MW-vi-CTRL
REC-vi-CTRL ~
MW-v»-SHAM
REC-vt-SHAM"
MW-vt-REC
-0.5
0.0
0.5 -0.5
SAR = 12.5mW/g
FIGURE 6:
0.0
0.5 -0.5
SAR = 125mW/g
0.0
0
12.5 and 125mW/g
Time course of input resistance; tests for MW effect. For
each exposure level, and both together, AR/R of MW irradiated
and control neurons is plotted for (1) initial control, (2)
MW exposure, 30<ts60 min, and (3) post-exposure recovery.
Below the plots, bars delimit 0.95 confidence intervals for
the listed comparisons, first by t-tests, then by MannWhitney tests. * marks intervals which do not include 0;
compare Tables 2 and 3>
transmembrane voltage, particularly when the voltage is not far below
the AP threshold.
In an active neuron input resistance is a dynamic
quantity, and any changes due to MW have to be detected against a back­
ground of continuous ongoing voltage dependent changes.
In a silent
neuron, on the other hand, changes in input resistance due to MW would
be more evident, since most conductances would otherwise be steady.
Another difference from the previous work is that these experiments
were done at 20.9°C.
At 20.9°C, the input resistance effect seen by
Arber (Arber and Lin, 1983) was weaker than at 8°C.
The difference in the direction of change from that seen by Arber
(1981) needs some explanation.
Arber (Arber and Lin, 198^, 1985a.
1985b) thought that MW might mobilize intrace11ular1y stored Ca+* (sec.
1.5-2).
Calcium may lower the observed resistance mainly by gating on a
Ca +t dependent K* conductance.
This could result from overall heating,
which lowers input resistance (see section 5«2).
The present outcome seems not to be due to overall heating.
Its
direction is opposite from known thermal effects, and the effect was
clearly stronger at 12.5mW/g than at 125mW/g.
12.5mW/g had a sufficient
effect on AR/R to remain evident even when 12.5mW/g cells were grouped
along with 125mW/g cells, which by themselves did not show effects.
A more reasonable explanation would be that MW exerted a local
degenerative effect on the somatic membrane.
The lipid components of
the membrane are held apposed by strong electrostatic forces.
tein components, by contrast, are much more labile.
The pro­
Especially the ion
channel proteins respond to gating currents or transmitters (very weak
electric fields are sufficient) by undergoing conformational changes.
60
Gradually during an experiment a proportion of the channel moieties will
lose their patency and function.
As the total available number of con­
ducting paths decreases, resistance will increase.
It is this sort of
degradative effect which MW may enhance.
That the MW effect is degradative is suggested by the apparent
irreversibility of the effects.
Dissimilarity with an overall heating
effect does not rule out that the effect could be thermal or dissipative.
This point will be considered further in Chapter 6.
The resistance decrease in the control cells may have been caused
by a slowing down of the metabolic processes (e.g. Na+ and Ca*+ extru­
sion) which maintain transmembrane concentration gradients.
lead to an increase of internal Ca*+.
This could
In this view, the MW effects seen
by Arber (1981) would be an enhancement of a process which was occurring
in all prepared cells.
The present MW effect would represent degenera­
tion of a different type.
The difference would be evident in the paral­
lel comparison of MW and exposed cells after corresponding times.
The membrane time constant data were treated identically to the
resistance data.
Results are presented in Table
(corresponding with
Table 2) and Table 5 (corresponding with Table 3). as well as in Figure
7, which corresponds with Figure 6.
As a rule, membrane time constants covaried with input resistances.
Here, too, exposure to 12.5mW/g seemed more effective.
However, the
effects on time constants never reached statistical significance.
If membranes have a relatively constant specific capacitance (gov­
erned primarily by the highly stable lipid bilayer), resistance and time
constant ought to covary in a given cell.
Thus the time constant data
gave no evidence of a separate mechanism than the one which affected
resistances.
es.
The time constants were more variable than the resistanc­
This may be due to greater variability in the measurements.
TABLE 4:
MW EFFECT ON FRACTIONAL CHANGE IN TIME CONSTANT:
12,5mW/g
125mW/g
T-TESTS*
12.5 and 125mW/g
MICROWAVE -vs- INITIAL CONTROL:
n=40 1 .037±0.198
n=45 1 .020±0.196
t« 0.41 p=0.69 df=82
n=l6 1.086±0.I89
n=45 1.020±0.196
t= 1.20 p=0.24 df=27
n=56 1.05110.195
n=45 1 .02010.196
t= 0.80 p»0.42 df=94
RECOVERY -vs- INITIAL CONTROL:
n=32 1.099±0.352
n=45 1.02010.196
t= 1 .16 p=0.25 df-l»5
n=l1 0.97410.186
n=45 1.02010.196
t=—0.71 p=0.49 df=16
n=43 1.06710.321
n=45 1 .02010.196
t« 0.84 p«=0.40 df=69
MICROWAVE -vs- SHAM EXPOSURE:
n=40 1.03710.198
n=22 1.01810.181
t= 0.38 p=0.71 df=i*7
n=l6 1.08610.189
n=22 1.01810.181
t= 1.11 p=0.27 df=32
n=56 1.05U0.195
n=22 1.01810.181
t= O.70 p=0.49 df=4l
RECOVERY -vs- SHAM RECOVERY:
n=32 1 .09910.352
n=19 0.97210.200
t= 1.65 p=0.11
df=49
n=l 1 0.97410.186
n=19 0.97210.200
t= 0.03 p=0.98 df=22
n=43 I.O6710.321
n=19 0.97210.200
t= 1.42 p=0.l6 df=53
n=l6 1.08610.189
n=l1 0.97410.186
t- 1.52 p=0.14 df=22
n-56 1.05110.195
n=43 1.06710.321
t—0.30 p«0.77 df=65
MICROWAVE -vs- RECOVERY:
n«40 1.03710.198
n=32 1.09910.352
t—0.90 p=0.37 df-46
* indicates no changes in time constant were significant at p£0.05<
TABLE f>:
MW EFFECT ON TIME CONSTANT:
12.5mW/g
MICROWAVE -vs- INITI
125mW/g
MANN-WHITNEY TESTS*
12.5 and 125mW/g
CONTROL:
n-40 MED- 0.986
n-45 MED- 1.006
E—0.000 W-1720
p-1.000
n-16 MED- 1.051*
n«45 MED- 1.006
E- 0.060 W- 567
p-0.244
n=56 MED= 0.994
n-45 MED- 1.006
E- 0.019 W=2928
p=0.625
RECOVERY -vs- INITIAL CONTROL:
n=32 MED= 1.019
n-45 MED= 1.006
E= 0.046 W-1324
p-0.432
n-11 MED- 1.022
n-45 MED- 1.006
E—0.022 W= 303
P-O.837
n-43 MED= 1.022
n-45 MED= 1.006
E= 0.021 W=1979
p-0.585
MICROWAVE -vs- SHAM EXPOSURE:
n-40 MED= O.986
n=22 MED- 1.029
E—0.009 W=1240
P-O.78O
n-16 MED= 1.054
n-22 MED- 1.029
E= 0.049 W= 334
p-0.515
n-56 MED= 0.994
n=22 MED= 1.029
E= 0.002 W=2215
p-0.978
RECOVERY -vs- SHAM RECOVERY:
n-32 MED- 1.019
n-19 MED= 0.980
E- 0.086 W= 897
p-0.209
n=l1 MED= 1.022
n-19 MED- 0.980
E- 0.008 W= 173
p-0.931
n-43 MED= 1.022
n-19 MED- O.98O
E= 0.060 W-1422
p-o.306
n-16 MED- 1.054
n-11 MED- 1.022
E- 0.087 W- 246
p-0.278
n-56 MED- 0.994
n-43 MED- 1.022
E—0.003 W-2788
p-0.938
MICROWAVE -vs- RECOVERY:
n-40 MED- O.986
n-32 MED- 1.019
E—0.028 W-1401
p-0.507
* indicates no changes in time constant were significant at p£0.05-
63
FRACTIONAL DEVIATION IN TIME CONSTANT
1.5-1
1-
I
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T-TEST: 0.95 CONFIDENCE INTERVALS
MW-vi-CTRL
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MW-v»-CTRL
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FIGURE
i
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-0.5
0.0
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I
0.0
12.5 and 125mW/g
0.5 -0.5
Time course of time constant; tests for MW effect. For each
exposure level, and both together, ATC/TC of MW irradiated
and control neurons is plotted for (1) initial control, (2)
MW exposure, 30<t*60 min, and (3) post-exposure recovery.
Below the plots, bars delimit 0.95 confidence intervals for
the listed comparisons, first by t-tests, then by MannWhitney tests. * marks intervals which do not include 0;
compare Tables k and 5*
Chapter IV
MICROWAVE EFFECTS ON NEURON ACTIVITY
i*. 1
k.1.1
EVIDENT FEATURES OF THE DATA
Features of the Action Potent i al Records
It was indicated
in sec. 2.2.1 that neurons were used in the sta­
tistical study if they yielded enough APs to analyze under each condi­
tion.
The absolute lower limit was 1 OA APs in a condition, as this num­
ber was required to yield a testable serial correlogram (see Appendix
C).
No record was kept of the total number of experiments that was dis­
carded for having too few APs, as loss of spiking was most often accom­
panied by other pathologies, such as excessive drifts.
These defects
were considered to be due to technical errors, and not in the realm of
possible MW effects (sec. 2.2.1).
No effects of MW were visible in the raw spiking record of any cell
that was used in the statistical study.
Segments of the record from
neuron A021986, of type E6, which was exposed to 12.5mW/g, appear in
Figure 8.
Included are five-minute segments near the end of the initial
control period (25 min, A), during MW exposure (30 min, B; 50 min, C),
and during recovery (30 min, D).
Figure 9 shows corresponding spiking segments from neuron A02157
(initial control: 5 min (A) and 25 min (B); MW: 30 min (C) and 50 min
65
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FIGURE 8:
,j;
Segments of raw AP data; experiment A02196, neuron E6,
12.5mW/g. (a): Initial control, 25 min. (b): MW exposure,
30 min. (c): MW exposure, 50 min. (d); Recovery, 30 min.
:
-t--l
i
(D); recovery: 30 min (E)).
This F1 neuron initially had a moderately
pronounced bursting character, but tended to more regularity during the
course of the experiment, in that it fired longer bursts.
rons which did not fire bursts fired relatively regularly.
rate drifted gradually up and down.
Type F1 neu­
Usually the
Irregular interval sequences as in
Figure 8 were not seen in F1 neurons.
Figure 10 shows data from a highly regular neuron, AO9106.
This
cell, exposed at 125mW/g, was identified as type E7. but was grouped
with the unidentified neurons for treatment.
It was one of the most
stable cells recorded, particularly in AP height and offset drift.
The
figure shows initial control data (A; 1 min), MW exposure at 20 min (B)
and 55 min (C), and recovery (45 min; D).
Slight drifts in the AP rate
are visible during MW (C), but also appear in the control record (A).
Panel E shows that some time after temperature was lowered by i4°C, the
AP rate slowed and the AP height increased.
the temperature was reset.
Strip E starts 5 min after
An increase in rate during the first part of
strip E may be an anomalous transient (see sees. 1.6 and 3*3•1) The
temperature effect reversed on returning to 20.8°C (not shown).
Two neurons which were not used in the statistical analysis showed
specific changes during MW irradiation.
(unidentified) exposed at 12.5mW/g.
Figure 11 shows neuron A042186
Activity was robustly stable and
regular initially (control, 5 min, A), and early during MW (20 min, B) ,
but the AP height decreased, and firing became quite irregular, after 25
min (C).
After record C, the first input resistance measurement during
MW was made.
The original pattern of regular APs returned briefly (not
shown), but then disappeared (D; 35 min).
After a second resistance
67
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FIGURE 2:
Segments of raw AP data; experiment A02157, neuron Fl,
12.5mW/g. (a): Initial control, 25 min. (b): MW exposure,
30 min. (c): MW exposure, 50 min. (d): Recovery, 30 min.
68
(A)
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A091086
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IM»n^i:<»;;r 1 i i;> k ;ii;j111: i •f ?i ^:i ui j t.f r^'u li i-<:nn:iiiI;Ki:;f'rf tn:I:j t jf n ftifi; UifrWiii i.f11 r;f
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RECOVERY. 45 min
""TEMP Jo 17.4C. 5 min
30 sec "
FIGURE JO:
Segments of raw AP data; experiment A09106, 125mW/g. (a):
Initial control, 1 min. (b): MW exposure, 20 min. (c):
MW exposure, 55 min. (d): Recovery, US min. (e): Record
starting 5 min after resetting temperature to 17.1»°C.
n »m
: „,,^|ri
69
measurement, AP firing returned and remained through the rest of the
experiment (MW 50 min, E; recovery 35 min, F).
The F1 neuron in Figure 12 initially fired somewhat regularly (con­
trol 1 min, A; 25 min, B) , but developed a pronounced bursting character
within two minutes after the onset of MW at 125mW/g (C; arrow marks MW
onset).
As time progressed during the exposure, the AP pattern reverted
to more regularity (D; MW 30 min).
occurred at or after MW offset.
No hint of a corresponding transient
During recovery (E, 25 min), irregular­
ities which fell short of bursts were evident.
Shortly after the onset
of a second MW exposure, also at 125mW/g, a transient also occurred (F),
but this was not very distinct from transients that occurred at other
times in the recording.
The increasing phase of the transient started
before the full MW power level was reached (F, arrow).
These two cells represent unique single occurrences of obvious
reversible changes.
Referring first to the cell
in Figure 11, in numer­
ous instances a cell that stopped spiking during MW exposure was held
through and after the exposure period, so that any recovery of spiking
could be seen; resistance measurements were also continued.
The cell in
Figure 11 was unlike all other cells that stopped spiking, in that no
others recovered beyond producing a few APs over many minutes.
In almost all neurons, AP firing, inhibited during a resistance
measurement, sped up for a few seconds afterward.
A transient depolar­
izing release of charge which had accumulated by the end of the measure­
ment current pulse probably stimulated firing after a measurement.
A
capacitative discharge may have restarted AP production in the cell of
Figure 11, but the question of why firing stopped remains unanswered.
70
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FIGURE 11:
Experiment with an apparently reversible MW effect (I).
Neuron A042186 (unidentified), 12.5mW/g. (a): Initial con­
trol, 5 min. (b): MW exposure, 20 min. (c): MW 25 min,
showing gradual loss of amplitude and increasingly frequent
disruption of spiking. APs returned briefly when resistance
was measured after this record. (d): MW 35 min, showing
total loss of APs. (e): MW 50 min, showing return of spik­
ing after a resistance measurement. (f): Recovery, 30 min.
I'11': j':
71
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FIGURE 12;
Data which appeared to show a reversible MW effect (II). F1
neuron A072287* 125mW/g. (a): Initial control, 1 min.
(b): Initial control, 25 min. (c): MW onset (arrow), with
severe bursting. (d): MW, 30 min, with only weak bursts,
(e): Recovery, 30 min. (f): MW onset (arrow), with single
severe transient.
Inhibition through increased K* conductance (either direct or mediated
by Ca ++ ) seems unlikely, as the level of polarization hardly shifted
(F i gure 11, c).
Regarding the cell of Figure 12, many regularly or irregularly fir­
ing cells showed several short bursts or speedups of activity during an
experiment.
Also, F1 neurons tended to gain or lose bursting character
gradually during an experiment (see Figure 9).
The cell in Figure 12 is
unlike these other cells, because its bursting character changed quickly
and to an extreme degree, and the change occurred only once.
Bursting
may have resulted from a change in the interplay of Ca** and K* conduc­
tances (see sections 1.5-2 and 2.1.1).
Here, too, though, the question
as to what acted as a stimulus can not be answered.
From known temperature dependencies of neurons (see sec. 1.6), from
the known response time of the temperature controller (see sec. 2.1.4),
and from our own observations of temperature dependencies (see sec.
3-3). it would seem that the cell
temperature disturbance.
in Figure 12 experienced a transient
However, the temperature record revealed
changes only within the specified ±0.3°C tolerance.
It seems reasonable to conclude for these cells that there was some
pathology or disturbance of normal functioning, possibly from the out­
set.
For the cell in Figure 11, a MW induced effect may have occured,
but in the case of Figure 12, the rapid onset argues against effects of
the types suggested in section 1.5.
Denaturing MW effects on protein
structures, as were suggested for the resistance data, seem unlikely for
these cells, owing to the apparent reversibility.
Because of their rarity, observations on cells like those of
Figures 11 and 12 provide no direct insight into possible MW mechanisms.
They mainly indicate the need to base modeling and interpretation on
secure and repeatably observable phenomena.
4.1.2
Features of Reset. Threshold and Interspi ke Interval
For each experiment, the time course of the reset, threshold, and
maximum of the AP, along with the ISI, were plotted over the entire
duration.
(The AP maximum was not used in the analysis, but provided a
qualitative check on stability.)
These data are shown for five MW
experiments, in Figures 13 through 17Figure 13 is from an F1 neuron (A03286) which received 12.5mW/g.
No effect of exposure is evident.
This neuron had quite regular AP fir­
ing, compared with other F1 neurons, and was quite stable over the dura­
tion of the experiment.
The recovery period lacks very long intervals,
but this may have been a chance occurrence.
In Figure 14, an E6 neuron (A02056) was exposed, also to 12.5mW/g.
The quite erratic interval record was typical of E6 neurons.
The inter­
vals seem on average slightly to have lengthened during the exposure, as
compared to the control period, and they clearly shortened during the
recovery period.
Except for the unusual neurons in Figures 11 and 12
(section 3.2.1.1), these data give the strongest visual impression of a
MW response of all that were recorded.
Figure 15 has data from an F1 neuron (A02157; 12.5mW/g).
AP pattern in this cell was bursting (see Figure 9)•
The basic
In this cell, like
other bursting cells, the bursting character is evident i.n the reset,
71*
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FIGURE li:
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(Dos) iVAaaiNi 3>iidsa3iNi
MW exposure at 12.5mW/g; experiment A03286, neuron Fl.
Except for the lack of very long intervals in the recovery
period, no effect of MW is visible. In this and the follow­
ing figures, arrows mark times of input resistance measure­
ments.
FEATURES OF THE AP RECORD. EXPT. A02056CE6) 12.5mW/g
50-i
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AP MAXIMUM
25-
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100
125
•»j
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threshold and AP maximum.
As time progressed, this cell produced longer
bursts and longer interburst intervals.
during the exposure and did not reverse.
This change occurred mainly
It was typical of F1 neurons
that the AP interval pattern was stable or changed quite gradually, in
contrast with the E6 neurons.
The reset, threshold, and AP maximum
undergo more slow drift in this experiment than those of any other but
one.
Figure 16 shows E6 neuron A0219& (12.5"iW/g) , for which segments of
AP data appeared in Figure 8.
As in neuron A02056 (Figure 14), a gradu­
al tendency to longer intervals is evident.
Here, though, the interval
properties had already begun to change before MW onset.
The threshold
and reset in this experiment diverged considerably, and the reset varied
inversely with the gradual changes in the interval pattern.
By con­
trast, in the experiment of Figure 15. the threshold and reset covaried,
in a manner not apparently related with the variations in intervals.
This neuron produced 4670 APs during the experiment.
A white area
appears in Figure 16 because the plotting device could not resolve fully
these dense data.
Figure 17 holds data from an E6 neuron exposed to 125mW/g (A03177)•
The AP rate slowed through the experiment, but was particularly erratic
toward the end.
The reset, threshold, and maximum do not show the mark­
ed instability that is in the interval record.
The interval data in
this experiment are among the least stable of all experiments that were
accepted.
None of the five other neurons exposed at 125"iW/g (two E6,
two Fl, one not identified; see Figure 10) showed similar instabilities.
77
ca1") sanindwv
FIGURE 15:
( 3«s)
ivAaaiNi 3>udsa3iNi
MW exposure at 12.5mW/g; experiment A02157. neuron Fl. This
neuron gradually began to produce longer intervals, and the
other AP variables were relatively unstable.
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FEATURES OF THE AP RECORD. EXPT. A02196(E6) 12.5mW/g
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k.2
DESCRIPTIVE STATISTICS OF INTERSPIKE INTERVALS
k.2.1
Interspike Interval Histograms
Histograms were calculated and compared across experimental condi­
tions as described in Appendix C.
Data from each experiment were divid­
ed into three sections (before, during, and after exposure for the MW
experiments, and sections of corresponding length for the control-only
experiments).
An approximately x 2 distributed goodness-of-fit statistic
was calculated to compare each MW or second control segment and then
each recovery or third control segment against the initial control seg­
ment.
The number of bins (i.e., classes for interval
chosen for the histograms of each experiment.
length) had to be
The optimal number of
bins would give the x 2 test a statistical power of 0.5; that is, it
would cause the probabilities of Type I and Type II errors to be equal.
It depends on the number of data points (i.e., the total frequency), and
the desired significance level of the x 2 test (p=0.05 was used), and was
found using an algorithm from the International Mathematical and Statis­
tical Library (198^4; GTCN).
As indicated in Appendix C, data had to be concatenated for the x 2
test until each bin in the reference histogram (initial control) had a
minimum frequency of five.
Histograms made using the number of bins
chosen by algorithm GTCN had mainly sparsely populated bins.
When these
histograms were concatenated, much of the mass of the histogram moved
into the concatenated bins, leaving little of the original shape of the
histogram.
Probably the algorithm performed defectively because it did
not take into account the distribution of the data, but rather assumed
that they were not far from uniform.
The actual choice of binwidth was based on the shape of the histo­
gram for the initial control condition, and on the span between the min­
imum and maximum interval.
The goal in selection was to produce a rela­
tively smooth histogram in which changes in features such as the mean,
range, and skewness could be identified visually.
For highly regular
neurons, whose maximum interval was only several times the minimum, a
bin width of about one-quarter of the minimum interval was chosen.
For
irregular cells, and especially for bursting cells, there was a signifi­
cant proportion of intervals up to 100 or more times as long as the min­
imum.
Intervals longer than 200 times the bin width were discarded as
outliers.
For these cells, the bin width was set long enough to include
nearly all of the longer intervals within the span of the histogram.
The resulting bin width was usually equal to or slightly greater than
the minimum interval.
Interspike interval histograms are shown in Figures 18 through 22
for the five MW experiments whose AP variables appeared in Figures 13
through 17, respectively.
Figure 18 (F1 neuron A03286, 12.5mW/g)
reveals the most common feature found in the histograms, a tendency for
the width to increase, and for the skewness to become more negative,
over the course of an experiment.
In Figure 13, this feature was not
evident, because Figure 13 was scaled to include the rare long intervals
(>10 sec), which do not appear in the histogram.
In Figure 19 (E6 neuron A0205&, 12.5mW/g), the appearance of longer
intervals during MW irradiation and their disappearance afterward, as
82
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n=880
AT=200ms
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X 2 = 2574. 15df
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8
10
MICROWAVE (38 to 90 min)
n=1051
0.3-
RECOVERY (91 to 117 min)
n=452
0.3-
0.2 H
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0.4 -i
2
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INTERVAL (Sec)
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to
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A03286(F1) 12.5mW/g
FIGURE 18:
Interspike interval histograms, A03286(F1), 12.5mW/g. AT
indicates the bin width for all three histograms. Also for
the histogram of each condition, the number of intervals and
the time span (to the nearest minute) are indicated. For
each histogram other than the initial control, the value of
the x 1 test statistic from a comparison with the initial
control is shown.
10
was seen in Figure 18, is evident.
The shape of the histogram during
recovery is not very similar to its initial shape.
The histogram thus
belies the possibility, suggested in the discussion of Figure T», of a
reversible MW effect.
Figure 20 (F1 neuron A02157 12.5mW/g) shows a bimodal histogram
typical of bursting neurons.
This plot shows the relative frequency of
long intervals (the longest interval was 6O.83 sec; see Figure 15)Long intervals were not discarded as outliers, but rather concatenated
into the 7*6 to 8.0 sec class.
Figure 21 (E6 neuron A0219&, 12.5mW/g) shows clearly the lengthen­
ing of the average interval that was evident in the record of its AP
variables (Figure 16).
More striking, though, is the radical
increase
in the interval variance.
Figure 22 (E6 neuron A03177. 125mW/g) shows not only longer inter­
vals and greater variance but also quite drastic changes in the shape of
the histogram, as time progressed.
The histograms reflect the relative
instability of the interval data, as seen in Figure 16.
Figure 23 shows histograms for an unirradiated E6 neuron (A03117).
This set of histograms shows that the distributions of intervals changed
similarly in MW and control only neurons.
Table 6 holds the values of the goodness of fit statistic comparing
initial with MW and initial with recovery histograms for all MW exposed
neurons, and corresponding segments for control only neurons.
In both
comparisons in every experiment the value of the statistic was signifi­
cant, when checked using x 2 values, at p < 0.001.
84
0.4 n
CONTROL (0 to 26 min)
0.4-1
RECOVERY (78-110 min)
n*424
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15
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A02056(E6) 12.5mW/g
FIGURE 1 2 :
I n t e r s p i k e i n t e r v a l h i s t o g r a m s , A02056(E6), 12.5mW/g.
v e n t i o n s a r e as i n F i g u r e 1 8 .
