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Investigation of beam property correlation in a mixed field beam using collimators of different compositions

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ABSTRACT
INVESTIGATION OF BEAM PROPERTY CORRELATION IN
A MIXED FIELD BEAM USING COLLIMATORS OF
DIFFERENT COMPOSITIONS
Joshua Michael Ernst, M.S.
Department of Physics
Northern Illinois University, 2010
Thomas Kroc, Director
Concrete-polyethylene interchangeable collimators are used to
determine the field size and allow for flexibility in treatment planning at the
Northern Illinois University Institute for Neutron Therapy at Fermilab. New
collimator material is being evaluated to improve durability and safety during
use. To this end, an effort has been undertaken to design epoxy-based versions
that could effectively replace the current models. The leading candidate of the
epoxy-based collimators was chosen to undergo beam property investigations
and comparisons between the two collimator models were made. Dose buildup measurements were taken and dose components of the mixed field were
calculated using the epoxy and concrete-polyethylene collimators. Beam
properties tested were found to deviate by less than 3% between the different
collimators in both areas of this investigation.
NORTHERN ILLINOIS UNIVERSITY
DEKALB, IL
MAY, 2010
INVESTIGATION OF BEAM PROPERTY CORRELATION IN
A MIXED FIELD BEAM USING COLLIMATORS OF
DIFFERENT COMPOSITIONS
BY
JOSHUA MICHAEL ERNST
A THESIS SUBMITTED TO THE GRADUATE SCHOOL
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE
MASTER OF SCIENCE
DEPARTMENT OF PHYSICS
Thesis Director:
Thomas Kroc
UMI Number: 1477025
All rights reserved
INFORMATION TO ALL USERS
The quality of this reproduction is dependent upon the quality of the copy submitted.
In the unlikely event that the author did not send a complete manuscript
and there are missing pages, these will be noted. Also, if material had to be removed,
a note will indicate the deletion.
UMI 1477025
Copyright 2010 by ProQuest LLC.
All rights reserved. This edition of the work is protected against
unauthorized copying under Title 17, United States Code.
ProQuest LLC
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P.O. Box 1346
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ACKNOWLEDGEMENTS
Several members of the NIU Physics Department Faculty and the NIU
INT staff were instrumental to the fulfillment of this report, and to all of them I
am sincerely thankful. Dr. Thomas Kroc, my thesis advisor, was instrumental
in building any knowledge I may have acquired in the area of medical physics
from the ground up over the past two years and also in directing me in every
aspect of this investigation, and to him I am sincerely thankful and
appreciative. I would also like to thank Mark Austin and Linda Schneider,
who were both always willing to help with the set-up of equipment or the
answering of questions during my time at NIU INT, along with the rest of the
staff who I learned so much from through osmosis over the course of this
investigation. Dr. Dave Hedin, who helped facilitate my relationship with NIU
INT and Dr. Suzanne Willis, for her academic advisement, also have my
gratitude for their help over the past two years.
TABLE OF CONTENTS
Page
LIST OF TABLES ............................................................................................. v
LIST OF FIGURES ........................................................................................... vi
LIST OF APPENDICES ................................................................................. viii
Chapter
1.
INTRODUCTION ...................................................................... 1
2.
Northern Illinois University Institute for
For Neutron Therapy .................................................................. 4
NIU INT Treatment Set-Up.................................................. 4
Neutron Production,Collimation,
Treament Room .............................................................. 4
Neturon Beam Controls
And Monitoring System ................................................. 8
3.
METHODS AND MATERIALS ............................................... 9
Dose Build-Up Investigation ................................................ 9
Equipment Used in Experiment.................................... 10
Experimental Method ................................................... 15
Mixed Beam Investigation ............................................................................... 15
Equipment Used in Experiment.................................... 18
Experimental Method ................................................... 23
Chapter
4.
iv
................................................................................... Page
RESULTS ................................................................................. 26
Dose Build-Up Investigation
Measurements ..................................................................... 26
Mixed Beam Investigation
Measurements and Calculations ......................................... 28
Measured Values .......................................................... 28
Dn and Dg Calculation .................................................. 30
5.
DISCUSSION AND CONCLUSIONS .................................... 35
BIBLIOGRAPHY ................................................................................ 38
APPENDICES ...................................................................................... 40
LIST OF TABLES
Table .............................................................................................................. Page
1.
Build-up measurements for
concrete-polyethylene collimator ............................................. 27
2.
Build-up measurements for epoxy collimator .......................... 27
3.
G-gamma values from Cesium 137
exposure measurements using ion chambers
127 and 462 with 5 mm build up caps and a
constant gas flow rate of 0.3 cm3/min of pure
Argon and TE gas respectively................................................. 29
4.
Corrected open air response rates in ion chambers
127 and 462 placed at 190 SAD in a
10 x 10 cm2 field....................................................................... 30
5.
Dose component calculations as computed
using the paired-chamber method at NIU INT ......................... 33
Dose calculation table for given number of
beam pulses. Can be manipulated to calculate
different dose related quantities using scroll bars. ................... 43
7.
Mixed Beam investigation data table ....................................... 51
8.
Dose component calculation spreadsheet ................................. 53
9.
Portion of spreadsheet used to identify range of values for ku.
Dg was divided by Dn and the resulting equation was rearranged
to solve for Ru... ........................................................................ 55
LIST OF FIGURES
Figure ............................................................................................................. Page
1.
Damaged concrete-polyethylene collimators
that can no longer be used in treatment ...................................... 3
2.
Epoxy collimator (right) in comparison to concretepolyethylene (left) ...................................................................... 3
3.
NIU INT beam line and treatment setup adapted from [3] ........ 5
4.
NIU INT Collimation System [5] ............................................... 7
5.
Absorbed dose (D) compared to kerma (K) as a function of
depth in a medium, taken from [8].]. ........................................ 11
6.
EG&G 114TG Parallel Plate Ion Extrapolation Chamber,
adapted from [11] ..................................................................... 12
7.
Tissue equivalent phantom and experimental set-up for dose
build-up investigation ............................................................... 14
8.
0.5 cm3 Exraden ionization chamber with build-up cap, redrawn
from [17] ................................................................................... 19
9.
Gas regulation cart used for gas filled chamber dosimetry at
NIU INT ................................................................................... 21
10.
Close-up of image of gas flow instrument panel ...................... 21
11.
Mixed beam experimental set-up schematic ............................ 22
12.
Actual mixed beam experimental set-up .................................. 23
13.
Dose build-up curves for concrete-polyethylene and epoxy
collimators in TE phantom at 180 cm SSD in a 10 x 10 cm2
field ........................................................................................... 28
vii
............................................................................................... Page
Figure
14.
Component dose measured as a function of collimator and MU
given as calculated using the paired-chamber method ............. 34
15.
Collimator Schematics.............................................................. 41
16.
G-gamma exposure factor measurement set-up ....................... 48
17
Surface plot representation of ku
determination spreadsheet. ....................................................... 56
LIST OF APPENDICES
Appendix
............................................................................................... Page
A.
COLLIMATOR SCHEMATICS.............................................. 40
B.
NEUTRON BEAM DOSE AND PULSE
MANIPULABLE SPREADSHEET ......................................... 42
C.
A-150 TISSUE EQUIVALENT PLASTIC AND GAS ........... 44
D.
CESIUM 137 RADIATION SOURCE EXPOSURE FACTOR
CALCULATION AND INFORMATION ............................... 46
E.
MIXED BEAM INVESTIGATION DATA TABLE............... 50
F.
DN AND DG CALCULATION SPREADSHEET.................... 52
G.
