54 mongrel dogs of either sex weighing 8–12 kg were used as experimental animals as approved by the IACUC at the University of Florida, College of Medicine. All animals were kept in runs and observed for 3 weeks prior to the experiment and passed requirements for good health set by the animal department. All had normal white blood cell count, hematocrit and sedimentation rate. The dogs were not screened for heartworms or intestinal parasites. For initial anesthesia each received 30 mg of sodium pentobarbital per kilogram of body weight intravenously (IV). This was supplemented as needed during the experiment with additional doses of IV pentobarbital. The left leg was shaved and the muscle used was cleared from other tissues and attached to a pneumatic myograph, which is described later in detail, used for measurements of mechanical activity (Fales et al., 1958). The animals were humanely euthanized under anesthesia at the end of the experiment with pentobarbital and IV potassium chloride.

The perfused denervated dog gastrocnemius (Fales et al., 1956) and semitendinosus (Stainsby and Barclay, 1971) with isolated intact circulation is a unique model because unlike almost all other preparations it gives the experimenter the ability to change almost all variables in muscle physiology except recruitment of motor units which all fire at once when the nerve is stimulated directly. Temperature, initial length, load (preload and afterload), stimulation frequency and determination of the elastic properties can all controlled independently (See Figure 1).

Fresh biopsy samples both gastrocnemius-plantaris and semitendinosus muscles were quick frozen and liquid nitrogen and placed on frozen section chucks for sectioning. Half micron sections we’re stained for myofibrillar ATPase pH 9.4 and succinate dehydrogenase (27). These sections were then viewed on an upright microscope, photographs were taken, and the fibers typed according to their staining properties.

After completing a series of dynamic length tension curves, the blood vessels to the muscle were isolated and the muscle perfused in situ, with fixation solutions while still attached to the lever so that fixation would be done a known initial length. Each muscle studied was fixed at a different initial length that was used to measure isometric tension for the Length:Tension Curve. This was done so that a sarcomere length-tension relationship could be ascertained relative to the active length tension curve. After fixation, initial embedding was done using a one-to-one ratio propylene oxide and araldite-epon mixture for 2 h and then followed by 12 h in a one to two mixture. The specimens were then cut into still smaller pieces and placed longitudinally in the tips of small plastic capsules and covered with 100% araldite-epon mixture. This was allowed to polymerize for 3 days at 60°C. At first 5 µ thick sections were made to ascertain fiber orientation after which the blocks were trimmed and thin sectioned (∼400–600 Å) and placed on 300 mesh coated copper grids. These were viewed in a Hitachi 11 TC electron microscope. Photographs were made on Kodak high resolution electron sensitive plates and printed on Brovira #6 photographic paper. Sarcomere lengths were determined by measuring the distance between the midpoints of two adjacent Z dash lines. I band and A band widths were also measured.

Either the semitendinosus or the gastrocnemius plantaris was used as the experimental muscle. Only one muscle was used for each animal. Isolation of the muscle was performed following the techniques of Stainsby and Barclay (Stainsby, 1970; Stainsby and Barclay, 1972). Briefly, the semitendinosus was isolated through a wide anterior medial incision and was cleared of its connective tissue attachments to the skin, being careful to preserve the blood supply (see Figure 1). Next, its two tendons were cut from their insertions and placed into a lightweight aluminum tendon clamp, the leg was then turned over and a posterior incision made, the nerve to the semitendinosus was exposed carefully isolated, ligated at the central end, cut between the ties and the distal end laid down on a silver wire stimulus electrode imbedded in a tubular dental acrylic nerve holder. The distal cut end of the nerve was loosely tied in place and the holder was filled with isotonic saline and the ends were sealed with silastic grease. The posterior wound was then closed around the electrode leads with skin clips and the leg turned over and a bone nail was placed into the bony pelvis parallel to the leg and perpendicular to the pelvis and attached to a strut which butted against the tip of the myograph support. The tendon clamp was attached to the myograph (See Figure 1). The strut and bone nails provided mechanical stability by preventing the muscle from pulling the animal up towards the lever. The gastrocnemius plantaris was isolated similarly using an anterio-medial incision (See Figure 1). Its tendon was removed from its insertion to the calcaneus and was placed in the tendon clamp. The proximal sciatic nerve was isolated and treated in the same fashion as the semitendinosus nerve. Two bone nails were placed into the femur at 90° to the pull of the muscle these were clamped to the myograph stand with struts which screwed into bone nails. A large strut was placed parallel to the pull of the muscle between the bone nail and the myograph preventing both lateral and rotational movement as well as providing the vertical stability needed because of the large tensions developed by this muscle. Again, the tendon clamp was attached to the myograph, and measurements made.

