Effects of oxidation on the power of chemically skinned rat soleus fibres

Oxidation alters calcium sensitivity, and decreases maximum isometric force (Po) and shortening velocity (Vmax) of single muscle fibres. To examine the effect of oxidation on the curvature of the force-velocity relationship, which determines muscle power in addition to Po and Vmax, skinned rat type I fibres were maximally activated at 15°C in a solution with pCa 4.5 and subjected to isotonic contractions before and after 4-min incubation in 50 mM H?O? (n=10) or normal relaxing solution (n=3). In five oxidised and four control fibres the rate of force redevelopment (ktr), following a rapid release and re-stretch, was measured. This gives a measure of the sum of the rate constants for cross-bridge attachment (f) and detachment (g?): (f+g?). H?O? reduced Po, Vmax and ktr by 19%, 21% and 24% respectively (P<0.001), while the shape of the force-velocity relationship was unchanged. Fitting data to the Huxley cross-bridge model suggested that oxidation decreased both the rate constant for cross-bridge attachment (f), and detachment of negatively strained cross-bridges (g?), similar to the effect of reduced activation. This suggests that oxidative modification is a possible cause of the variation in contractile properties between muscle fibres of the same type.     

The mechanics of mouse skeletal muscle when shortening during relaxation

The dynamic properties of relaxing skeletal muscle have not been well characterised but are important for understanding muscle function during terrestrial locomotion, during which a considerable fraction of muscle work output can be produced during relaxation. The purpose of this study was to characterise the force-velocity properties of mouse skeletal muscle during relaxation. Experiments were performed in vitro (21 degrees C) using bundles of fibres from mouse soleus and EDL muscles. Isovelocity shortening was applied to muscles during relaxation following short tetanic contractions. Using data from different contractions with different shortening velocities, curves relating force output to shortening velocity were constructed at intervals during relaxation. The velocity component included contributions from shortening of both series elastic component (SEC) and contractile component (CC) because force output was not constant. Early in relaxation force-velocity relationships were linear but became progressively more curved as relaxation progressed. Force-velocity curves late in relaxation had the same curvature as those for the CC in fully activated muscles but V(max) was reduced to approximately 50% of the value in fully activated muscles. These results were the same for slow- and fast-twitch muscles and for relaxation following maximal tetani and brief, sub-maximal tetani. The measured series elastic compliance was used to partition shortening velocity between SEC and CC. The curvature of the CC force-velocity relationship was constant during relaxation. The SEC accounted for most of the shortening and work output during relaxation and its power output during relaxation exceeded the maximum CC power output. It is proposed that unloading the CC, without any change in its overall length, accelerated cross-bridge detachment when shortening was applied during relaxation.     

Could an increase in airway smooth muscle shortening velocity cause airway hyperresponsiveness?

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma. It has been proposed that an increase in the shortening velocity of airway smooth muscle (ASM) could contribute to AHR. To address this possibility, we tested whether an increase in the isotonic shortening velocity of ASM is associated with an increase in the rate and total amount of shortening when ASM is subjected to an oscillating load, as occurs during breathing. Experiments were performed in vitro using 27 rat tracheal ASM strips supramaximally stimulated with methacholine. Isotonic velocity at 20% isometric force (Fiso) was measured, and then the load on the muscle was varied sinusoidally (0.33 ± 0.25 Fiso, 1.2 Hz) for 20 min, while muscle length was measured. A large amplitude oscillation was applied every 4 min to simulate a deep breath. We found that: 1) ASM strips with a higher isotonic velocity shortened more quickly during the force oscillations, both initially (P < 0.001) and after the simulated deep breaths (P = 0.002); 2) ASM strips with a higher isotonic velocity exhibited a greater total shortening during the force oscillation protocol (P < 0.005); and 3) the effect of an increase in isotonic velocity was at least comparable in magnitude to the effect of a proportional increase in ASM force-generating capacity. A cross-bridge model showed that an increase in the total amount of shortening with increased isotonic velocity could be explained by a change in either the cycling rate of phosphorylated cross bridges or the rate of myosin light chain phosphorylation. We conclude that, if asthma involves an increase in ASM velocity, this could be an important factor in the associated AHR.     