KU SURFACE PLOT AND DATA TABLE ............................ 54
CHAPTER 1
INTRODUCTION
Collimation is used in radiation therapy to adjust beam size and allow
for variation and optimization in treatment planning. Collimation systems at
most modern treatment facilities consist of steel plates contained within a
gantry that can be adjusted to allow for the spreading or narrowing of the beam
to accommodate the treatment plan, called multi-leaf collimators or MLC.
Unlike other facilities, the Northern Illinois University Institute for Neutron
Therapy (NIU INT) at Fermilab does not use an enclosed gantry system but
instead utilizes a rotating patient platform and a three-stage collimation system
that includes interchangeable concrete and polyethylene collimators that are
placed in the beam opening to adjust beam height and width. This treatment
setup leads to everyday wear and tear on the removable collimators and thus
possible safety concerns due to irradiated dust and debris for the radiation
therapy staff that physically exchange the collimators as dictated by the
treatment plan. Because of this, an investigation into replacing the concrete
2
and polyethylene collimators with an epoxy version that would be both more
durable and alleviate safety concerns has been undertaken.
This report investigates the beam properties of the leading candidate of
the epoxy collimators as compared to those of the existing concrete and
polyethylene. The epoxy collimator that was used in this investigation was
chosen based on the correlation seen in response rate during daily beam
calibration procedures as compared to the concrete-polyethylene collimator.
The epoxy versions solve existing problems as they are more durable,
eliminate dust and debris, and decay much faster from the neutron activation
that occurs during irradiation in the neutron beam. However, further analysis
must be completed to ensure that known beam properties remain unchanged
when treatment is conducted with the epoxy collimators. Tests were
conducted and data collected of the dose build-up and mixed beam components
using both collimators and the results are presented in this report. High
correlation between the beam properties must be seen in order for the epoxy
collimators to be used in future treatment. See Appendix A for collimator
schematic.
Figure 1 and Figure 2 show examples of the concrete-polyethylene and
epoxy collimators.
3
Figure 1. Damaged concrete-polyethylene collimators that can no longer be
used in treatment.
Figure 2. Epoxy collimator (right) in comparison to concrete-polyethylene
(left).
4
CHAPTER 2
NORTHERN ILLINOIS UNIVERSTY INSTITUTE
FOR NEUTRON THERAPY
NIU INT Treatment Set-Up
The Northern Illinois University Institute for Neutron Therapy at
Fermilab is one of only a handful of facilities in the world that uses neutron
radiation to treat cancer patients. Neutron therapy is most effective in treating
inoperable, radioresistant tumors and the facility has treated over 3,000
patients since opening its doors three decades ago [1]. NIU INT is part of the
Fermi National Accelerator Laboratory, located in Batavia, Illinois and was
designed to operate off the extra beam that is created by the Linear Accelerator
that is not used for the high energy experiments that take place at FNAL. The
creation of neutrons using the Linac beam in series with a three-tier
collimation system and a two-level treatment room combine to form the
treatment facility.
Neutron Production, Collimation, Treatment Room
The neutron beam used at NIU INT is created as 66 MeV protons are
bent from the Linac with dipole magnets and further steered by quadrupole
magnets into a gold backed beryllium target [2], as seen in Figure 3.
5
66 MeV Proton Beam
Tank 5
Bending
Magnets
Tank 4
Quadrupole Magnets
Collimation
System
Gray Areas are
heavy concrete
shielding walls.
Gold Backed
Beryllium Target
Neutron
Beam
Treatment
Room
Figure 3. NIU INT beam line and treatment setup adapted from [3].
6
The emerging neutrons enter the collimation system that is composed
of three parts that effectively funnel the beam and shape it to the needs of the
treatment plan. First a fixed steel collimator directs the neutron beam and
funnels it into a second collimator that is made of steel and Benelex [4]. This
secondary collimator was designed to hold the interchangeable concrete and
polyethylene collimators that ultimately shape the beam to provide the desired
field height and width size at the isocenter, located 190 cm downstream from
the neutron target.
The treatment room consists of a patient platform that can be rotated
and translated to allow for isocentric treatment from different angles. This
platform sits on an elevator that is used to lower the patient down to the level
of the beam, four feet below floor level. Using the platform, the treatment area
in the patient is placed at the isocenter of the beam and, depending on the
treatment plan, the patient can be rotated so that the target area remains at the
isocenter while the beam enters from different directions. This process allows
for the same multi-beam treatment method that a gantry provides. Figure 4
shows the comparisons that can be made between these two setups.
7
Figure 4. NIU INT Collimation System as compared to conventional setup [5].
8
Neutron Beam Controls and Monitoring System
NIU INT is supplied with protons from the Linac at a pulse rate of 15
Hz [6]. The pulse length can be adjusted depending on the needed dose rate
and consists of micro pulses that send a beam every 66 milliseconds. Each
micro pulse delivers 1x109 protons and combines in 57 microsecond macro
pulses that deliver .039 cGy of Dose, see Appendix B. This dose is measured
by a transmission chamber that is located directly downstream from the source,
Figure 4, and is adjusted for temperature and pressure corrections. A treatment
computer receives the output from the chamber in monitor units – where 1 MU
= 1 Gy of dose, 10 cm deep in a tissue equivalent liquid for a 10x10 cm2 field
at the isocenter.
CHAPTER 3
METHODS AND MATERIALS
The dose build-up region in a material due to irradiation and the
gamma component of the treatment beam are two properties that can be
affected by the collimation material. Investigations looking into these
properties as compared between the two collimator types were completed and
are detailed below.
Dose Build-up Investigation
Dose build-up refers to the phenomenon that leads to the skin-sparing
effect that is seen in radiation therapy. This phenomenon is explained by the
differences that exist between the quantity kerma (K) and the absorbed dose
(D) in the same medium. Both (K) and (D) have units of Gray or Joules/kg
and are defined in the following way:
K=
dE tr
dm
3.1.1
D=
dE
dm
3.1.2
10
When beam is incident on a slab of material, the energy transferred to
the medium, kerma, does not necessarily stay in that region due to the range of
the secondary energized particles that are released [7]. However, at some
point, the number of charged particles entering a region will equal those
exiting, and charged particle equilibrium will be reached. Because of this,
while kerma is at a maximum at the surface and linearly decreases with depth,
the absorbed dose builds up to a maximum inside the medium at some depth
dmax, occurring in an area of CPE, before decreasing at the same rate as kerma,
shown in Figure 5. This build-up region allows for the maximum dose to
occur at a depth below the surface, thus sparing the skin.
Due to the importance of this relationship, verification of the matching
of the absorbed dose curves between the concrete-polyethylene and epoxy
collimators was necessary. Differences in leakage or dose due to scatter within
the collimators could be exposed in a dose build-up investigation.
Equipment Used in Experiment
An effective and accepted way to measure build-up is by using an
extrapolation chamber inside a tissue-equivalent phantom that allows for the
chamber to be positioned with its face on the beam-facing surface of the
phantom and also for layers of phantom material to be added to the window,
simulating depth in the human body [10]. See Appendix C for more
information on tissue-equivalent plastic.
11
Kerma
Dose
Build-Up
Region
Dose or Kerma
dmax
Depth in Medium
Figure 5. Absorbed dose (D) compared to kerma (K) as a function of depth in
a medium, redrawn from [8]. At the surface kerma is larger due to the
depositing of energy deeper in the medium by the released excited particles.
After dmax, this deposited energy boosts the absorbed dose to a level slightly
higher than kerma. Kerma decreases as depth increases due to the energy lost
to scatter and absorption. Absorbed dose decreases after dmax as the beam
creates less secondary particles [9].
