close

Вход

Забыли?

вход по аккаунту

?

Effects of distribution of muscle fiber length on active length-force characteristics of rat gastrocnemius medialis.

код для вставкиСкачать
THE ANATOMICAL RECORD 239:414-420 (1994)
Effects of Distribution of Muscle Fiber Length on Active
Length-Force Characteristics of Rat Gastrocnemius Medialis
GERTJAN J.C. ETTEMA AND PETER A. HUIJING
Department of Anatomical Sciences, The University of Queensland, Queensland, Australia
(G.J.C.E.); Vakgroep Functionele Anatomie, Faculteit der Bewegingswetenschappen, Vrije
Uniuersiteit, Amsterdam, The Netherlands (P.A.H.)
ABSTRACT
Background: The length-force curve of mammalian skeletal
muscle is often wider than expected on basis of the optimum length of the
muscle fibers. Two important effects may explain this discrepancy: muscle
pennation and distribution of fiber lengths in the muscle. In the present
study the effects of a Gaussian distribution of fiber lengths on muscle
length-force characteristics were investigated in rat gastrocnemius medialis.
Methods: Fiber length-force characteristics and parameter values of the
Gaussian distribution were derived from literature data (Stephenson et al.,
1989, J. Physiol., 410:351366; Heslinga and Huijing, 1990, J. Morph. 206:
119-132; Zuurbier and Huijing, 1993, J.Morphol., 218167-180). Three different constructions of the distribution model were compared with experimental data. Pennation effects were incorporated in the model.
Results: Two constructions gave reasonably good results: 1) the model
with a fiber optimum distribution, in which fibers acted at the same absolute length at a given muscle length; 2) the model in which fiber optimum
length was uniform but absolute length at a given muscle length was distributed.
Conclusions: In rat gastrocnemius medialis, the magnitude of the effects
of these distributions is similar to pennation effects. The current results
help to explain the relative wide working range of skeletal muscles in human movement and the differences in specific muscle tension as affected by
muscle type, species, and age. o 1994 Wiley-Liss, Inc.
Key words: Rat, Skeletal muscle, Length-force curve, Gastrocnemius,
Modelling
It has been widely accepted that skeletal muscle
length-force (length-tension) curves cannot be predicted solely on the length-force curve of a single fiber
or sarcomere. The active working range of entire skeletal muscles is much wider than that of a single fiber of
similar length. In the last few decades the effects of
muscle pennation on the shape of the length-force diagram have been studied extensively (e.g., Gans, 1982;
Huijing and Woittiez, 1984, 1985; Woittiez e t al., 1984;
Otten, 1988). [Also see Kardel (1990) for a historical
review.] Although geometrical changes during muscle
shortening are very well described by several models
(Huijing and Woittiez, 1984; Zuurbier and Huijing,
1991, 1992), it appears that pennation effects can only
partly explain the discrepancy between the width of
the length-force curve of entire muscle and a single
fiber (Huijing and Woittiez, 1984, 1985; Huijing et al.,
1989).
Also, attention has been paid to effects of distribution of lengths of fibers and motor units within the
muscle (Lewis et al., 1972; Bagust et al., 1973;
Stephens et al., 1975; Huijing, e t al., 1989; Bobbert et
Q 1994 WILEY-LISS, INC
al., 1990; van Eijden and Raadsheer, 1992). Although
data on fiber distributions are available (Bagust et al.,
1973; Stephens et al., 1975; Holewijn et al., 1984;
Heslinga and Huijing, 1990; Zuurbier and Huijing,
19931, the effects of distribution of fiber lengths were
not studied systematically. Especially it is not known
yet how much a certain distribution of fiber lengths
contributes to the width of the length-force curve. The
answer to this question is of importance for explaining
the biomechanics of human movement. For example,
Herzog and ter Keurs (1988) found that the length
range over which the human rectus femoris was able to
produce active force was much wider than could be expected on basis of the muscle fiber length. Furthermore, the maximum force appeared to be much lower
than expected on cross-sectional area of the muscle.
Received October 26, 1993; accepted March 8, 1994.
Address reprint requests to G.J.C. Ettema, Department of Anatomical Sciences, The University of Queensland, Queensland 4072, Australia.