The isotonic and isometric lever system used for these experiments was a modification of the pneumatic isotonic lever system describe by Fales (Fales et al., 1958). (See Figure 1). The muscle exerts its force against the air in the bellows. To maintain the bellows air pressure nearly constant during the compression phase a surge chamber 1,000 times the volume of the bellows was connected to the bellows by a 2″ bore tube. Further, the range of complete excursion made by the bellows during the maximum contraction produced a volume change of less than 1/3 of the volume in the bellows. Therefore, a contraction altered the gas volumes by a maximum ratio of only 1–3000 making pressure quite constant in the bellows throughout the contraction. The inertial load of the air column in the tube was very small and when added to that of all the mechanical parts of the lever, the total inertia is equal to about an 86 g mass at the end of the lever which is approximately 1.9 g/g of either muscle. The stiffness of the bellows was overcome by a spring adjusted to be exactly equal and opposite to the stiffness of the bellows as described in detail by Fales et al. (1958). An aluminum rod with regular indentations was used to connect the muscle clamp to the force transducer on the lever. The distance between the indentations in the rod was 6 mm. A stainless-steel wire was used to connect the tendon clamp to the rod.

Muscle shortening was measured using a Statham strain gauge linear displacement transducer placed about 8 mm forward of the pivot point of the lever. Its output was linear over 4.5 cm of travel which was the maximum allowed by the lever. A small range (1 cm) of non-linearity near the top of the travel of the lever was illuminated by a stop above the after-load screw which was always left in place. Tension (P) was measured using two bonded semiconductor strain gauges placed on a 1/4 in thick by 1/2 in wide by 1 in long aluminum bar which ended in the clamp for the muscle attachment rod. The compliance of the rod and the transducer and lever system was approximately 10^–4 cm/kg tension development. This allowed a maximum movement that was less than 1% a muscle rest length (Lr) at the maximum isometric tension development. Velocity and the rate of tension development during the isometric contraction phase were measured by taking the amplified signal from the length and tension transducers respectively and placing it through a R/C op-amp differentiated network. The addition differential R/C op amp circuits constructed to have a resistance and time constant for maximum sensitivity and linearity over the range studied (0–100 Hz natural frequency). For quick release to measure the series elastic component, a delay circuit was built which powered a solenoid near the end of its travel to allow maximum acceleration of a stop which held the lever. 100 msec after initiation of a contraction, the solenoid was activated and the stop was pulled, releasing the lever. This allowed an almost instantaneous change (4.0 msec) in the length of the muscle from its rest isometric length to the new isometric length corresponding to the new load.

All recorded signals were conditioned with a Honeywell Accudata 113DC bridge amplifier (Honeywell Inc. Newport TN). Excitation voltage to the position and tension transducers was 4.5 V DC. The output of the amplifier was transmitted to a Honeywell M1650 galvanometer and the light signal from the galvanometer recorded on Kodak 1895 linograph light sensitive paper. The M1650 galvanometers had a frequency response which was linear to 1000 Hz (10X the natural frequency of the event). The paper speed for recording was run between 100 and 2,000 mm/sec. The output of the amplifiers was also monitored on a single beam eight channel oscilloscope. Filters were then placed at a frequency of five times that of the maximum expected requirements (60 Hz for muscle length and tension and 100 Hz for the differential signals) to assure less than 1% error in the actual measurements. The signal to the differentiators was taken after filtering but before it reached the recording galvanometer so the differentiated signal would be in phase with the non-differentiated length and force outputs. In the final version, signals from the length and tension amplifiers were conditioned to 500 Hz and that from the differentiators to 1000 Hz using three pole Butterworth filters at a rate of 4DB/octave. The response was checked with a signal generator using both sine and triangular wave forms from 1 to 100 Hz for phase and amplitude linearity and was found to be linear and in phase over the entire range. All instruments were calibrated daily with constant input source in (1 cm for length transducers, 4.4 kg for tension transducers). The differentiated output was calibrated by applying a 10 Hz triangular wave signal to the length or tension amplifiers and recording the wave function height, frequency and 1/2 maximum excursion of the square-wave differentiated output.