The extrapolation chamber used in this experiment was an
EG&G Model 114TG parallel plate ion extrapolation chamber with an
electrode spacing of 2.3 mm. Ion chambers are a type of dosimeter and are
used to measure the energy due to ionizing radiation at the point in air or
medium in which they are placed. Extrapolation chambers are designed
specifically for measuring surface dose as their cavities are of cylindrical shape
with a thin tissue-equivalent wall on its face, Figure 6.
12
Thin TE Foil
Wall
Electrode
Gas/Ionization Cavity
Conducting Wall
Lucite Cup
High Voltage
Cable
Signal Cable to
Electrometer
Figure 6. EG&G 114TG Parallel Plate Ion Extrapolation Chamber, adapted
from [11].
Voltage can be applied to the chamber, an electrode measures the ionization
inside the volume of the gas-filled chamber and a signal line sends this
information to an electrometer. In this investigation, the chamber was filled
with air and a high voltage of 400 volts was applied across the cavity. A series
of tissue-equivalent disks with varying thicknesses were included with this
chamber and were used as the phantom material that simulated build-up
material.
The tissue-equivalent phantom used in this experiment was
parallelepiped with dimensions of 23.3 cm high x 27.4 cm wide x 16 cm deep,
13
with a cylindrical hole drilled through it from face to back, to accommodate
the extrapolation chamber and 4 cm diameter tissue-equivalent disks. Also, a
slab of aluminum extended from the back of the phantom and served as a
support for the chamber. Figure 7 shows the experimental setup.
The signal cable of the extrapolation chamber was connected to a Keithley
6514 electrometer, serial number 0768667.
14
54.5 cm
Isocenter: SAD = 190 cm
TE 4 cm Diameter
Disks
BEAM
Extrapolation
Chamber
HV and Source
Outputs
23.3 cm
Support Base
16 cm
25.9 cm
180 cm SSD
Elevation View
27.4 cm
Front View
Figure 7. Tissue equivalent phantom and experimental set-up for dose buildup investigation.
15
Experimental Method
Dose build-up measurements were taken with the parallel plate ion
extrapolation chamber inserted into the tissue-equivalent phantom with
different depths of build-up material. The phantom was placed at 180 cm SSD
(source to surface distance) and the TE disks were used in series creating
depths from .037 cm to 9.277 cm. The high voltage source was set to +400
volts. The field size chosen was 10 x 10 cm2 and the chamber response as a
function of depth was recorded in nC from the Keithley Electrometer using
both the epoxy and concrete-polyethylene collimators. Measurements were
repeated until a method was found in which measurements could be
reproduced within +/- 1%. At this point, a full set of response vs. depth
measurements were taken using both collimators. The charge measured per
monitor unit given was normalized to the maximum values and were plotted
against depth in the phantom.
Mixed Beam Investigation
According to AAPM Report No. 7 (1980):
Neutron fields are always accompanied by gamma rays originating
from the neutron-producing target, the primary shielding, the fieldlimiting or collimating system, the biological object or phantom being
irradiated, and from the surroundings. (p. 4).
When everyday dosimetry is done in a mixed beam field, the dosimeter
measures the total ionization due to both the neutron and gamma ray
16
component of the beam. While this is useful in everyday calibrations, it does
not take into consideration the differences in biological effectiveness of the
two components of radiation [12], and although the original treatment design is
always developed to minimize the dose due to gammas, the perfect neutron
beam does not exist. Because of this, it is necessary to determine the dose due
to each component of the field separately to understand the radiation treatment
that is actually being given.
Several methods to determine the dose due to neutrons (Dn) and the
dose due to gamma rays (Dg) have been developed through the years, but the
most commonly used method is referred to as the paired-chamber technique
[13]. In the paired-chamber technique, two ion chambers of different
composition are chosen to be irradiated by the mixed beam. One chamber
should be made of a tissue-equivalent material and filled with a tissueequivalent gas. This chamber is chosen because it is known to have a
relatively equivalent response rate to both the neutron and gamma ray
component of the beam. The other chamber is chosen to have a reduced
sensitivity to the neutron component of the beam as compared to the gamma
component and is filled with an appropriate gas. If the sensitivities to the
neutrons and gamma rays for both chambers are known, Dn and Dg can be
calculated using the following equations [14]:
17
Dn =
hU RT − hT RU
hU kT − hT kU
2.2.1
Dg =
k T RU − kU RT
hU k T − hT kU
2.2.2
where hU and hT are the ratios of the sensitivities of each ion chamber to the
photon component of the beam and the gamma rays used for calibration, kU
and kT are the ratios of the sensitivities of the two chambers to the neutron
component of the mixed field and the gamma rays used for calibration, and RU
and RT refer to the response rate of the two chambers divided by their
sensitivities to the gamma rays used for calibration [15]. For example:
kU =
Sensitivity of mg chamber to neutrons in beam
S (mg , n)
=
S (mg , calγ ) Sensitivity of mg chamber to calibration gammas
2.2.3
The subscript T is used to identify the TE ion chamber and the subscript U is
used to identify the Magnesium chamber.
Because the gamma rays discussed above originate as nuclear collisions
occur between the incident neutrons and the atoms of the material they are
passing through, one of the major contributing factors to the dose due to the
photon component of the beam originates from the collimation material; the
calculation of Dn and Dg using both collimators must be conducted to confirm
the plausibility of completing the replacement process.
18
Equipment Used in Experiment
To complete the paired-chamber technique of calculating the
component doses in the mixed beam at NIU INT, a pair of thimble ion
chambers, that meet the aforementioned criteria along with a gas regulation
system that can be used to fill the chambers at a constant flow rate with the
appropriate gas, were needed. Also, a method for measuring each chambers’,
sensitivity to gamma rays used for calibration, and an experimental set-up to
measure the response rate in each chamber in open air at the isocenter was
developed.
The two thimble ion chambers used in this investigation were chosen to
have a cavity volume of 0.50 cm3 and were manufactured by Exradin, now
called Standard Imaging, Inc. [16]. The TE ion chamber, serial number 462,
and the Mg ion chamber, serial number 127, were both used in conjunction
with 5 mm thick caps that were made of the same material as their outer walls.
Both chambers were also equipped with input and output gas lines that allowed
their chambers to be filled with gas as needed for the experiment. See Figure
8.
NIU INT has a gas regulation system that is mounted to a portable cart
that is used for gas-filled-chamber dosimetry at the facility. For this
experiment, the cart was fitted with a TE gas tank and an Argon gas tank that
each had their own regulation valves and could be hooked up to the regulation
system; see Appendix C for composition of TE gas. The cart also came
19
Insulator
Collector
Triax Cable
Outer Shell
6.1 mm
Input/Output
Gas Lines
Guard Ring
Build-Up Cap
5.0 mm
Figure 8. 0.5 cm3 Exraden ionization chamber with build-up cap, redrawn
from [17].
equipped with input and output gas lines enclosed in rubber tubing that were
long enough to reach from outside the treatment room, where the cart was
located, to the experimental set-up, located four feet below floor level at the
isocenter of the beam, Figure 9 and Figure 10.
The Cesium 137 radiation source that is used to measure the exposure
factor (Dose/charge) of chambers in daily calibration was used in this
20
experiment to calculate the chamber sensitivities’ (charge/Dose) to gamma
rays, as sensitivity is the inverse of exposure. See Appendix D for more
information on the Cesium 137 radiation source and the exposure factor
calculation at NIU INT.
A system of rods and clamps were used to position the chambers at the
isocenter of the beam at 190 SAD and the same Keithley Electrometer as
described earlier was used in the measuring of ionization within the chambers
during the open air beam tests; see Figure 11 and Figure 12.
21
Figure 9. Gas regulation cart used for gas filled chamber dosimetry at NIU
INT.
Figure 10. Close up of image of gas flow instrument panel.
