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

код для вставкиСкачатьTHE 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.

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