Direct nerve stimulation was done using square pulses of 0.1 Msec duration and 8 V amplitude for the normal voltage experiments and for the reduced voltage experiments from the amplitude of the voltage used was 0.12–0.30 V which reduced the force development at L₀ to 0.5–0.8 (mean 0.65) P₀. The stimuli were produced by using a single or two S5 grass stimulators coupled in series. Two types of experiments were done using the same stimulus pulse characteristics. 1. Twitch: one 0.1Msec impulse per second. Brief Tetanic: 200 msec duration trains of 0.1 Msec 100 Hz impulses at a rate of 12 per minute. This rate and duration of stimulation for tetanic contractions was chosen empirically as the lowest frequency of stimulation that resulted in smooth fused tetanic contractions with no decline in force over time. At the commencement of the experiment or after any change in experimental conditions, for example change in length, stimulus voltage or load, a minimum of 10 brief tetanic or 20 twitch contractions were allowed to pass unrecorded, being observed only on the oscilloscope to allow for the staircase potentiation effect (Hamada et al., 1985; Peyton and Lowe, 2022) when quiet muscles are first stimulated. After this the data points were gathered for analysis. This procedure was used to reduce errors from changes in contractility due to “staircase effects” because of the changes in load or length.

All raw data were taken from the records analyzed and curves fitted with the University of California Biomedical Computing BMD statistics package. Force:Velocity curves were fitted with the 3 and 5 parameter functions using the nonlinear least squares regression analysis (BMDX85) and R values were calculated after obtaining the sums of squares for y with the BMD02D package. For stress:strain of the series elastic component the raw data were fitted using a BMD02R linear regression analysis program. Differences were considered significant if the p value was <0.05.

Before the data are presented for the force:velocity relationship a brief description of the terms and methods of analysis are made to clarify the data which will follow. The force:velocity relationship of an active skeletal muscle has been said to follow the classical relationship first described by Hill (1938) as described the methods section: V=b ( P 0 − P ) ( P+a ) (B1)

In Eq. B1, P, V and P₀ are all measured experimentally. a and b are constants chosen to give the best fit of the equation to a series of observed values of velocity and force. The constant “a” has as its dimensions force and the constant “b” has the dimensions of velocity. While a has the dimensions of force it is most often used in the expression a/P₀ which is dimensionless and has been proposed to be stable over a wide range of muscle lengths and temperatures (Hill, 1938). While constant b has the dimensions of velocity as is most often expressed as b/L₀ has the dimensions of seconds⁻¹. Hill (1938) states that this ratio may vary enormously according to the functional role and size of the muscle. This relationship however can only hold true when L_i = L₀. If other rest lengths are to be used, by definition, P₀ must be changed to the maximum isometric tension at the new initial length according to the active length tension curve.

In studying the muscle using lower power electron microscopy on sections from muscles held at L_r which prior to fixation, the muscles are rich in mitochondria throughout suggesting that they have a highly oxidative metabolism. The micrographs also show that as expected the SR forms “triads” at the A-I junction with the lateral sacs of the SR being adjacent to the t-tubules. Fiber typing done using standard methods available at the time the experiments were done showed that both the semitendinosus and gastrocnemius-plantaris were made up of a mosaic of High and Low myosin ATPase staining fibers and as predicted by the abundance of mitochondria, all fibers had high SDH staining, indicating that the muscles studied were made up of both Slow (Type I) and Fast (Type II presumably type IIa) high oxidative fibers. This is in concurrence with more recent fiber type data showing that using myosin ATPase staining in dog skeletal muscle has both fast IIa and IIx and slow fibers, all with high oxidative capacity (Amann et al., 1993; Acevedo and Rivero, 2006; Toniolo et al., 2007; Schiaffino and Reggiani, 2011). In addition there is no evidence that we could find that showed that fiber type had any relationship with muscle activation (Schiaffino and Reggiani, 2011) which might have effected mechanical properties.