415
S K E L E T A L MUSCLE LENGTH-FORCE C U R V E
Herzog and ter Keurs (1988)hypothesised that a distribution of fiber lengths in the rectus femoris could
have caused this discrepancy.
The aim of this study was to elucidate quantitatively
the effects of distributed fiber optimum lengths on the
active length-force curve. The characteristics of passive
muscle, although of significance a t large muscle
length, were not considered in this study. The effects of
three different distributions were studied.
The rat gastrocnemius medialis m i w c ! ~WIP t&es zs
a model, for three reasons. First, a substantial amount
of information on its fiber length-force characteristics
and fiber length distribution is available (Stephenson
and Williams, 1982; Holewijn et al., 1984; Heslinga
and Huijing, 1990; Zuurbier and Huijing, 1993). Second, a t the origin and insertion the muscle is equipped
with a tendon. This implies that all motor units have
the same mechanical effects during activity. This
makes it unlikely that essential functional (i.e. mechanical) differences, and thus differences in functional
properties, are related to the organisation of the gastrocnemius muscle in motor units. Thus, a systematic
distribution of fiber lengths along different motor units
is less likely than in muscles with large origin and
insertion sites. Third, in rat gastrocnemius all fibers
are organised in parallel, no in-series connections are
present (Holewijn et al., 1984). This fact symplifies the
modeling of the fiber length-force curve.
METHODS
Simulation Model
A simulation model was developed incorporating a
length-force curve of a single muscle fiber, based on the
length-force curve of a single sarcomere. Sarcomere optimum length was set a t 2.3 Fm (Heslinga and Huijing,
1990), and active slack lengths were set at 60% (-1.39
Fm) (Heslinga and Huijing, 1990) and 175% (-4.00
pm) (Stephenson and Williams, 1982). The ascending
limb and the range around optimum length of the
length-force curve (1.39-2.56 p.m) were described by a
parabolic function, and the descending limb (2.56-4.00
pm) by a linear function. The transition point between
these two functions was continuous. The length-force
curve of a single muscle fiber consisted of a n in series
summation of the sarcomere curves. It should be noted
that it is assumed t h a t sarcomeres are uniformly distributed within a fiber. Effects of non-uniformity of sarcomeres on the length-tension curve of muscle fibers
have been described, e.g. by ter Keurs et al. (19781, and
should not be ignored when interpreting the results of
the current study (see Discussion).
In mammalian muscle, most of the passive muscle
force is thought to be exerted by extracellular connective tissue (Borg and Caulfield, 1980). Therefore, passive force of the entire muscle is not necessarily directly related to the length of individual fibers. Thus,
the effects of fiber length distribution on passive
length-force characteristics were not studied, and we
exclusively described the active component of the
length-force characteristics.
The distribution of the number of sarcomeres connected in series within a single fiber, i.e. the distribution of optimum fiber lengths (1,) within the muscle,
was described by a Gaussian distribution, determined
by a mean (pIf,)and a standard deviation (ulfo):
(A,
Model I1
.........
....
,
..........
....
,
I
,
I
I
I
l
,
t
I,
k
,
lo
,
,
1>10
,
F]im
Model III
............
........
.............
.......
tendon
1
I
,
'
<lo
,
'
'1
lo
]>lo
0sarcornere
Muscle Length
Fig. 1. Left: Fiber length-force curves of five fiber groups for model,
I, 11, and I11 (dashed curves are not represented in right side figures).
Fiber forces are plotted against muscle length. Right: Schematic representation of three fibers a t three different muscle lengths relative to
optimum length (lo):<lo, lo, and 11,. Differences in fiber lengths are
compensated for by tendinous structures. All length changes of the
muscles are taken up by the fibers (the small amount of extension of
the short pieces of tendinous tissue is ignored).
=
(2%&
1/2*e{( -(ix-&L)/"I2),2}
(1)
where y is the probability of occurrence of fiber length
x. The integration of y with respect to x resulted in
unity. In the model, y was multiplied by maximal isometric force for the entire population of muscle fibers
(Fa),so that the summation of all forces was equal to Fa.
F, was set a t a n arbitrary level, since its absolute value
was not of interest in this particular study.