22
4-Way Connector
Temperature
Gauge
Input/Output
Gas Lines
Triax Cable
Beam Field
Thimble
Ionization
Chamber
Treatment Chair
Signal Line
Triax Splitter
High Voltage
Figure 11. Mixed beam experimental set-up schematic.
23
Figure 12. Actual mixed beam experimental set-up.
Experimental Method
Exposure chamber calibration factor measurements were made using
the TE thimble ionization chamber: model number T2, in the Cesium 137
radiation source. A 5 mm thick TE build-up cap was used on the chamber as
appropriate for the energy range, and the chamber was filled with TE gas at a
constant flow rate, 0.3 cm3/min. Before the measurements were made, gas
lines were connected and the lines and chamber were purged to ensure that
24
only TE gas was present within the chamber. The chamber was held at +400
volts, and the exposure was integrated and corrected for temperature and
pressure by the facility’s treatment computer. Multiple measurements were
made on several different days over a period of two weeks until a method was
established and results were repeatable. The process was repeated with the Mg
thimble ion chamber using pure Argon gas and a 5 mm thick magnesium buildup cap. From these measurements, the sensitivities to the gamma rays during
calibration could be extrapolated from the measured exposure. Values were
reproduced within +/- 1.2% from the average.
The open air beam test set-up was then constructed and the chambers
were each in turn positioned so that the center of chamber curvature was
located at the isocenter, 190 cm SAD. The voltage setting at which the
chambers were held was alternated between +400 V and -400 V so that
corrections could be made due to polarity, and the chambers were irradiated
with doses of 0.5 and 1.0 monitor units (MU). This process was done using
both the epoxy and concrete-polyethylene collimators that correspond to 10 x
10 cm2 field size at the isocenter. The signal line fed into the previously
described Keithley Electrometer that was switched to the charge setting and
displayed the ionization in nC. A total of eight measurements were made for
each chamber and their responses were corrected for temperature and pressure,
and for the actual MU given. The equivalent absolute values corresponding to
positive and negative voltages were then averaged to account for any
25
electromagnetic noise or leakage that occurred from either polarity setting.
Measurements were made on multiple days and values were reproduced to
within +/- 4.2% from the average.
CHAPTER 4
Results
Dose Build-Up Investigation Measurements
Table 1 shows the data gathered during the build-up investigation using
the concrete-polyethylene collimator. The Q/MU was normalized to the
average of the three peak values so that when plotted, the peak would be
located near 100 percent of dose at dmax. Table 2 shows the measurements
collected for the epoxy collimator, normalized in the same manner.
Figure 13 shows the Q/MU per Depth build-up curves for both type
collimators. The initial normalized Q/MU values for both collimators were
found to agree to the fourth decimal place and both curves have the shape
expected from theory. Furthermore, dmax was found to be lie between 1.24 cm
and 1.34 cm for both collimators, which is in agreement with measurements
that have been made in the past at NIU INT [18]. The epoxy and concretepolyethylene curves show high correlation and data points at equal depths
differ less than 1%.
27
Table 1. Build-up measurements for concrete-polyethylene collimator.
Depth (cm)
Signal Voltage
Temp 5
Pressure
TPCOR
Corrected Q (nC)
MU Given
Q/MU
0.037
0.4932
20.15
996.15
1.011
0.4985
0.5000
0.9970
Normalized
0.5904
0.053
0.522
20.24
995.82
1.011
0.5280
0.5006
1.0547
0.6246
0.087
0.5722
20.19
995.8
1.011
0.5787
0.5001
1.1571
0.6852
0.104
0.5928
20.25
995.8
1.011
0.5996
0.4998
1.1997
0.7105
0.138
0.6242
20.38
995.8
1.012
0.6317
0.5006
1.2618
0.7472
0.154
0.6385
20.25
995.5
1.012
0.6460
0.5006
1.2905
0.7642
0.205
0.671
20.38
995.27
1.012
0.6794
0.5014
1.3550
0.8024
0.239
0.6906
20.22
994.61
1.013
0.6993
0.5014
1.3947
0.8259
0.356
0.7409
20.46
994.58
1.013
0.7509
0.5023
1.4949
0.8852
0.516
0.7822
20.38
994.58
1.013
0.7925
0.5020
1.5787
0.9349
0.823
0.8204
20.24
994.58
1.013
0.8308
0.5021
1.6547
0.9799
1.211
0.842
20.36
994.14
1.014
0.8534
0.5012
1.7027
1.0083
1.246
0.8431
20.24
993.99
1.013
0.8543
0.5009
1.7056
1.0100
1.347
0.8374
20.24
994.24
1.013
0.8483
0.4995
1.6983
1.0057
1.736
0.8403
20.22
994.58
1.013
0.8509
0.5000
1.7018
1.0078
2.094
0.8339
20.38
994.53
1.013
0.8449
0.4995
1.6916
1.0017
9.277
0.5825
20.37
994.46
1.013
0.5902
0.4996
1.1814
0.6996
Table 2. Build-up measurements for epoxy collimator.
Depth(cm)
Signal Voltage
Temp 5
Pressure
TPCOR
Corrected Q (nC)
MU Given
Q/MU
Normalized
0.037
0.493
20.21
994.18
1.013
0.4994
0.5006
0.9976
0.5908
0.087
0.5732
20.24
994.18
1.013
0.5807
0.5005
1.1603
0.6871
0.138
0.6229
20.35
994.53
1.013
0.6311
0.5005
1.2609
0.7467
0.205
0.6701
20.34
994.32
1.013
0.6790
0.5002
1.3575
0.8039
0.356
0.7334
20.39
994.02
1.014
0.7435
0.5002
1.4864
0.8802
0.516
0.776
20.25
993.97
1.013
0.7864
0.5000
1.5727
0.9313
0.823
0.816
20.38
993.97
1.014
0.8273
0.5001
1.6542
0.9796
1.211
0.8353
20.39
993.83
1.014
0.8470
0.5001
1.6936
1.0029
1.246
0.8325
20.37
993.54
1.014
0.8443
0.5000
1.6887
1.0000
1.347
0.8347
20.38
993.53
1.014
0.8466
0.5001
1.6929
1.0025
1.736
0.8358
20.36
993.38
1.014
0.8478
0.5002
1.6949
1.0037
2.094
0.8276
20.41
994.57
1.013
0.8386
0.4997
1.6782
0.9938
9.277
0.5769
20.5
994.58
1.014
0.5847
0.4997
1.1702
0.6930
28
1.2
1
Q /M U (n C /J ig G ra y )
0.8
ConcretePolyethylene
0.6
Epoxy
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
Depth in TE Phantom (cm)
Figure 13. Dose build-up curves for concrete-polyethylene and epoxy
collimators in TE phantom at 180 cm SSD in a 10 x 10 cm2 field.
Mixed Beam Investigation Measurements and Calculations
Measured Values
Table 3 shows the results of the Cesium 137 exposure measurements
for both the 127 Mg ion chamber and the 462 TE ion chamber. The percent
error column refers to the variation from the average for each G-gamma value
29
that was calculated. See Appendix D for information regarding the G-gamma
calibration procedure and calculation.
Table 3. G-gamma values from Cesium 137 exposure measurements using ion
chambers 127 and 462 with 5 mm build up caps and a constant gas flow rate of
0.3 cm3/min of pure Argonne and TE gas respectively.