Con-
85
0.8
.
0.8
CONTROL (0 to 28 min)
n=H68
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n«1276
X2= 155.0 19df
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INTERVAL (Sec)
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INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A02157(F1) 12.5mW/g
FIGURE 20:
I n t e r s p i k e i n t e r v a l h i s t o g r a m s , A02157 ( F 1 ) . 12.5mW/g. Long
i n t e r v a l s were concatenated and p l o t t e d a t 7 * 8 s e c . Conven­
t i o n s as i n F i g u r e 1 8 .
8
86
0.4 -i
CONTROL (0-38 min)
n=1325
0.4 -i
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RECOVERY (94-183 min)
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8
INTERVAL (Sec)
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killlllli.1
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0.0
2
4
6
10
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A02196(E6) 12.5mW/g
FIGURE 2 1 :
I n t e r s p i k e i n t e r v a l h i s t o g r a m s , A02196(E6), 12.5mW/g.
v e n t i o n s as i n F i g u r e 18.
Con­
10
87
0.4-i
CONTROL (0-32 min)
n=996
0.3
AT=200ms
04
RECOVERY (89-125 min)
n=638
°-H
X2= 145480.
O
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0.1
i
0.0
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0.4 -j
0.0 J
2
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6
8
10
MICROWAVE (33-89 min)
Jill
2
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6
8
INTERVAL (Sec)
n=1721
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X2= 4625. 9df
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0.0-
2
4
6
B
10
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A03177(E6) 125mW/g
FIGURE 22:
I n t e r s p i k e i n t e r v a l h i s t o g r a m s , A03177(E6), 125mW/g.
conventions see F i g u r e 1 8 .
For
10
9df
88
0.4-n
CONTROL 1 (0-42 m
n=712
AT=500ms
0.3-
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0.4 -
0.3-
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at
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CONTROL 2 (42-92 min)
n=712
0.0-
X 2 = 1.883x10' 9df
•••••lllllllh.
3
6
9
12
INTERVAL (Sec)
X 2 = 1672. 9df
O
11-
,
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CONTROL 3 <92-151 min)
n=712
0.2-
0.1-
0.0-
Jill
3
6
9
12
i
15
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A03117CE6) CONTROL
FIGURE 2 ^ :
I n t e r s p i k e i n t e r v a l h i s t o g r a m s , A03117 ( E 6 ) . c o n t r o l o n l y .
Conventions as i n F i g u r e 1 8 .
15
89
TABLE 6:
HISTOGRAM x a VALUES, MW AND CONTROL EXPERIMENTS*
F1 NEURONS
E6 NEURONS
df
MW/CT1
REC/CT1
15
Ht
19
61*8.6l
2257-12
200.29
2573.56
5161.66
155.01
16
18
171*5.1*8
1906.06
1575J».19
31*52.19
df
CT2/CT1
CT3/CT1
9
17
20
1550.60
81»ll» .74
10383-01*
1267.33
df
MW/CT1
REC/CTl
A02056
A02196
A05216
13
15
21*
66.11
7l»92.U6
175.96
1396.99
7315.78
536.73
A03177
A03227
A0l»067
9
11
13
l»625.M
21*5.35
3601.92
ll*5l*8l .25
1351*.99
111*1*3.50
df
CT2/CT1
CT3/CT1
16
1*959.1*0
99-10
1671.78
581*10.75
1*01.11*
18825.20
12.5mW/g
A03286
A 1201*6
A02157
125mW/g
A09036
A0l*057
CONTROL
A02057
B04067
C0l»067
1*87 • 26
527.30
B02196
A10166
A03117
21
9
UN IDENTFI ED NEURONS
df
MW/CT1
REC/CTl
11*
20
29
16397.15
1271.19
70921*. 13
957A8.1*!*
3301*.1*9
53932.32®
11*
601*2.63
6l96.56 a
df
CT2/CT1
CT3/CT1
23
20
726.36
61*71.06
88921*.94
i*6i*3.77a
12.5mW/g
A0l*11*6
A03316
A022l*7
125mW/g
A09106
CONTROL
A07026
A062l*6
a
indicates all values were significant, p£0.001.
indicates neurons with highly regular AP interval patterns.
Because all deviations were highly significant, MW and control
experiments could not be distinguished directly from the interval histo­
grams.
A larger value of the test statistic indeed indicates a greater
relative deviation between the histograms being compared, as follows
from Equation C-2.
Beyond this, however, it is not possible quantita­
tively to compare or test the values.
This is because Equation C-2 was
derived assuming that the null hypothesis (no change in the histograms)
was true (Blum and Rosenblatt, 1972).
It becomes a poor approximation
for the underlying likelihood ratio, when the deviations become large.
The statistics reported in Table 6 tested the hypothesis that MW
did not affect any aspect of the interval PDF.
The highly significant
changes in the interval histograms during an experiment indicated nonstationarities that may not have been related to the presence or absence
of MW.
The question arises as to what property of the data caused the his­
tograms to diverge as they did.
In a few data sets, the initial control
segment was subdivided into two parts, and histograms from each part
were compared, again using the x 2 test.
This check showed that even
under constant conditions, interval statistics often changed signifi­
cantly.
Common treatments for nonstationary data include removing lin­
ear (y = at + b) or square law (y = ait + a2t 2 + b) trends in the mean.
In the few data sets tried, significant linear and quadratic trends
could in fact be fitted to the entire experimental record; clearly, data
such as A0219& (Figures 8,16, and 21) could have been "improved" by
removing an overall trend.
Systematic detrending of entire experiments
was rejected for several reasons.
Removing an overall trend in the mean
did little to change the data within an experimental condition.
Also,
it was just as often the variance which had a trend as the mean.
Final­
ly, trend removal was not appropriate for the analysis of time dependent
properties (sec. **.3)t particularly because detrending resulted in neg­
ative intervals.
The histogram will change whenever there is a change in the mean,
variance, or higher moments of the data.
Therefore it can be asked
whether the particular changes that were seen represent changes in all
or just some of these parameters.
To answer this question, the hypothe­
sis was tested that MW did not affect any aspect of the interval PDF,
disregarding unknown changes m the mean.
A further test was made,
using the hypothesis that MW does not affect the PDF, disregarding
unknown changes in its mean and variance.
For these tests, the mean or the mean and variance of intervals in
the initial control condition was first found.
Then data from MW and
recovery conditions (or later control conditions in control only experi­
ments) were scaled so their mean or mean and variance matched those of
the initial condition.
Finally the histograms were recalculated.
Data
treatment and statistical justification for these tests are in Appendix
C (see equation C-l).
They should not be identified with tests for MW
effects specifically on the mean or specifically on the variance.
(Tests on these parameters are described below in sec. ^.3.1.)
These hypothesis tests are explorations to identify distinguishing
features of the data, and should not be regarded as physiological.
Physiological hypotheses predicting changes in interval PDFs could be
generated if specific assumptions about AP generation were made.
For
example, Gestri and Petracchi (1969) showed that certain retinal neurons
tend to act as pure integrators, with respect to effects of light stimu­
li.
If input integration was taken into account, light did not change
the interval histograms.
Unfortunately, in the present study, no prior
information is available to support physiological predictions of proper­
ties of interval PDFs.
Figure 24 shows how standardizing the mean and variance affected
the histograms from neuron A02196, for which histograms of the untreated
data appear in Figure 21.
Figure 25 shows the effect of this same stan­
dardization on neuron A03117» and can be compared with Figure 23Tables 7 and 8 present the
x 2 values obtained for all three
hypothesis tests on interval histograms.
In each entry, the first line
repeats the corresponding entry of Table 6, the second shows the test in
which variations in the mean interval are ignored, and the third shows
the result of ignoring both mean and variance.
the
As would be expected,
x2 test statistic was almost always substantially smaller when mean
values were standardized.
Usually it decreased further when both mean
and variance were standardized.
Nonetheless, all of the
x2 values
remained significant across all conditions in all experiments, both MW
and control-only, regardless of the particular hypothesis being tested.
This was true even of the neurons (marked
a
in Tables 6 and 8) with
highly regular and apparently stable interval patterns.
In experiment
AO3286, the MW histogram differed from the control histogram, when means
were standardized, at 0.005 > p > 0.001.
significant at p < 0.001.
All other test values were
93
0.4
.
o
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0.3H
u-
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CONTROL (0-38 min)
0.4-1
RECOVERY (94-183 min)
n=2067
n=1325
AT=200ms
0.3-
X2= 146.6 13df
0.2
LU
0.1
0.1-
0.0J
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10
0.4-1
MICROWAVE (39-94 min)
0.0J
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4
6
8
INTERVAL (Sec)
n=1278
.
0.3
X2= 326.0 13df
O
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0.2
0.1-
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—•••-——|
2
4
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6
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8
10
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS, A02196(E6) 12.5mW/g
MEANS AND VARIANCES MATCHED
FIGURE 2 k i
Histograms, A02196(E6), means and variances standardized.
Compare with Figure 21.
to
9*
0.60i
CONTROL (0-32 min)
0.60 -i
RECOVERY (89-125 min)
n=638
n=996.
AT=200ms
0.45
o
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0.45 -
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0.30H
0.30-
0.15-
0.15-
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0.60 -
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~r
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6
8
10
MICROWAVE (33-89 min)
iL
o.oo-1
0
2
4
6
8
INTERVAL (Sec)
n=1721
0.45
Oi.
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X2= 208.7
7df
0.30-
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0.15-j
0.00^ r
0
imii.
2
4
6
8
10
INTERVAL (Sec)
INTERSPIKE INTERVAL HISTOGRAMS. A03177(E6) 125mW/g
MEANS AND VARIANCES MATCHED
FIGURE 25;
Histograms, A03117(E6), means and variances standardized.
Compare with Figure 23>
10
95
TABLE 7:
x2 VALUES, RAW AND ADJUSTED, IDENTIFIED NEURONS*
F1 NEURONS
E6 NEURONS
df
MW/CT1
REC/CT1
df
MW/CT1
REC/CT1
A03286
15
14
13
648.61
36.63a
63.18
2573-56
697-21
708.92
A02056
13
12
11
66.11
75.39
5*.13
1396.99
90.34
89-954
A12046
lit
13
12
2257.12
619.36
62.28
5161.66
2837. 14
128.78
A02196
15
14
13
7492.46
2903.14
325.98
7315.78
2757.12
146.58
A02157
19
18
17
200.29
198.84
1793-^5
155-01
107.95
2389.15
A05216
24
23
22
175.96
110.48
98.31
536.73
216.89
113.20
16
15
lit
17it5.it8
919.08
13232.77
15754.19
20060.20
936.03
A03177
9
8
it625.it4
5008.it5
208.70
Iit5it8l .25
31973.77
it02.11
18
17
16
1906.06
1274.89
799.87
3452.19
1141.63
890.85
A03227
9
2^5-35
180.36
192.45
135^.99
1166.65
949.74
13
12
11
3601.92
609.19
106.52
11443.50
1493.00
54.69
df
CT2/CT1
CT3/CT1
12.5mW/g
125mW/g
A09036
A04057
7
A04067
11
10
df
CT2/CT1
CT3/CT1
9
8
8414.74
1098.32
164.20
B02196
7
1550.60
1176.16
224.69
16
15
14
4959-40
148.49
86.71
58410.75
10816.43
391.81
B04067
17
16
15
487.26
224.87
3391.67
10383.04
1878.50
3004.77
A10166
21
20
19
99-10
813-41
60.66
401.14
2030.40
224.70
C04067
20
19
18
527.30
409.13
3444.45
1267.33
2101.48
4813-97
A03117
9
8
1671.78
1456.59
184.20
18825.20
2766.37
180.69
CONTROL
A02057
7
* indicates all values are significant at p£0.001.
a indicates value was significant at 0.001<p<0.005.
TABLE 8:
x* VALUES, RAW AND ADJUSTED, UNIDENTIFIED NEURONS*
UN IDENTFI ED NEURONS
df
MW/CT1
REC/CT1
11*
13
12
16397.15
55731-28
739.5**
95748.44
52254.35
2091.71
A03316
20
19
18
1271.19
185.68
52.97
3304.49
584.26
152.75
A022A7
29
28
27
70924.13
3503.00
4276.26
53932.32®
1371.12
2358.65
14
13
12
6042.63
757.31
295.89
6196.56®
3859.23
658.59
df
CT2/CT1
CT3/CT1
A07026
23
22
21
726.36
259.06
110.48
88924.94
21536.41
412.38
A06246
20
19
18
6471.06
1077.85
556.34
12.5Mw/G
A04146
125mW/g
A09106
CONTROL
4643.77a
1786.79
597-67
* indicates all values were significant at p£0.001
a indicates neurons with highly regular firing patterns.
In summary of the histogram data, histograms changed radically
across experimental conditions, and there was no possibility of discern­
ing differential effects due to MW.
One limitation on the goodness of fit analysis of the histograms
originates with use of the observed data in the initial control condi­
tion as representing the expected or hypothetical distribution for each
experiment.
Because the data in the reference or null histogram are
random, the x2 test statistic may be overestimated.
However, given that
the underlying form of the distribution is not known, this choice makes
the best use of the available information.
*•.2.2
Ser i al correloqrams of the I nterval s
To assess dependencies among intervals, the serial correlogram was
measured from data within each condition, using Equation 1 .7—2.
The
conditions chosen correspond to those used for the histogram analysis.
Within a condition, only continuous subsegments with enough data points
for the test of renewal properties (Appendix C) could be used.
Whenever
more than one long enough continuous subsegment of data in a given con­
dition was available, a second correlogram was made.
In every experi­
ment, the first correlogram for a condition is from data recorded start­
ing when that condition was set.
Figures 26 through 30 show the correlograms for the experiments
whose AP variables appeared in Figures 13 through 17 and whose histo­
grams appeared in Figures 18 through 22.
Each figure shows, in the left
column, the serial correlograms for the imposed conditions, in temporal
order.
The bold line in each panel
is the correlogram of the actual
data, and the faint line is a correlogram of the same set of intervals,
but shuffled.
The correlogram of the shuffled data shows roughly how
much variability should be expected in correlograms estimated using the
given number of points.
function.
The correlogram is not in fact a continuous
Correlogram values at successive lags have been connected for
clari ty.
The correlograms in Figure 26 (neuron A03286, Fl, 12.5mW/g; compare
Figures 13 and 18) indicate adjacent and near adjacent intervals with
positively correlated lengths.
as did some Fl neurons.
fashion.
This cell did not exhibit frank bursting
The rate drifted up and down in a slow wavelike
The positive correlation among nearly adjacent intervals
reflects the gradualness of the drifts.
During and after MW irradia­
tion, positive correlation peaks at longer lags become increasingly evi­
dent.
This correlation at long lags indicates that the rate drift was
pseudoperiodic.
In Figure 27 (E6 neuron A02056, 12.5mW/g), the correlogram has
detected the slow oscillation in rate that occurred in the control con­
dition (compare Figure 1*0 .
The weakness of the negative correlations
(around lag 50) in control and MW conditions indicates that the oscilla­
tion was heavily damped or not truly periodic.
ed during MW, but damped out during recovery.
The oscillation persist­
The recovery correlogram
indicates that the dominant feature of the recovery period was a slow
drift in rate.
Slow drifts, up or down, appear as sustained positivi-
ties in the correlogram.
Figure 28 (F1 neuron A02157 12.5mW/g) , like Figure 26, shows rather
weak positive correlations among intervals that are not nearly adjacent.
99
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RECOVERY (99-117 min)
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0.1
0.2
0.3
0.4
0.5
FREQ (Neper)
SERIAL CORRELOGRAM AND SPECTRUM OF INTERSPIKE INTERVALS
EXPERIMENT A03286(F1) 12.5mW/g
FIGURE 26:
Serial correlogram of interspike intervals, A03286(F1),
12.5mW/g. F1 neuron, 12.5"iW/g. Initial control, then MW
(from MW onset), MW (from 28 min MW) and recovery. Left
panels: Bold line connects correlation coefficients; faint
line connects correlation coefficients found after random
reordering of intervals. Right panels: x2 test statistic H
for flatness of spectrum. Bold line segments centered on
smoothed spectral coefficients; faint line connects sample
points of raw spectrum.
100
1.0
CONTROL (0-21 min)
o
H = 9.7756
n = 351
ll_*
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1.0 -i
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r
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0.1
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H = 41.236
df=9
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1.0 n
MICROWAVE (27-60 min)
n = 566
0.3
0.80.6-
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uj
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100
0.0
RECOVERY (78-110 min)
1.0
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0.5
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0.2
0.3
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H = 36.397
df=9
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50
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100
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1
1
1
1
1
0.1
0.2
0.3
0.4
0.5
SERIAL CORRELOGRAM AND SPECTRUM OF INTERSPIKE INTERVALS
EXPERIMENT A02056(E6) 12.5mW/g
FIGURE 27:
Serial correlogram of interspike intervals, A02056 (E6),
12.5mW/g. The MW correlogram is based on data taken start­
ing at the onset of MW. Conventions are as in Figure 26.
101
This neuron fired quite evident bursts (see Figures 9 and 20).
The cor-
relogram of a periodically bursting neuron will show repeated positivities at lags that are multiples of the number of APs in a burst.
Peri­
odicity was somewhat more evident in correlograms from other F1 neurons
that fired bursts than in this one.
Excepting the peaks related to interburst intervals, evidence of
correlation is lacking in the correlograms of this and other bursting F1
neurons.
In this respect, bursting neurons contrasted with non-bursting
neurons, whether of type F1 (Figure 26) or E6 (Figure 27).
Non-bursting
neurons almost universally had correlograms with positivity that per­
sisted at least over the shorter lags.
Figure 29 (E6 neuron A02196, 12.5mW/g), like Figure 27, shows
effects of slow drifts.
Unlike neuron A02056 (Figure 27), this neuron
initially had a monotonical1y drifting rate (in this case downward), and
later, during NW irradiation, tended toward slow oscillations of rate.
A gradual shift from monotonic to wavelike rate variations, or from
wavelike to monotonic, was characteristic of the E6 neurons.
During the control and MW conditions, the correlation of immediate­
ly adjacent intervals is distinctly negative.
At least a relative neg­
ativity persists in the correlogram for the recovery period.
Sustained
negativity in the correlation of intervals separated by roughly half the
period was a feature of neurons with periodically drifting rates.
This
can be seen in the recovery correlogram of neuron A03286 at the bottom
of Figure 26.
In contrast with Figure 26, only the first lag of the
correlograms of neuron A02196 is negative.
102
CONTROL (0 TO 24 min)
1.0-1
n = 1290
0.0
UtXi
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MICROWAVE (28-60 min)
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MICROWAVE (60-83 min)
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100
0.0
0.1
0.2
0.3
0.4
0.5
FREQ (Neper)
SERIAL CORRELOGRAM AND SPECTRUM OF INTERSPIKE INTERVALS
EXPERIMENT A02157(F1) 12.5mW/g
FIGURE 28:
Serial correlogram of interspike intervals, A02157(F1),
12.5mW/g. Conventions are as in Figure 26.
103
A relative negativity confined to the first lag was found in sever­
al of the E6 neurons.
strong example.
Neuron A0219& (Figure 27) is a particularly
It was most evident during the initial control period.
This feature was not characteristic of the F1 neurons.
An initial neg­
ative peak indicates that long intervals tend to be followed immediately
by short intervals.
This pattern could resut from an interaction
between refractoriness and synaptic inputs.
It would be most evident
during the initial control period if this were the time when a cell were
being driven most strongly by active synaptic inputs, or when the ref­
ractory period were longer.
Figure 30 (E6 neuron A03177. 125mW/g) shows the same pattern of
changes as neuron A02056 (Figure 27) but more dramatically.
Neurons
A03177 and A0205& change from periodic to monotonic, the opposite of the
change in neuron A02196 (Figure 29).
The shapes of the serial correlograms captured salient details of
AP patterns.
They seemed more to describe particular neurons than the
type of neuron.
Only one feature of the correlograms seemed possibly to
be related to MW irradiation:
over the time course of an experiment,
the correlation properties of a cell changed gradually.
The correlo­
grams of MW exposed neurons appeared to change more than those of unex­
posed neurons.
As indicated in Appendix C, serial correlograms can not be compared
directly by any quantitative method.
In order to describe each correlo-
gram and provide a metric for characterizing changes, the corrsponding
frequency spectrum was examined.
The question of interest for the spec­
tra was whether they were flat, as a flat spectrum would result from an
uncorrelated interval sequence (uncorrelated point process).
10l»
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MICROWAVE (94-144 min)
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H •= 14.393
df=9
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RECOVERY (148-183 min)
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df=9
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0.0
0.1
0.2
0.3
0.4
0.5
FREQ (Neper)
SERIAL CORRELOGRAM AND SPECTRUM OF INTERSPIKE INTERVALS
EXPERIMENT A02196(E6) 12.5mW/g
FIGURE 29;
Serial correlogram of interspike intervals, A02196(E6),
12.5mW/g. Conventions are as in Figure 26.
105
o
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CONTROL (0-27 min)
Ul
n = 863
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MICROWAVE (33-65 min)
1.0-1
H - 86.277
df=9
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1.0-1
i.o-
50
75
160
0.0
RECOVERY (89-125 min)
n * 638
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df=9
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50
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LAG (Intervals)
100
0.0
0.1
0.2
0.3
0.4
0.5
FREQ (Neper)
SERIAL CORRELOGRAM AND SPECTRUM OF INTERSPIKE INTERVALS
EXPERIMENT A03177(E6) 125mW/g
FIGURE ^0:
Serial correlogram of interspike intervals, A03177 (E6),
125mW/g. Conventions are as in Figure 26.
106
To the right of each correlogram in Figures 26 through 30 is the
corresponding estimate of the spectral density.
The spectra were tested
for flatness by the procedure described in Appendix C, section C.2.
Sample points of the raw spectra, which are shown by the faint lines,
were first smoothed.
ing.
The bold bars show the sample points after smooth­
Next the smoothed spectra were tested for constancy of variance,
yielding the x2 statistic H which appears on each spectral plot.
The vertical scaling on the spectral plots was chosen to clarify
whether the spectra were flat.
The overall scalings of the plots for
different conditions may differ.
Although the spectral estimates have
only a finite resolution, proportional to the number of data in the cor­
relogram, the underlying functions are continuous.
Of the spectra, those of non-bursting neurons were low-pass, as in
neuron A03286 (Figure 26).
Bursting neurons had periodic or pseudoper-
iodic variations in their correlogram spectra, similar to but often
stronger than neuron A02157 (Figure 28).
Correlograms of neurons A02196
(Figure 29) and A062^6 (not illustrated), which had initial negative
peaks, show a band-reject character not seen in any others.
Tables 9 and 10 show the H statistics from all of the MW and
control-only experiments, respectively.
Below each value is the number
of degrees of freedom used in testing H as a x2 random variable.
The
starred values are significant at p=0.05No specific feature (such as the type of neuron) seemed to deter­
mine whether H would be significant at the start of an experiment.
In
general, the form of the correlogram tended to change quite gradually
over the course of an experiment.
In 8 out of the total of 23 experi-
TABLE 9:
TESTS OF HO:
CT1
F1
12.5
mW/g
A03286
A12046
F1
125
mW/g
E6
12.5
mW/g
E6
125
mW/g
NO ID
12.5
mW/g
CT2
CT3
12.61
9df
160.62* 142.24* 118.71*
8df
7df
6df
MW1
MW2
10.06
9df
3.84
5df
148.95*
7df
A02157
0.57
9df
0.45
9df
A09036
8.07
9df
11.11
9df
A04057
12.44
9df
8.45
A02056
9.78
6df
41 .24*
9df
A02196
11.05
9df
7.63
9df
A05216
38.03*
9df
29-17*
9df
A03177
86.28*
9df
143-64*
9df
A03227
2.01»
5df
4.43
5df
A04067
4.03
5df
3-54
3df
A041
*••99
9df
7.69
9df
A02247
A03316
NO ID
125
mW/g
INTERVALS ARE NOT SERIALLY CORRELATED (MW)
A09106
9df
RC2
1.65
4df
3.19
2df
80.81*
9df
153-77*
7df
0.11
9df
1.45
9df
26.73*
9df
4. 16
9df
4.94
9df
5.63
9df
36.40*
9df
14.39
9df
12.68
6df
33.95*
9df
78.49*
9df
81.93* 132.91*
9df
9df
0.89
2df
27.55*
9df
0.55
ldf
3.76
9df
11.16
9df
2.13
3df
176.81* 121.11* 160.59* 147-58*
9df
9df
9df
9df
* marks values which are significant at p-0.05.
RC3
48.82*
5df
178.52* 131 .49* 169.86* 100.86*
9df
9df
9df
9df
237.82*
9df
169.31*
9df
RC1
99.08*
9df
108
TABLE 10;
TESTS OF HO:
CT1
F1
A02057*
B04067*
C04067
EG
NO ID
INTERVALS ARE NOT SERIALLY CORRELATED (CONTROL)
CT2
41.46 110.19
9df
9df
191.62
9df
83.82
9df
l».67
9df
3-22
9df
CT3
CT4
CT5
CT6
CT7
CT8
63.60 158.91
5df
9df
x»o. 17 118.05 113.59 104.93 115.48
9df
9df
9df
9df
9df
5-49
9df
2.23
9df
3.78
9df
B0219&
30.93* 34.50*
9df
9df
33-31**
9df
14.09
2df
A10166
26.80* 45-38*
7df
9df
55-18*
8df
45-50*
9df
A03117
11.84
7df
20.69*
9df
29.37*
8df
25.55*
7df
A06246
22.16* 20.83*
9df
9df
28.96*
9df
33.68*
9df
A07026
89.22* 61.1*3*
9df
9df
57.15* 112.58*
i+df
8df
* marks values that are significant at p=0.05.