Three distribution models were tested. In model I all
fibers in the muscle were assumed to work at the same
absolute length, giving the same distribution of sarcomere lengths for all muscle lengths. In model I1 all
fibers were assumed to act at their own optimum
length a t muscle optimum length, resulting in a changing distribution of sarcomere length as a function of
muscle length; a t muscle optimum length there is no
distribution of sarcomere length. In model I11 no distribution of fiber optimum length was incorporated
(ulfo= O), but a Gaussian distribution was applied to
their absolute length (lf) a t muscle optimum length.
Fiber optimum length was taken as the average fiber
length a t muscle optimum (pkf),and the standard deviation (u,Jwas taken the same a s ulfo.Thus, in model
I11 there is a changing sarcomere length distribution a t
all muscle lengths. The principles of these models are
shown in Figure 1. For illustrative reasons, only five
fiber groups are shown.
416
G.J.C. ETTEMA AND P.A. HUIJING
For all models the entire fiber population was divided in 100 groups with different fiber lengths. This
number was well above the critical value where a constant model output was obtained, independent of the
number of groups. The difference in fiber optimum
length or acting length (model 111) between adjacent
groups was chosen such that the longest and shortest
fiber groups had a probability of occurrence of near
zero.
The parameter values for the simulations were based
on results from Holewijn e t al. (1984), Heslinga and
Huijing (1990), and Zuurbier and Huijing (1993). In
these studies, the number of sarcomeres in series
within fibers was determined at different regions in the
muscle belly. These data allow for a reasonable estimate of the average optimum fiber length and the standard deviation value of the distribution of fiber
lengths.
The effect of muscle pennation was also included in
the models. Pennation effects calculated by means of
the planimetric model, presented by Woittiez and Huijing (1984, 1985) and further elaborated by Otten
(1988), were incorporated. Pennation angles were deduced from Heslinga and Huijing (1990) and Zuurbier
and Huijing (1992). For all models, muscle force was
calculated a t muscle length intervals of 2% of the chosen average fiber optimum length, from about 5 mm
above optimum length to slack length, i.e. the same
region for which experimental data are available.
Experimental Data
The experiments were performed on five young adult
male Wistar rats (body mass 228-246 g), who were
anaesthetised with pentobarbital (initial dose 10 mg/
100 g body mass i.p.1. The GM was freed from its surrounding tissues leaving muscle origin and blood supply intact. The distal tendon and part of the calcaneus
were looped around a steel wire hook, tightly knotted
with suture, and glued with tissue glue (Histoacryl).
The steel wire was connected to a strain gauge force
transducer. This procedure ensured a solid fixation,
preventing slippage during force exertion. All measurements were done at a n ambient temperature of
25°C on a multipurpose ergometer (Woittiez et al.,
1987). The muscle was excited by supramaximal stimulation of the distal end of the severed nerve (square
wave pulses; 0.4 msec duration, 3 mA, 100 Hz). Lengthforce characteristics of the muscle-tendon complex
were determined by applying this stimulation protocol
at very short lengths, where hardly any active force
was exerted, to lengths about 4 mm above optimum
length. To find the actively generated muscle force, the
passive force exerted a t the same muscle length was
subtracted from total isometric force. Length increments between two subsequent contractions amounted
to 0.5 mm. Optimum length of the muscle-tendon complex (lo), was defined a s that length a t which active
isometric muscle force was highest (F,), and was determined with a n accuracy of 0.5 mm. Force-compliance
characteristics of the series elastic component were determined using quick length decreases of 0.2 mm
within 3 msec during the same isometric tetanic contractions (Bobbert et al., 1986), and thus for the whole
range of isometric force levels. Compliance of the series
elastic component was calculated as the ratio of length
and force change of the muscle-tendon complex during
the quick release. By integration of compliance with
respect to force, elongation of the series elastic component could be calculated for each isometric force measurement. The length-force data were corrected for this
elongation. It should be noted that this correction includes extension of series elasticity within the muscle
fibers. For rat GM this extension is limited however,
i.e. 0.21 mm at F, (Ettema and Huijing, 1993), and
therefore ignored in this study.