Both the passive length:tension relation of the parallel elastic component and the active length:tension relationship of the contractile component were examined. From these data, a well-defined optimum length (L₀) was established for maximal isometric tension during brief-tetanic contractions. Studies were not carried out beyond 1.20 L₀ because attempts to make measurements beyond this length early in the study had resulted in permanent damage to the muscle demonstrated by reduced tension development at optimum length as had been previously observed in other mammalian muscles by Bahler et al. (1968). The exact mechanism for this is unknown as this is not the case for amphibian muscle. From our electron microscopic length:tension study (see Figure 5) it can be seen that the relationship between sarcomere length and active developed tension follow the findings of Gordon et al. (1966) in that the degree of overlap of myofilaments appeared to govern tension development. The sarcomere length at L₀ is 2.75 microns which is about the same as the sarcomere length at L₀ measured in frogs and other mammalian muscles studied in situ or in vitro (Parmley et al., 1970; Gregor et al., 1988).

Our results agree with the length tension relationship for twitch contractions in mammalian muscles studied previously (Close, 1964; Geffen, 1964; Close, 1965; Bahler et al., 1968). The relationship obtained for twitch contractions differs from brief tetanic contractions in two ways, the shape of the length tension curve for twitches is a smoother function, and the apparent optimum length of the muscle is 12% greater for twitches than for brief tetanic contractions. One explanation which has been offered for these differences is that tension development is not only related to the overlap of the thick and thin myofilaments, but also to the fact that the degree of activation of the contractile elements is not complete during a single twitch (Bahler et al., 1967; Rack and Westbury, 1969; Lambert et al., 1979). This relationship between length and activation is not as important for brief tetanic contractions as it is in twitch contractions, because the duration of stimulation is long enough to fully activate the muscle, regardless of length. This theory is unproven and could not be refuted or supported by the present study because no measurements of active state were made.

All of the force:velocity data collected in these experiments were subjected to nonlinear least squares analysis and the parameters were adjusted to give the curve the best fit. When the force: velocity relationship of the contractile component was studied under optimal conditions, L_i = L₀ with supramaximal stimulus voltage and either twitch or brief tetanic stimulation, the best fit curves showed the relationships illustrated in Figures 9A,B. These data generally conform to the relationship defined by Eq. 1 as suggested by Hill (1938). In previous descriptions of the mechanics of skeletal muscle these constants have either been used at the beginning of the experiment from previous reported constants or have been taken from the first L_i = L₀ F:V curve and held constant throughout the rest of the analysis. In our analyses here however, these values are not held to be constant but rather adjustable parameters to allow the best fit for the equation. Secondly, P₀ in Eq. 1, which had previously been taken as a constant from an experimental curve, was also allowed to act as parameter “c” because there was no justification for that single observed point being more valid than any other observed experimental point. This yielded the equation: V=b ( c-P ) / ( P+A ) (1A)

(see Figure 12).

The constants from Eq. 1A obtained by fitting the general equation to the observed data of a single experiment using the above stimulus conditions were: a/P₀ = 0.63 and b = 2.83. The correlation coefficient between the curve fitted by Eq. 2 and the observed data was 0.9887, p < 0.001, indicating that Eq. 2 closely describes these observed data values for the a/P₀ ratio reported previously from isolated mammalian muscles (0.115–0.60) becoming higher in fast muscles than in slow muscles (Donald et al., 1972; Amann et al., 1993; 83). The speed of the muscles currently studied are relatively fast so that the a/P₀ ratio would be expected to be at the upper part of the range.