B04067 are significant.
1.48
9df
49-71 106.75
9df
9df
2.29
9df
All values in A02057 and
ments, the correlogram changed enough to change the significance judg­
ment of H at some time during the experiment.
Either H was insignifi­
cant at the start and then became significant (see, for example Figures
26, 27. and 29) or H lost significance that it had initially.
In two
experiments a change occurred and then reversed.
The 8 experiments where the significance of H changed amounted to 6
out of 15 microwave experiments, and 2 out of 8 control only experi­
ments.
CT9
109
If only neurons exposed at 12.5mW/g are considered, then k out of 9
experiments showed a change in H, as judged by its significance.
If
only 125mW/g experiments are taken, MW affected 2 out of 6.
None of the experiments on unidentified neurons showed a change in
the significance of the correlogram.
This may reflect that fact that
three of the unidentified cells fired regularly.
The question of whether the MW and control proportions were signif­
icantly different was judged using a binomial model.
An experiment with
one or more changes in the significance of the correlogram was consid­
ered a "success."
Two tests were applied to the proportions.
First, the observed
proportion p of control experiments with a change in the significance of
H was taken as an estimate of the expected proportion p under the
hypothesis of no effect.
The observed number x of MW experiments with a
change, out of a total of n MW experiments, was then assigned a prob­
ability under the null hypothesis according to (Walpole, 197^+) i
x-1
P = 1.0 - 2 ( J ) px (1 - p)n"x.
0
This test has the weakness that proportion p has to be estimated from a
small sample of actual data.
The other test was based on confidence limits which can be assigned
to observed proportions in binomial experiments with the number of tri­
als given (Blum and Rosenblatt, 1972).
These limits are quite conserva­
tive, as they are based on the Chebyshev inequality.
To apply this
test, confidence limits were assigned to the proportion (x/n) of MW
110
experiments with a change in H.
The proportion of control experiments
with a change in H was then taken as a point estimate and judged not to
be part of the same population if if it fell outside the limits.
Table 11 shows that MW affected the stability of H, as judged by
whether the significance of H changed.
However the test based on
expected proportions did not reach a significance level of 0.05.
Nor
did the proportion of control experiments with a change in the signifi­
cance of H fall outside the confidence bounds for the observed propor­
tion of MW experiments showing a change.
Both tests failed when only
12.5mW/g or only 125mW/g experiments were considered, as well as when
all neurons were included.
MW EFFECT ON THE SIGNIFICANCE OF C0RREL0GRAM xJ STATISTIC H
TABLE 11:
OBSERVED
(MW)
EXPECTED
(CONTROL)
PROB(obs.|p)
obs.
prop.
conf. 1imi ts
lower upper
obs.
12.5mW/g
V9
O.kkh i
0.068
0.897
2/8
0.250
0. 165
125mW/g
2/6
0.333
0.029
0.89l»
2/8
0.250
0.1*51
12.5 and 125
6/15
0.i»00
0.082
0.832
2/8
0.250
0. 11*8
P
An alternative method for classifying the values of the H statistic
was based on how much the value of H changed during each experiment,
without regard to whether the value itself was significant at a particu­
lar level.
To apply this method, the ratio of H in each condition to H
during the initial control condition was calculated.
Ill
Values of H are essentially sample variances from normal popula­
tions (Cox and Lewis, 1966).
Further, H values for successive correlo­
grams were determined from independent samples of data.
Therefore it is
acceptable to form the ratio of H values, which follow a x2 distribu­
tion, and expect the ratio to follow approximately an F distribution.
A matrix was formed, to show the ratio of the H statistic for each
correlogram to the H statistic for every other, within each experiment.
Table 12 shows which entries in each matrix were significant at p=0.10.
(The F-ratio test is two-tailed.)
Entries marked 0 indicate no change,
while those marked + mean the degree of correlation was significantly
larger, and those marked - mean the degree of correlation was signifi­
cantly smaller.
Entries for MW experiments in the table correspond with
each possible comparison of a correlogram in one condition against cor­
relograms for the others.
For instance, in experiment A120^*6, three
control correlograms were compared against the single MW correlogram and
then against the single recovery correlogram.
In control only experi­
ments, the first control correlogram was compared with each of the fol­
lowing correlograms.
No comparisons of correlograms later than the
first with subsequent correlograms revealed significant differences in
control experiments.
The significance judgments on the F ratios were also treated as
binomial data, exactly as were the significance levels of the H statis­
tic.
An experiment with one or more significant F ratios was considered
a "success".
Considering all experiments, without regard to neuron
type, 8 out of 23 experiments revealed significant changes in statistic
H.
These were 7 out of 15 MW irradiated neurons and 1 out of 8 control
112
TABLE 12:
CHANGES IN THE VALUE OF CORRELOGRAM xa STATISTIC H
12.5mW/g
125mW/g
Control
RECV / MW
A03286
A1201*6
A02157
0a _c
0 0 0
0 -
0
+
+
0
0
A09036
A0l»057
0
0
0
0
0
0
0
A02057
B0l»067
C0l»067
125mW/g
+
CTRL[n]
/
0
0
0
+
0
0
0
+
0
CTRLtl]
0
0
0
0
0
0
+
0
0
+
0
0
0
0
0
0
0
0
A03177
A03227
AOJ4O67
0
0
0
0
0
0
0
+
0
/
+
+
0
+
0
0
+
0
CTRL[1]
B0^067
0
0
0
0
A10166
A03117
0
0
0
0
0
0
0
RECV / MW
RECV / CTRL
0
A0M46
0 0
00
A022i»7
A03316
00
0
000000000
0
0
A09106
0000
0000
0000
CTRL[n] / CTRL[1]
Control
0
A02056
A02196
A05216
MW / CTRL
125mW/g
+
0
RECV / CTRL
OTHERS
12.5mW/g
+
RECV / MW
CTRL[n]
Control
+b
MW / CTRL
E6
12.5mW/g
RECV / CTRL
MW / CTRL
F1
A06246
A07026
0
0
0
0
0
0
0
a 0 indicates H did not change (F-ratio test, p>0.10).
k + indicates an increase in H (F-ratio test, p£0.10).
c - indicates a decrease in H (F-ratio test, pSO.lO).
113
only neurons.
Considering only neurons of types F1 and E6, H changed
significantly during or after exposure in 7 out of 11 neurons exposed to
microwave.
Only one out of 6 control experiments showed a significant
change.
Tests on the F ratios on neurons grouped by exposure level appear
in Table 13.
In the case of 12.5mW/g, the proportion of MW experiments
with a change is significantly larger, when judged using summed binomial
probabilities, but fails the test based on confidence bounds.
Cells
exposed to 125mW/g did not have changes in the value of H significantly
more often than unexposed cells.
The total population of MW exposed
cells is very nearly significantly more affected than controls.
TABLE Ji:
MW EFFECT ON THE VALUE OF CORRELOGRAM x2 STATISTIC H
OBSERVED
(MW)
EXPECTED
(CONTROL)
PROB (obs.|p)
obs.
prop.
conf. 1imi ts
1 ower upper
obs.
12.5mW/g
5/9
0.555
0. 102
0.931
2/8
0.250
0.048*
125mW/g
2/6
0.333
0.029
0.89^
2/8
0.250
0.451
12.5 and 125
7/15
0.467
0.108
0.863
2/8
0.250
0.056
P
* indicates significance at p£0.05.
Taking into account both the significance (Tables 10 and 11) and
the value (Tables 12 and 13) of statistic H, the six test groups were
consistent in the direction of a possible MW effect.
However, only the
value of H changed more under MW at a level of p<0.05. and this only for
1u
cells exposed to 12.5mW/g and only using the less conservative test
bassed on summed probabilities.
The serial correlogram reflects the spiking properties of a partic­
ular cell.
Referring to the integrator model (equation 1.7~3) * temporal
correlation in one or more of the threshold value of v(t), the reset
value v(to), or the input current i (t) will impart correlation among
intervals.
Formally, these variables can be viewed as having undergone
filtering by the action of dynamic phenomena not included in equation
1.7-3.
Physically, serial correlation can result on the one hand from
processes intrinsic to normal cell function.
For instance, an initial
negativity was indicated in the discussion of Figure 19 possibly to rep­
resent refractoriness.
Refractoriness results from channel inactivation
processes which have been characterized pharmacologically (Hi lie, 198^4) .
On the other hand, as a preparation ages, the serial correlation
gradually changes in a nonspecific way.
Neither the direction nor the
time of onset of correlation changes had any consistent pattern.
Physically, these changes may occur because the ganglia, lacking blood
circulation, maintain needed concentrations of oxygen and nutrients, and
dispatch metabolic wastes, quite imperfectly.
Microwave appears marginally to speed up or magnify ongoing changes
in the serial correlation of AP intervals.
In explaining MW induced
increases in input resistance, possible denaturation or other degenera­
tion of channel proteins was indicated.
Destabi1ization of correlation
properties could also result from this process, but because consistency
is lacking in the type and direction of effect, this connection remains
speculative.
115
4.3
EFFECTS ON TIME-DEPENDENT ACTION POTENTIAL PROPERTIES
As noted in section 4.1, MW may just as well affect the mean
or the standard deviation
and correlation properties.
151 of AP intervals, as their distributional
In addition, MW effects could appear in.
properties of the input current
grator model (section 1.7)•
misi
mAT/C
which was postulated in the inte­
Variables related to the input current
include not only the mean yU| and standard deviation
, but also autore-
gressive coefficients AR1 (I) and AR2O), which compactly describe its
correlation properties (see section 4.3.2).
The analyses of input resistances (Chapter 3), interval histograms,
and serial correlograms (sections 4.1 and 4.2), required the assumption
that a steady state be reached during each experimental condition.
The
AP-related variables can also be treated assuming steady states; i.e.,
using a point estimate for each condition in each experiment.
An advan­
tage of this treatment is that it is selective for effects that are all
in the same direction.
On the other hand, as detailed in Appendix E, the estimation situ­
ation for the AP-related variables is more favorable, and sequential
estimates can be made from short subsegments of the data records to cre­
ate explicit functions of time.
The advantage of the sequential esti­
mates is that they admit of straightforward analysis using linear
regression, and that each cell can be tested individually for a MW
effect.
116
4.3.1
Effects on the Mean and Standard Deviation of Intervals
4.3-1.1
Steady State Case
For each experimental condition (initial control, MW, and recovery
in each MW experiment, and corresponding records in each control only
experiment), a single value of i"isi
anc ' a lSI
were
®ach found.
The data
segments used matched exactly those used in the histogram analysis.
As in the treatment of the resistance data, M|S| or CT|j| were
expressed as a fraction of their values during the initial control peri­
od, in each experiment.
Fractional deviations in M|g| and cr151 can not
be interpreted directly in terms of probabilities of effects, as was
done for the input resistance data (Chapter 3).
However, fractional
deviation is an appropriate measure for these data, because, like the
resistance data, their absolute values depend on factors not related to
MW.
Mann-Whitney tests were used in preference to t-ratio tests for
differences of means or F-ratio tests for ratios of variances.
This is
because the usual distributional assumptions (normal and x2> for M|$|
and cr|5|, respectively) can not confidently be applied to ratio or frac­
tional deviation data (see Chapter 3)Table 14 presents the results of Mann-Whitney tests for the hypoth­
eses that fractional changes in M|SI were not different for MW exposed
and control neurons, while Table 15 shows the same analysis for f|si*
In each table, MW exposed and control only neurons are compared at cor­
responding times, during and after MW exposure.
cant at level p (type I error).
Statistic W is signifi­
Variable E represents the difference in
location (mean or median) of the distributions for the two conditions.
117
TABLE lk:
MW EFFECT ON MEAN INTERSPIKE INTERVAL (STEADY STATE)*
12.5mW/g
MICROWAVE
CONTROL
RECOVERY
CONTROL
125mW/g
12.5 and 125mW/g
n= 9 MED= 0.8337
n= 8 MED* 0.8690
n- 6 MED= 0.8238
n- 8 MED= 0.8690
n=15 MED= 0.8337
n= 8 MED= 0.8690
E=-0.06l W= 77.5
E«= -0.091 W= 1* 1.0
E= -0.063 W=172.5
p= 0.7728
p= O.65U
P= 0.651^
n= 9 MED= 0.851»3
n= 8 MED= 0.5723
n= 6 MED= 0.8^419
n= 8 MED= 0.5723
n-15 MED= 0.85^3
n= 8 MED= 0.5723
E= 0.203 W« 89.O
E=
E=
p= 0.U7O5
p= 0.5613
0.190 W= 50.0
0.197 W=193-0
p= O.i+197
* indicates none of the differences were significant at pS0.05.
Experiments were subgrouped by SAR (12.5mW/g, 125mW/g, or both) for
both tables.
It appears that M|$| decreased slightly more during MW in
MW exposed cells, while it decreased more during (sham) recovery in con­
trol only cells.
C|S| increased over time in control only cells; MW
tended to mitigate the increase.
However, these effects did not reach
significance (using pS0.05 as a criterion) in the population of experi­
ments or in either subgroup.
Cells were also grouped by type (F1, E6,
or unidentified; not shown in table).
Although the numbers of samples
in these subgroups were too small to support confident statistical judg­
ments (see discussion in Chapter 3). they revealed no apparent effects.
The absence of all MW effects on the steady state estimates of M|$| and
<7|5I certainly lends no support to the idea that specific MW effects
might exist.
118
TABLE 15:
MW EFFECT ON SD OF INTERSPIKE INTERVALS (STEADY STATE)*
12.5mW/g
MICROWAVE
CONTROL
125mW/g
12.5 and 125mW/g
n« 9 MED= 0.9916
n= 8 MED= 1.4357
n» 6 MED= 0.9321
n= 8 MED= 1.4357
n«15' MED= 0.93^7
n= 8 MED= 1 .^357
E«=-0.500 W= 63.O
E= "0.219 W= 43-0
E«= -0.375 W=l60.0
p» 0.0922
p= 0.8465
P» 0.208l
n«= 6 MED= 1.1616
n= 8 MED= 1.2646
n-15 MED= 0.9108
n- 8 MED= 1.2646
E—0.343 W= 68.0
E= -0.073 W= 43.0
E= -0.252 W=165.0
p= 0.2290
p= 0.8465
P= 0.3493
RECOVERY
n= 9 MED= 0.7054
CONTROL
' n= 8 MED= 1.2646
* indicates none of the differences were significant at p£0.05.
4.3•1•2
Time Dependent Case
The steady state analysis is clearly unable to reveal anything
about the time course over which effects might evolve.
It could be
falsely sensitive to random effects which occurred approximately cotemporally with MW, but did not follow causally (see, for example, Figure
16).
It statistical power is related to the size of sample available,
and it is unable to yield judgments about individual cells.
To overcome these possible limitations, /jjgi and cr 15( were estimat­
ed as explicit functions of time.
As described in Appendix E, section
E-2, subsegments of the AP interval record from each experiment were
defined using a window which was moved through the record in overlapping
steps spaced each three minutes.
The mean and standard deviation of the
119
intervals within the window defined each sample point of time dependent
functions which can be denoted Misi^)
an ^ crisi^t^»
respectively.
To analyze each MW experiment, M|$|(t) and erj5j (t) were regressed
separately on an indicator variable representing the on or off condition
of MW exposure at each sample time by the values 1 and 0, respectively.
In treating the control only experiments, the indicator variable was set
to switch from 0 to 1 at the time that delineated the initial from the
second control segment, and to return at the starting time of the third
control segment, the segments bfeing the same as used in the histogram
analys i s.
As was indicated in Appendix E, two different models for MW effects
were considered.
On the view that MW effects are instantaneous or stat­
ic, rather than being filtered through any of the dynamic properties
that govern AP generation, the observed values of misi(*)
and
^ISI ^
were regressed directly on the values of the indicator at corresponding
times (Equation E-6):
f (t) = W0I (t)
where
f (t) is either of M j s) C t) or c?is|(t)»
Wo is the coefficient expressing the relative strength of effect,
and
I(t) is the indicator variable.
In general /U|g|(t) or C|s|(t) would depend on a single regressor (the
indicator variable) according to y "a + bx.
Microwave would not affect
the mean of m 15
|
(t) and cr j 5 j (t) over an entire experiment.
For this
120
reason, and because some of the variance in the data would otherwise be
explained as variance in the estimate of a, which could somewhat dilute
a significance test on b, overall means were calculated separately and
the regressions were done without constant terms.
Data for M|s|(t) and f|S( (t) for four representative experiments
appear in Figure 31 and Figure 32.
In each figure, the faint line rep­
resents the data while the bold line represents the fit of the regres­
sion model.
Each fit (prediction) was made using
f (t) = Wq I (t) + (mean)
The overall means of m|sI
and
aISI ^
were added back in to the model
predictions for plotting.
At the bottom of the plot is the course of the indicator variable.
Microwave was applied gradually, over several sec, in an experiment.
However, the gradual onset and offset slopes on the indicator plots in
Figures 31. 32, and later figures do not indicate specifically the onset
and offset rates.
Rather, they resulted from applying the same (over­
lapping boxcar) averaging to the indicator sequence as was applied to
the AP interval sequence.
In Figure 31 are two MW experiments with 12.5mW/g.
pare Figures 13, 18, 26) no MW effect on misi
In A03286 (com­
's visible in the pre­
diction, but a weak effect on c|s|(t) can be discerned.
In A0219& (com­
pare Figures 8, 16, 21, 2k, 29) effects on both parameters were
predicted by the static model.
In Figure 32, the top experiment
(A09106; compare Figure 10) shows a quite weak effect on M|s|(t), but
121
EXPERIMENT A03286CF1) 12.5mW/g
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STATIC MODEL
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180.0
INDICATOR
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0.0
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150.0
120.0
150.0
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TIME (min)
FIGURE 21:
MW effects on mean and SD of ISI (static model; I). Above:
A03286 (FI, 12.5mW/g); Below: A02196 (E6, 12.5mW/g). In
each panel, bottom plot has misi(*) (faint line) and its
prediction (bold line); top plot has C7|S| (t) (faint line)
and its prediction (bold line). Beneath the plots is the
indicator variable.
122
EXPERIMENT A09106(NQ ID) 125mW/g
u
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w
OO
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O
OO
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STATIC MODEL
1.00.80.60.40.20.00.0
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30.0
45.0
60.0
75.0
90.0
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105.0 120.0 135.0 150.0
MW ON
INDICATOR
MW OFF
0.0
15.0
30.0
45.0
60.0
75.0
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105.0 120.0 135.0 150.0
EXPERIMENT B02196CE6) CONTROL ONLY STATIC MODEL
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TIME (min)
FIGURE 3 2 :
MW e f f e c t s o n mean and SD o f I S I ( s t a t i c m o d e l ; I I ) . Above:
A09106 (Not i d e n t . , 125mW/g); Below: B0219& (E6, c o n t r o l
o n l y ) . C o n v e n t i o n s a r e as i n F i g u r e 31•
123
none on cr|£|(t), while the bottom experiment (B02196) shows strong
effects on both.
This is surprising enough, as A09106 was irradiated at
125mW/g, while B02196 was an unirradiated control.
The feature that most distinguishes A0219& and B02ig6, which showed
strong effects of the indicator, from A03286 and A01906, which did not,
is the instability of ?is|(t) in A0219& and B0219&-
Particularly
because of the outcome in B0219&, the possibility of nonstationarities
in the AP functions which fortuitously mimic MW effects because they are
coincident in time, has to be taken seriously.
The alternative view of MW effects considered in Appendix E was
that they may represent an input (forcing function) to the dynamic sys­
tem that governs AP generation (Equation E~7) '•
f(t) - V,f(t-1) + V,f(t-2) + ... + V f(t-n) +
WQI (t) + W,l1t-1)
k
+ . . . + Wml"t-m)
-l~2
where
f (t) is again one of the six functions of neuron activity,
1
V j , i=l,...,n express the natural dynamic response of the system,
and
Wj, j=0,...,m express the strength with which I forces a response.
This view takes explicit account of the possibility of delayed and/or
gradually developing effects, as suggested in sec. 1.8.3.
this situation, time series regression was used.
To analyze
Figure 33 and Figure
34 show dynamic model predictions for the same experiments whose static
predictions appear in Figures 31 and 32.
12U
EXPERIMENT A03286(F1) 12.5mW/g
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0
0
CO
0.80.60 .40.20.0-
o.o
to
Z>
o
u
UJ
£
u
•
V
30.0
60.0
90.0
30.0
60.0
90.0
—i
120.0
—i
r
150.0
180.0
150.0
180.0
3:0-1
2 .4-
m
1.8-
z
<
Ui
1.2-
*
DYNAMIC MODEL
1.0-1
0.6-
0.0-
—i
0.0
y
MW OFF -
x
INDICATOR
1
0.0
120.0
1
30.0
1
1
60.0
1
1
T"
90.0
—I
120.0
150.C
180.0
TIME (min)
FIGURE 2 1 :
MW e f f e c t s o n mean and SD o f I S I (dynamic m o d e l ; I ) . Above:
A03286 ( F l , 12.5mW/g); B e l o w : A02196 (E6, 12.5mW/g). Com­
pare wi th F igure 31•
125
EXPERIMENT A09106(NC> ID) 125mW/g
u
•
DYNAMIC MODEL
1.0-j
0.8-
w
00
toI
$Q£
0.6-
0.40
0
to
0.20.0-
0.0
UJ
u
U1
QC
UJ
52
Z
<
Z
£
Q
0.0-
u
«
.
£
l
I
I
45.0
60.0
75.0
:
I
l
l
90.0 105.0 120.0 135.0 150.0
INDICATOR
1
1
1
1
1
15.0
30.0
45.0
60.0
75.0
1
1
1
1
90.0 105.0 120.0 135.0 150.0
EXPERIMENT B02196CE6) CONTROL ONLY DYNAMIC MODEL
O
UJ
l
30.0
J
0.0
GO
o
KJ
I
15.0
-
U_
LO
90.0 105.0 120.0 135.0 150.0
0.2-
MW OFF
£
UJ
75.0
MW ON-
Z
<
UJ
60.0
0.4-
Q
h—
l/>
Q
z
<
45.0
0.6-
0.0
>
UJ
30.0
0.8-
UJ
V
O-
15.0
1.0 -1
O
O
to
7.0-|
5.64.22.81.40.0o.o
u
e
VI
S-S
30.0
60.0
90.0
30.0
60.0
90.0
120.0
150.0
180.0
11.On
8.8
6.6
z
<
4.4-j
UJ
2.2
€
0.0
—i
—I
0.0
ON i
Z OFF
/
1
0.0
1
30.0
120.0
1
60.0
1
1
180.0
INDICATOR
X
1
150.0
—i
1—
90.0
120.0
150.0
TIME (min)
FIGURE 3 ^ :
MW e f f e c t s o n mean and SD o f I S I (dynamic m o d e l ; I I ) .
Above: A09106 ( N o t i d e n t . , 125mW/g); B e l o w : B02196 (E6,
c o n t r o l o n l y ) . Compare w i t h F i g u r e 3 2 .
180.0
126
It is clear that the dynamic model is a far superior representation
of each set of observed data.
Most of the variation in both M|s|(t) and
er|s|(t) seem to be predictable from the intrinsic dynamics; the effect
of the indicator is not visible in the predictions, Other than for
A09106.
On data from a few experiments, the static and dynamic models were
compared by checking the residuals for autocorrelation.
The first few
autocorrelation coefficients for the static models were universally
larger than those of the dynamic model, indicating that the static model
was inferior.
Despite this, the static model has the advantage of high
sensitivity, since all of the variance in the data which the model can
explain is loaded directly on the indicator.
To analyze the static regression models for m15 1 (*)
an{* CTISI
^»
the overall significance of each model was checked using an F-ratio
test.
an^
To analyze the dynamic models for
^ISI^' ^ ratio
tests (Equation E-10) were applied to determine if the model was signif­
icantly better when it included the indicator as a forcing function than
when it represented an unforced system (all Wj=0 in Equation k.$-2).
As
indicated in Appendix E, an F-ratio test provides an overall comparison
of models without the difficulties attached to judging individual coef­
ficients (Neter and Wasserman, 1971*) •
Table 16 summarizes the regression analysis of m|5|(t) and Table 17
lists the same features of models for CT|<j| (t) First, the Ra value and
F-ratio for a test of overall significance of each dynamic model,
including the forcing function, is shown.
Next appears the same test
for the model without the forcing function.
Among all dynamic models
127
for m i s i (*)
and aIS|(t)'
nificant in every case.
both
the
forced and unforced models were sig1
Third in Tables 16 and 17 are F-ratios for the
hypothesis that the forced model is no better than the unforced.
Final­
ly F-tests for the overall significance of each static model are includ­
ed.