Markers (0.05 mm in diameter) were inserted in the
muscle a t the distal and proximal end of the most distal
fiber bundle (running from proximal aponeurosis to
achilles tendon). With the use of dividers, the length of
the most distal fiber bundle was measured at 1, as the
linear distance between the two markers. Real fiber
optimum length of this distal bundle was estimated a s
follows. First, the measured fiber length at 1, was corrected for elongation of the series elastic structures a t
F,. Sarcomere optimum length was assumed to be 2.3
pm (Heslinga and Huijing, 1990). From data of
Heslinga and Huijing (1990) and Zuurbier and Huijing
(1993), i t can be deduced that the ratio of calculated
fiber optimum length (optimum sarcomere length multiplied by the number of sarcomeres) and measured
length a t muscle optimum length is about 1.11 (see also
Discussion section). Therefore, the measured fiber
length, corrected for series elastic elongation, was multiplied by 1.11 to get a n estimate of fiber optimum
length (at sarcomere optimum length).
RESULTS
The distal fiber length of the five GM muscles
amounted to 12.26 2 0.53 mm, and 11.24 2 0.56 mm,
when corrected for series elastic elongation. Therefore
the average optimum length of these fibers was estimated to amount to 11.24 * 1.11 = 12.48 mm.
For the simulation model a n average optimum fiber
length (plf,)of 12.48 mm was chosen. It should be noted
that this value was chosen in a somewhat arbitrary
way. The value of 12.48 mm is a n estimate of the optimum length of the distal fibers, not of the average
optimum length of all fibers. However, data of Zuurbier
and Huijing (1992b) show that similar lengths also occur in the mid-region of the GM muscle, whereas only
in the proximal region substantially shorter fibers are
present. Therefore, it was reasoned that p,fowas close
to the optimum length of the distal fibers. On basis of
proximal-distal differences in rat GM (Holewijn et al.,
1984; Heslinga and Huijing, 1990; Zuurbier and Huijing, 1992b), a standard deviation of the distribution of
fiber lengths (alf,and alf)of 2.0 mm (16% of plfo)was
chosen.
In Figure 2A the simulation results for parallel fibered muscles are shown. Models I and 111 obviously
cause the largest widening of the length-force curve.
Model I1 does not have large effects on the width of the
curve. In Figure 2B the effects of pennation and fiber
distribution according to model I are compared. For the
given ulfo(2.0 mm) and pennation angles (line of pullfiber angle 20°, line-of pull-aponeurosis angle 100) the
pennation effect is somewhat larger for most of the
length-force curve below optimum length. For the ab-
417
S K E L E T A L MUSCLE LENGTH-FORCE CURVE
0.9
7
0.8
:A
0.9
0.8 -
-
v
8
0.7
0.6
0
3 0.5
Uniform
-
-
P d e l Uniform
P d e l Model I
PeMate Uniform
0.2
0.2
0.1
Pemata Model I
010 -1.5
-5
-2.5
0
2.5
relative length (rnm)
5
010 -7.5
-5
-2.5
0
2.5
relative length (mm)
5
Fig. 2. Simulation results: A Muscle length-force curves of parallel fibered muscles. B Parallel and
pennate muscle models (uniform muscle, model I, and model 111).
solute width, i.e. optimum-slack distance, the effects models: not all fibers work at their own optimum
are similar. The combined effect is quite large, leading length when the muscle is a t its optimum. A distributo a n increase of about 5 mm (40% of plfo)of the width tion exclusively of number of sarcomeres in series
within fibers, without any shift of fiber optimum
of the curve.
In Figure 3, models I and 111, including pennation lengths relative to muscle optimum length, must be
effects, and the uniform pennate model are compared considered inadequate to predict this width appropriwith the experimental data. It appears that a ulfoof 2.0 ately (model 11).
mm gives reasonable results for model 111. In model I
The question arises which model best predicts the
the length-force curve is still underestimating the force length-force curve of rat GM. A similar simulation a s
along most of the ascending limb of the curve. There- model I11 has been previously applied, with reasonable
fore, a second run of model I was made with a n ulfoof success, to rat extensor digitorum longus (Bobbert et
3.0 mm. This resulted in quite a good prediction of the al., 1990). Furthermore, in the present study, a stanexperimental data, similar to model I11 with ulf = 2.0 dard deviation of 2.0 mm (16% of fiber optimum length)
mm. However, the shape of the ascending limb is not was sufficient for a reasonable overall prediction,
well described in either simulation: in the middle part whereas in model I 3.0 mm (24%)was needed. This last
of the ascending limb the force prediction tends to be value seems rather high, given the experimental data
lower than the experimental data, whereas a t the on differences in fiber lengths (Holewijn et al., 1984;
shortest lengths there tends to be a n overestimation of Heslinga and Huijing, 1990; Zuurbier and Huijing,
relative force (Fig. 3B). Figure 3 also shows that the 1993), but is of the same order of magnitude a s shifts
effects of fiber distribution are of a similar magnitude of muscle optimum length with derecruitment of motor
to those of series elastic elongation.