When both semitendinosus and gastrocnemius plantaris muscles were studied under non-optimal conditions (Li ≠L0 and/or twitch contractions) a/P₀ became larger and more variable ranging in magnitude from 1 to 2.5^.10⁴ the a/P₀ ratios indicate the relative concavity of the force velocity curve. Elevated a/P₀ ratios indicate little curvature, and the force velocity curve is nearly a straight line, but there is no quantitative relationship between shape and the magnitude of the a/P₀ ratio. The data from contractions done at all conditions demonstrate a wide variation in the quantitative results between different muscles. In contrast, force velocity data from previously reported experiments done under optimal conditions had been more consistent for muscle to muscle (Fenn and Marsh, 1935; Wilkie, 1949; Ritchie, 1954; Rosenblueth and Rubio, 1959a; Close, 1965; Gordon et al., 1966; Lawrence McCrorey and Alpert, 1966; Joyce and Rack, 1969; Parmley et al., 1970; Ameredes et al., 19851992; Perreault et al., 2003; Hakim et al., 2013; Herzog, 2017) Variation in the data obtained among different muscles however, is not unique to the present study. It has been observed previously by Stainsby (1970), Stainsby and Barclay (1971), Stainsby and Barclay (1972) and Fales et al. (1956), who used preparations identical to those used in the present study. The cause of the wide variation of data from muscle to muscle was not determined.

Deliberately decreasing the muscles ability to contract maximally causes changes in the force:velocity relationship other than just altering the a/P₀ ratio. When L_i was reduced below L₀ the maximum isometric contraction strength was reduced and shortening velocity was reduced at all loads (see Table 1). The mechanism for the reduction in velocity has not been adequately explained but may be due to delayed complete activation of the contractile elements because of reduced L_r. The present study offers no data on differences in activation at lower lengths as all motor units were activated simultaneously. The reduction seen in predicted V_max was much less (2–12%) than the reduction in maximum tension (10–50%). These data concur with other studies in which initial length was reduced (Rosenblueth and Rubio, 1959b; Rosenblueth and Rubio, 1960; Pennycuick, 1964; Joyce and Rack, 1969). Reducing the muscle’s ability to contract maximally by lowering stimulus voltage, thereby reducing the functional cross-sectional area, reduced the maximal isometric tension between 50 and 80% of maximal isometric tension for super maximal stimulation. Associated with the decrease in maximal isometric tension was a smaller reduction and predicted V_max. The percent change in V_max was between 1/3 and 1/5 as great as the corresponding change in tension. If L_i is lowered at the same time as stimulus voltage isometric tension is further reduced from that seen at L₀ for reduced stimulus voltage. This is accompanied by a modest further decrease of predicted V_max for sub maximal voltage at L₀. It appears from the above that the effects of submaximal voltage and reduced initial length are additive if the two conditions are superimposed. Deliberately lowering stimulation voltage to decrease contractility is a condition which is unique to the present study. As a result, these data could not be compared to the work of other investigators.

The force:velocity relationship for twitch contractions at L₀, full stimulus voltage, appear similar to the force:velocity relationship for a brief tetanic contractions when the contractile state is reduced. Maximal isometric tension development is approximately ½ of that developed during brief tetanic contractions at the same stimulus voltage and rest length. Predicted V_max is reduced less than 5% at L₀ and the percent reduction in V_max is a third to a fifth as great has the corresponding reduction in isometric tension development at all initial lengths. It appears that in twitch contractions, as in brief tetanic contractions, the effects of lowering stimulus voltage and reducing rest length are additive. Despite the similarity of changes in force and velocity brought about by reduced stimulus voltage, reduced L_i and twitch contractions the mechanisms for the reduction and contractile state among the different conditions may be different. In twitch contractions all the fibers are activated but duration of activation may be so short that the muscle is unable to realize its maximum potential for either tension development or speed of shortening. Alternatively, reduced stimulus voltage reduces isometric tension development by reducing the total number of active contracting fibers and reduces the maximum velocity by adding the mass of the unstimulated fibers to the inertial load which the remaining muscle fibers must accelerate; this in turn reduces velocity. Changing L_i above or below L₀ reduces force and velocity by reducing the degree of overlap between the actin and myosin in the sarcomere. Changing L_i reduces the number of active sites which are available for potential crossbridge formation, thereby reducing the potential for tension development and/or shortening.