Maximum shortening velocity of smooth muscle: zero load-clamp vs. afterloaded method

Previous reports from this laboratory of force-velocity relationships of canine tracheal smooth muscle (TSM) have presented maximum shortening velocities (Vmax) mathematically derived from the linearized transformation of the Hill equation (A. V. Hill, Proc. Roy. Soc. London, Ser. B., 126:136-195, 1938). Recent technical advances enable us to measure Vmax directly using an electromagnetic lever system that can instantaneously clamp to a zero load, thus we compared values of Vmax derived mathematically and those directly measured on the same TSM strips. Derived Vmax values from afterloaded isotonic shortening curves for loads greater than preload were 0.328 +/- 0.021 optimal length (lO)/s and were not significantly different from zero load-clamp measurements of 0.301 +/- 0.022 lO/s from the same (n = 15) muscles. These data indicate that Vmax values mathematically derived for TSM from conventional isotonic afterloaded force-velocity curves are valid estimates of zero load velocity, because they were not significantly different from values obtained by direct measurement using the zero load-clamp technique.     

Force-velocity constants in smooth muscle: afterloaded isotonic and quick-release methods

In using pharmacologic stimuli, force-velocity (FV) curves are usually obtained by the method of quick release (QR) and redevelopment of shortening at peak tetanic tension; the advantage of the method being that the active state is at maximum. However, the QR may itself reduce the intensity of the active state and result in reduced values of FV constants. We tested this by delineating FV curves in canine tracheal smooth muscle using both conventional afterloaded isotonic contractions (ALI), and redevelopment of shortening after QR methods. For both these studies a supramaximal tetanizing electrical stimulus was used. The analysis of 11 experiments revealed that the latter method resulted in statistically significant reductions of all FV constants except for Po (maximum isometric tetanic tension). The means and standard errors for the sets of constants for the ALI and QR, respectively, are as follows: Vmax (maximum velocity of shortening) = 0.275 lo (optimal muscle length)/s +/- 0.024 (SE), and 0.216 lo/s + 0.023; a (hyperbolic constant with units of force) = 294 g/cm2 +/- 35 and 236 g/cm2 +/- 32; b (hyperbolic constant with units of velocity) = 0.059 lo +/- 0.004 and 0.039 lo/s +/- 0.005; a/Po = 0.214 +/- 0.028 and 0.182 +/- 0.026; and Po = 1.362 kg/cm2 +/- 0.106 and 1.294 kg/cm2 +/- 0.097. These data clearly show that the quick-release method for measuring force-velocity relationships in canine smooth muscle results in significant underestimates of muscle shortening properties.     

Some proposals in cardiac muscle mechanics and energetics

Based on A. V. Hill's three-component model, mechanical properties of the contractile element (CE), such as velocity and tension, were determined as muscle shortening and loads in quick-release or afterloaded isotonic contraction. The method is applicable for studying cardiac mechanics, to obtain force-velocity data of the same CE length at varous afterloads. Analysis of the energetics of cardiac muscle was based on simulation studies of cardiac mechanics (Wong 1971, 1972). By proper derivation, the conventional contractile element work (CEW) was found to be a minor energy determinant. The tension-time integral and tension-independent heat (Ricchiuti and Gibbs, 1965) represent energy utilization for activation and maintenance of tension, the primary energy determinant.     