units (Huijing and Baan, 1992). Also Otten (1988), reFigure 4 shows the effects of fiber length distribu- ferring to Stephens et al. (1979, calculated a standard
tions on the maximal force (F,) exerted by muscles with deviation of about 16% of fiber optimum length distriequal physiological cross-section. The effects of the fi- bution for cat GM. On the other hand, the same data
ber distribution and pennation used in this study are (Stephens et al., 1975) point out that substantial difsimilar in magnitude and amount to about 12% reduc- ferences in fiber optimum lengths must be present
tion in tension. The combined effect of pennation and within rat GM muscle, ruling out the feasibility of
fiber length distribution amounts to a 23% reduction. model 111. A good possibility might be a combination of
models I and 111: that is, model I with a smaller uIf0,but
DISCUSSION
with a larger shift of acting fiber lengths at muscle
The aim of the present study was not to determine optimum. The effect of such a shift is a widening of the
the exact distribution of fiber lengths within a single length-force curve relative to model I. It would mean
skeletal muscle, but rather to test the feasibility of that the somewhat shorter fibers of the population, but
different fiber length distributions. The simulations in- longer than in model I, would have their optimum
dicate that the width of the length-force curve of rat length a t shorter muscle lengths than in model I.
GM can a t least partly be explained by means of a
From the difference in shape between actual lengthpopulation standard deviation of about 16% of fiber force data and simulations it can be deduced that the
optimum length or acting length in combination with distribution in fiber lengths is not of a Gaussian type.
effects of pennation (models I and 111).The differences Skeletal muscle is organised in separate motor units
between directly measured fiber length and fiber with separate functions. Although this organisation
lengths based on sarcomere counts (Heslinga and Hu- makes a systematic and skewed distribution of fiber
ijing, 1990; Zuurbier and Huijing, 1993) may be a n lengths plausible, data on 89 motor units of cat GM
important indication for the occurrence of these two (Stephens and Williams, 1982) do not support such a
G.J.C. ETTEMA AND P.A. HUIJING
418
1
0.9
"
0.8
W
8
0.7
b
0.6
2 0.5
a 0.4
8
d
0.3
0.2
0.1
n
u
-
-10
-7.5
-5
-2.5
2.5
0
5
relative length (mm)
Fig. 3. Comparison of experimental data and model calculations. A Total length-force curve. B: Part
of the ascending limb. Vertical bars indicate standard deviation of experimental data. s.d., standard
deviation of fibre length distribution.
n
' c-
0.9
0.8 n
2 0.7
E
8
0.6
0.5
v1
.r(
-
0.4
Uniform Parallel
-
-
Model I Parallel
Model III Parallel
0.3
d
..
0.1
....... Uniform Pennate
0.2
<*'.:<
0.
-10
"\a
?
,
:
'
4(:
Model I Pennate
I
-. q,'
-<'
-... ' , ' "
-7.5
-5
Model III Pennate
" ' ' l ' . ~ ' l . ' "
-2.5
0
2.5
5
relative length (mm)
Fig. 4.Normalised muscle force as a function of length for uniform,
distributed, parallel, and pennate muscles. Force is expressed relative
to maximal force of the uniform parallel fibered muscle.
hypothesis. GM is a muscle running from tendon to
tendon. Therefore, all motor units will produce a force
in the same direction a t the joints involved, and thus
they have the same qualitative mechanical action. This
makes a skewed distribution along motor units less
likely. Still, symmetric and random fiber distributions
other than the Gaussian distribution might be present
in skeletal muscle.