Ch. ID
127
127
127
127
127
462
462
462
462
Gas
Arg
Arg
Arg
Arg
Arg
TE-Mix
TE-Mix
TE-Mix
TE-Mix
G-gamma
(R/C)
5.72E+09
5.74E+09
5.85E+09
5.77E+09
5.85E+09
7.26E+09
7.27E+09
7.20E+09
7.25E+09
Average G-gamma (R/C)
5.78E+09
7.25E+09
Percent
Error
-1.2%
-0.9%
1.1%
-0.3%
1.2%
0.2%
0.3%
-0.7%
0.1%
Table 4 shows the average measured response values for both ion
chambers in the open air mixed beam tests. The charge recorded has been
corrected for temperature and pressure and for the actual MU given during the
test. See Appendix E for complete data sheet.
30
Table 4. Corrected open air response rates in ion chambers 127 and 462 placed
at 190 SAD in a 10 x 10 cm2 field. Same color columns correspond to same
experimental settings between the concrete-polyethylene and epoxy
collimators.
Chamber Collimator HV (V) MU Req (MU) Mean MU Given (MU)
127
Epoxy
(+) 400
0.5
0.500
127
Epoxy
(-) 400
0.5
0.500
127
Epoxy
(+) 400
1.0
1.001
127
Epoxy
(-) 400
1.0
1.002
127
Concrete (+) 400
0.5
0.501
127
Concrete (-) 400
0.5
0.501
127
Concrete (+) 400
1.0
1.001
127
Concrete (-) 400
1.0
1.001
462
Epoxy
(+) 400
0.5
0.501
462
Epoxy
(-) 400
0.5
0.501
462
Epoxy
(+) 400
1.0
1.006
462
Epoxy
(-) 400
1.0
1.001
462
Concrete (+) 400
0.5
0.500
462
Concrete (-) 400
0.5
0.501
462
Concrete (+) 400
1.0
1.002
462
Concrete (-) 400
1.0
1.002
Mean Corrected
∆Q (nC/MU)
9.470
-9.309
9.591
-9.431
9.505
-9.312
9.505
-9.354
17.291
-17.199
17.262
-17.198
17.690
-17.750
18.130
-17.891
Dn and Dg Calculation
We saw earlier that the equations for calculating the dose components
in a mixed field are as follows:
Dn =
hU RT − hT RU
hU kT − hT kU
2.2.1
31
Dg =
k T RU − kU RT
hU k T − hT kU
2.2.2
Because hU and hT are ratios of sensitivities of each chamber to the gamma rays
in the mixed field to the gamma rays used in calibration, these values are very
close to unity and are assumed to equal 1 [19]. RT and RU refer to the response
rates of each chamber in the mixed field divided by their sensitivities to the
gamma rays used for calibration. The response rates are what were measured
by the open air investigation and the sensitivities of each chamber to the
gamma rays used for calibration are the inverse of the exposure factor that was
measured in the Cesium 137 radiation source. kT can be calculated using the
following equation [20]:
kT =
W C (S w, g )C K C
•
•
W N (S w, g )N K N
4.2.2
where the W factors are the average energy required to produce an ion pair in a
60
Co gamma ray beam and neutron beam respectively, the S factors refer to the
ionization chamber gas-to-wall conversion factors for dose measurement in the
respective beams, and the K values refer to the kerma factor ratios for both
beams. All values needed to calculate kT are known values at NIU INT. The
final quantity needed to complete the dose component calculation is the kU
value, or the ratio of the sensitivity of the neutron-insensitive ion chamber to
32
the neutron component of the mixed field to its sensitivity to the calibration
gamma rays. This value cannot reliably be calculated in the same manner as
kT due to fragmented data and most times must be measured. There are several
different methods for measuring this value, including the spectral difference
method and a lead filtration method [21]. However, because the concretepolyethylene collimators were designed to minimize the dose due to gamma
rays and that this percent has been measured multiple times and is known to lie
between 0 and 4%, a value for kU was calculated as follows.
By dividing equation 2.2.2 by equation 2.2.1 and rearranging to solve for RU:
 D g


 RT − kU RT 

D
n


RU = 


 Dg
k T − 
Dn 


4.2.1
Because the Dg/Dn value is well known for the concrete-polyethylene
collimators, kT is known, and the high certainty due to reproducibility of our
measured RU and RT values – a surface plot was constructed which calculated
RU by treating kT and RT as constants, for varying values of Dg/Dn and kU.
From this plot, it was found that in order for our value of RU to be measured in
a mixed beam that contained between 0 and 4% of gamma rays, kU must lie
between 0.38 and 0.41; see Appendix F for more information.
Table 5 shows the calculated average values for Dn and Dg for the four
different values of kU as the ration Dg/Dn. See Appendix E for complete
calculation.
33
Table 5. Dose component calculations as computed using the paired-chamber
method at NIU INT, discrepancy in %Difference due to rounding.
kU value
0.38
0.39
0.40
0.41
Collimator
Concrete
Epoxy
Concrete
Epoxy
Concrete
Epoxy
Concrete
Epoxy
Dg/Dn
5.26E-02
8.32E-02
3.53E-02
6.54E-02
1.80E-02
4.76E-02
7.71E-04
2.98E-02
%Dose from Gamma
4.99%
7.68%
3.41%
6.14%
1.77%
4.54%
0.07%
2.89%
%Difference
2.7%
2.7%
2.8%
2.8%
Figure 14 shows comparisons between the total dose, dose due to neutron
component, and dose due to gamma ray component for each experimental setup.
34
1.60E+02
1.40E+02
1.20E+02
D o s e /M U (R /J ig G y )
1.00E+02
Dose Due to Neutrons
8.00E+01
Dose Due to Gammas
Total Dose
6.00E+01
4.00E+01
2.00E+01
0.00E+00
1
2
3
4
Epoxy (.5 MU), Epoxy (1.0 MU), Concrete (0.5 MU), Concrete (1.0 MU)
Figure 14. Component dose measured as a function of collimator and MU
given as calculated using the paired-chamber method for a kU value of 0.40.
CHAPTER 5
DISCUSSIONS AND CONCLUSIONS
An effort to improve the interchangeable collimators that are currently
used at NIU INT led to an investigation into the possibility of replacing them
with epoxy-based versions. The epoxy-based version that showed the closest
correlation to the concrete-polyethylene collimators in beam calibration water
phantom tests, was chosen to undergo further investigation to ensure the
integrity of known beam properties while collimating the field with the epoxy
version.
A dose build-up investigation was conducted using both collimator
versions and the Q/MU vs. Depth curves that they produced were nearly
identical. Both collimators showed the same initial dose and peaked at the
same dmax depth in the material. From this investigation it is safe to assume
that no significant differences exist between the two material collimators in the
areas of leakage or collimator scatter and that the integrity of the known skinsparing information would be kept in the replacement of the concretepolyethylene collimators.
36
A beam composition investigation was also completed using the pairedchamber technique. The percent dose due to the gamma ray component of the
field was calculated and found to only deviate by a few percent from the
concrete-polyethylene collimators to the epoxy version. However, due to the
manner in which kU was calculated instead of being measured, there is concern
that the percent dose due to the gamma ray component of the field may vary
from what was calculated in this investigation. A calculation was also
attempted using a kU value from an investigation that took place 30 years ago
at Fermilab [22], but this was proven to be inaccurate due to the fact that the
same model Mg/Ar chambers can have vastly different kU values when
irradiated in the same beam conditions [23]. However, since we were mainly
concerned with the correlation between the values calculated between the two
collimator versions, only a relative value for kU was needed. By using the fact
that the Dg/Dn value has been calculated in the past using the concretepolyethylene collimators [24], we were able to calculate a range that the value
for kU must fall within, and no matter what value from this range is chosen, the
epoxy collimators have shown to vary from the concrete-polyethylene by less
than 3%.