Interpretation of these latter two tests will be given in sec.
^ - 3 - 3•
128
TABLE 16:
ANALYSIS OF TIME DEPENDENT MODELS FOR MEAN AP INTERVAL
STATIC MODEL
DYNAMIC MODELS*
FULL
REDUCED
F-RAT 10
df=(3, )
R-sq
F df-O, )
R-sq
F df-(l, )
I
R-sq F df=(1, )
F1
12.5
mW/g
A03286
A12046
A02157
0.708
O.586
0.413
4
92.05(38)
60.85(43)
25.30(36)
0.665
0.574
0.384
81.51 (41)
61.93(46)
24.36(39)
1
1.84(38)
0.42(43)
0.58(36)
0.001
0.139
0.021
4
0.06(42)
*7-58(47)
0.85(40)
F1
125
mW/g
F1
ctr I
A09036
A04057
0.882
0.132
284.68(38)
6.22(41)
0.848
0.113
228.52(41)
5-59(44)
*3.70(38)
0.30(41)
0.000
0.000
0.00(42)
0.01 (45)
A02057
B04067
C04067
0.612
0.881
0.551
61.39(39)
445.75(60)
75-97(62)
0.602
0.874
0.491
63.59(42)
435.52(63)
62.70(65)
0.31(39)
1.30(60)
2.74(62)
0.045
0.042
0.001
2.02(43)
2.80(64)
0.09(66)
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
I
I
R-sq F df=(1, )
I
E6
12.5
mW/g
A02056
A02196
A05216
0.693
0.932
0.623
1
65-53(29)
728.57(53)
92.72(56)
0.654
0.918
0.599
60.49(32)
631.03(56)
88.10(59)
1 .24(29)
*3-57(53)
1.22(56)
0.272 *12.30(33)
0.073 *4.49(57)
0.093 *6.18(60)
E6
125
mW/g
A03177
A03227
A04067
0.825
0.684
0.850
146.62(31)
77.97(36)
203.94(36)
0.789
0.654
0.811
127.47(34)
73-67(39)
167.63(39)
2.13(31)
1.15(36)
*3-10(36)
0.153
0.140
0.001
E6
ctr 1
B02196
A10166
A03117
0.978 2173-53(49)
0.947 648.10(36)
0.795 155.21 (40)
0.977 2231.46(52)
0.944 655-55(39)
0.789 161.15(43)
0.54(49)
0.80(36)
0.37(40)
0.204 *13-54(53)
0.185 *9-09(40)
1.50(44)
0.033
F df-(l, )
i
df«(3, )
R-sq F df=(1, )
1
R-sq
NO ID A04146
12.5
mW/g
A02247
A03316
NO ID A09106
F df=(1, )
I
R-sq
1
0.996 9432.56(39)
88.48(40)
0.689
0.834 181.09(36)
0.996 10150.73(42) 0.01 (39)
0.609
67-07(43) *3.40(40)
0.816 172.66(39)
1-33(36)
0.542
0.419
43-85(37)
28.90(40)
*3.31 (37)
0.730 151.65(56)
0.975 1692.53(43)
0.55(53)
0.39(40)
*6.34(35)
*6.49(40)
0.02(40)
0.033
0.072
0.002
1.46 (43)
*3-43(44)
0.07(40)
0.024
1.00(41)
125
mW/g
NO ID A06246
Ctrl
A07026
0.738 149-62(53)
0.976 1621 -10(i+O)
* indicates significance at p£0.05 (one-tailed test).
and r e d u c e d dynamic models m e t p £ 0 . 0 5 .
0.053
3.19(57)
0.209 *11.61 (44)
All F-ratios for full
TABLE 17:
ANALYSIS OF TIME DEPENDENT MODELS FOR SD OF AP INTERVAL
DYNAMIC MODELS*
FULL
R-sq
STATIC MODEL
REDUCED
F df-(l, )
R-sq
F-RATIO
F df«(l, )
df= (3» )
i
I
R-sq F df=(1, )
i
I
F1
12.5
mW/g
A03286
A12046
A02157
0.448
0.737
0.487
30.87(38)
120.50(43)
34.17(36)
0.407
0.721
0.472
28.19(41)
118.80(46)
3^-80(39)
0.94(38)
0.88(43)
0.36(36)
0.003
0.028
0.112
0.12(42)
1.36(47)
*5-04(40)
F1
125
mW/g
A09036
A04057
0.927
0.371
485.86(38)
24.16(41)
0.912
0.351
423.08(41)
23-76(44)
2.76(38)
0.44(41)
0.010
0.001
0.42(42)
0.06(45)
F1
Ctrl
A02057
B04067
C04067
0.244
0.506
0.549
12.59(39)
61.40(60)
75.50(62)
0.231
0.461
0.531*
12.62(42)
53.94(63)
74.40(65)
0.22(39)
1.80(60)
0.71 (62)
0.004
0.16(43)
0.188 *14.79(64)
0.016
1.09(66)
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
R-sq F df=(1, )
i
I
i
E6
12.5
mW/g
A02056
A02196
A05216
0.688
0.877
0.611
64.07(29)
378.90(53)
87.86(56)
0.621
0.872
0.591
52.52(32)
382.21 (56)
85.19(59)
1
2.08(29)
0.73(53)
0.95(56)
0.291 *13.55(33)
0.091 *5.72(57)
O.O89 *5.87(60)
E6
125
mW/g
A03177
A03227
A04067
0.837
0.350
0.596
159.69(31)
19.M (36)
53.03(36)
0.836
0.248
0.404
173.59(34)
12.90(39)
26.46(39)
0.08(31)
1.88(36)
*5.68(36)
0.003
0.10(35)
0.201 *10.06(40)
0.081 *3.51 (40)
E6
ctr 1
B02196
A10166
A03H7
0.761
0.852
0.606
156.17(49)
207.86(36)
61.51 (40)
0.756
0.844
0.588
161.15(52)
211.51 (39)
61.34(43)
0.35(49)
0.65(36)
0.61 (40)
0.163 *10.33(53)
0.303 *17.38 (40)?
2.64(44)
0.057
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
R-sq F df=(1, )
y
I
I
I
NO ID A04146
12.5 A02247
mW/g A03316
0.929
0.592
0.543
509.91 (39)
58.03(40)
42.82(36)
0.925
0.533
0.508
516.50(42)
49-10(43)
40.35(39)
0.76(39)
1.92(40)
0.91 (36)
0.003
0.001
0.002
0.11 (43)
0.03(44)
0.09(40)
NO ID A09106
125
mW/g
O.388
23(37)
0.310
17.94(40)
1 -58(37)
0.018
0.75 0»D
NO ID A06246
ctrl
A07026
0.389
0.951
33.71 (53)
768.35 0»0)
0.377
0.948
33-95(56)
779.79(^3)
0.33(53)
0.75(^0)
0.067 *4.12(57)
0.186 *10.05(44)
* indicates significance at p£0.05 (one-tailed test).
and reduced dynamic models m e t p £ 0 . 0 5 .
All F-ratios for full
130
1*.3-2
Effects on the Properties of the Input Current
Input current parameter mA T /C of the integrator model (equation
1.7~^) was estimated as in Appendix D and thereafter treated as an
experimental variable.
Examples of the input current appeal- in Figure
35 (E6 neuron A0205&; compare Figures 1 i*,19. and 28) and
(F1 neuron A02157. compare Figures 9, 15. 19. and 27).
in Figure 36
A universal fea­
ture of the input current data is that they are strongly negatively cor­
related overall with the lengths of intervals, as model 1.7~^ would pre­
dict. * Often, however, the input current and interval sequence differed
in detail.
In Figure 35» for instance, the variability of the input
current tends to be constant, while the variability of intervals (Figure
14) increased during MW and decreased during recovery.
In each figure, the residual errors that are plotted were backtransformed (unweighted) so that they could be expressed in mV (Equation
E-12) .
The model generally performed best, in the sense of smaller var­
iance of residual errors, on data from neurons where the rate did not
change abruptly.
In Figure 36, for instance, negative peaks in the
residual error occurred at the same times as long interburst intervals.
The variables of interest in /uAT/C were its mean /Uj, standard devi­
ation cr| , and autoregressive coefficients ARi(l) and AR2O).
Coeffi­
cients AR1 and AR2 describe the autocorrelation of time series data.
As
shown in Box and Jenkins (1976) and in appendix E, the coefficients are
found by fitting the data to a linear difference equation which is to
represent the action of a linear dynamic system (a filter) on uncorre­
cted white noise:
Pint(t) - AR! x(t-l) + AR2x(t-2) + v(t)
l».3"3
£ 0.040
§
C 0.032
£ 0.024
OC
3 0.016
U
i \y
=5 0.008
Q.
z
11
•
1
A1
A
A
i
i
i
1
~ 0.010
® 0.008
^ 0.006
q 0.004
0.002
A
1
40
t
20
<
0
3
9
-20
CO
LU
OH
>i iLlJ^^uULiiUk^lLdiiyikatbkijk
-40
MICROWAVE LP
CONTROL
i
i
i
RECOVERY
i
i
i
TIME (min)
FORGETFUL RECURSIVE ESTIMATION OF INPUT CURRENT EXPERIMENT A02056CE6)
12.5mW/g
» 0.060
§
~ 0.048 H
2 0.036
C*L
CX.
3 0.024
U
Z> 0.012-
CL
Z
~ 0.040
£ 0.032
> 0.024
q 0.0160.008
00
A
^uaiUAMl/VV
60
=1
30
<
z>
0
g
to
UJ
-30
OtC
-60
r
0
MICROWAVE LP
CONTROL
i
25
50
RECOV
75
100
I
125
TIME (min)
FORGETFUL RECURSIVE ESTIMATION OF INPUT CURRENT
EXPERIMENT A02157CF1) 12.5mW/g
133
in which
$ j nt(t)
are the values of the interpolated input current series at
times t,
ARi and AR2 are the autoregressive coefficients, and
vt is a hypothesized uncorrelated white-noise process.
The choice of a second order model is justified in Appendix E.
Obtaining mean /U|, standard deviation tr| , and autoregressive coef­
ficients ARi(I) and AR2 (I) from the estimate $ of mAT/C (Figures 35 and
36) required a number of steps, which are shown in Appendix E.
0 was
interpolated and resampled to put it on a uniform time increment axis,
the resulting function being designated as 3;nf
Treatment of 0jnt was different for the steady state and time
dependent cases.
For the steady state case, subsegments of 3;nt were
defined to correspond exactly in time with the subsegments of the ISI
data used in the histogram analysis and the analysis of /U|SI
and
^ISI*
Each of the four features of the input current was estimated from the
data in a subsegment using MlNITAB (Ryan e t a I . , 1980).
For the time dependent case, a window was moved in overlapping
steps through an entire record of 3;nt> to define subsegments, just as
was done to the interval data to obtain >u | c; j (t) and <?|5| (t) .
and cr|
were calculated directly from the data in the window, and thereafter
designated M| (t) and a| (t) , respectively.
Within a window, ARi (I) and
AR2(1) were found using a maximum likelihood algorithm from the
International Mathematical and Statistical Library (IMSL-FTML, 198^+) ,
and thereafter denoted as ARi(l;t) and AR2(l;t), respectively.
13*4
4.3.2.1
Steady State Case
The steady state values of the input current features are compared
for MW and control experiments in Tables 18, 19, 20, and 21.
These data
were expressed as fractional deviations and tested using the
Mann-Whitney test, just as were M|$| and cr|s| (see section 4.3.1).
As
was the case for steady state values of M|si and cr151» no MW effects
were discernible in the groupings of neurons at either SAR level.
TABLE 18:
MW EFFECT ON MEAN OF
125mW/g
12.5mW/g
MICROWAVE
CONTROL
RECOVERY
CONTROL
INPUT CURRENT (STEADY STATE)*
12.5 and 125mW/g
n= 9 MED= 1.1307
n« 8 MED= 1.1829
n« 6 MED= 1.0465
n= 8 MED= 1.1829
n=15 MED= 1.1041
n- 8 MED= 1.1829
E" 0.159 W= 89.0
E= -0.045 W= 44.0
E=
p« 0.^705
p= 0.9485
p= 0.6748
n-= 9 MED«= 1.3201
n« 8 MED«= 1 .2421
n= 6 MED«= 1.2557
n= 8 MED= 1.2421
n-15 MED= 1.3201
n= 8 MED= 1.2421
E= 0.081 W- 84.0
E=
E-
p= 0.8099
p= 0.8465
0.073 W= 47.0
0.119 W=l87-0
0.081 W=I85.O
P= 0.7715
* indicates none of the differences were significant at p:£0.05.
135
TABLE 12s
MW EFFECT ON SD OF INPUT CURRENT (STEADY STATE) *
12.5mW/g
n= 15 MED- 1.1791
n= 8 MED- 1.1712
n- 6 MED= 0.9^2i»
n= 8 MED= 1.1712
E- 0.208 W= 87.O
E-
P= 0.5966
P= 0 . 9 k & 5
p= O.67U8
n= 9 MED- 1 .6796
n= 8 MED- 1 .5879
n= 6 MED= 1.5108
n= 8 MED= 1.5879
n-15 MED- 1.6796
n= 8 MED- 1.5879
E—-0.181 W= 79-0
E=
E=
P= 0.8852
P= 0.5613
W= U6.0
0.15 w= 50.0
E=
0.132
O
*-r
00
7
3
RECOVERY
CONTROL
12.5 and 125mW/g
n- 9 MED- 1 • 3985
n= 8 MED- 1 .1712
O
O
X-
MICROWAVE
CONTROL
125mW/g
0.069 W-183.0
P= O.8718
.
A indicates none of the differences were significant at p£0.05.
MW EFFECT ON ARi PARAMETER OF INPUT CURRENT (STEADY STATE)*
12.5mW/g
P= 0.3123
P= 0.9485
P= 0.5397
n- 9 MED- 0.8287
n- 8 MED- 0.9l»90
n- 6 MED- 0.9152
n= 8 MED- 0.9490
n-15 MED- 0.8336
n- 8 MED- 0.9490
E- -0.091 W= 42.0
E- -0.101+ W-173.0
P= 0.7^69
P= 0.671*8
E—
p= 0.7363
•^4
-^j
0
E-
*:
n
E—-0.099 w= 70.0
1
O
n- 6 MED- 0.9769
n- 8 MED- 0.9339
0.010 W- 46.0
n-15 MED- 0.9^^1
n= 8 MED- 0.9339
E-
* indicates none of the differences were significant at p£0.05.
0
0
—1
II
RECOVERY
CONTROL
12.5 and 125mW/g
n- 9 MED- 0.9224
n- 8 MED- 0.9339
NJ
O
MICROWAVE
CONTROL
125mW/g
O
O
00
TABLE 20:
136
TABLE 21:
MW EFFECT ON AR2 PARAMETER OF INPUT CURRENT (STEADY STATE)*
12.5mW/g
MICROWAVE
CONTROL
n- 9 MED- 0.8013
n- 8 MED= 1.0264
n- 6 MED- 0.9168
n= 8 MED- 1.0264
n-15" MED- 0.8947
n= 8 MED- 1.0264
E~-0.171 w= 69.0
E-
P= 0.2685
p= 0.3329
P= 0.2081
n= 9 MED- 0.9909
n- 8 MED= 1. li*69
n- 6 MED- 1.1211
n- 8 MED- 1.1469
n= 15 MED- 0.9909
n- 8 MED- 1.1469
E=--O.IJ46 w= 73.0
E=
E= -0.057 W=173•0
P= 0.^705
P= 0.9485
MC
12.5 and 125mW/g
0
1
RECOVERY
CONTROL
125mW/g
W- 37-0
0.079 W«= 46.0
E= -0.147 W-160.0
P= 0.6748
* indicates none of the differences were significant at p£0.05.
4.3.2.2
Time Dependent Case
Variables M|(t) , cr( (t), AR1 (I; t) and AR 2(I;t), of the input current
were tested for dependence on MW using regression analysis of static and
dynamic models exactly as were the AP interval variables M|s|(t) and
ffIS|W
Observed and predicted values for
AR 2 (I ; t) for the four experiments whose
(t) , cr| (t) , ARt (I;t) , and
anc'
^ISI^ were shown
in Figures 31 and 32 (static models) and 33 and 34 (dynamic models) are
shown in Figures 37 through 40 and 41 through 44, respectively.
In
these figures also, the faint line traces the data while the bold line
traces the fit of the regression model.
tor variable.
Below can be found the indica­
137
Comparison between static and dynamic models for any of the input
current functions shows the differences that were seen when static and
dynamic models for M|$|(0
and aiSI ^ were
compared.
Again, the exoge­
nous influence can often be seen clearly in the static prediction (m|(t)
of A09106, Figure 39)# but it is susceptible to nonstationarities (m|(t)
of B02916, Figure kO).
The dynamic models fit impressively, but it is
hard to discern visually whether there is an exogenous influence.
Tables 22, 23, 2 k , and 25 contain the evaluations of the regression
models for the mean, SD, and parameters AR1 and AR2 of the input cur­
rent.
Whenever the mean ISI was susceptible to the exogenous variable
(significant F-ratio), quite likely the mean current was also.
General-
ly, cr|5|(t) was more susceptible to being changed than was tr| (t).
Along
with <7j (t) , correlation parameters AR1 (1st) and AR2(I;t) proved to be
somewhat noisier and yielded models with lower R2 than did M| (t).
In
fact, in Tables 23, 2k, and 25, a few even of the dynamic models (marked
with
a)
did not pass F-ratio tests for overall significance.
138
EXPERIMENT A03286CF1) 12.5mW/g
STATIC MODEL
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Predicted instantaneous effects on input current,
A03286 ( F 1 ) . F l ; MW 12.5mW/g. C o n v e n t i o n s a r e as i n F i g u r e
31.
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EXPERIMENT A02196CE6) 12.5mW/g
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FIGURE 38:
Predicted instantaneous effects on input current,
A02196 (E6).
38.
E 6 ; MW 12 .5mW/g. C o n v e n t i o n s a r e a s i n F i g u r e
140
EXPERIMENT AO9IO6CNO ID) 125mW/g
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P r e d i c t e d i n s t a n t a n e o u s e f f e c t s o n i n p u t c u r r e n t , AO91O6(N0
I D ) . NO I D ; MW 125mW/g. C o n v e n t i o n s a r e a s i n F i g u r e 3 1 •
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FIGURE 1»0:
Predicted instantaneous effects on input current,
B02196 ( E 6 ) . E 6 ; c o n t r o l o n l y . C o n v e n t i o n s a r e as i n F i g u r e
38.
11*2
EXPERIMENT A03286CF1) 12.5mW/g
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FIGURE 41:
Predicted effects on dynamics of input current, A03286(F1).
Fl; MW 12.5mW/g. Conventions are as in Figure 31•
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FIGURE J»2:
P r e d i c t e d e f f e c t s o n dynamics o f i n p u t c u r r e n t , A02196 (E6)
E 6 ; MW 12.5mW/g. C o n v e n t i o n s a r e a s i n F i g u r e 3 8 .
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EXPERIMENT A091()6(NO ID) 125mW/g
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FIGURE 1»3:
P r e d i c t e d e f f e c t s o n dynamics o f i n p u t c u r r e n t , A09106(N0
I D ) . NO I D ; MW 125mW/g. C o n v e n t i o n s a r e a s i n F i g u r e 3 1 •
H5
EXPERIMENT B02196CE6) CONTROL ONLY DYNAMIC MODEL
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TIME (min)
Predicted effects on dynamics of input current, B02196(E6).
E6; control only. Conventions are as in Figure 38-
TABLE 22s
ANALYSIS OF TIME DEPENDENT MODELS FOR MEAN INPUT CURRENT
DYNAMIC MODELS*
FULL
R-sq
STATIC MODEL
REDUCED
F df-
( l ,
)
F-RAT 19
R-sq
F df=(1, )
df=(3. )
0.597
0.673
0.670
4
60.67(41)
9^.83 C»6)
81.19(40)
4
1.34(38)
0.72(43)
1 .07(37)
R-sq F df=(1, )
0.000
0.040
0.155
4
0.00(42)
1.97(47)
*7-54(41)
0.09(44)
*6.97(45)
mW/g
A03286
A12046
A02157
0.635
O.689
0.696
4
66.18(38)
95-24(43)
84.83(37)
F1
125
A09036
A04057
0.783
0.575
144.59(40)
55.51 (41)
0.771
0.561
145.02(43)
56.33(M)
0.74(40)
0.44(41)
0.002
0.134
A02057
B04067
C04067
0.599
0.714
0.620
58.16(39)
149.65(60)
104.60(64)
0.590
0.693
0.579
60.44(42)
142.14 (63)
92.06(67)
0.28(39)
1.46(60)
2.34(64)
1.49(43)
0.033
0.153 *11.54(64)
0.34(68)
0.005
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
R-sq F df=(1, )
A02056
A02196
A05216
0.710
0.855
0.447
4
68.70(28)
312.62(53)
45.3^(56)
0.650
0.836
0.411
4
57-64(31)
284.91 (56)
41.21 (59)
4
1.94(28)
2.35(53)
1.22(56)
4
0.234 *9.79(32)
0.163 *11.06(57)
0.021
1.31(60)
A03177
A03227
A04067
0.769
0.713
0.870
109.58(33)
81.86(33)
248.40(37)
0.733
0.684
0.820
99-06 (36)
77.83(36)
1 8 1 . 9 8 (40)
1.67(33)
1.11 (33)
*4.81 (37)
O . 3 6 8 *14.34(37)
0.107 *4.41(37)
0.011
0.46(41)
B02196
A10166
A03117
0.964 1358.43(51)
0.856 244.70(41)
0.755 129.09(42)
0.964 1429-48(54)
0.853 254.91(M)
0.729 121.12(45)
0.10 (51)
0.35(41)
1.45(42)
0.183 *12.29(55)
0.347 *23.96(45)
0.095 *4.84(46)
F df-(l, )
df=(3. )
R-sq F df=(1, )
4
0.995 9567.82(44)
60.42(43)
0.584
0.881 287-77(39)
4
0.74(41)
1.21 (40)
0.5^(36)
F1
12.5
mW/g
F1
C t r l
E6
12.5
mW/g
E6
125
mW/g
E6
ctr 1
R-sq
NO ID A04146
12.5 A02247
mW/g A03316
NO ID A09106
125
F df=(1, )
4
0.996 9397-97(41)
64.97(40)
0.619
0.886 279.28(36)
0.599
55-20(37)
R-sq
38.10 (40)
*3-M (37)
0.832 278.18(56)
0.964 1189.00(45)
1.70(53)
0.44(42)
0.488
0.008
0.009
0.006
4
0.34(45)
0.40(44)
0.25(40)
0.213 *11.12(41)
mW/g
NO ID A06246
ctrl
A07026
0.847 293-75(53)
0.965 1145.92(42)
* indicates significance at p£0.05 (one-tailed test).
and reduced dynamic models met p£0.05.
0.138
0.081
*9.10(57)
*4.04(46)
All F-ratios for full
147
TABLE 21:
ANALYSIS OF TIME DEPENDENT MODELS FOR SD OF INPUT CURRENT
DYNAMIC MODELS*
FULL
STATIC MODEL
F-RATIO
REDUCED
R-sq
F df-(l, )
R-sq F df=(1, )
R-sq
F df-(l, )
df-(3. )
0.454
0.461
0.255
4
34.03(41)
39-38(46)
13-72 (40)
4
0.63(38)
0.3M43)
0.63(37)
0.013
0.000
0.043
4
0.57(42)
0.01 (47)
1.83(41)
1.14(44)
1.07(45)
F1
12.5
mW/g
A03286
A12046
A02157
0.479
0.474
0.291
4
35.00(38)
38.70(43)
15.21 (37)
F1
125
mW/g
A09036
A04057
0.626
0.080
66.99(40) 0.614
3.5* 0»l)a 0.070
68.46(43)
3.31(M)a
0.42(40)
0.14(41)
0.025
0.023
F1
ctr 1
A02057
B04067
C04067
0.354
0.482
0.294
21.35(39)
55-86(60)
26.62(64)
22.78(42)
49-33(63)
24.63(67)
0.04(39)
1.66(60)
0.75(64)
0.001
0.03(43)
0 . 1 6 2 *12.36 (64)
0.31 (68)
0.005
F df«(l, )
d f =(3. )
R-sq F d f =(1, )
4
2.13(31)a
113.56(56)
25-74(59)
1
0.69(28)
0.79(53)
0.23(56)
0.025
0.114
0.007
R-sq
F d f =(1, )
0.352
0.439
0.269
R-sq
4
4.l4(28)a 0.064
114.68(53) 0.670
25.^3(56) 0.304
4
0.81 (32)
*7.36(57)
0.40(60)
E6
12.5
mW/g
A02056
A02196
A05216
0.129
0.684
0.312
E6
125
mW/g
A03177
A03227
A04067
0.463
0.491
0.440
28.42(33)
31.87(33)
29-07(37)
0.3*7
0.477
0.408
19.16(36)
32.77(36)
27-52(40)
2.36(33)
0.32(33)
0.71 (37)
0.371 *21.86(37)
0.114 *4.75(37)
1.66(41)
0.039
E6
ctr 1
A10166
A03117
B02196
0.710
0.345
0.421
100.52(41)
22.15(42)
37.09(51)
0.708
0.336
0.372
106.94(44)
22.78(45)
31.96(54)
0.08(41)
0.20(42)
1.45(51)
0 . 1 8 2 *10.02(45)
0.02(46)
0.001
0.014
0.81 (55)
R-sq
F d f =(1, )
R-sq
F d f =(1, )
d f =(3. )
R-sq F d f = ( 1, )
NO ID A04146
12.5 A02247
mW/g A03316
0.496
0.657
0.194
4
40.31 (41)
76.52(40)
8.64(36)
0.468
0.558
0.148
4
38.69(44)
5^ - 33(43)
6.75(39)
4
O. 7 6 (41)
*3.82(40)
0.68(36)
0.005
0.003
0.031
4
0.21 (45)
0.11 (44)
1.26(40)
NO ID A09106
125
mW/g
0.381
22.76(37)
0.208
1 0 . 5 3 0»o)
*3-44(37)
0.005
0.22(41)
NO ID A06246
ctr 1
A07026
0.510
0.210
55-08(53)
1 1.20(42)
0.432
0.203
42.57(56)
11.46(45)
*2.80(53)
0.13(42)
0.039
0.019
2.30(57)
0.89(46)
* indicates significance at p£0.05 (one-tailed test).
a i n d i c a t e s dynamic models where F - r a t i o t e s t d i d n o t meet p<0.05«
t e s t s o n f u l l and r e d u c e d dynamic models met p £ 0 . 0 5 .