Two modifications were made in our regression analysis of the force:velocity relationship which differ from previous analyses. (1) P₀ was made into a third variable parameter, c, and (2) the remaining parameters in this model are not fixed constant as they had been previously but are allowed to change until the lowest mean square for the regression is obtained. As a result of these changes there is a broad variation in derived parameters: a, b, c, P₀. Variations in the parameters were so great from one muscle to another that despite individual muscle trends and obvious differences in means there is no statistical difference from one condition to another when group data are evaluated. This method of analysis has only been used once previously by Donald et al. (1972) and they also found a great variability in the parameters obtained. Their range of a/P₀ ratios was from 0.12 to 3.4 × 10⁴ concurring with the results of the present study.

Donald et al. (1972) also found that the predicted P₀ from Eq. 1 or Eq. 1A was greater than the observed P₀. The observed drop in velocity was sufficiently great in some reported instances that only the upper 2/3 of the curve was used when data were analyzed (Devrome and MacIntosh, 19852007; Gregor et al., 1988; Edman, 1993). In other cases, the authors appeared to have ignored the graphic discrepancy between their data and the predicted curve and accepted the statistical fit of the Hill model (Ritchie, 1954; Günther et al., 2018). When we employed this technique in the present study, the statistical fit of the data to Eq. 1A was good, but velocity at high loads dropped more rapidly than predicted. To correct this we devised a 5-parameter equation, Equation 2, which better accounted for the abrupt decrease in velocity at high loads (see Figure 12). V=b ( c-P ) / ( P+a ) + d ( 1- e ( f ( P-c ) ) ) (2)

This is not the first alternative to the Hill equation that has been proposed. Alternatives were first espoused by Fenn and Marsh (1935), Donald et al. (1972) and Perreault et al. (2003) tried several different models among which were polynomials of different degrees, exponentials or a combination of exponentials, fourier series etc.

From Table 1 lowering rest length and or reducing stimulus voltage tended to increase the a/P₀ ratio, especially at initial lengths below 0.8 L₀. Extrapolated V_max was also significantly reduced at rest lengths below 0.8 L₀. This indicates a length dependent factor in the force velocity relationship. In all cases (twitch or brief tetanic), the percentage reduction of developed tension after reducing initial length and or stimulus voltage (up to 50%) is far greater than the reduction in extrapolated V_max (up to 15%). It is visually apparent for most of the curves that the five-parameter curve with its downward inflection, near P/P₀ = 1 fits the observed data better than the simple rectangular hyperbola. (Figure 13) When compared statistically as a group, 14 experimental semitendinosus brief tetanic force:velocity curves had significantly better fits to the five than to the three-parameter equation due to the five-parameter equation’s ability to predict P₀ better than the three-parameter equation. The difference between the observed and predicted P₀ was 0.004 for the five-parameter equation compared to a mean difference of 0.088 for the three-parameter equation (p < 0.05).

The mean values for the derived parameters from curve fitting for the three-parameter and five-parameter equations for each stimulus condition for gastrocnemius plantaris are seen in Table 1. Fitted curves for Eqs 1A,2 for conditions 3 and 7 are seen in Figure 14. The five-parameter equation had a statistically better fit the observed data for the gastrocnemius plantaris than the three-parameter equation (p < 0.05). The difference was again especially exemplified by the differences between observed and predicted P₀. The main difference between observed and predicted P₀ for the five-parameter curve model was 0.012 compared to a mean difference of 0.061 for the three-parameter model (p < 0.05). Equation 2 is unquestionably necessary to describe the force:velocity relationship when velocity is carried through zero, to negative velocities (lengthening). Mashima et al. (1972) using frog skeletal muscle fiber bundles and Joyce and Rack (1969) using in situ cat soleus have measured the relationship of force-lengthening as well as force-shortening (Rack and Westbury, 1969). Their curves are in fact a double curve like ours, the upper half of which is hyperbolic and the lower half a negative exponential. This similar to what we found. The force component of computer fitted curves was carried through zero and velocity allowed to be negative. In all cases the transition occurs near zero velocity. To further justify the 5-parameter equation by calculating the velocity at tensions greater than P₀ the parameters obtained from the regression after fitting Eqs. 3, 4 to a single set of observations. Five examples were carried out and the results were qualitatively the same in all cases.