Another concern in the mixed beam investigation comes from the
variation of values that were calculated initially for the exposure factor of the
chambers. However, these variations subsided as it was found that a flushing
time of around 40 minutes at a rate of 0.3 cm3/min was needed to ensure
37
electronic equilibrium was reached inside the chamber and all foreign gases
were removed. Using this method, values became highly reproducible for both
chambers, leading us to believe that the measured values were indeed valid for
the calculation.
The results from the mixed beam investigation suggest that there is a
high level of correlation between the dose components of the beam in each
version of the interchangeable collimators. A future study that re-examined
these calculations using a measured value for the sensitivity of the Mg/Ar
ionization chamber used in the paired-chamber technique or using a different
method such as the proportional counter method [25], would be useful in the
further verification that the percent dose from each component of the field was
consistent between the epoxy and concrete-polyethylene collimators.
However, we believe that enough evidence of correlation has been shown in
this report to support the replacement of the concrete-polyethylene
interchangeable collimators with the more durable and safer epoxy-based
collimators. A full set of the epoxy-based collimators matching the existing
range of concrete-polyethylene collimators have been put into production and
will be introduced into patient treatment at NIU INT.
BIBLIOGRAPHY
[1] L. Cohen, M. Awschalom., The Cancer Therapy Facility at the Fermi
National Accelerator Laboratory: A Preliminary Report., FN-291, 1976.
[2] M. Awschalom, I. Rosenberg., Fermilab Cancer Treatment Facility:
Neutron Beam Calibration and Treatment Planning., TM-834, 1978, p. 2-4.
[3] Ibid., p. 31.
[4] Benelex consists of 95 to 98% wood fiber, 0 to 3% polyethylene plastic,
and some unknown amount of phenolic resin. It also has a density of 1.2 to 1.4
g/cm3.
[5] Tom Kroc., NIU INT Neutron Production and Collimation Schematics.
NIU INT Internal Document., October, 2007.
[6] Phillip Prior., Investigation of Standard Approximations in Clinical
Treatment Planning Systems., Master’s Degree thesis, Northern Illinois
University, 2003.
[7] E.B. Podgorsak, Technical Ed., Radiation Oncology Physics: A Handbook
for teachers and Students., IAEA, 2005, p. 48-9.
Pub1196_web.pdf –
http://www-pub.iaea.org/MTCD/publications/PDF/pub/1196_web.pdf
[8] Ibid., p. 59.
[9] F. Kahn., The Physics of Radiation Therapy, 2nd Ed., Williams & Wilkins,
1994, p. 133-34.
[10] Ibid., p. 111.
[11] Ibid., p. 113.
[12] P. Wootton, et. al., AAPM Report No. 7., American Institute of Physics,
1980, p. 4.
39
[13] F. Kuchnir, M. Awschalom, L. Grumbowski, and M Sabau.,
Determination of the Sensitivity of a Mg-Ar Chamber to High Energy Neutrons
by use of two Independent Methods., Presented at the international workshop
on ion chambers for Neutron Dosimetry, September, 1979.
[14] F. Waterman, F. Kuchnir, et. al., Energy Dependence of the Neutron
Sensitivity of C-CO2, Mg-Ar and TE-TE Ionisation Chambers., Phys. Med.
Biol., 1979, Vol. 24, No. 4, p. 721-733.
[15] [12]., p. 4.
[16] Standard Imaging, Inc., 7601 Murphy Drive, Middleton, Wisconsin,
53562-2532., Phone: 608-831-0025, Internet: www.standardimaging.com
[17] [6]., p. 10.
[18] Gordon Holmblad, Tom Kroc., Dose Build-Up Measurements with Tissue
Equivalent Build-Up Apparatus and EG&G Model 114TG Parallel Plate Ion
Extrapolation Chamber., NIU INT Internal Document. December, 1997.
[19] [12]., p. 5.
[20] Ibid., p. 16.
[21] T. Stinchcomb, F. Kuchnir, and L. Skaggs., Comparison of the
Microdosimetric Eevent-Size Method and the Twin-Cchamber Method for
Separating Dose into Neutron and Gamma Components., Phys. Med. Biol.,
1980, Vol. 25, No. 1, p. 51-64.
[22] [13].
[23] J. Zoetelief, D. Schlegel-Bickmann, H Schraube, and G. Dietze.,
Characteristics of Mg/Ar Ionization Chambers used as Gamma-Ray
Dosimeters in Mixed Neutron-Photon Fields., Phys. Med. Biol., 1986, Vol. 31,
No. 12, p. 1339-135.
[24] [1]., p. 16.
[25] U. Schrewe, H. Brede, and G. Dietze., Dosimetry in Mixed NeutronPhoton Fields with Tissue-Equivalent Proportional Counters., Radiation
Protection Dosimetry., 1989, Vol. 29, No. 1/2, p. 41-45.
[26] M. Awschalom, R. Goodwin, et. al., High Precision in Dose Delivery:
Routine Use of a Microcomputer., FNAL Internal Document. November, 1982.
APPENDIX A
COLLIMATOR SCHEMATICS
41
Figure 15. Collimator schematic as drawn by Mark Austin, NIU INT
Engineer.
APPENDIX B
NEUTRON BEAM DOSE AND PULSE
MANIPULABLE SPREADSHEET
43
APPENDIX B
NEUTRON BEAM DOSE AND PULSE MANIPULABLE SPREADSHEET
Table 6. Dose calculation table for given number of beam pulses. Can be
manipulated to calculate different dose related quantities using scroll bars.
Dose Calculation for Given Number of Beam Pulses at NTF
Frequency (Hz)
Time of 1 Pulse
(s)
15
0.066666667
=1/A4
Minimum Pulse Time Elapsed (s)
10
9
8
7
6
5
4
3
2
1
0.667
0.600
0.533
0.467
0.400
0.333
0.267
0.200
0.133
0.067
=A7*B4
Number of
Pulses
x time of one
Pulse
Beam Time
per Pulse Current (A)
(s)
0.000062
0.035
Actual
Beam Time
0.00062
0.000558
0.000496
0.000434
0.000372
0.00031
0.000248
0.000186
0.000124
0.000062
Absorbed
Radiation
Dose/Time
0.35
Gy/s
0.005833
Dose Given (Gy)
=A7*D4
0.00389
0.00350
0.00311
0.00272
0.00233
0.00194
0.00156
0.00117
0.00078
0.00039
=G4*B4*A7
Explanation
Dose/second x
Beam Time of
Pulse x Number
of Pulses
Number of
Pulses
x Beam
Time/Pulse
Scroll Bar Calculations
# of Pulses
4500
900
Dose Given
1.75
3500
Actual
Beam Time
(seconds)
Time Elapsed
(seconds)
300
=A21*B4
=A21*D4
Actual
Beam Time
(seconds)
Time Elapsed
(seconds)
300
0.279
Dose Given (Gy)
=F25*B4
0.279
Time Elapsed
(minutes)
Actual
Beam Time
(minutes)
5
0.00465
1.75
=G4*B4*A21
# of Pulses
=F25*D4
4500
=(A25/(G4*D4)
APPENDIX C
A-150 TISSUE EQUIVALENT PLASTIC AND GAS
45
APPENDIX C
A-150 TISSUE EQUIVALENT PLASTIC AND GAS
As taken from AAPM Report No. 7, p. 10-11:
3.2.1 Tissue-equivalent plastic
A common electrically conductive plastic used in the
construction of TE ionization chambers has been a particular muscleequivalent formulation designated A-150. A-150 plastic can be
obtained as small chips or granules suitable for use in molding, or in
various sizes of stock and custom-molded shapes for direct use. It
consists of a homogeneous mixture of polyethylene, nylon (DuPont
Zytel 69), carbon, and calcium fluoride…The A-150 TE plastic is not
identical in elemental composition to ICRU muscle tissue because of
the large admixture of carbon in the plastic formulation…The density
of molded A-150 plastic is 1.127 +/- .005 g/cm3 …
3.2.2 Tissue-equivalent gas
Tissue-equivalent gas is recommended for use in homogeneous
TE ionization chambers for measuring the total absorbed dose. The
recommended formulation and composition of the TE gas is: 64.4
percent CH4, 32.4 percent CO2, and 3.2 percent N2.