All other
TABLE 24:
ANALYSIS OF TIME DEPENDENT MODELS FOR ARi OF INPUT CURRENT
DYNAMIC MODELS*
FULL
STATIC MODEL
REDUCED
R-sq
F df-(l, )
R-sq
0.189
0.363
0.147
F-RATIO
F df=(1, )
i
df=(3. )
R-sq F df= (1, )
i
F1
12.5
mW/g
A03286
A02157
A12046
0.426
0.435
0.149
1
28.22(38)
28.48(37)
7.17(41)
F1
125
mW/g
A09036
A04057
0.741
0.429
114.51 (40)
29.99(40)
0.715
0.395
108.06(43)
28.03(43)
1.33(40)
0.79(to)
0.003
0.083
0.13(44)
*4.00(44)
F1
A02057
B04067
C04067
0.348
O.687
0.194
20.84(39)
131.67(60)
14.64(61)
0.348
0.660
0.182
22.37(42)
122.24(63)
14.20(64)
0.01 (39)
1.73(60)
0.30(61)
0.000
0.014
0.004
0.00(43)
0.88(64)
0.29(65)
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
R-sq F df=(1, )
C t r l
9.56(41)
22.80(40)
7.60(44)
I
*5.23(38)
1.57(37)
0.03(41)
0.066
0.019
0.002
2.96(42)
0.81 (41)
0.08(45)
I
I
E6
12.5
mW/g
A02056
A02196
A05216
0.180
0.592
0.305
6.13(28)
76.93(53)
24.58(56)
O.O63
0.560
0.286
2.08(31)a
71 .20(56)
23.68(59)
1
1.33(28)
1.40(53)
0.50(56)
4
1 .04(32)
0.031
0.150 *10.08(57)
0.41 (60)
0.007
E6
125
mW/g
A03177
A03227
A04067
0.321
0.257
0.589
15.60(33)
11.41 (33)
51.63(36)
0.149
0.153
0.539
6.30(36)
6.52(36)
45-58(39)
2.79(33)
1.53(33)
l.47(36)
0.088
0.169
0.146
*3.55(37)
*7-54(37)
*6.86(40)
E6
ctr 1
B02196
A10166
A03117
0.613
0.495
0. 186
80.79(51)
40.16(41)
9-58(42)
0.556
0.485
0.174
67.60(54)
41.41 (44)
9-46(45)
2.51 (51)
0.27(41)
0.21 (42)
O.O85
0.048
0.002
*5-12(55)
2.25(45)
0.10(46)
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3. )
NO ID A04146
12.5 A02247
mW/g A03316
0.937
0.544
0.241
1
608.65(41)
47-75(40)
11.^5(36)
0.926
0.424
0.135
NO ID A09106
125
mW/g
0.365
21.25(37)
NO ID A06246
C t r l
A07026
0.180
0.613
11.42(52)
66.45(42)
i
R-sq F df=(1, )
552.64(44)
31.70(43)
6.07(39)
1
2.30(41)
*3.50(40)
1.69(36)
0.002
0.032
0.012
4
0.11 (45)
1.43(44)
0.48(40)
0.247
13-14(40)
2.28(37)
0.121
*5.62(41)
0.132
0.556
8.33(55)
56.43(45)
1.03(52)
2.04(42)
0.002
0.09(56)
0.314 *21.03(46)
* indicates significance at p£0.05 (one-tailed test).
a i n d i c a t e s dynamic models where F - r a t i o t e s t d i d n o t meet p < 0 . 0 5 .
t e s t s o n f u l l and reduced dynamic models met p £ 0 . 0 5 .
All other
149
TABLE 2£:
ANALYSIS OF TIME DEPENDENT MODELS FOR ARz OF INPUT CURRENT
DYNAMIC MODELS*
REDUCED
FULL
R-sq
STATIC MODEL
F df-(l, )
R-sq
F-RATIO
F df=(1, )
I
df=(3. )
R-sq F df-(l, )
I
F1
12.5
mW/g
A03286
A12046
A02157
0.335
0.117
0.257
4
19.12(38)
5.43(41)
12.81 (37)
0.131
0.034
0.221
6.21 (41) *3.87(38)
1.55(44) a 1.28(41)
11 .33(40)
0.60(37)
0.188
0.001
0.017
i
*9-74(42)
0.04(45)
0.69(41)
F1
125
mW/g
A09036
A04057
0.549
0.643
48.77(40)
71 .99(40)
0.520
0.623
46.65(43)
70.98(43)
0.86(40)
0.75(40)
0.005
0.064
0.21 (44)
3.01 (44)
F1
A02057
B04067
C04067
0.325
0.336
0.383
18.78(39)
30.30(60)
37-79(61)
0.320
0.319
0.335
19.80(42)
29.45(63)
32.17(64)
0.09(39)
0.51 (60)
1.58(61)
0.000
0.029
0.001
*0.00(43)
1.94(64)
0.04(65)
R-sq
F df-(l, )
R-sq
F df=(1, )
df=(3, )
0.278
0.445
0.047
Ctrl
I
R-sq F df=(1, )
i
11.95(31)
44.94(56)
2.90(59)a
1
0.29(28)
1.38(53)
1.15(56)
0.016
0.078
0.023
E6
12.5
mW/g
A02056
A02196
A05216
0.300
0.485
0.102
1
1 1.97(28)
49-98(53)
6.37(5o)
E6
125
mW/g
A03177
A03227
A04067
0.485
0.244
0.233
31.05(33)
10.66(33)
10.96(36)
0.440
0.178
0.058
28.30(36)
7.80(36)
2.38(39)a
0.95(33)
0.96(33)
2.75(36)
3-10(37)
0.077
2.16(37)
0.055
0.203 *10.20(40)
E6
ctr 1
B02196
A10166
A03117
0.309
0.410
0.172
22.80(51)
28.49(41)
8.75(42)
0.229
0.300
0.164
16.01 (54)
18.89(44)
8.82(45)
1.98(51)
2.54(41)
0.14(42)
0.099 *6.04(55)
0.281 *17.56(45)
0.21 (46)
0.005
R-sq
F df=(1, )
R-sq
F df=(1, )
df=(3, )
R-sq F df= (1 , )
NO ID A04146
12.5 A02247
mW/g A03316
0.606
0.364
0.186
62.98(41)
22.84(40)
8.24(36)
0.591
0.342
0.179
63.56(44)
22.32(43)
8.51 (39)
1
0.51 (41)
0.46(40)
0.10(36)
0.001
0.039
0.009
0.05(45)
1.78(44)
0.37(40)
NO ID A09106
125
mW/g
0.358
20.59(37)
0.156
7.40(40)
*3-87(37)
0.075
3.31 (41)
NO ID A06246
ctr J
A07026
0.596
0.570
76.76(52)
55.78(42)
0.490
0.569
52.86(55)
59.40(45)
*4.55(52)
0.05(42)
0.073
0.025
*4.41 (56)
1.18(46)
i
i
0.52(32)
*4.80(57)
1.40(60)
I
* indicates significance at p£0.05 (one-tailed test).
a i n d i c a t e s dynamic models where F - r a t i o t e s t d i d n o t meet p < 0 . 0 5 t e s t s o n f u l l and r e d u c e d dynamic models met p £ 0 . 0 5 .
All other
150
4.3.3
Overa 11 tests of HO: MW affected time-dependent AP properties
The time-dependent AP functions were considered separately for
their possible susceptibility to MW.
The static and dynamic models were
also evaluated separately.
For the models fit to a particular function, each experiment repre­
sented an independent test for MW effects.
According to the F-ratio
tests for the regression models, each experiment thus represented a
"success" or "failure" to reject the hypothesis that MW exerted no
effect.
Thus, as was done to test the relative stability of the inter­
val serial correlograms, the result of each experiment was considered to
be an outcome in an experiment whose overall structure was one of
repeated binomial trials.
As in the serial correlogram analysis, two methods were used to
evaluate the binomial results.
First, a probability was found using as
the expected probability of "success" (if the hypothesis of no MW effect
were true) the proportion of control-only experiments that showed
effects.
Secondly, confidence bounds for the proportions of MW effects
seen in actual exposures were checked as to whether they encompassed the
proportions observed in control-only experiments.
The proportions of "success" with and without MW exposure are list­
ed for comparison, along with the corresponding probabilities under HO:
MW has no effect, in Tables 26 and 27.
Data from all cells exposed at
12.5mW/g and at 125mW/g were checked separately.
cells were grouped.
Then all identified
Finally, to secure the best possible discriminatory
power, all exposed and control cells were compared, without regard to
power level or cell type.
Table 26 covers the static models while the
151
dynamic models are summarized in Table 27.
Data for each of the six
functions are shown separately.
In Table 27, several estimates of the expected probabilities are
zero.
To judge the significance in these cases, the expected probabili­
ty was assumed to be 0.05, for the calculation based on binomial sums.
These probabilities are marked with
a
in the table.
It would be impossible from these data to build a case for MW
effects on any time-dependent feature of neuron activity other than the
mean interval
of the input current.
and
t*ie
first autoregressive coefficient ARi(l;t)
Even for these two features, a confident judgment
of effects can hardly be maintained, as arguments below will show.
For almost every feature and both models, the proportion of MW
affected cells was lower when the test groups included all neurons, as
opposed to only identified neurons (types F1 and E6). This may have
occurred because the sample of all neurons included 3 neurons (1 each at
12.5mW/g, 125mW/g, and unexposed) with highly stable and regular firing.
From Tables 22 Gu|S|(t)), 23 (a|Sj(t)), 2U (m|
(t)) , and 25 (cr j (t)) ,
it appears that the regression analysis may have done just as well at
discriminating F1 from E6 neurons, whether or not MW irradiated, than at
discriminating MW irradiated from control neurons.
This impression
could not be verified statistically, in the tests on proportions (Tables
26 and 27), as not enough data were available.
However, it is consis­
tent with the observation that the AP properties of E6 neurons were gen­
erally less stable than those of F1 neurons.
The proportions of experiments, either MW or control, with and
without effects, reveal striking differences in the sensitivities of the
152
TABLE 26:
TESTS of HO: HW DID NOT AFFECT ISI OR CURRENT (STATIC MODEL)
EXPECTED
(CONTROL)
OBSERVED
(MICROWAVE)
"IS (t)
rISI
(t)
M1 (t)
01 (t)
ARi (I)
ARj (I)
obs.
prop,
lower
upper
obs.
5/9
2/6
6/11
7/15
0.555
0.333
0.545
0.467
0.103
0.029
0.115
0.108
0.932
0.894
0.917
0.863
3/8
3/8
2/6
3/8
0.375
0.375
0.333
0.375
4/9
0.444
0.333
0.545
0.400
0.068
0.897
2/6
6/11
6/15
0.029
0.115
0.082
0.894
0.917
0.832
5/8
5/8
3/6
5/8
3/9
4/6
6/11
7/15
0.333
0.667
0.545
0.467
6/8
6/8
4/6
6/8
1/9
2/6
3/H
0.111
0.333
0.273
3/15
1/9
5/6
5/11
6/15
0.040
0.106
O.856
0.3148
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0.625
0.625
0.500
0.625
O.926O
0.8535
0.5000
0.9790
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0.750
0.750
O.667
0.750
0.9987
0.8784
0.9958
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
2/8 0.250
2/8 0.250
0.9249
0.4661
0.7652
0.7639
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0.9249
0.0046*
0.0247*
0.1484
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0.9805
0.9844
0.7652
0.9408
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0.108
0.200
0.005
0.029
0.033
0.024
0.753
0.894
0.806
0.719
0.111
0.833
0.454
0.400
0.005
0.161
0.083
0.082
0.753
0.992
0.885
0.832
2/8 0.250
2/8 0.250
2/9
0.222
0.019
0.808
1/6
3/11
3/15
0.167
0.273
0.200
0.008
O.838
4/8 0.500
4/8 0.500
0.033
0.024
0.806
2/6 0.333
0.719
4/8 0.500
* indicates significance at p£0.05.
0.2166
CLASS
ALL
ALL
ALL
ALL
0.971
0.917
0.863
0.115
P(obs.|p)
2/6 0.333
2/8 0.250
1/6 0.167
2/8 0.250
O.7258
0.1216
0.8306
TABLE 22:
TESTS of HO.: MW DID NOT AFFECT ISI OR CURRENT (DYNAMIC MODEL)
OBSERVED
(MICROWAVE)
EXPECTED
(CONTROL)
P(obs.|p)
CLASS
obs.
prop,
lower
upper
obs. p
M|5|(t)
2/9
3/6
3/11
5/15
0.222
0.500
0.273
0.333
0.019
0.061
0.033
0.060
0.809
0.939
0.806
0.797
0/8
0/8
0/6
0/8
0.050a
0.050a
0.050a
0.0503
0.0712
0.0022*
0.0152*
0.0006*
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
r,5,(t)
0/9
0/6
1/11
1/15
0.000
0.000
0.091
0.067
0.004
0.003
0.705
0.625
0/8
0/8
0/6
0/8
0.050a
0,050a
0.050a
0.050a
1.0000
1.0000
1.0000
1.0000
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
0/9
1/6
1/11
2/15
0.000
0.167
0.091
0.133
0.008
0.004
0.011
0.839
0.705
0.674
0/8
0/8
0/6
0/8
0.050a
0.0503
0.0503
0.0509
1.0000
0.2649
0.4312
0.1710
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
1/9
1/6
0/11
2/15
0.111
0.167
0.000
0.133
0.006
0.008
0.011
0.754
0.839
O.bjk
1 /80.125
1/8 0.125
0/6 0.0503
1/8 0.125
0.6993
0.5512
1.0000
0.5759
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
2/9
0.222
0.019
0.809
0/6
0.000
0/8 0.050 3
0/8 0.050 a
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
ALL
ALL
ALL
ALL
12.5mW/g
125mW/g
F1 AND E6
NEURONS
M|(t)
CT| (t)
AR1 (I)
ARs(l)
a
1/11
2/15
.0.091
0.133
0.004
0.011
0.705
0/6 0.050a
0.674
0/8 0.050 a
0.0712
1.0000
0.4312
0.1710
1/9
1/6
1/11
2/15
0.111
0.167
O.636
0.133
0.006
0.008
0.004
0.011
0.754
0.839
0.705
0.674
1/8
1/8
0/6
1/8
0.6993
0.5512
0.4312
0.5759
0.125
0.125
0.050a
0.125
indicates no effects observed; expected probability was set to 0.050.
* indicates significance at p£0.05.
15*
static and dynamic models to particular features of the data.
Data in
many of the control-only experiments have similar nonstationarities to
data in MW experiments.
The static model seems particularly sensitive
to coincidental occurrences that have nothing to do with MW (for exam­
ple, B02196; Figures 32 and kO).
By contrast, the dynamic models rarely
attributed significance to random noncausal relationships between the
modeled function and the indicator.
In their context, it seemed suffi­
cient to explain the vast majority of variations in most groupings,
whether MW or control, by the history of the feature under study.
Despite these diverse sensitivities, the static and dynamic models could
be expected to perform similarly when the criterion of judgment is a
difference of proportions.
Referring first to M|si
» the proportion of MW experiments with
an effect on the mean interval was larger, but it only reached signifi­
cance (p<0.05) when the dynamic model was used, and even then only if
cells exposed to 125mW/g were included in the test group.
For coeffi­
cient ARi(l;t), the proportion of affected cells was also significantly
larger, but in this case only with identified cells making up the test
group, and not with a group of all exposed cells.
Also in contrast with
M|5|(t)> only the static model revealed an effect on AR1 (I;t).
To interpret the effects on M|$|(t) and AR1 (1;t), two properties of
the result have to be examined.
One is the sensitivity of each outcome
to the particular test, criterion, or test group used.
For instance,
given the arguments above, the static and dynamic regression analyses
ought to have yielded similar judgments, when they in fact did not.
So
also, the tests on proportions ought not to have been sensitive to the
155
choice of confidence bounds or expected binomial probabilities as the
test method, nor to p£0.05 (which was priorly chosen) or some other but
similar value of p as a criterion.
Yet had confidence bounds been
insisted upon as the test method, ARi (I;t) would not have been judged to
be affected by MW.
The other property is the direction of the effects seen.
The
direction of effect can be established by inspecting the sign of the
single coefficient on the indicator variable in each static regression
that showed an effect.
(This was not convenient to do for the dynamic
models, because the three coefficients on the lagged indicator had div­
erse signs).
In the case of M|s|(t), the group of all neurons showed MW
effects in the proportion seven out of fifteen.
increases and two decreases in the mean.
These amounted to five
Of the three control only
cells that showed apparent effects, two had decreases and one an
increase.
For. ARi(l;t), the proportion of cells exposed at 125mW/g was
five out of six.
These amounted to three decreases and two increases.
In summary of the regression analysis of AP features, the infrequency of effects overall, and the high sensitivity of each significance
judgment to the choice of test, criterion, or grouping, combine to tem­
per any statistical conclusion that the data contain a MW effect.
These
properties and the lack of consistent direction of effects strongly sup­
port a physical conclusion that MW affected AP properties of this sample
of neurons minimally or not at all.
156
Chapter V
TEMPERATURE EFFECTS; COMPARISON WITH MICROWAVE EFFECTS
Temperature sensitivities of neuron activity have been investigated
in the past (sec. 1.6).
Even so, it was essential in this study to have
normative data on temperature responses.
Emphasis was put in sees. 1.3»
1.1», and 1.5 on attempts to distinguish thermal from other types of MW
effect.
As indicated in sees 1.3 and 1.8, the design of this study
required establishing a threshold temperature change below which changes
in AP properties due to temperature would not occur.
Further, apparently MW related changes observed while temperature
was constant could be distinguished from temperature dependent changes,
if recorded temperature responses were available whose character was
quite different.
Finally, study of temperature change induced responses
can provide essential confirmation of the correct operation of the sta­
tistical analysis.
In 19 experiments the temperature was changed with no MW exposure
by resetting the temperature of the coolant.
Some neurons were exposed
to MW either before or after their temperature responses were recorded.
Cells were exposed to various large (up to 5°C) and small (0.5°C or
less) temperature steps, from a reference temperature of 20.8°C.
Any
imposed temperature condition was held for 20 min or more.
Usually if a cell fired approximately 1 AP/sec or faster, tempera­
ture was lowered from the reference value to elicit a response.
Quite
157
slow cells (1/3 AP/sec or less) were given a temperature increase.
Neu­
rons seemed most sensitive to temperature when they were firing APs at
rates intermediate between these extremes, although neither the influ­
ence of initial rate nor of reference temperature were investigated.
Input resistances and time constants were measured on all neurons
in the temperature study.
Five neurons were given the identical statis­
tical analysis as was used for the MW experiments.
(Only one of these,
A09106, was also exposed to MW).
5.1
EVIDENT FEATURES OF THE DATA
In contrast to the situation with MW irradiation, responses to
temperature changes were directly evident in raw AP records.
For the
larger temperature steps, AP rate increased obviously with increasing
temperature, and vice versa.
The AP waveform also changed obviously
(shorter duration at higher temperature).
Examples of AP records showing obvious temperature responses appear
in Figures kS and 46.
Figure
shows a continuous record from neuron
A03166 (E6), which responded profoundly and repeatedly to a two degree
temperature change.
reset to 22.8°C.
At the start of each underbar, the temperature was
At the end, temperature was moved back to 20.8°C.
Temperature commands were steps.
The neuron's response took,siightly
longer than the time constant of the temperature controller, four to six
minutes.
The time course of the imposed temperature change (not shown)
was very similar to that in Figure 3»c.
A rapid reversible response of
this form stands in sharp contrast to anything seen in any MW experi­
ment, even including the two unusual experiments of Figures 11 and 12.
158
FIGURE i»5:
Rapid reversible response to +2.0°C steps, A03l66(E6).
Recording was continuous (top to bottom traces). Each
underbar marks temperature of 22.8°C; absence of underbar
indicates 20.8°C. R marks times when input resistance was
checked.
159
In Figure 1»6 temperature and MW step responses are compared, for F1 neu­
ron A05206.
Though the cell Was recorded continuously, only segments pf
interest are shown.
(This neuron was not used in the statistical study,
because of defects in the magrvetic tape record).
In comparison with
cell AO3166 (Figure kS), this cell had a faster response, which also
depended on the rate of temperature change (this point was not examined
in neuron AO3166):
a fast change in either direction caused a sharp
overshooting response, while a slower change to the same end point
caused a smaller response.
malous transients.
This neuron provides a clear example of ano­
Once a change was complete, the cell's firing rate
was positively correlated with temperature, but during the transition,
the rate changed oppositely.
These observations can help distinguish MW from temperature respon­
ses.
If the onset of MW irradiation raised the local temperature, the
change should be a quick one, as the more highly absorbing materials
have only a small mass.
Thus, if MW effects are like temperature chang­
es, they should be like rapid ones.
the onset and offset of MW.
At the bottom are records made at
No change was evident in the AP pattern at
the MW transition or at any time during MW.
160
FIGURE ht>:
Contrast between temperature and MW effects, neuron
A05206(F1). A: fast increase. The spiking rate increased
with temperatures, but during the transition, the rate
decreased anomalously. B: fast decrease; rate increased
transiently then decreased. C: slower increase; the anoma­
lous response was weaker than in A. D: slower decrease;
comparable to C. E: onset of MW, 12.5mW/g (dark bar); no
response is evident. F: offset of MW (end of dark bar); no
response is evident.
161
5.2
RESISTANCE AND TIME CONSTANT
Figure h~] shows an analysis of the temperature dependence of input
resistance (top) and time constant (bottom).
In this figure, tempera­
ture dependent resistance and time constant data were treated as frac­
tional deviations, 1+AR/R, as in the study of MW effects (Chapter 3).
Temperatures were expressed as absolute deviations from 20.8°C.
This is
in accord with data treatment in other empirical temperature studies, in
which measures such as the Q10 (the fractional change in a variable for
a 10°C increment in temperature) were reported.
For reference measurements, the earliest measurement pair (resis­
tance with time constant) at 20.8°C in each experiment was used, provid­
ed that MW irradiation did not intervene between the reference and other
temperature related measurements.
In experiments with no MW, and in
those where temperature responses were investigated before MW was
applied, the reference measurement pair was usually at the end of an
initial control period.
In experiments in which MW was applied, and
temperature responses were studied afterward, a measurement made at
20.8°C during the recovery period was used as a reference.
The refer­
ence measurement was assigned the value 1.0.
Other than the reference datum, all measurements on a cell which
were not separated by a MW irradiation period from the reference were
accepted, without regard to temporal order.
Included were data measured
when the temperature was returned to 20.8°C after a different tempera­
ture had been set.
In order to take advantage of the largest possible
number of measurements, temperature response data from all available
experiments were combined, without regard to cell type.
162
DEPENDENCE OF INPUT RESISTANCE ON TEMPERATURE
0.50 -|
AR/R - -0.0213 AT
0.25-
^
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0.00
-0.25-
-0.50-7.5
-5.0
-2.5
0.0
2.5
5.0
7.5
ATEMP. deg
DEPENDENCE OF MEMBRANE TIME CONSTANT ON TEMPERATURE
0.50-1
ATC/TC •= -0.0470 AT
0.25-
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0.00-
-0.25-
-0.50
-7.5
-5.0
-2.5
0.0
2.5
77"
7.5
ATEMP. deg
FIGURE
Temperature effects on input resistance and time constant
The regression line through the data is shown on each plot.
Despite the wide scatter in the data, both regression coefficients are
significant (p<0.05).
They indicate that resistance decreases as temp­
erature increases, with a Qio of -0.213±0.00613. and that time constant
decreases as temperature increases with a Qioof -0.^70±0„008U6.
The
direction of the resistance change is the same as was reported by Kerkut
and Ridge (1962; see sec. 1.6).