Close, in his review (Close, 1972), stressed the importance of using units fiber lengths per second or sarcomere lengths per second rather than muscle lengths per second for expressing the velocity of muscle contraction. This is especially important if comparisons of different muscles are to be done. This importance of using the proper units is reemphasized in the present study when comparisons were done between semitendinosus and gastrocnemius plantaris. When muscle lengths per second are used the mean predicted maximal velocity for gastrocnemius plantaris is 1.97 compared to a mean of 9.61 for the semitendinosus. This would suggest that the gastrocnemius plantaris is much slower muscle than the semitendinosus. A major difference in speed between the two muscles would be unexpected in the light of observed similarities in the fiber type composition. When the two muscles maximum velocities were calculated using estimated fiber length rather than muscle length, the velocities were not significantly different, 7.88 for gastrocnemius plantaris versus 9.61 for the semitendinosus. Unfortunately, because it is really not possible to measure exact fiber length of every fiber in an intact pennate muscle, even with modern monitoring techniques, the estimated fiber length we used here is probably as close as can be measured. Analysis of the small difference between the two muscles that does exist leads to the hypothesis that fiber arrangement in the gastrocnemius plantaris is designed for strength rather than for speed. This hypothesis is supported by Azizi et al. (2008) who suggest that the pennation angle acts with the load acting like an automatic transmission system allowing the muscle to shift from high gear with low load allowing high velocity contractions to low gear as the load increases where forceful contractions are needed. However this view is somewhat controversial as Lieber suggests that muscle pennation has little if any functional significance (Lieber, 2022).

The stress: strain properties of the series elastic component using the standard quick release method of Wilkie (1949) were described in the methods section. The records obtained demonstrated a two-phase velocity record following release which concurs with the findings of previous studies (Hill, 1950; Bahler, 1967; Lieber et al., 2017). At L₀, full stimulus voltage, the gastrocnemius plantaris series elastic component has a slightly greater compliance than the semitendinosus. Some of the reason for the difference in compliance between the two muscles may be due to the parallel elastic component, which must be stretched in the gastrocnemius to achieve L₀. The effects of adding the parallel elastic to the series elastic would be to add the energy from the parallel elastic to the overall energy for shortening after the quick release. It is possible that the contractile element could also add its energy to the initial phase of shortening but it is assumed that it does not travel fast enough to play a significant role. The parallel elastic will only be a factor here if the muscle was stretched beyond L₀ and would release all its energy by the time the muscle had reached L₀ while shortening. However, the result of the addition of parallel elastic energy to the series elastic component would be an overestimation of the true series elastic. A second difference between the two muscles which may affect the series elastic is the quantity of series tendon within the two muscles. In the gastrocnemius plantaris the short muscle fibers are attached obliquely the parallel tendons which run through the muscle and a large thick tendon at the muscle clamp end of the muscle. These tendons may also add to the contractile element series elastic. The semitendinosus only has one thin tendonous inscription internally and a thin tendon at the muscle clamp end of the muscle. Thus, overall parallel tendon mass is probably less in semitendinosus than in gastrocnemius-plantaris. The combination of effects from parallel elastic and tendon probably accounts for the difference between the compliance values of the two muscles series elastic component at L₀ full stimulus voltage.

Deliberately reducing muscle contractility by lowering stimulus voltage or rest length had no significant effect on the compliance of the serious elastic component in either muscle. However, when voltage and rest length were lowered simultaneously, there was an increase in the compliance of the serious elastic component in both muscles. Some of the possible explanations are as follows: (1) reducing stimulus voltage leaves some motor units completely inactivated, (2) reducing initial length is thought to reduce activation, and (3) there is a difference in the strength among different sarcomeres (Gordon et al., 1966; Rack and Westbury, 1969; Donald et al., 1972; Lambert et al., 1979; Allinger et al., 1996; Hou, 2018). Hill (1950) has proposed that inactivated or weak fibers will function as series elastic when the muscle contracts. Although, none of the differences for contractile state cause a significant increase and the series elastic separately, in combination the inactivated fibers and weak fibers could act together and significantly increase the total muscle serious elastic. This, however, is speculation and the actual mechanism for this increase in compliance is not certain.