APPENDIX D
CESIUM 137 RADIATION SOURCE EXPOSURE FACTOR
CALCULATION AND INFORMATION
47
APPENDIX D
Gγ Calculation from Cesium 137 Chamber Calibration Process at NTF
Introduction
The Cesium 137 calibration exposure factor is measured in daily
calibration to ensure that all dosimeters are working to their nominal values.
The Cesium 137 source was built to provide an extremely reproducible
constancy check for ion chambers [26]. NIU INT regularly sends a chamber to
an Accredited Dosimetry Calibration Laboratory (ACDL) for calibration and a
correlation of +/- .5% exists between the two methods. The following provides
information to the theory and procedure that govern the determination of the
exposure factor at NIU INT.
Theory
By irradiating an ionization chamber in a Cesium 137 radiation source
and measuring the charged accumulated over an elapsed time and correcting
for the pressure and temperature conditions on a particular day; the following
equation to calculate the chamber exposure factor (Gγ):
G factor • Fdecay
(D.1)
∆Q
TPCOR1 •
∆t
Where Gfactor and Fdecay are both constants specific to NTF and refer to
the strength of the source in R/s its decay over time respectively, ∆Q and ∆t
refer to the accumulated charge and elapsed time, and TPCOR1 is the
temperature/pressure correction given by the following equation:
Gγ =
TPCOR1 =
Temp + 273.15 1013.25
•
295.15
Pr essure
where temperature and pressure are measured in Celsius and millibars,
respectively.
Apparatus
•
•
•
Cesium 137 Radiation pig
TE Ionization Chamber (#120-TG)
Keithley 6514 Electrometer (#0768667) – normal
(D.2)
48
•
•
•
Keithley 6514 Electrometer (#1153180) – backup
TENNELEC TC563P Timer/Scaler (#23436)
NTF Control Software (R0712181011)
Source Line
High Voltage
Ionization
Chamber
Cesium 137 Pig
Figure 16. G-gamma exposure factor measurement set-up.
Procedure
The TE ionization chamber was placed in the Cesium 137 radiation
source Pig and the source and high voltage lines were connected to the
ionization chamber. The Keithly 6514 Electrometer was used in tandem with
the TENNELEC TC563P Timer/Scaler to measure the accumulated charge in
the chamber over approximately 120 second intervals. This measurement was
taken through eight runs at which point the system was switched to use the
backup up Keithly Electrometer. Eight more runs of approximately 120
seconds were completed using the backup electrometer. Upon completion, the
source line was switched over so that the measurements would be read by the
NIU INT treatment computer and the Gγ was computed by the computer
software over a series of nine runs. The two values of Gγ were compared to
check for consistency.
Results
After calculating the eight values of the chamber exposure factor (Gγ) using the
two different Keithley Electrometers, values of 3.66016E9 and 3.6561E9 were
found to be the averages. The NIU INT treatment computed value was
3.67E9, yielding correlations of 99.6% and 99.5% with those found using the
49
manual calculation method and the Keithley Electrometers. All three values
were well within the norm when compared to historical values from weekly
calibration.
APPENDIX E
MIXED BEAM INVESTIGATION DATA TABLE
51
APPENDIX E
Table 7. Mixed Beam investigation data table.
Collimator
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Epoxy
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Concrete
Chamber
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
127
462
462
462
462
462
462
462
462
462
462
462
462
462
462
462
462
Gas
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
ARG
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
TE-Mix
HV (V)
(+)400
(+)400
(+)400
(+)400
(+)400
(+)400
(-)400
(-)400
(-)400
(-)400
(-)400
(-)400
(+)400
(+)400
(+)400
(+)400
(+)400
(+)400
(-)400
(-)400
(-)400
(-)400
(-)400
(-)400
(+)400
(+)400
(+)400
(+)400
(-)400
(-)400
(-)400
(-)400
(+)400
(+)400
(+)400
(+)400
(-)400
(-)400
(-)400
(-)400
MUReq
0.5
0.5
0.5
1
1
1
0.5
0.5
0.5
1
1
1
0.5
0.5
0.5
1
1
1
0.5
0.5
0.5
1
1
1
0.5
0.5
1
1
0.5
0.5
1
1
0.5
0.5
1
1
0.5
0.5
1
1
MU Given
0.4998
0.5
0.4993
1.0012
1
1.0021
0.4999
0.5009
0.4993
1.0014
1.0012
1.002
0.4997
0.5027
0.5006
1.0001
1.0018
1.0002
0.5015
0.5027
0.5001
1.0005
1.0005
1.0012
0.5005
0.5012
1.0011
1.011
0.5
0.5024
1.0006
1.0007
0.5005
0.5002
1.0009
1.0026
0.501
0.5009
1.001
1.0024
∆Q (nC)
4.662
4.729
4.522
9.285
9.728
9.195
-4.565
-4.638
-4.482
-9.16
-9.55
-9.05
4.637
4.748
4.611
9.267
9.453
9.219
-4.561
-4.654
-4.504
-9.128
-9.296
-9.081
8.421
8.561
16.911
17.125
-8.37
-8.542
-16.751
-17.01
8.773
8.589
18.379
17.203
-8.889
-8.552
-18.012
-17.12
TPCOR1
1.022
1.026
1.013
1.022
1.027
1.014
1.022
1.026
1.013
1.022
1.027
1.013
1.023
1.025
1.014
1.023
1.026
1.015
1.023
1.026
1.014
1.023
1.026
1.014
1.028
1.012
1.028
1.013
1.027
1.012
1.027
1.012
1.028
1.011
1.029
1.012
1.028
1.011
1.029
1.011
APPENDIX F
DN AND DG CALCULATION SPREADSHEET
53
Appendix F
Table 8. Dose component calculation spreadsheet.
Set-up Variables
Rt
Abs. Rt
Ave. Rt
Ru
Abs. Ru
Ave. Ru
DN (R/MU)
DG (R/MU)
Total Dose (R)
DG/DN
5.48E+01
5.48E+01
5.43E+01
1.21E+02
7.22E+00
1.28E+02
5.98E-02
-5.38E+01
5.38E+01
Epoxy, 127, +400, 1
5.55E+01
5.55E+01
5.50E+01
1.19E+02
8.47E+00
1.28E+02
7.10E-02
Epoxy, 127, -400, 1
-5.46E+01
5.46E+01
5.44E+01
1.26E+02
5.11E+00
1.32E+02
4.04E-02
5.45E+01
1.30E+02
3.92E+00
1.34E+02
3.02E-02
Epoxy, 127, +400, .5
Epoxy, 127, -400, .5
Epoxy, 462, +400, .5
1.25E+02
1.25E+02
Epoxy, 462, -400, .5
-1.25E+02
1.25E+02
Epoxy, 462, +400, 1
1.25E+02
1.25E+02
Epoxy, 462, -400, 1
-1.25E+02
1.25E+02
1.25E+02
1.25E+02
Concrete, 127, +400, .5
5.50E+01
5.50E+01
Concrete, 127, -400, .5
-5.39E+01
5.39E+01
Concrete, 127, +400, 1
5.50E+01
5.50E+01
Concrete, 127, -400, 1
-5.41E+01
5.41E+01
Concrete, 462, +400, .5
1.28E+02
1.28E+02
Concrete, 462, -400, .5
-1.29E+02
1.29E+02
1.28E+02
Concrete, 462, +400, 1
1.31E+02
1.31E+02
1.31E+02
Concrete, 462, -400, 1
Wc
-1.30E+02
Wn
1.30E+02
(Sw,g)C
(Sw,g)N
KC
KN
kt
ht
hu
ku
3.37E+01
Values needed for Dose
Calculations
3.58E+01
1.14E+00
1.16E+00
1.05E+00
1.00E+00
9.76E-01
1.00E+00
1.00E+00
3.90E-01
APPENDIX G
KU SURFACE PLOT AND DATA TABLE
55
APPENDIX G
Table 8. Portion of spreadsheet used to identify range of values for ku. Dg was
divided by Dn and the resulting equation was rearranged to solve for Ru. Column A
was filled with possible values for ku ranging from 0.01 to 0.50 and Row 52 was
filled with possible values for Dg/Dn ranging from 0.0025 to 0.2000. Rt and kt were
inserted into the spreadsheet as constants and the inner cells were assigned the
equation to calculate Ru based on the Rt and kt constants, and corresponding column
and row values for ku and Dg/Dn, respectively. Calculated Ru values that matched
our measured values were highlighted and the range of ku was determined from the
Ru values that occurred for Dg/Dn values between 0 and 4%.