The time constant change may be a
direct consequence of the change in resistance.
The temperature dependent measures of resistance and time constant
are subject to the same nonstationarities as the MW related measures.
Although nonstationarities must have increased the scatter in the
regression estimates, it is unlikely that bias was induced, as tempera­
ture steps of various sizes, up or down, were imposed in various orders,
either early or late in the experiments.
In sec. 1.3 it was indicated that a threshold temperature change is
needed to support discrimination of MW from temperature effects.
figures provide a definition of such a threshold.
These
At 20.8°C, 0.95 con­
fidence intervals for the resistance and time constant, respectively,
are ±0.013^ and ±0.0177-
(These figures assume normally distributed
data, but take the sample size (85)
into account, so are slightly great­
er than ±2SD; see Johnson and Leone, 1977)-
The temperature deviations
at which the regression predictions just reach the 20.8°C confidence
bounds are 0.63°C for the resistance and 0.38°C for the time constant.
It is thus safe to conclude that temperature changes seen during the MW
experiments, which never in the worst case exceeded ±0.3°C, were not
able by themselves to evoke responses.
164
5-3
5.3*1
DESCRIPTIVE STATISTICS OF INTERVALS
Interval Hi stoqram
In general interval histograms from the neurons subjected to temp­
erature changes revealed the same sorts of nonstationarities as did his­
tograms from MW exposed neurons.
Histograms from the initial data sub-
segment (20.8°C, except neuron A05046: 27.8°C), were compared with
histograms for all later subsegments, again using the approximately
x2
distributed statistic G.
Illustrative histograms appear in Figures 48 through 50.
Figure 48
(F1 neuron A02117) shows a trend in the shape of the histograms which
obscures possible temperature related changes.
erature was twice stepped up then down 0.5°C.
In this experiment temp­
In successive segments,
the histogram skewed further to the right, while the relative frequency
of longer intervals fell.
These features of the histogram are consis­
tent with a trend which was evident in the raw AP records:
grew less intense.
bursting
That is, bursts were longer and reached lower peak
AP rates, and interburst intervals were shorter.
Figure 49 shows F1 neuron A03126, for which reversible temperature
effects were evident despite an overall nonstationarity.
First, temper­
ature was moved down 2°C and returned; when the first, second, and third
histograms are compared, an unmistakeable temperature related shift in
the mean interval can be seen.
Next, a -4.5°C step was made.
By the
time the temperature was returned to 20.8°C, the interval pattern had
broadened greatly.
However, the bimodal character which appeared in the
16.30C segment (frequent intervals of 3-6 sec or greater) largely
reversed when the temperature was finally returned to 20.8°C.
165
0.60 -i
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20.9C (0-32 min)
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HISTOGRAM OF INTERSPIKE INTERVALS
EXPERIMENT A02117(F1) TEMPERATURE STUDY
FIGURE 48:
Interval histograms, A02117(F1). +0.5°C steps
r~
12
15
166
0.60 n
20.8C (0-41 min)
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HISTOGRAM OF INTERSPIKE INTERVALS
EXPERIMENT A03126 (Fl) TEMPERATURE STUDY
FIGURE
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6
Histograms, A03126(F1), -2.0°C then -4.50C step
8
10
8df
Neuron A03166 (E6; Figure 50) demonstrated an unequivocal speeding
up of AP rate and narrowing of the distribution for repeated +2.0°C
steps.
Although the AP rate showed an overall increasing trend, the
reversible temperature dependent changes are clear.
Table 28 holds the x 2 G statistics for the temperature dependent
histogram analysis.
In this table, as in Tables 7 and 8, the first val­
ue for each entry represents raw interval data, the second represents
the data for histograms with standardized means, and the third charac­
terizes histograms after both means and variances were standardized.
Here, as for the histograms from MW exposed cells, the large x2 values
make rigorous comparisons impossible.
However, taking the statistic
only as an overall measure of deviation, it is clear that reversible
temperature effects occurred in all neurons except A02117» which was
studied with small (±0.5°C) steps in temperature.
5.3*2
Ser i a 1 Correloqram
The serial correlograms of MW exposed neurons tended to undergo
more changes than in control neurons, when change was measured as change
of the value of statistic H.
For neurons exposed to temperature chang­
es, analysis of the correlograms was somewhat moot, as the size of temp­
erature responses was large enough that the firing patterns of the neu­
rons were changing essentially always.
An exception was A02117-
This
neuron did not respond noticeably to the ±0.5°C steps that were imposed.
Its firing pattern was initially bursting, and as was true for other
bursting neurons (see Figure 27). the correlogram was flat.
It regular­
ized gradually, and as this happened, positive correlation between
168
intervals began to appear.
The remaining correlogram sequences showed
marked instability in the value of H; H was not correlated with tempera­
ture.
TABLE 28:
F1 TEMP
A02117
18DF
17DF
I6DF
F1 TEMP
A03126
8DF
7D F
6DF
NO ID TEMP
A09106
16DF
15DF
1ADF
9DF
8DF
7DF
E6 T E M P
A0501463
15DF
II4DF
13DF
a
21.k
20.9
21.I4
1181*.03
935-10
817.^8
1190.58
658.75
2M3.90
1163.23
21+17.56
18.8
20.8
6956.77
237.69
7589.23
17.lt
E6 TEMP
A0316 6
HISTOGRAM x2 VALUES, TEMPERATURE STUDIES*
832l»5-75
29675 - 3^
IO5U8.58
520. ko
711»-00
751.90
7617.55
lllh.Ul
20.8
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26I4I46.59
H310.21
17987.18
21592.14O
230I43.I40
20.8
989.83
190.51
6 6 . 14O
1476.22
20.8
25.5
2667.99
609.79
75696.13
147277.814
397•5^
f>07U.15
IU76.U5
20.9
22.8
H46I4.8I
16.3
20.9
138.11
67.10
1412.75
170.23
301.28
22.8
1255 •39
190•51
814.32
23.8
387.51
221.H
1172.92
25.8
302.39
261.96
1812.814
25.8
*79-*7
3I40.17
182.95
Indicates that the reference histogram was made at 27*8°C. Ref­
erence histograms of all other neurons were made at 20.8°C.
* indicates that all x2 values were significant at p£0.05>
169
0.4 n
20.8C (1-54 min)
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HISTOGRAM OF INTERSPIKE INTERVALS
EXPERIMENT A03166(E6) TEMPERATURE STUDY
FIGURE 50;
Interval histograms, A03l66(E6) +2.0°C steps
40
170
5.k
EFFECTS ON TIME-DEPENDENT ACTION POTENTIAL PROPERTIES
In studying MW effects, the mean /x|sI
and
standard deviatipn <r(5(
of AP intervals, as well as the mean M|, standard deviation <7|, and
autoregress i ve coeff ici-ents ARi(l) and AR2(1), were expressed as point
estimates in each condition for the steady state analysis, and as time
dependent functions for the time series regression analysis.
For the
temperature experiments, insufficient data were available with any given
pair of temperatures to define samples for t-ratio, Mann-Whitney, or
similar tests.
Therefore the steady state analysis was not done.
For the time-dependent functions, the regression analysis was iden­
tical to that used for the MW studies.
indicator variable.
The only difference was in the
When two step changes of temperature of two differ­
ent sizes were given, the size of the non-zero portion of the indicator
was scaled in proportion to the size of each change during the corre­
sponding period.
5.1*. 1
Effects on the Mean and Standard Dev i at i on of I nterva 1 s
Figures 51 and 52 show, respectively, the static and dynamic model
analyses of neurons A03126 (Fl) and A09106 (not identified; see Figures
10, 32, 3^» 39t and J»3) .
In Figure 51, the temperature was moved from
20.8 to 18.8, back to 20.8( to 16.3» then back to 20.8°C.
In Figure 52,
the temperature was moved down to 17.*»°C from 20.8 and returned (compare
Figure 10).
Substantial effects are evident in both the static and
dynamic model cases.
Even in the dynamic case the pattern of the exoge­
nous variable is evident in the model prediction, unlike the situation
in the MW experiments.
171
It can be seen in Figures 51 and 52 that the standard deviation of
intervals is larger at low spiking rates; i.e., when the mean interval
is larger.
Although it was not verified statistically, this relation­
ship held across cells, also.
This outcome is consistent with the find­
ing in O'Neill, et. al. (1986) that the mean input current (smaller at
low spiking rates) countervaried (also across cells) with the standard
deviation of intervals.
It differs from the expectation for a Poission
model (mean rate equal to standard deviation of rate) and from observa­
tions on some other neural systems (Levine, 1980).
172
EXPERIMENT A03126CF1) TEMPERAI URE STUDY
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FIGURE 51:
Effects on mean and SD of ISI, A03126(F1), +2.0°C steps.
Temperature was lowered by 2.0 then 4.5°C. In this figure,
the indicator moves down for lower temperature.
240
173
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S.h.2
Effects on the Properties of the Input Current
Figures 53 through 56 hold example responses of features of
the input current to temperature.
For neuron A03126, the static models
for m| and AR1 (I) show obvious influence of the temperature input (Fig­
ure 53)-
In the dynamic models for this cell (Figure 5*0 » temperature
appears to affect every variable.
For neuron A09106, the strongest
effect in both static (Figure 55) and dynamic (Figure 56) models seems
to be on ctj, but the other features are clearly also affected.
In gen­
eral the influences apparent in Figures 53 through 56 were strongest in
neurons A03126 and A050A6 (not illustrated), which showed the most obvi­
ous temperature effects in their raw spiking records.
The analysis of temperature responses using linear regression and
F-tests appears in Table 29-
Temperature effects on M|5|(t) and M|(t)
appear consistently in the static models (except for A02117» ±0.5°C).
aj5|(t) but not C7| (t) was consistently affected, while effects on
AR1 (I;t) and AR2(l;t) were evident but not lawful.
Neuron A09106 illustrates a difference in sensitivity between the
static and dynamic models.
As seen in Figures 10, 55. and 56, this neu­
ron appeared to be affected by a -3.^°C temperature step.
The influence
of temperature was judged significant for the static model, but in the
case of the dynamic model, it is not possible to reject the hypothesis
that the interval pattern resulted from the neuron's own intrinsic
dynamics.
175
.
EXPERIMENT A03126 (Fl) TEMPERATURE STUDY
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Effects on input current, A03126(F1), +2.0°C step (static).
Temperature was stepped down 2.0 then
In this fig­
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176
EXPERIMENT A03126(F1) TEMPERATURE STUDY DYNAMIC MODEL
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FIGURE 51*:
Effects on input current, A03126(F1), +2.0°C step (dynamic).
Temperature was moved down 2.0 then 4.5#C. In this figure,
the indicator moves down for lower temperature.
177
EXPERIMENT A09106 (NO ID) TEMPERATURE STUDY
10^
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STATIC MODEL
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Effects on input current, A09106(N() ID), -3.J»°C (static).
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178
EXPERIMENT A09106 (NO ID) TEMPERATURE STUDY
' °1
DYNAMIC MODEL
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Effects on input current, AO91O6(N0 ID), -3-i*°C (dynamic).
In this figure, the indicator moves up for lower tempera­
ture.
90.0
179
TABLE 22:
TEMPERATURE EFFECTS ON AP INTERVALS AND INPUT CURRENT
DYNAMIC MODELS*
FULL
R-sq
STATIC MODEL
REDUCED
F df=(1, )
F-RATIO
R-sq
F df=(1, )
df= (3. )
i
I
i
R-sq F df =(1, )
M1 s1(0
A09106
A02117
A03126
A03166
A05046
44.04(22)
0.667
0.668
94.44(47)
0.944 1109.21 (66)
0.948 926.09(51)
102.79(34)
0.751
0.572
0.609
0.928
0.920
0.591*
33.47(25)
77.72(50)
885.58 ( 6 9 )
620.66(54)
54.17(37)
2.08(22)
2.79(47)
*6.32(66)
*9.07(51)
*7.17 (31*)
"I SI ^
A09106
A02117
A03126
A03166
A05046
0.490
0.692
0.806
0.894
0.479
0.284
0.667
0.793
0.852
0.389
9.90(25)
100.37 (50)
264.55(69)
309.76(54)
23.51(37)
2.96 (22)
1.2M47)
1.47 (66)
*6.84(51)
1.98(34)
0.291 *10.69 (26)
0.116 *6.69(51)
0.361 *39.50(70)
O . 5 6 8 *72.22(55)
0.155 * 6 . 9 6 ( 3 8 )
21. 1 1 (22)
105-53(47)
274.38(66)
430.79(51)
31.30(34)
1
0.235 *8.00(26)
0.042
2.21 (51)
0.452 *57.63(70)
O. 6 3 8 *96.98(55)
0.420 * 2 7 . 4 8 ( 3 8 )
|
M (t)
A09106
A02117
A03126
A03166
A05046
0.692
5^.03(24)
0.681
102.62(48)
0.972 2396.22(68)
0.885 423.11(55)
0.847 188.84(34)
0.595
39.70(27)
0.630
86.81 (51)
0.964 1911 .00(71)
0.860 357.09 (58)
0.767 121.95 (37)
2.53(24)
2.58(48)
*6.76(68)
*3-9M55)
*5.96(34)
0.292
0.001
0.321
O. 5 2 9
0.361
*11.53(28)
0.06(52)
*34. 10(72)
*66.34(59)
*21.50 (38)
A09106
A02117
A03126
A03166
A05046
0.600
0.398
0.452
0.610
0.461
35-98(24)
31 -74(48)
56.13(68)
86.07(55)
29.07(34)
0.489
0.363
0.444
0.538
0.227
25-79(27)
29.06(51)
56.80(71)
67.59 (58)
10.84(37)
2.23(24)
0.93(48)
0.32(68)
*3-38(55)
*4.93(34)
0.093
2.88 (28)
0.029
1-53(52)
0.000
0.00(72)
0.339 *30.2 9 ( 5 9 )
O.328 *18.52(38)
30.26(21)
58.85(48)
137. 17 (68)
204.78(55)
37-94(34)
0.491
0.522
0.644
0.767
0.301
23-13(24)
55.72(51)
128.54(71)
190.89 (58)
15-93 (37)
1.85(55)
*5.43(3M
0.104
2.90(25)
0.075 *4.20(52)
0.003
0.24(72)
0.377 *35-69(59)
O . 1 8 9 *8.85(38)
31.51 (21)
89-09(48)
185.27(68)
51.39(55)
41.95(34)
0.310
0.629
0.659
0.452
0.342
10.79(24)
86.42 (51)
137.01 (71)
47.90(58)
19.25(37)
*5.07(21)
0.96(48)
*6.15(68)
1.09(55)
*5.32(3*0
0.054
1.43(25)
0.087 *4.93(52)
0.449 *58.77(72)
0.054
3-37(59)
0.241 *12.04(38)
<7| (t)
AR,(I)
A09106
A02117
A03126
A03166
A05046
0.590
0.551
0.669
A09106
A02117
A03126
A03166
A05046
0.600
0.650
0.788
0.527
1.70(21)
1.02(48)
1 . 6 7 (68)
AR 2 (I)
0.732
0.483
0.552
* indicates significance at p£0.05 (one-tailed test).
dynamic models had p£0.05<
A l l f u l l and reduced
180
Chapter VI
CONCLUSIONS
The input resistance of MW exposed neurons increased after fifty
minutes or more, while the input resistance of unexposed controls
decreased after the same length of time.
The change in MW cells and the
difference between MW and control only cells were significant at p<0.05
for 12.5mW/g, but not 125mW/g exposures.
They were still significant
when all neurons were grouped together, without regard to type or expo­
sure.
Type E6 neurons seemed to be affected more often, but this could
not be verified statistically.
The time constant of the resistance
response also increased more in MW exposed cells, but not significantly.
Analysis of interspike interval histograms did not yield a conclu­
sion about MW effects.
X2
The differences among histograms, described by
statistic G, was so large that assumptions required for comparisons
were violated.
This remained true even after the mean or the mean and
variance of the interval data were standardized across conditions, in
order to isolate higher order properties that shaped the histograms in
detai1.
Interspike interval serial correlograms were characteristic of the
firing pattern of each cell.
A
x2
statistic, H, was generated to
describe how far each correlogram deviated from that of an uncorrelated
point process (renewal process).
The initial value of H followed no set
pattern, but it changed more in MW exposed than in control neurons.
181
These changes were quantified both as jumps above or below a criterion
(p"0.05 was chosen) and as significant changes in the ratios, of the ini­
tial value to values measured during and after MW (two-sided F-ratio
test, p=0.10).
Because jumps in both the significance and the magnitude of statis­
tic H occurred also in unexposed cells, all experiments were treated as
binomial outcomes.
The frequency of changes in MW exposed neurons was
higher by both criteria, but only reached significance for the ratio
changes, and then only when the weaker of two statistical tests was
used.
Moreover, the ratios changed more frequently only for a sample
made up of neurons exposed at 12.5mW/g, although the effect nearly
reached p=0.05 with a sample including all recorded neurons, regardless
of SAR or type.
The correlograms of all neurons were checked visually
for consistency in form or direction of changes; none was found.
The mean and variance of interspike intervals, as well as the mean,
variance, and first two autoregressive parameters of the input current
(integrator model) were first expressed as steady state values, held
throughout an experimental condition.
When MW and control groups were
compared for differences in the amount of deviation over time, no MW
effects whatever were found.
Each of these features was also checked for dependence on MW using
time series regression.
This analysis had the advantage of rendering a
judgment on each cell individually.
Sometimes apparent dependencies on
a sham MW exposure emerged in control experiments.
Therefore, as in the
serial correlogram analysis, the presence or absence of an effect was
judged as a binomial outcome.
182
When studied using static models predicting only instantaneous MW
effects, only the the ARi parameter describing the autocorrelation of
the input current was affected by MW, and the effects reached p£0.05
only if unidentified neurons were excluded from the sample,' or if neu­
rons exposed at 12.5mW/g were excluded.
Models which included contribu­
tions from the intrinsic dynamics revealed effects much less frequently
than static models for the same data.
Spurious effects in control
experiments were almost absent in the dynamic models.
However, except
in the case of the mean interspike interval, no MW effects on any AP
time dependent feature were revealed, which could not be explained using
the neuron's own dynamics.
Further, although the effects of MW on
M151U) and ARi (I;t) were significant, they were not consistent in
direction, across cells.
In contrast with all MW observations, temperature changes produced
clear effects on input resistance, time constant, interval distribu­
tions, means and standard deviations of intervals, and features of the
input current.
(Not every feature was affected in every experiment.)
Thresholds for temperature effects on input resistance and time constant
were found.
These were larger than any changes that occurred in MW
experiments, assuring that the latter were not contaminated by system
temperature changes.
This study was intended to determine whether a MW effect could be
demonstrated reliably.
No evidence was found of a consistent MW effect
at constant temperature.
A reliable demonstration might imply physical
mechanisms, perhaps unique to biological systems, involving cooperativity, amplification, or nonlinear effects.
Such a demonstration might
also contribute to understanding of environmental exposure hazards.
183
Determining whether the effects were reliable was at the start a
statistical task.
The strength even of the significant effects can be
questioned, when it is considered that the judgment depended on the par­
ticular grouping by cell type (all effects), on the particular choice of
test used (serial correlogram and regression analyses), or on the sig­
nificance criterion (serial correlogram).
At the same time, different tests applied to each feature of the
data showed consistency (resistance data) or at least lack of systematic
differences (compare the static and dynamic regression analyses for each
of M|s| (t) and AR1 (I;t)).
This suggests that the results are not due to
weaknesses in the statistical procedures.
Also, most tests were veri­
fied on generated data of known characteristics.
Even if the effects seen on individual cells were granted to be
robust, the question of reliability has to be addressed in terms of an
overall picture.
Criteria for reliability include lack of susceptibili­
ty to external conditions that ought not to affect the experimental sys­
tem, as well as consistency of direction (see, for instance, Michaelson
and Lin, 1987)-
The latter was specifically shown to be absent from the
present data.
Another reasonable requirement is that an effect be reversible.
In
this study, the time series regression analysis was preferentially sen­
sitive to reversible effects, because of the form of the indicator vari­
able.
However, the other analyses would not have selected against find­
ing a reversible effect, had one emerged.
If these criteria are invoked, the overall conclusion of this study
is that MW effects are lacking under the conditions used.
Even the
strongest effects seen had to be reported with specific qualifications.
I8i»
Physically, the view that MW effects might involve cooperative phe­
nomena, long range coherent interactions, and similar behaviors of high­
ly organized systems was not supported by the results.
The single explanation most consistent with all of the effects
observed is that membrane proteins which serve as conductive ion chan­
nels, underwent more rapid degeneration under MW irradiation.
Referring
to the resistance effect, it appears that a proportion of channels grad­
ually stopped operating.
The increase in resistance can not by itself
indicate which of the multitude of types of channel were affected.
Some
insight into this might have come from the serial correlation or inter­
val data, had there been a consistent effect.
For instance, a systemat­
ic lowering of rate might have indicated loss of Na* channels relative
to K* channels.
The explanation involving membrane channel proteins implies some
selectivity.
However, it is not inconsistent with a local uncontrolled
or uncompensated temperature increase, on a multimolecular scale corre­
sponding with the sizes of structures which could mediate cooperative
effects, but microscopic relative to the temperature sensing system.
Particularly the interaction between water and membrane ion chan­
nels should be considered.
This interaction contributes importantly to
the ion selectivity, voltage dependence, response to gating signals, and
total conductance of channels.
Water associated with the channel pro­
teins could be made especially susceptible to thermal agitation by MW,
if by the association its resonant frequency were lowered into the MW
range.
185
One feature of the MW effects which distinguishes them from expect­
ed responses to changing the system temperature was that 125mW/g did not
usually cause more effects than 12.5mW/g.
For instance, M|s|(t) and
ARi(I;t) were affected more at 125mW/g, but the resistance and correla­
tion properties were changed more at 12.5mW/g.
Lack of consistency
between MW and system thermal effects could be explained by the highly
localized nature of the MW interaction.
Other workers have hesitated to commit themselves to the conclusion
that effects they saw were truly nonthermal (McRee and Wachtel, 198O;
Seaman and Wachtel, 1978).
In some cases, e.g. Seaman and Wachtel
(1978), doubts may have arisen out of legitimate technical concerns.
In
this study, technical issues such as temperature control and dosimetry
were handled conservatively.
Thus questions about temperature constancy
relate to the actual character of the system.
It may be suggested that
the distinction between "thermal" and "nonthermal" MW effects becomes
somewhat moot, once it has been assured temperature has been controlled
properly.
From thermodynamics it may be argued that no process proceeds
at a finite rate without dissipative losses.
This applies no less to
biochemical processes in living cells than to other systems.
Confidence in the technical correctness of this study leads to more
freedom in designing future experiments.
First, it would be valuable to
modulate the MW source and express responses in terms of correlation
with the modulating waveform.
This could yield answers on MW effects
from short data records, without violating the requirement for a long
total period of exposure.
Secondly, potential targets of MW effects
might be defined better, especially by manipulating the preparation
pharmacologically, as has been started by Arber (Arber and Lin, 198^).
186
Appendix A
USE OF ONE MOLAR POTASSIUM CHLORIDE FILLED ELECTRODES
A.1
INTRODUCTION
Intracellular recording in a MW field can be complicated by the
relatively high conductivity of recording electrodes.
Generally, MW
energy absorption by the electrodes will be disproportionately high in
relation to their volume.
The MW field about a neuron could distort, causing errors in the
estimation of the specific absorption rate (SAR).
Although nonlinear
effects of MW are unlikely at the power levels in this study (see sec.
1.2), charges could accumulate and currents could fl.ow, causing arti­
facts in the recorded potential.
If enough energy were absorbed to heat
the electrolyte, diffusion of the contents of the electrode into the
cell along the existing gradient could be enhanced.
Inhibitory postsy­
naptic potentials (IPSPs) generated by increases in CI" conductance, are
most likely to be affected (Coombs, Eccles, and Fatt, 1955)•
To minimize energy absorption effects, 1.0M KC1 was used in the
recording electrodes, rather than the usual 2.5 or 3-OM.
1,0M KC1
filled electrodes behaved similarly to 2.5M electrodes in passive prop­
erties, and there was no degradation of recording quality.
187
A.2
A.2.1
PASSIVE PROPERTIES OF ELECTRODES
Results
Figures 57 through 59 show representative data from comparing the
current-voltage laws of sixteen 1.0M with seventeen 2.5M electrodes.
Current-voltage behavior of an electrode contaminates measurements of
membrane resistance; the electrode contribution can be subtracted only
when it is a nearly pure and constant resistance.
Nonlinear current-
voltage behavior might also serve as a model for rectified currents that
can flow when electrodes are exposed to high MW powers.
Figure 57 shows transient responses as tested with square wave cur­
rents of ±1.0nA peak-to-peak at 1 kHz, for four different electrodes.
Although the transient response is shaped by the network properties of
the shunt capacitance neutralizer in the electrometer, lower resistance
electrodes have more heavily damped responses, regardless of the elec­
trolyte concentration.
The 1.OM and 2.5M filled electrodes all have
bandwidths of several kHz, certainly adequate to record snail
neuron
action potentials, whose bandwidth was estimated from rise times to be
less than 400 Hz.