The use of a parabolic function to describe the ascending limb and the optimum region of the lengthforce curve of a single fiber might not be totally appropriate. Data in literature (Stephenson and Williams,
1982; Stephenson et al., 1989) indicate that the plateau
of the mammalian fiber length-force curve around its
optimum might be broader than described by the function used here. This is likely due to non-uniformity of
sarcomeres within a single fibre (ter Keurs et al.,
1978), which was not implemented in our models. We
tested the effects of implementing such a sarcomere
length-force curve. The shape of the curve was based on
filament lengths reported by Heslinga and Huijing
(1990). The optimum plateau was taken from 1.98 pm
to 2.30 pm, and fiber optimum length was assumed to
coincide with the middle of the plateau, i.e. 2.14 km.
The results are presented in Figure 5. The curves for
the uniform parallel muscles, resembling the sarcomere curves, are quite different. (Note that the points of
the optimum plateaus coinciding with a sarcomere
length of 2.3 pm are presented as zero length.) However, most of these differences seem to disappear due to
the effects of pennation and distribution of optimum
lengths (model I, ulfo = 2.0 mm). Especially the differences in shape have disappeared. The curve based on
the optimum-plateau sarcomere curve is only narrower
than the original curve. This is caused by the fact that
the ascending limb of the optimum-plateau sarcomere
curve is steeper, and that muscle optimum length in
the pennate muscle with fiber length distribution coincides with a n average sarcomere length of 2.14 pm.
Compared to the original model, this length is closer to
slack length of the ascending limb. We repeated the
same simulation with a sarcomere optimum plateau
from 2.19 pm to 2.69 pm, based on filament lengths
reported by Stephenson and Williams (1982). In that
case, the length-force curve of the pennate muscle with
distribution of fiber lengths (model I) appeared almost
exactly the same a s in the original simulation. Therefore, we concluded that the exact shape of sarcomere
length-force curve cannot explain any discrepancies between muscle and simulated length-force curves.
Clearly, substantial information about the shape of the
ascending limb of the fiber length-force curve is essential to elucidate this problem entirely. Here, effects of
sarcomere distributions within a single fibre seem to be
of major importance (e.g. ter Keurs et al., 1978).
419
SKELETAL MUSCLE LENGTH-FORCE CURVE
a
;. 0.5
a
0
0.4
c
0.3
0.2
0.1
-
/
/
.
/
1’
.
,’
7:
.
/I
:
I:
Uniform Parallel
Distributed Pennate
point
...... Uniform Parallel
--
Distributed Pennate
relative length (mm)
Fig. 5. Length-force curves of uniform, parallel muscles and of pennate muscles with fiber length
distributions (model I, ulf0 = 2.0 mm). Curves indicated by ‘plateau’ are based on a sarcomere lengthforce curve with a n optimum plateau from 1.98-2.3 pm; curves indicated by ‘point’ are based on the
originally used sarcomere length-curve with an optimum point at 2.3 pm.
Of course, it can be disputed that the average fiber
optimum length used in the simulations was a n accurate estimate of the real average length. We used the
length of the most distal fiber bundle for this purpose.
To our knowledge this value is rather a n overestimation than a n underestimation of the true average fiber
optimum length (Holewijn et al., 1984; Zuurbier and
Huijing, 1993). Therefore, we must conclude that the
true average fiber optimum length can only be smaller.
As a consequence, a larger and less likely mlfo will be
needed to predict the muscle length-force curve satisfactorily. Thus, despite the reasonable simulation results on distributions of fiber lengths, it is still disputable whether these distributions can entirely explain
the discrepancies between sarcomere and muscle
length-force curves. However, i t is clear that the effects
are of such magnitude that they cannot be ignored.
In the model presented in this study, pennation was
taken into account. However, a distribution of pennation angles was not considered. Although in rat GM
differences in pennation angles between the line of pull
and aponeurosis do occur, they could not be demonstrated for the more important angle between line of
pull and muscle fiber (Zuurbier and HJijing, 1993).