ku
0.5
4.53E
+01
4.67E
+01
4.80E
+01
4.93E
+01
5.06E
+01
5.19E
+01
5.33E
+01
5.46E
+01
5.59E
+01
5.72E
+01
5.86E
+01
5.99E
+01
6.12E
+01
6.25E
+01
6.39E
+01
6.52E
+01
6.65E
+01
4.55E
+01
4.69E
+01
4.82E
+01
4.95E
+01
5.08E
+01
5.21E
+01
5.35E
+01
5.48E
+01
5.61E
+01
5.74E
+01
5.87E
+01
6.01E
+01
6.14E
+01
6.27E
+01
6.40E
+01
6.53E
+01
6.67E
+01
4.58E
+01
4.71E
+01
4.84E
+01
4.97E
+01
5.10E
+01
5.23E
+01
5.37E
+01
5.50E
+01
5.63E
+01
5.76E
+01
5.89E
+01
6.02E
+01
6.16E
+01
6.29E
+01
6.42E
+01
6.55E
+01
6.68E
+01
4.60E
+01
4.73E
+01
4.86E
+01
4.99E
+01
5.12E
+01
5.25E
+01
5.38E
+01
5.52E
+01
5.65E
+01
5.78E
+01
5.91E
+01
6.04E
+01
6.17E
+01
6.30E
+01
6.44E
+01
6.57E
+01
6.70E
+01
4.62E
+01
4.75E
+01
4.88E
+01
5.01E
+01
5.14E
+01
5.27E
+01
5.40E
+01
5.54E
+01
5.67E
+01
5.80E
+01
5.93E
+01
6.06E
+01
6.19E
+01
6.32E
+01
6.45E
+01
6.58E
+01
6.71E
+01
4.64E
+01
4.77E
+01
4.90E
+01
5.03E
+01
5.16E
+01
5.29E
+01
5.42E
+01
5.55E
+01
5.68E
+01
5.82E
+01
5.95E
+01
6.08E
+01
6.21E
+01
6.34E
+01
6.47E
+01
6.60E
+01
6.73E
+01
4.66E
+01
4.79E
+01
4.92E
+01
5.05E
+01
5.18E
+01
5.31E
+01
5.44E
+01
5.57E
+01
5.70E
+01
5.83E
+01
5.96E
+01
6.09E
+01
6.22E
+01
6.35E
+01
6.48E
+01
6.62E
+01
6.75E
+01
4.68E
+01
4.81E
+01
4.94E
+01
5.07E
+01
5.20E
+01
5.33E
+01
5.46E
+01
5.59E
+01
5.72E
+01
5.85E
+01
5.98E
+01
6.11E
+01
6.24E
+01
6.37E
+01
6.50E
+01
6.63E
+01
6.76E
+01
4.70E
+01
4.83E
+01
4.96E
+01
5.09E
+01
5.22E
+01
5.35E
+01
5.48E
+01
5.61E
+01
5.74E
+01
5.87E
+01
6.00E
+01
6.13E
+01
6.26E
+01
6.39E
+01
6.52E
+01
6.65E
+01
6.78E
+01
4.72E
+01
4.85E
+01
4.98E
+01
5.11E
+01
5.24E
+01
5.37E
+01
5.50E
+01
5.63E
+01
5.76E
+01
5.89E
+01
6.02E
+01
6.15E
+01
6.27E
+01
6.40E
+01
6.53E
+01
6.66E
+01
6.79E
+01
4.74E
+01
4.87E
+01
5.00E
+01
5.13E
+01
5.26E
+01
5.39E
+01
5.52E
+01
5.65E
+01
5.77E
+01
5.90E
+01
6.03E
+01
6.16E
+01
6.29E
+01
6.42E
+01
6.55E
+01
6.68E
+01
6.81E
+01
n
0.002
5
0.005
0.007
5
0.01
0.012
5
0.015
0.017
5
0.02
0.022
5
0.025
0.027
5
0.34
0.35
0.36
0.37
0.38
0.39
0.4
0.41
0.42
0.43
0.44
0.45
0.46
0.47
0.48
0.49
Dg/D
kt
9.76E
-01
Rt
1.30E
+02
56
7.60E+01-7.80E+01
7.40E+01-7.60E+01
7.20E+01-7.40E+01
7.80E+01
7.60E+01
7.40E+01
7.20E+01
7.00E+01
6.80E+01
6.60E+01
6.40E+01
6.20E+01
6.00E+01
5.80E+01
5.60E+01
5.40E+01
5.20E+01
5.00E+01
4.80E+01
4.60E+01
4.40E+01
4.20E+01
4.00E+01
3.80E+01
3.60E+01
3.40E+01
3.20E+01
3.00E+01
2.80E+01
2.60E+01
2.40E+01
2.20E+01
2.00E+01
1.80E+01
1.60E+01
1.40E+01
1.20E+01
1.00E+01
8.00E+00
6.00E+00
4.00E+00
2.00E+00
0.00E+00
7.00E+01-7.20E+01
6.80E+01-7.00E+01
6.60E+01-6.80E+01
6.40E+01-6.60E+01
6.20E+01-6.40E+01
6.00E+01-6.20E+01
5.80E+01-6.00E+01
5.60E+01-5.80E+01
5.40E+01-5.60E+01
5.20E+01-5.40E+01
5.00E+01-5.20E+01
4.80E+01-5.00E+01
4.60E+01-4.80E+01
4.40E+01-4.60E+01
4.20E+01-4.40E+01
4.00E+01-4.20E+01
3.80E+01-4.00E+01
3.60E+01-3.80E+01
3.40E+01-3.60E+01
3.20E+01-3.40E+01
3.00E+01-3.20E+01
2.80E+01-3.00E+01
2.60E+01-2.80E+01
2.40E+01-2.60E+01
2.20E+01-2.40E+01
2.00E+01-2.20E+01
S49
S37
S25
1.80E+01-2.00E+01
1.60E+01-1.80E+01
1
4
7
10
13
16
19
22
25
28
31
34
37
40
43
46
49
52
55
58
61
64
67
70
73
76
79
S13
S1
1.40E+01-1.60E+01
1.20E+01-1.40E+01
1.00E+01-1.20E+01
8.00E+00-1.00E+01
6.00E+00-8.00E+00
4.00E+00-6.00E+00
Figure 17. Surface plot representation of ku determination spreadsheet.
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