Figure 57 also includes an example to show that high
frequency currents up to ±25 nA do not cause severe non1inearities.
In Figure 58 are tests of settling times and steady state resis­
tances, made with 1 Hz square wave currents of ±1,5>10« and 25nA.
In
this figure the gain factors were scaled inversely with the applied cur­
rents to make relative changes in resistance apparent.
In the second
column from the left are the responses of a 1.0M electrode, in snail
Ringer solution.
The electrode is severely nonlinear at the higher cur-
188
±1.0nA
±5.0nA
±10.nA
±25.nA
F IGURE 52:
Transient responses of l.OM and 2.5M KCl filled electrodes.
The test signal was a train of short (0.5 mS) current puls­
es. Traces in left column show that step response of an
electrode did not depend specifically on concentration.
Traces in right column, made with a l.OM electrode, show
that at high frequency an electrode had a linear resistance.
Traces on right were scaled inversely with test current.
189
rents.
In the leftmost column the traces are from the same electrode,
but the bathing medium was changed to 1.0M KC1.
The apparent resistance
is about 50% smaller and the nonlinearity is gone.
A 2.5M electrode
behaves the same way, as shown in the right two columns.
Figure 59 shows that the amount of non1inearity, expressed as addi­
tive deviation from linear resistance behavior, does not depend on the
concentration.
The data in this figure are the quasi-steady values of
the responses in low frequency tests like the one in Figure 58.
Since
the average resistance of the 1.OM electrodes (measured with 1.0 nA) is
higher, these data could indicate that electrodes of higher resistance
are not necessarily more nonlinear.
In fact, when electrodes were
grouped by resistance only, disregarding the concentration, nonlinearity
had no systematic dependence on resistance.
190
o*| E
LUilT)
Vu0l+
FIGURE
Vu0l+ v u sz+
Low frequency responses of 1.OM and 2.5M KCl electrodes.
Test signal was a 1Hz square wave. Left: 1.OM KCl elec­
trode, first in 1.0M KCl then in Ringer solution (0.12M).
Right: 2.5M KCl electrode, first in 2.5M KCl then in Ringer
solution. Electrodes were linear in equimolar KCl; they
were nonlinear and resistance was higher in Ringer. Traces
scaled inversely with test current.
191
\ o
r v cm
m 1.0 M, R=12.1m
SI
<J
IT)
>
LU
2.5 M, R=5.9m
\
Q 8
6<n<17
•7
o°
I—
s
O
<°
Y?/Z
tS
I
-25
FIGURE 59:
-10
-5
5
CURRENT (nA)
10
Deviation of electrodes from linear resistance behavior.
Fractional deviation from linearity is expressed as depen­
dent on the test current. Resistances found from final val­
ues of the responses to 0.5 sec current pulses as shown in
Figure 58.
25
192
A.2.2
Discussion
For every electrode the form of the nonlinearity was the same:
for
positive currents the electrode settled slowly to a resistance at or
below the small signal value, while for negative currents the resistance
rose slowly to a resistance substantially larger than the small signal
value.
Studies of Rubio and Zubieta (1961) and of Firth and deFelice
(197U suggest why this is so.
In the presence of the concentration
gradient, there is an osmotic pressure difference, which will cause some
volume flow of less concentrated solution into the electrode tip.
When
a current flows, the amount of flow and the concentration in the tip
will be influenced by the concentrations as weighted by the mobilities
of the various ion species.
The nonlinearity would be explained if
there were less volume flow or if the dominant carriers were more mobile
for positive currents, resulting in a higher momentary concentration in
the tip.
There would be more volume flow or less mobile carriers for
the negative currents, leading to a lower momentary concentration.
A.3
RECORDING QUALITY
Figure 60 shows data from two examples of neuron E6.
The example
on the left was recorded with a 1.0 M electrode, while the data on the
right were taken with a 2.5M electrode.
The spiking rate, polarization, and membrane time constant differ
in the two examples, but the spike waveform and size, and the magnitude
of the membrane resistance, agree closely.
All of these measures have
ranges of variation comparable to those that can be observed in a given
neuron type with a fixed electrolyte concentration (see, for instance,
Gainer, 1972a).
193
WAVEFORM AND POLARIZATION
MV
40 H
40r
0
60n
60
~i—i—r
0
~~i
i
80
r
l i—i—r
0
160
T
i—r
MSEC 160
80
INTERVAL PATTERN
MV
40"
40
o-i
h
0
UJJJ:
r
r r i
60-
60
1
20 '
RESISTANCE MEASURE
i
40
1 =1.0 A
i
i
i
i
20
i
i
SEC
i—r
40
MV
31.5J
\
1
FIGURE 6 0 :
-
I
2.5 s1
TC 0.19 SEC
2.5 S '
TC 0.32 SEC
Recording quality of 1.0M and 2.5M KC1 filled electrodes.
Records made with 1.0M (left) and 2.5M (right) electrodes on
two E6 neurons. Variations in waveform, polarization,
interval pattern, membrane resistance, and time constant
were all within range found across E6 neurons with a con­
stant electrode concentration.
19^
Appendix B
EMPIRICAL THRESHOLD ESTIMATION
For an inactive neuron, threshold could be defined using parameters
of a stimulus which led with a fixed probability to the firing of an AP.
A probabilistic definition can account for variations in the initial
state of a neuron, and in its inputs, but the choice of probability and
test stimulus are subjective.
A probability based definition is not
suited to an active neuron, as its probability of firing an AP is one
(Holden, 1976; O'Neill et al., 1986).
Ma (1985) tested a number of methods for estimating the AP thresh­
old from the intracellular voltage record.
The method summarized here
was chosen because it proved best in two ways: the set of estimated
thresholds had the smallest sample variance among all methods tried, and
the sequence of threshold values was uncorrelated and normally distrib­
uted.
It also consistently placed the threshold at the point where the
slope of the intracellular voltage record just began to increase visi­
bly.
The method is shown in Figure 61.
For each AP, 100 to 150 samples
(interval 0.2 mSec) previous in time to the AP peak had been saved from
the data acquired off the tapes.
The detection algorithm was started by
defining a test point at which the voltage was positive-going and well
before the AP peak, but was above any threshold so far measured, nearly
always between 0 and -lOmV.
When 100 points had been saved, the twenti-
195
O
O-i
to :
AVERAGE AP WAVEFORM. A02056CE6). INITIAL CONTROL
in
THRESHOLD = -23.28 +/- 1.85 mV
AP MINIMUM (RESET) = -48.19 +/- 0.74 mV
O
O
to
o
o
fSJ
o
d
CO
Oo
?" d
o
r\j
o
o
ro
o
d
oin
CDCD
o:
do
CO
0.0 4.0
8.0 12.0 16.0 20.0 24.0 28.0 32.0 36.0 40.0 44.0 48.0 52.0 56.0 50.0
MERN SPIKE DflTR POINTS (MSECS)
FIGURE 61:
Detection of action potential threshold and reset. The
average waveform for 150 APs from an F1 neuron is shown,
with mean ±SD of the threshold and reset marked.
196
eth point before the AP peak was chosen, for 125 points, the forty-fifth
point before the peak was chosen, and so on, leaving a record of eighty
points.
For a window of five points previous in time to the test point, the
mean and standard deviation of the voltage were estimated.
The test
sample point was checked as to whether it was within the window's mean
+SD.
If the test point was above the window's mean +SD, the window and
the test point were each shifted one point backward in time and the test
repeated, and so on, until the test was passed.
The midpoint of the
first window (latest in time) for which the test point was within mean
+SD was taken as threshold.
If all seventy-five possible test points
were exhausted, an error was reported.
When this occurred, the data for
the threshold were reacquired from- the tape, with a longer segment of
data saved, and the threshold was recalculated using an earlier portion
of the rising phase of the AP.
As shown in Figure 61, the threshold was localized quite closely in
the transition from the steeper to the shallower sloped part of the AP
waveform.
However, an algorithm using a test for changes in the esti­
mated slope of the AP waveform performed inferiorly to the present one.
197
Appendix C
CALCULATIONS AND TESTS FOR INTERVAL STATISTICS
C.l
INTERVAL HISTOGRAMS: COMPARISON USING A CHI-SQUARED TEST
The three hypotheses on interval PDFs (section ^».l) were tested by
comparing histograms using a
x2
goodness of fit test.
Interval data were first put in groups (segments) to correspond
with the experimental conditions to be compared, i.e., control, micro­
wave, and recovery for the exposure experiments, and a sequence of three
or more segments of comparable length for the control experiments.
For
the temperature experiments, a new segment was defined each time the
temperature was changed.
A temperature change started at the beginning
of a segment was complete within four to five minutes.
Data recorded
during the initial time were included in each segment.
All interval data for a particular condition were used in a histo­
gram.
Because recordings were interrupted for input resistance measure­
ments, the data do not usually represent a single continuous record.
The mean and variance of the intervals were calculated from the raw
data in each segment.
'a,n "
C
1
The data were adjusted according to:
r,n " ^'r.n)
+
^('rj) 3'C ^'r.l''
CT ('r,n)
in which
l rin is the set of raw (observed) intervals for segment n,
l
a n
is the set of adjusted
intervals for segment n,
3
C_1
198
M(l R>J) is the sample mean of intervals in segment j,
o-(l R>J) is the sample standard deviation of intervals in segment j.
The adjustment was not applied, except when differences in mean were to
be ignored (then the denominator was set to one), or when differences in
both mean and variance were to be ignored.
Next a bin width was chosen, as described in section 4.1.
A fre­
quency histogram was formed for each experimental segment, by adding one
to the cell whose range included each interval within the segment.
maximum of 200 bins was allowed.
A
Occasionally intervals longer than 200
times the binwidth existed in a data set.
Also, in most cases, adjust­
ment C-l generated a few intervals longer than 200 binwidths or shorter
than zero.
These out-of-range intervals were discarded as outliers.
These outliers were not included in calculating the total frequencies in
the histograms.
The test statistic G for the hypothesis that a histogram has a par­
ticular form is an approximation to a log likehihood ratio (Johnson and
Leone, 1977) '•
i=k
G = 2 [ 0
C -2
n
- E
1
3
2
/ E
1
i =l
i n wh i ch
i
indexes the histogram cells, of which there are k,
0(n) is the observed frequency in experimental segment n,
E (1) is the expected frequency.
The expected frequencies for each experiment were taken as the observed
frequencies in the first (control) experimental segment.
199
Statistic G follows approximately a x 2 PDF
all cells are at least five.
if the frequencies in
Intervals which were quite long or short,
but had not been discarded as outliers, usually filled the corresponding
cells of the histograms with frequencies less than five.
Cells at the
long and at the short end of the first (control) histogram were combined
until no cell contained less than five counts.
Corresponding cells in
the test histograms (MW, temperature change, recovery) were combined the
same way as the cells in the control histogram.
The number of degrees of freedom for testing G is the number of
cells, less the number of pieces of information used to calculate the
frequencies (Johnson and Leone, 1977; Walpole, 197^)•
In constructing
the test, the total frequency over all bins in each test histogram is
matched to the total
of freedom.
in the control histogram, with loss of one degree
When means in the data are matched, one additional degree
of freedom is taken.
Finally, one degree of freedom is also lost when
the variances are matched.
The histogram analysis was verified by comparing interval sequences
from a uniform integer generator against a deterministica11y uniform
sequence.
The analysis is limited somewhat by the fact that no underly-
ing form is known for histograms under control conditions.
C.2
TESTS ON THE SERIAL CORRELOGRAM OF INTERVALS
The serial correlogram was estimated by Equation 1.7~2.
correlogram requires a continuous record of
intervals.
The serial
Data were
grouped into segments as nearly as possible in the same way as for the
histogram analysis, except that within a given condition, only the long­
est available continuous record was used.
200
The variability of a correlogram estimate will suffer at larger
lags, as the number of overalapping interval pairs falls.
The specific
number of lags was additionally constrained by the requirements of the
test described below.
The maximum lag was chosen from
... as
the nearest value to twenty-five per cent of the number of intervals in
a segment, or 10^, whichever was smaller.
Individual serial correlation coefficients can be tested for sig­
nificance, but no method has been described to assess the overall func­
tion.
A question which can be asked for the overall correlogram, and
which is fundamental, is whether the underlying process is of renewal
type, i.e., whether it has independent interval lengths.
To answer this question, an impression of whether each correlogram
was flat was first obtained in Monte Carlo fashion.
Each correlogram
was compared with a correlogram estimated from the same data, after the
order of the data had been shuffled randomly.
The actual test for renewal
Lewis (1966).
properties was done following Cox and
In the test, a periodogram estimate of the energy density
spectrum of the intervals was made by Fourier transforming the correlo­
gram.
The periodogram is useful for statistical testing of the correlo­
gram because it represents uniform samples from an underlying spectrum
which is continuous.
The energy spectrum is defined by:
k=+°°
C-2
f («) • (l/27r) 2 p^ cos(kw)
k"- 08
in which P is the true serial correlation coefficient at lag k.
spectrum is estimated by:
This
201
C-3
k"n0-1
I («p) - (1/2TT) 2 R^* COS(kcOp)
k^-ng+l
in which
ft
Rk
- Rk (1 - |k| / n0 )
is a weighted function of the estimated serial correlogram,
no is the maximum number of lags which were estimated, and
«p are samples of the continuous spectrum at frequencies
27r/no, W/no,..• ,7r.
Weighting of the sample correlogram is necessary to prevent major
leakage or splatter errors in the spectrum which would be caused by an
abrupt truncation.
Frequency samples at intervals spaced 27r/no are suf­
ficient to represent the spectrum.
Notice that the frequency resolution
improves when more data (more lags) are available.
A renewal process will have a flat energy density spectrum, f (top) =
cr2/27r, for each p.
To determine whether the periodogram estimate I (w p )
represented a renewal process with this spectrum, a test for homogeneity
of variance was used.
Boxcar smoothing was applied to the spectral points.
They were
summed into j groups of length m points each, ignoring «=0 and to=7r.
value of five was set for m.
A
The maximum number of lags no was set so
that no/2 was mj+2; j=2 corresponded to 2^ lags, j=3 to
and so on,
up to j•= 10 for 10^ lags.
im
s j 2 • 2[ I (w p ) / f («p) ]
p= (i -1)m + 1
C -4
202
y(t) = +0.75 y(t-l) + a(t)
n = 1000
1.0
1
0.3H
u
"a.
C
.2
E
<
o.o-
B
«
o
-1.0
—I—
—I—
25
50
75
y(t) = +0.50
1.0
O
0.2-
0.0
+ a(t)
n = 1000
D
0.5
"o.
E
<
o.o-
o
€>
>
-0.5-
O
u
€>
-1.0 - 1
50
75
o.o
~5_
i>
>
o
0.5
0.40.2-
X 2 = 30.820
df=9
-L_/l
in
0.1
0.2
0.3
0.4
0.5
i)
X 2 = 10.446
df=9
0.8
0.6
0.4-
0.2
Ckl
u
-1.0
r
—i—
25
0.0-1
-I—
50
75
0.0
100
y(t) = aO)
n = 1000
1.0
T
~r
0.1
0.2
0.3
0.4
TJ
3
0.5
"5.
0.0-
0.6
*>
0.4
-0.5-
o
U
v
X 2 = 2.8891
df=9
0.8
E
<
>
1
0.2
Aa
,I
r
c*.
-1.0
50
75
LAG (Intervals)
V
0.0J
"1—
25
0.5
1.0
«
•
100
-1
0.0
0.1
0.2
0.3
FREQ (Neper)
SERIAL CORRELOGRAM OF INTERSPIKE INTERVALS
FIGURE 62:
0.4
1.0 -i
E
<
j5
«
L.
V.
0.3
i
i
0.0
0
-o
3
n = 1000
.2
o
U
c
o
0.6-
100
y(t) = +0.25 yCt-1) + a(t)
1.0-
0.5-
0.2
0.025
«
0.8-
Ck:
o
u
c
0.1
1.0-
"0
4>
«
IK
0.0
100
U
c
.2
V
oc.
J
—i—
0.6
0.4-
-0.5
X 2 = 68.076
df=9
0.8
v
>
u
0)
1.0-1
O
TJ
3
Operation of the test for a renewal process of intervals
(I). The value of statistic H increases proportionally to
the degree of serial correlation of the process; positive
correlations shown.
0.4
0.5
203
yCt) • -0.25 y(t-l) + a(t)
n = 1000
1.0-,
«
o
'0.5-
u
c
o 0.0
3
o
l. - 0 . 5 H
l.
Q.
o
-1.0
r
i.Oi
y(t) *
50
75
a.
E
<
0.0-
«>
>
0.1
0.2
0.3
0. 4
D
—I—
X 2 = 26.922
df=9
0.8J
0.6 H
0.4
AA
)
'•
0.2
o.o-J
—I—
50
75
!
0.0
100
y(t) « -0.75 y(t-1) + a(t)
0.1
Q0.0-
3
«
t -0.5
u
o
u
0.3
0.4
0.5
1.0
~§
0.5-1
,
1
0.2
tt
n = 1000
X 2 = 7 5.&+3
df=9
j\
0.8 J
E
<
0.6-
«>
>
0. 4 .
to
at
n
0.2
0.0J
-1.0
25
50
75
100
0.0
0.1
0.2
0.3
0.4
SERIAL CORRELOGRAM OF INTERSPIKE INTERVALS
FIGURE 63;
0.5
at.
25
1.0-1
0.0J Tl
1.0
I)
~3
0.5
r r~h
0.2
0.0
-0.50 y(t -l) + aO)
n *= 1000
-1.0
c
o
0. 4 -
100
o
a>
u
1. - 0 . 5
o
u
D
O
u
«>
>
—i—
25
c
o
0.6-
V
X 2 = 7.2145
df=9
0.8 -j
E
<
oc
V
a
o
U
1.0
«>
*3
Operati-on of the test for a renewal process of intervals
(II). The value of statistic H increases proportionally to
the degree of serial correlation of the process; negative
correlations shown.
0.5
20k
in which i,i«l,2,...,j, indexes the groups.
J
The test statistic,
J
c-5
H •[ 2q ln(2 S j 2 / 2q) - 2 2m 1 n(s j
I >= 1
2
/ 2m ) ] (6m-3) / (6m-2) ,
i =l
in which q=mj , is approximately
x2
distributed, with j-1 degrees of
freedom.
The function and appropriateness of this test were verified on gen­
erated data.
First, a sequence of integer intervals with known correla­
tion properties was generated, according to an autoregressive process:
T,(k) = a 0 J ] (k-1) + T 0 (k) + /u.
in wh i ch
To(k) is a sample from a sequence of independent uniform random
integer intervals of zero mean,
T1 (k) is the resulting sequence,
M is an appropriate mean, and
ao takes on values -0.75#-0.5."0.25,0.0,0.25,0.5t and 0-75The result is shown in Figures 62 and 63One limitation on the spectral test has its origin in the use of a
weighting function.
Contributions to serial correlation at longer
lags,
such as would result from a drifting'or nonstationary interval process,
are deemphasized.
Thus, two correlograms which are dissimilar only in
their long lag dependencies might not be distinguished.
A second limi­
tation is that the test is sensitive to the amount of dependence, but
not to the details.
For instance, it does not distinguish a low-pass
filtered process from a high-pass filtered process.
205
Appendix D
ESTIMATION AND VERIFICATION OF THE INTEGRATOR MODEL
The pure integrator model with random reset, threshold, and input
current density was given by equation
Although 1.7_Jt is a single
input single output system, we treat the linear model
in vector-matrix
form (single output with k inputs) to maintain genera 1 ity.
The model is:
Y = X 3 + V
D-l
in which (when n observations are available):
Y • [y (1) ,y (2) ,... ,y (n)] T is the output vector with elements y(i),
xli • [x (1,1) ,x (1,2)
X (1 ,k)]
X T 2 - [x (2, 1) ,x (2,2),...,x (2,k)]
xl n - [x (n,1),x (n,2),...,x(n,k)] are the row vectors of input matrix
X, whose dimensions are (n x k).
3 is a parameter vector of length k (in our case k=l and 0 will
estimate mAT/C in equation 1.7-6)• and
V • [v(l),v(2)
D.l
v(n)] T is the sequence of disturbances.
WEIGHTED LEAST SQUARES ESTIMATION
Because the variance of the disturbances V is not constant but pro­
portional for each v(i) to the corresponding x(i), D-l can not be esti-
206
mated by ordinary least squares (OLS).
A weighted least squares (WLS)
estimator is required in which less significance is given to noisier
data.
In this study
it was hypothesized that 3 changes with MW irradia­
tion and/or temperature.
In testing this, it was first assumed that 3
changed only with a new experimental condition and rapidly reached a
steady state.
The data were segmented by condition and 3 was estimated
separately for each segment.
The following shows the nonrecursive (off
line) WLS estimate of 3 that was applied in this case (Johnston, 198^4;
Ma, 1985)•
This estimator, like the OLS estimator, is best (smallest
variance) among estimators which depend linearly on the observed data,
and is unbiased.
The covariance matrix of the disturbances assumed to be:
a^
0
0
a*
Cov (V) = E (V V T )
0
0
al
0
0
0
D-2
is
If each v (i) were transformed to v*(i) such that cov(V*)=<721 , an OLS
problem would result.
If cov (V) is symmetric and positive definite, then nonsingular
matrix P exists such that
PP T « (1/cr2) Cov (V)
This is guaranteed because cov(V) is diagonal with all independent posi­
tive elements.
T
P
Premultiplying by P" 1 ,
2
-
-
(1/<T ) E [ P
I
T
V V ]
207
Taking the transpose,
2
- I T
P - (1/a ) E [ V (P
V)
]
Again premultipiying by P" 1 ,
2
-1
I = (1/c7 ) E [ P
-1
V (P
T
V)
-1
] - Cov(P
V).
To form the OLS estimator, we premultiply not only V but also Y and X by
P" 1 , with no effect on 3.
Matrix P" 1 is:
1A*1
0
0
0
l/<*2
0
0
0
0
0
0
l/«3
..
..
• ..
0
0
0
i/a.
Then the transformed equation is:
ft
Y
*
-X
*
3 + V
in which Y* • P" X Y and X* = P" l X.
The OLS estimator
3 - [ x* T x* r 1 [ X*TY* ]
D-3
is a WLS estimator of equation D-l.
This estimator was used by Ma (1985) and by O'Neill et al. ( 1 9 8 6 ) .
It was used in this study to obtain the results shown in section
4.3*2.1, on steady state values of
and ctj.
Validation of the estimates is covered by Johnston (1984).
On a
few experimental data sets in this study, the quality of the integrator
208
model was chrecked as follows.
Each parameter estimate was tested
against the hypothesis that its true value was zero, with a one-sample
t-test.
The autocorrelation (ACF) of the residual errors from the WLS
regression was also inspected.
The ACF will be flat if model form D-l
is appropriate and covariance matrix D-2 is diagonal, as was assumed.
Generally, as O'Neill et al. (1986) found, the ACF was not flat.
Rather
than impugning the integrator model, this probably indicates that D-2 is
not truly diagonal.
Possibly the properties of the cell membrane filter
the input current process somewhat.
Bias can also occur if D-2 has off-diagonal terms or D-l is not a
good model, but this possibility was not tested.
D.2
FORGETFUL RECURSIVE WEIGHTED LEAST SQUARES ESTIMATION
As was indicated in sec. 1.8.1», improved tests for MW effects
require that 3 (mAT/C) be estimated as a function of time.
Ljung and
Soderstrom (1983) describe numerous recursive estimation algorithms,
among which is one derived from the nonrecursive (off-line) OLS estima­
tor.
This estimator is readily specialized to WLS and to time-varying
parameters, and is explicated here following mainly their arguments.
The nonrecursive OLS estimator is made recursive as follows.
From
the nonrecursive estimator:
0 = [ XTX I"1 [ XTY ]
def i ne:
^n ™ *n^*n
d-k
209
in which Xn means X using all data including the current observation,
and
Rn.
n-1
=
A n-1
x n-l
in which Xn_] means the current observation is not yet known.
Provided
that cov(V) is diagonal:
R n-1
+
D-5
*n *n
Then
( XJ XN )
( Rn'
0n
( Rn
(
Xn-1T Yn-1 +
( V
(
Rn-1
{ Rn
+
*n v W )
([ Rn - xn Xp ] 3n-i + xn y(n) )
(
( Rn
* ^n-1
Bn-1
*n V >
+ Rn
Rn
*n ) C y ( n ) ~ *n
^n-1
^ *n ( y
®n-1 ^ )
D-6
~ *n ^n-1 ^
Equations D-5 and D-6 constitute the recursive OLS (ROLS) estimator.
Ljung and Soderstrom (1983) showed that updating R then inverting it can
be avoided by substituting
^
R
~1
K
n
Rn-] ^
x n xT R n _^ 1
D-7
<n-l
'
for equation D-5.
+
*n
R
n-T ^ *n
The ROLS estimator preserves every property of the
OLS estimator provided only that cov (V) is diagonal.
Within the assump-
210
tions it is proper to convert the ROLS estimator to recursive weighted
least squares (RWLS) by premultipiying each datum x(n,i) or y(n) by the
corresponding element p(n,n) of weighting matrix P as these become
available.
The result, shown in Ljung and Soderstrom (1983) » can be
verified by carrying through the derivation of D-6 and D-7 starting with
D~3 instead of D-4.