What is more important, it is theoretically impossible
that a random and independent distribution of pennation angles occurs in a muscle: all fibers are aligned
along each other, allowing only a systematic change of
pennation angles from distal to proximal regions.
lmplications for Human Movement
Like pennation, the distribution of fiber lengths has
important effects on physiological and mechanical
properties of skeletal muscle. It broadens and flattens
the length-force curve of the muscle, allowing a wider
active working range. Furthermore, the maximal
forces that can be exerted become less dependent on
muscle length. This is important for incorporation of
muscle models in models of the locomotor system. For
example, Bobbert and Ingen Schenau (1990), using a
uniform muscle model, found discrepancies between
modelling isometric plantar flexion moments as a function of ankle ankle angle and actual experimental
data. They stated that these discrepancies might be
due to distributions of fiber optimum lengths. The
same argument was raised by Herzog and ter Keurs
(1988) to explain the wide length-force curve of the
human rectus femoris. Huijing (1985) showed that for
the human gastrocnemius fiber length differences between proximal and distal part of the medial and lateral head could be about 9%. Differences between the
two heads were even larger, about 18%. The present
study shows that incorporating a distribution of fiber
lengths, based on experimental data, improves muscle
models considerably. Therefore, discrepancies between
locomotor models and experimental data can be very
well caused by a distribution of fiber lengths.
Specific Tension
Another important consequence of fiber length distribution in skeletal muscle concerns the specific tension that can be exerted. It has been generally accepted
that, at the level of muscle fibers, specific tension (force
per cross-sectional area) is more or less the same for
different muscles and fiber types (Close, 1972). How-
420
G.J.C. ETTEMA AND P.A. HUIJING
ever, this might not be the case at the level of the entire
muscle. A distribution of fiber optimum lengths will
decrease F, for a given cross-sectional area. Herzog and
ter Keurs (1988)reported a discrepancy of about 60%
between expected and measured maximal isometric
force for in vivo human rectus femoris, which was
thought to be caused by a n overestimation of the physiological cross-esectional area of the muscle. However,
a considerable part of this difference might be due to
fiber distribution.
Recently, de Haan et al. (1992) found a clear increase
of specific tension of rat GM during growth, and similar
results were found for rat extensor digitorum longus
(Lodder e t al., 1991). The authors did not give a specific
cause for these changes. One could hypothesise that a
more widely spread fiber length distribution in the
younger animals narrows during growth and development to suit the appropriate functional needs. More
research is needed to elucidate such hypotheses.
Since the effects of fiber distribution can account for
a reduction in specific tension of about 12% in rat GM,
they must be considered when dealing with specific
muscle tension.
LITERATURE CITED
Bagust, J., S. Knott, D.M. Lewis, J.C. Luck, and R.A. Westerman 1973
Isometrics contractions of motor units in a fast twitch muscle of
the cat. J. Physiol., 231:87-104.
Bobbert, M.F. and G.J. van Ingen Schenau 1990 Isokinetic plantar
flexion: experimental results and model calculations. J . Biomechanics, 23: 105-1 19.
Bobbert, M.F., C. Brand, A. de Haan, P.A. Huijing, G.J. van Ingen
Schenau, W.H. Rijnsburger, and R.D. Woittiez 1986 Series-elasticity of tendinous structures of rat EDL. J . Physiol., 377r89P.
Bobbert, M.F., G.J.C. Ettema, and P.A. Huijing 1990 The force-length
relationship of a muscle-tendon complex: experimental results
and model calculations. Eur. J . Appl. Physiol., 61r323-329.
Borg, T.K. and J.B. Caulfield 1980 Morphology of connective tissue in
skeletal muscle. Tissue Cell, 12,197-207.
Close, R.I. 1972 Dynamic properties of mammalian skeletal muscles.
Physiol. Rev., 52:129-197.
Eijden, T.M.G.J. van and M.C. Raadsheer 1992 Heterogeneity of fiber
and sarcomere length in the human masseter muscle. Anat. Rec.,
232 :78 -84.
Ettema, G.J.C. and P.A. Huijing 1993 Contributions to compliance of
series elastic component by tendinous structures and crossbridges in rat muscle-tendon complexes. Neth. J . Zool., 43:306325.
Gans, C. 1982 Fibre architecture and muscle function. Exercise Sport
Sci. Rev., 1Or160-207.
Haan. A. de. C.J. de Ruiter. A. Lind. and A.J. Sareeant 1992 Growthrelated change in specific force but not in specific power of rat fast
skeletal muscle. Exp. Physiol., 77505-508.
Herzog, W. and H.E.D.J. ter Keurs 1988 Force-length relation of in
-
vivo human rectus femoris muscles. Pflugers Arch., 411r642647.