The linear stress: strain curve of the series elastic component from here does not agree with most of the reported findings of previous investigators. Most previous mechanical studies on skeletal and cardiac muscle have reported that the stress: strain curve of the elastic component is defined by an exponential function (Hill, 1950; Pennycuick, 1964; Parmley et al., 1970; Sonnenblick and Skelton, 1974; Herbert and Gandevia, 19852019; Mayfield et al., 2016; Herzog, 2017; Lieber et al., 2017; Lieber and Binder-Markey, 2021). From reviewing the results of these investigators, the following relationship can be drawn concerning the differences between their data and the data from this study: (1) They were done at lower temperatures (0°C–4°C). Because the bend of the exponential function (the point of most rapid slope change) occurs at relatively low loads while at higher temperatures (17°C–25°C) the bend occurs at higher loads. Jewell and Wilkie (1958) and Yeatman et al. (1969) compared the stress strain curves from the same muscle at increasing temperatures and found the shape of the curve was altered significantly as temperature increased in the manner described above. If this effect can be extrapolated to 37°C perhaps the bend in the exponential would occur beyond P/P₀ = 1 and therefore the curve would appear linear over the range of loads studied in this experiment. (2) Some of the previously reported stress strain curves are nearly linear and it appears they would fit either a linear or exponential model equally well (Ritchie, 1954, Donald et al., 1972). The majority of these studies were performed between 32^oC and 37°C and the choice of an exponential may have just been due to the bias of the author (Joyce and Rack, 1969). Over damping of the signals may have distorted the data from the experimental quick release records presented by other authors. Almost, if not all the reported data from these studies demonstrate a much lower rate of oscillation in the length records after the quick release than is seen here (Hill, 1950; Pennycuick, 1964; Parmley et al., 1970; Sonnenblick and Skelton, 1974; Herbert and Gandevia, 19852019; Mayfield et al., 2016; Herzog, 2017; Lieber et al., 2017; Lieber and Binder-Markey, 2021). The slower oscillations may indicate a difference in the degree of damping and/or greater inertia in their system compared to the system used in the present study. The increased damping could have arisen from either increased damping in the muscle caused by the increased viscosity which occurs when the temperature is lowered, by over damping the lever or damping induced by the recording apparatus itself. Both latter possibilities could cause a linear relationship to become non-linear especially as change in load and length increases.

A final possibility for the difference is that the lever system used for this study was different than the ones used in previous mechanical studies because it used an air-spring lever without significant viscous damping (Fales et al., 1958). The inertia of our lever was only 1.9 g per Gram of muscle, a value much less than the relative inertia of lever systems employed in previous experiments e.g., Bahler (1967) lever had an inertial load of 6 g per Gram of muscle. Our studies measuring the compliance of simple springs by both quick release and static measurements confirmed the accuracy of the lever system and have shown our lever system is minimally damped. When quick releases from simple springs were compared to a quick release of the muscle there is no doubt that the serious elastic component is significantly damped by the muscle. The release curves from spring releases had a very high resonant frequency. However, if the springs were deliberately damped by manually holding the spring, the resulting results resembled actual muscle releases. Bahler (1967) found the damping of the series elastic component to be 300 dyn per square centimeter at 17.5°C. Thus, muscle viscosity must be responsible for some, if not all, of the damping of the series elastic component and would certainly be demperature dependent. A report by Wise et al. (1973) has shown that the stress:strain curve from glycerinated rabbit fibers to be either linear or to bend in the opposite direction from previously reported data. The records they present demonstrate oscillations which are similar in frequency to those we found here. This supports the data from our study and encourages further investigation to prove what part of the measurement is really from the muscle and what is only an equipment or temperature artifact.