Ljung and Soderstrom (1983) modified the RWLS algorithm to produce
time dependent estimates by discounting previous data at a constant rate
per point.
The following show how equations D~5 and D~7. respectively,
change by the inclusion of both weighting and forgetfulness:
^n
=
3n-l
+
^n~1 *n p(n.n)"2 ( y (n)
Rn_1 •= (1 / X)[
Rn_]
D-8
xj en_, )
]
D-9
in which
X is the forgetting factor, X=<1, and
p(n,n) is element (n,n) of inverse covariance weighting matrix P.
This estimator can be referred to as forgetful weighted least
squares (FRWLS).
It was used to obtain the time dependent estimate of
the input current for the study of its mean M| (t) and standard deviation
(section 4.3.2.2), as well as for the study of its correlation proper­
ties (sections k.}.1.2 and 4.3-2.2).
A problem in its use is selection of X.
Whenever X is less than
one, the ideal (best linear unbiased) WLS properties will be lost, and
bias will be exacerbated.
%
A less forgetful estimator behaves more near-
ly ideally, but filters out systematic features of the input current
211
estimate.
On the other hand, a highly forgetful estimator will respond
faster than any actual variations in the input current, so will add spu­
rious noise.
Figure 6^ shows the behavior of the FRWLS estimator.
Data modeled
in this figure were generated directly from Equation 1.7—5of z(j) were taken from experimental data.
0.02v/sec and held for 100 samples.
'•OO samples
,uAt/C was set initially at
Then MAt/C was stepped abruptly up
to O.OW/sec (100 samples), down to O.Olv/sec (100 samples), then
returned to 0.02v/sec (also 100 samples).
The process e(r) was normally
distributed with zero mean and variance 0.02 (v/sec)2.
The resulting
sequence of simulated interspike intervals was modeled using FRWLS.
With X=1.0, the estimate is essentially unresponsive to the step
changes in MAt/C.
With X reduced to 0.95 then 0.90, increases in both
noise (the standard deviation of the estimate; not shown) and respon­
siveness become apparent.
It was found that the residual errors of estimation depended on X.
A criterion for selecting X was developed on this basis.
The sum of
squared residual errors (as defined below) fell steeply as X was reduced
from one.
In some data sets it reached a true minimum, but in most it
fell to a plateau, but did not rise again with further decreases in X.
X was chosen to give the minimum sum of squared residuals when this
existed.
For bursty or quite erratically firing cells, X was as low as
0.7, while for most other cells it was in the range of 0.8 to O.98.
Otherwise, X was set to a value above which the sum of squared residuals
started rapidly to increase.
212
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Demonstration of forgetful weighted least squares estima­
tion. Experimental reset and threshold data were used with
known values of mAT/C and computer random data to generate
simulated interspike intervals, from which 3 was estimated.
213
To choose X, the residual error that was summed and squared was the
recursive residual (Johnston, 198^):
E re s
* C y ( n ) ~ *n ®n - 0 / ( 1 .0 + x j R n - i '
^
D-10
Alternative error definitions include the prediction error:
Eres =
C V(n)
- xj 3n_,]
and the current residual error:
^res
=[
yW
*n ^n-J*
Neither of these error forms showed as obvious a dependence on X as did
the recursive residual.
2U
Appendix E
TESTING TIME-DEPENDENT AP PROPERTIES FOR MW EFFECTS
As was indicated in sec. 1.7» statistical properties of neuron
activity can most usefully be expressed as dependent on time, when
effects due to an exogenous experimental treatment such as MW irradia­
tion are to be examined.
The transfer function analysis that was used
to check for MW effects on interval
parameter of the integrator model
E.l
properties and on the input current
is described in this appendix.
TIME DEPENDENT MEASURE OF MEAN AND VARIANCE OF INTERVALS
Interval PDFs could be influenced by MW in a variety of ways.
In
sec. A.l, tests on interval histograms are reported for three different
hypotheses on interval PDFs.
First, no prior assumptions were made.
Next the mean interval was fixed, on the assumption that it might vary
in a way unrelated to the experimental treatment.
Finally, both the
mean and the variance were fixed, on the assumption that they could vary
independently of the experimental treatment.
Formally, these treatments
test the idea that essential properties of AP generation only govern the
shape of the interval PDF, and that shifting or scaling may occur by
independent or even spurious mechanisms that are of no consequence.
It
is just as sensible to suggest that properties of AP generation which
set the mean and variance of intervals are among the essential ones, and
that influences on the detailed shape of the PDF are not of interest.
215
To complete the process of checking for MW influences on the interval
PDF, the mean and standard deviation of intervals were also examined.
Analysis of interval histograms requires considerable numbers of
data.
The basic need is to estimate the relative frequency in each bin
with enough degrees of freedom to support a test (Appendix C).
In gen­
eral the properties of interval PDFs depend on time (sec. 1.8), but the'
requirement for many data makes a time dependent estimate of the histo­
gram itself impossible.
Instead, the AP interval generating process was
assumed to be in a steady state, and one histogram was estimated, during
each experimental condition.
In contrast, the mean and variance, being single parameters, can be
estimated usefully from a short data record.
To express the functional
dependence of the mean and standard deviation of intervals on time in
each experiment, a simple algorithm was designed.
It moved a sampling
window through a data record and repeatedly estimated the mean and stan­
dard deviation of the data within the window.
Sample times at intervals
of 3 minutes were chosen (the reason for this choice is given later).
The first interval in an experimental record which occurred at or after
a sampling time defined the central point in the window.
The window
extended a fixed number of intervals previous and forward in time.
The
number of intervals in each half of the window was determined by divid­
ing the sampling interval (3 min) by the mean interspike interval and
rounding to a convenient value.
Thus, on average, the window for each
sample reached back to the previous sample time and forward to the next.
Because the window had a length of approximately twice the sample inter­
val, yet was advanced only the length of the interval at each sample,
216
the possibility of aliasing was minimized.
The resulting time-dependent
functions of the mean and standard deviation of intervals contained
between 35 and 70 sample points, depending on the length of the experi­
ment.
E.2
PROPERTIES OF THE INPUT CURRENT
E.2.1
Interpolat ion and Un i form Resampli nq
Estimation of the integrator model (sec. 1.8) as described in
Appendix D, yielded a time-dependent input current (denoted by mAT/C in
equation 1.7~6, and by 3 in Appendix D).
Since each innovation in 3
occurred at the time an AP was fired, the samples of (3 fell on a nonuni­
form time increment axis.
A range of techniques is available for analyzing 0, but all require
that it be put on a uniform time axis.
A process of interpolating and
resampling is justifiable under the assumption that the input current
signal
is continuous (sec. 1.7).
To interpolate between nonuniformly spaced samples of a continuous
function 3 = f (t), the samples can be fit to a polynomial,
Pint ®
+ bju + b2U^ + bju^ + ... ,
E-l
in which
3 int is the interpolated continuous functional value,
£ I, i =0,1,..., are the fitting coefficients, and
u are arbitrary sample times for which a value of 3 is of interest.
217
Because a fit which sufficiently preserves details of the original func­
tion requires a polynomial of approximately the same order as the number
of samples available, it was impossible directly to interpolate the
input current function from an entire experiment.
of low order was fit recursively.
Instead, a polynomial
The fit was made by regressing 3 (t)
on time in a manner analogous with the estimation of the input current
parameter itself, using forgetful least squares.
Fitting was done using
equations D~7 and D-8, modified only to remove the weighting (the covariance properties of 0(t) were assumed constant).
These equations are
reproduced here with the appropriate variables changed.
B n = B n -! + R n " 1 l n ( 3(t(n)) - fT B n „!)
,
Rn
= (1 / X) C
,
Rp-f1
R n-1
1
^n ^n
E-2
R n-1
^
^"3
]
*
+ ll R
n-T 1 *n
In these equations,
(3 (t) is the FRWLS estimate of ,uAT/C,
§ is a vector of polynomial coefficients 6 j ,
i =0 , 1 , 2 , . . .
to be esti­
mated,
t (n) is the time at which interval n occurred,
t n is a vector [ t(n) t a (n) t 3 (n) ... ],
A is the forgetting factor (X=<1).
In carrying out the interpolation, equation E-l was made time dependent:
3int(k)
=
b0(n) + b1(n)u(k) + b2(n) u (k) 2+ b^(n) u (k) 3+ ... ,
E
It was then applied (as Equation E-^) at a sequence of uniformly spaced
sample times u(k).
At each uniform sample time, the values of B used
218
were those most recently estimated by equations E-2 and E~3» at times
t(n) , such that t (n) < u (k) < t(n+l).
^int O
=
3( n )
was
When u(k) •= t (n) occurred,
set -
In interpolating, it was necessary to decide on the interval
between uniform samples u(k), the maximum order for the polynomial coef­
ficients bj, and the forgetting factor X, as all of these can affect the
adequacy of the result.
The uniform sampling interval was fixed at one-half of the average
interspike interval as estimated over the entire experiment.
This rep­
resented a reasonable compromise between the need to recover rapid
changes in 0 that could occur when the AP rate was high, and the need to
avoid long sequences of samples that contained no new information.
To guide the selection of X and the order, a number of criteria for
a good interpolation can be suggested.
Ideally, the interpolated data
should match the original data in mean, variance, and distributional
properties.
The residual error between original and interpolated data
should also be as small as possible.
Preliminary tests were made on simulated data for 0, whose proper­
ties were at the extremes of any likely to be encountered in actual
data.
200 independent samples for 0 were generated.
The samples were
put on nonuniform intervals whose lengths were drawn in random order
without replacement from the integer sequence [1,2000] msec.
The ampli­
tudes of 0 were drawn in random order (not the same order as the inter­
vals) from an integer sequence then scaled to fit in [0.0002,0.0^].
The test data were interpolated using orders 0 through 3» and for X
from 1.0 through 0.1.
When order 2 was chosen for B, the interpolation
219
failed for A<0.3; for order 3 it failed if X<0.7 was picked.
Failures
were traced to a numerical overflow in calculating covariance matrix R
(Equation E~3).
Further testing showed that data interpolated at orders
0 and 1 with X of 0.75 and 0.50 underwent considerable filtering.
tering was evident in a persistent autocorrelation.
order 1 induced less autocorrelation than order 0.
Fil­
For a given X,
However, order 1
distorted the amplitude distribution of the data quite noticeably.
Therefore order 0 was chosen for all experiments.
(It will be observed
from Equation E-4 that choice of order 0 reduces coefficient vector B to
a scalar and removes its time dependence).
For the test data, X affected the quality of the interpolation
quite profoundly.
In experimental data, the choice of X seemed less
critical, but nonetheless, X was chosen specifically for each experi­
ment, as was done in estimating 0(t).
Sums of squared residual errors
of the three types defined at the end of Appendix D were were found for
each X.
To give a measure of effects on the distributional properties
of the data, the differences in mean and variance between (3 and (3j nt
were also found.
In all experiments, the summed squared recursive resi­
dual (Equation D-10) decreased sharply as X was reduced from 1.0, but
especially for X<0.5> the rate of decline became very gradual.
of 3 hardly differed from the mean of @j n f
The mean
The variance of 3jpt was
larger than the variance of 0 and usually grew with decreasing X.
X was
chosen for each experiment to fall in the broad region of decreasing
summed squared recursive residual and increasing variance 3; n f
220
E.2.2
Characterization of the Input Current
The interpolated input current parameter 0j nt was characterized by
its mean, variance, and correlation properties.
The mean and variance
of 0| n t were estimated using a moving window, exactly as was done to
find the mean and standard deviation of intervals.
Time series analysis (Box and Jenkins, 1976) compactly parameter­
izes the correlation properties of random data.
For a single time
series, such as 3; n t> the analysis assumes correlation has been induced
by the action of a linear dynamic system (a filter) on uncorrelated
white noise.
The dynamic system is described by the following differ­
ence equation:
x t = AR^Xt_i + AR2X t _2 + ... + AR n x t _ n +
MA 0 v t + MA lVt _ 2 + ... + MA m v t _ m
E-5
in which
x t are the values of the series, e.g.,
at
times t,
A R j , i=l,...,n are the autoregressive (AR) coefficients,
MAj, j=l
m are the moving average (MA) coefficients, and
v t is an uncorrelatecTwhite-noise process.
Characterizing the process consists of choosing the AR order n and the
MA order m, then fitting the model.
Orders m and n are chosen from the
correlation properties of the data by direct inspection of the auto­
correlation (ACF) and partial autocorrelation (PACF).
The PACF is a set
of nonlinear functions of the ACF, which can not be written directly in
closed form (see Box and Jenkins, 1976).
Data whose ACF damps out grad­
ually and whose PACF cuts off abruptly beyond lag n can be described by
221
a model that includes n AR coefficients and no HA coefficients.
Con­
versely, data whose PACF damps out gradually but whose ACF cuts off
beyond lag m can be fitted to a model with m MA coefficients and no AR
coeff i c i ents.
A special case occurs when the autocorrelation function of the data
neither damps out nor cuts off, but persists.
When the ACF of 0; n t was
calculated, it persisted in every one of 17 experiments tried.
This
behavior indicates nonstationary data which can not be described by the
action of a stable (bounded input/bounded output) system on white noise.
In this case it has to be assumed that the dynamic system that produced
the data operated in cascade with a pure integrator.
Therefore the data
were differenced:
x t * x t - x t _,
after which the model was re-identified using the ACF and PACF.
A differencing operation is justifiable when short-term correlation
properties of the data are of interest.
The persistent trends in 0j nt
are captured in the time dependent sequential estimates of its mean and
var i ance.
The ACF of the differenced 3; n t damped out gradually, and the PACF
cut off, indicating m=0, a pure AR model.
Although a few experiments
would have been fit better with n=3 or n=A, n=2 was indicated in the
remainder, so an AR2 model was chosen.
An AR2 model is a reasonable
choice, as it can account for a range of ACF shapes, including both sums
of real exponentials and damped sinusoids.
222
A sequence of estimates for autoregressive coefficients ai(i) and
a2 (i) was generated from (3jnt using the same moving window that generat­
ed estimates of the mean and variance.
Coefficients at (i) and a2(i)
were estimated by a maximum likelihood algorithm (Box and Jenkins, 1976)
using a commercial subroutine (International Mathematical and Statisti­
cal Libary, I98M .
Correct operation of the algorithm was verified by
.comparing it with a similar routine in Mini tab (Ryan, et. a 1 ., 1980) .
E.3
TESTING THE TIME-DEPENDENT SIGNALS FOR MW EFFECTS
In the previous two sections the generation of time-dependent sig­
nals for the mean M|S| and standard deviation cr151 of intervals, and for
the mean M|, standard deviation o-| , and autoregress i ve coefficients
(orders 1 and 2) ARt(l) and AR2(1) of the interpolated input current
$jnt were explained.
This section explains how these six functions were
tested for possible influence from MW, using regression analysis.
Results appear in sections A.3-1.1 and A.3.2.1.
Regression analysis can determine whether an exogenous treatment
such as MW irradiation has affected a system, if the treatment can be
described using a suitable indicator variable (Johnston, 1984; Neter and
Wasserman, 197^).
An indicator variable was defined as 0 or 1 to mark
whether MW was off or on, respectively, at the sample times of the above
six functions.
Whenever the window of data from which the functions
were found covered a transition in the MW regime, the indicator was set
to the proportion (0.0 < I < 1.0) of time that MW was on.
Two ideas can be suggested for possible MW influences.
On the one
hand, any response to MW may follow the MW regime essentially instanta­
223
neously.
A regression analysis constructed on this view has only the MW
indicator as an independent variable:
f (t) - W 0 I (t)
E-6
where
f (t) is any of the six functions of neuron activity defined above,
is the coefficient expressing the relative strength of effect,
Wo
and
I(t) is the indicator variable.
On the other hand, MW may be thought of as an input to the entire
dynamic system that determines which ever of the functions is being
investigated.
This view is more satisfactory, as it takes explicit
account for the possibility of delayed and/or gradually developing
effects, as suggested in sec. 1 .8.3.
series regression can be used.
To analyze this situation, time
Time series regression postulates a dif­
ference equation model to account for both natural and forced response
modes.
f(t) = V^U-l) + V2f(t-2) + ... + Vnf(t-n) +
W0I (t) + W,I (t-1) + ... + Wml (t-m)
E-7
where
f (t) is again one of the six functions of neuron activity,
V j , i=l,...,n express the natural dynamic response of the system,
and
Wj, j=0,...,m express the strength with which I forces a response.
22b
A dynamic time series model of the form E-7 is generally known ,as a
transfer function model (Box and Jenkins, 1976); it differs importantly
from the ARMA difference equation model (Equation E-5) in that here two
series, f(t) and I (t), which are explicitly known, are involved.
Models E-6 and E-7 were both estimated using ordinary least squares
linear regression.
Contrasting with the recursive forgetful estimation
of 0 and of 0j nt , one set of values of Vj or Wj was considered to
describe an entire experiment.
the estimation.
Mini tab (Ryan et al., 1980) was used for
The mean value of each f (t) and
I (t) was removed and
the regression was done without a constant term.
In estimating model
E-7, it was necessary to choose m and n.
In
analyzing a physical system, these can be chosen using inferences from
the system impulse response function (Box and Jenkins, 1976), but direct
estimation of this function is not possible when the forcing function is
an indicator variable.
In more general linear regression problems, the
choice of regressors has to be tied with the particular hypotheses to be
tested (Neter and Wasserman, 197*0 •
Fortunately, the test, described
below, that was used to detect MW effects, is not very sensitive to the
exact model specification.
In this study no physical information was available to help in the
choice of m and n.
Orders m and n wi11 be larger for a given system, if
the sampling interval of the data is made shorter.
An interval of three
minutes was picked so that time constants of about the length of the
interval could be modeled.
These would be reasonable time constants for
a system governing MW effects that evolved completely over tens of min­
utes.
225
Preliminary tests indicated that V (n) was seldom significant for
n >2.
Therefore, order n was set to two for all experiments.
If order
m > n were set, the model structure would imply dynamic properties of
the ,response which were not determined by the characteristic equation
f(t) =
V 1 f(t-1) + V 2 f (t-2) + ... + V n f(t-n)
of the system.
E-8
On the other hand, a major concern was that possible
influences due to MW not be missed.
Therefore order m=2 was also set.
A possible objection to estimating a dynamic model such as E~7 is
that the system dynamics cause lagged output variables f(t-1),...,f (t-n)
not to be truly independent of f(t) and of each other.
As is shown in
Johnston (198U), this situation causes a bias which is of minimal conse­
quence for relatively noisy data.
To test for MW effects, models E-6 and E-7 were tested for signifi­
cance.
It might be asked whether any of the Wj were significant; that
is, whether there was reason to reject the hypothesis that MW had no
effect.
The significance of an individual coefficient can be decided
using a t-test (estimated value/s.d.), but there is no appropriate way
to combine the tests into an overall judgment.
In addition, t-values
can be highly misleading, especially in time series regressions and oth­
ers where the regressors are partially correlated (Neter and Wasserman,
197*0 •
The significance of the W j as a group was decided using the analy­
sis of variance from each regression.
For static model E-6, an F-ratio
test was made on the overall significance of the model, since the only
regressor is Wo.
For dynamic model E~7, the test was done by comparing
226
mode) E-7, which can be referred to as a full model, with a model formed
from E-7, but in which none of the Wj appear (m=0), which is a reduced
model.
The influence of the Wj is significant if the full model
is sig­
nificantly better in the sense of having smaller residual errors than
the reduced model.
The following test statistic, which follows approxi­
mately an F distribution, was used (Neter and Wasserman, 197^+5 Ellis and
Duggleby, (1978):
F*
= _§§!J?L:J§L ( !L
df r - df f
/
_§§!i!L
df f
e-9
in which
SSE (R) is the sum of squared errors for the reduced model
lacking
Wj,
SSE (F) is the sum of squared errors for the full model, and
df r and dff are the respective degrees of freedom.
227
Appendix F
MICROWAVE DOSIMETRY
Microwave will irradiate the surface of a sample with a certain
intensity (flux density or power/area) but measuring this is insuffi­
cient for biological effects studies since absorption by the sample will
depend on its composition and geometry, as well as frequency.
To
describe tissue absorption, the specific absorption rate (SAR, power
absorbed per unit weight or volume) is used.
The SAR is related to
gross properties of tissues such as conductivity and attenuation factor
for the given frequency.
To the extent that the effect of energy
absorbed is thermal, SAR is quantitatively related to specific heat
capacity, temperature rise, and heat loss to the surroundings.
Background for the following material can be found in Paris and
Hurd (1969).
Referring to Figure 1, MW energy delivered into the waveguide is
propagated almost without loss to the interface between the dielectric
plate (matching device) and the water (z=0).
Reflective (reactive)
losses at the various interfaces are accounted for by taking as the net
power the difference (F-R) between forward and reflected powers as meas­
ured with a directional coupler.
The time-averaged power density is given by the complex Poynting
vector:
S - (1/2) E X H*
228
Owing to the dimensions of the waveguide and the frequency, the electric
(E) and magnetic (H) field components in the waveguide are strictly
those of propagation mode TE10.
For these components S in the.positive
z direction is:
2
(Sz) = (1/2) K] sin (rrx/a) u2
while S in the positive x direction is:
(Sx)= (1/2) j l<2 sin(7rx/a) cos (irx/a) ux
and S=0 in the y direction, where:
Ki and Kj subsume factors dependent on power, frequency, the geom­
etry, and the medium,
a is the x dimension of the waveguide, (0 <= x <= a).
Within the area of the x-y plane occupied by the brain (centered at
x=a/2, y=b/2), the x component of the power density practically vanish­
es.
Along the z direction within this area up to the dielectric plate/
water interface (z=0),
PD (z=0) • bSbx=a/2 = K-j / 2
E.l
The average power density in the z direction over the entire x-y
cross sectional area of the waveguide is:
p avg
=
a
/Q
E'2
bS z b dx
" K] / 4 •
Comparing equations E-l and E-2 it is seen that PD (z=0) is just twice
the average power density.
The average power density can be measured as
(F-R)/A, in which A is the area of the cross section.
Therefore
PD (2=0)-2(F-R)/A.
Beyond the dielectric plate (z>0), the water along with the brain
tissue, Ringer solution, and electrodes, will be considered to be homo­
geneously lossy.
The same power relations apply except that the media
absorb power at a constant rate per unit length.
To describe this, let
-2az
PD (z>0) = PD (z=0) e
The rate of absorption is just the partial derivative of this with
respect to z ,
-2az
SAR = ( 1 / p )
[2 (F-R)/A]
(-2a) e
Taking z=1.0cm, a=0.62, and p=l.Og/cm3 (the values for water) the SAR of
12.5mW/gram is associated with (F-R) =i*30mW.
density is 10mW/cm2.
set lOdB higher,
The corresponding power
In the 125mW/gram experiments these figures are
and 100mW/cmJ, respectively.
Little or no error is introduced by possible reflections at the
second water-air interface at the uppermost end of the waveguide.
As
the depth of water in the waveguide is 5 cm, only 0.002 of the power
incident at the matching plate reaches the second interface.
230
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VITA
Kenneth Stacey Ginsburg
Born 5/15A9» Cleveland, OH
Education:
BA, Biological Sciences, University of Chicago, Chicago,
IL, 1975
MS, Bioengineering, University of Illinois at Chicago,
Chicago, IL, 1983
PhD, Bioengineering, University of Illinois at Chicago,
Chicago, IL, 1987
Honors:
University of Chicago scholarships, 1967"1971
NSF Graduate Fellowships: honorable mention, 1976
University of Illinois tuition waivers, 197&~1980
Research
support:
Research Assistant (Dept. of Psychology, University of
Illinois at Chicago): "Rod and Cone Systems: Properties
and Interactions." MW Levine, JM Shefner, principal
i nvestigators.
Research Assistant (Dept. of Bioengineering, University
of Illinois at Chicago): "Microwave Interactions with
the Central Nervous System." JC Lin, WD O'Neill, princi­
pal investigators.
Abstracts:
Ginsburg, K. S., Levine, M. W., and Shefner, J. M.
(1978)» "Neighboring Ganglion Cells Share Components of
Long-Term Variability." ARVO Spring Meeting, Sarasota,
FL. Invest. Ophthal.. 17(supp): 128.
Ginsburg, K. S. (1983)* "Goldfish Retina: Dynamic Mod­
eling Using Time Series Methods." ARVO Spring Meeting,
Sarasota, FL. Invest. Ophthal.. 2k (supp): 218.
Ginsburg, K. S., Lin, J. C., and O'Neill, W. D. (1986).
"Snail Neuron Activity Under Varying Recording Condi­
tions." Bioelectromagnetics Society Meeting, Madison,
Wl.
238
Ginsburg, K . S., Lin, J . C . , and O'Neill, W. D . ( 1 9 8 7 ) •
"Microwave Effects on Snail Neurons: Statistical
Analysis." Bioelectromagnetics Society Meetihg, Portland
OR.
Article:
Ginsburg, K. S., Levine, M. W., and Johnsen, J. A. (1984)
"Common Noise in the Firing of Neighboring Ganglion Cells
in Goldfish Retina." J. Physiol. (London), 351s
433-450.
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