Heslinga, J.W. and P.A. Huijing 1990 Effects of growth on architecture and functional characteristics of adult rat gastrocnemius
muscle. J . Morphol., 206r119-132.
Holewijn, M., P. Plantinga, R.D. Woittiez, and P.A. Huiiing 1984 The
number of sarcomeres and architecture of the m. gastrocnemius
of the rat. Acta Morphol. Neer1.-Scand., 22t257-263.
Huijing, P.A. 1985 Architecture of the human gastrocnemius muscle
and some functional consequences. Acta Anat., 123:lOl-107.
Huijing, P.A. and G.C. Baan 1992 Stimulation level-dependent
length-force and architectural characteristics of rat gastrocnemius muscle. J . Electromyogr. Kinesiol., 2r112-120.
Huijing, P.A. and R.D. Woittiez 1984 The effect of architecture on
skeletal muscle performance: A simple planimetric model. Neth.
J . Zool., 34:21-32.
Huijing, P.A. and R.D. Woittiez 1985 Notes on planimetric and threedimensional muscle models. Neth. J . Zool., 35r521-525.
Huijing, P.A., A.A.H. van Lookeren Campagne, and J.F. Koper 1989
Muscle architecture and fibre characteristics of rat gastrocnemius and semimembranosus muscles during isometric contractions. Acta Anat., 135r46-52.
Kardel, T. 1990 Niels Stensen’s geometrical theory of muscle contraction (1667): a reappraisal. J . Biomechanics, 23:953-965.
Keurs, H.E.D.J. ter, T. Iwazumi, and G.H. Pollack 1978 The sarcomere length-tension relation in skeletal muscle. J . Gen. Physiol.,
72:565-592.
Lewis, D.M., J.C. Luck, and S. Skott 1972 A comparison of isometric
contractions of the whole muscle with those of motor units in a
fast-twitch muscle of the cat. Exp. Neural., 37:68-85.
Lodder, M.A.N., A. de Haan, and A.J. Sargeant 1990 The effect of
growth on specific tetanic force in the skeletal muscle of the
anaesthetized rat. J . Physiol., 438t151P.
Otten, E. 1988 Concepts and models of functional architecture in skeletal muscle. Exercise Sport Sci. Rev., 16t89-137.
Stephens, J.A., R.M. Reinking, and D.G. Stuart 1975 The motor units
of cat medial gastrocnemius: electrical and mechanical properties
as a function of muscle length. J . Morphol., 146r495-512.
Stephenson, D.G. and D.A. Williams 1982 Effects of sarcomere length
on the force-pCa relation in fast- and slow-twitch skinned muscle
fibres from the rat. J. Physiol., 333t637-653.
Stephenson, D.G., A.W. Stewart, and G.J. Wilson 1989 Dissociation of
force from myofibrillar MgATPase and stiffness at short sarcomere lengths in rat and toad skeletal muscle. J . Physiol., 410:351366.
Woittiez, R.D., P.A. Huijing, H.B.K. Boom, and R.H. Rozendall984 A
three dimensional muscle model: A quantified relation between
form and function of skeletal muscles. J . Morphol., 182:95-113.
Woittiez, R.D., C. Brand, A. de Haan, A.P. Hollander, P.A. Huijing, R.
van der Tak, and W.H. Rijnsburger 1987 A multipurpose ergometer. J. Biomechanics, 20:215-218.
Zuurbier, C.J. and P.A. Huijing 1991 Influence of muscle shortening
on geometry of gastrocnemius medialis muscle of the rat. Acta
Anat., 140:297-303.
Zuurbier, C.J. and P.A. Huijing 1992 Influence of muscle geometry on
shortening speed of fibre, aponeurosis and muscle. J . Biomechanics, 25r1017-1026.
Zuurbier, C.J. and P.A. Huijing 1993 “Changes in geometry of actively shortening unipennate rat gastrocnemius muscle.” J . Morphol., 218:167-180.
Документ
Категория
Без категории
Просмотров
0
Размер файла
769 Кб
Теги
fiber, effect, characteristics, muscle, distributions, length, activ, medialis, rat, force, gastrocnemius
1/--страниц
Пожаловаться на содержимое документа