Substrate and product dependence of force and shortening in fast and slow smooth muscle

To explore the molecular mechanisms responsible for the variation in smooth muscle contractile kinetics, the influence of MgATP, MgADP, and inorganic phosphate (P(i)) on force and shortening velocity in thiophosphorylated "fast" (taenia coli: maximal shortening velocity Vmax = 0.11 ML/s) and "slow" (aorta: Vmax = 0.015 ML/s) smooth muscle from the guinea pig were compared. P(i) inhibited active force with minor effects on the V(max). In the taenia coli, 20 mM P(i) inhibited force by 25%. In the aorta, the effect was markedly less (< 10%), suggesting differences between fast and slow smooth muscles in the binding of P(i) or in the relative population of P(i) binding states during cycling. Lowering of MgATP reduced force and V(max). The aorta was less sensitive to reduction in MgATP (Km for Vmax: 80 microM) than the taenia coli (Km for Vmax: 350 microM). Thus, velocity is controlled by steps preceding the ATP binding and cross-bridge dissociation, and a weaker binding of ATP is not responsible for the lower V(max) in the slow muscle. MgADP inhibited force and V(max). Saturating concentrations of ADP did not completely inhibit maximal shortening velocity. The effect of ADP on Vmax was observed at lower concentrations in the aorta compared with the taenia coli, suggesting that the ADP binding to phosphorylated and cycling cross-bridges is stronger in slow compared with fast smooth muscle.     

Influence of partial activation on force-velocity properties of frog skinned muscle fibers in millimolar magnesium ion

Segments of briefly glycerinated muscle fibers from Rana pipiens were activated rapidly by a brief exposure to 2.5 mM free calcium followed by a solution containing calcium buffered with EGTA to produce the desired level of force. Steps to isotonic loads were made using a servomotor, usually 3-5 s after the onset of activation. The relative isotonic forces (P/P0) and velocities from contractions obtained under similar circumstances were grouped together and fitted with hyperbolic functions. Under the condition of 6 mM MgCl2 and 5 mM ATP, there was no significant difference in the relative force-velocity relations obtained at full activation compared with those obtained at partial activation when developed force was approximately 40% of its full value. Control experiments showed that a variety of factors did not alter either the relative force-velocity relations or the finding that partial activation did not change these properties. The factors investigated included the decline in force that occurs with each successive contraction of skinned fibers, the segment length (over a range of 1-3 mm), the sarcomere length (over a range of 1.9-2.2 microns), the magnesium ion concentration (26 microM and 1.4 mM were tested), the ATP concentration, the presence of free calcium, and the age of the preparation (up to 30 h). Attempts to repeat earlier experiments by others showing a dependence of shortening velocity on activation were unsuccessful because the low ionic strength used in those experiments caused the fibers to break after a few contractions. The main conclusion, that the shortening velocity is independent of the level of activation, is consistent with the hypothesis that the cross-bridges act independently and that activating calcium acts only as an all-or-none switch for individual cross-bridge attachment sites, and does not otherwise influence the kinetics of cross-bridge movement.     

Adenosine diphosphate and strain sensitivity in myosin motors

The release of adenosine diphosphate (ADP) from the actomyosin cross-bridge plays an important role in the adenosine-triphosphate-driven cross-bridge cycle. In fast contracting muscle fibres, the rate at which ADP is released from the cross-bridge correlates with the maximum shortening velocity of the muscle fibre, and in some models the rate of ADP release defines the maximum shortening velocity. In addition, it has long been thought that the rate of ADP release could be sensitive to the load on the cross-bridge and thereby provide a molecular explanation of the Fenn effect. However, direct evidence of a strain-sensitive ADP-release mechanism has been hard to come by for fast muscle myosins. The recently published evidence for a strain-sensing mechanism involving ADP release for slower muscle myosins, and in particular non-muscle myosins, is more compelling and can provide the mechanism of processivity for motors such as myosin V. It is therefore timely to examine the evidence for this strain-sensing mechanism. The evidence presented here will argue that a strain-sensitive mechanism of ADP release is universal for all myosins but the basic mechanism has evolved in different ways for different types of myosin. Furthermore, this strain-sensing mechanism provides a way of coordinating the action of multiple myosin motor domains in a single myosin molecule, or in complex assemblies of myosins over long distances without invoking a classic direct allosteric or cooperative communication between motors.     

Contractile properties of the shortening rat diaphragm in vitro

Diaphragmatic fatigue has been defined in terms of the failure of the muscle to continue to generate a given level of tension. Appropriate shortening of the diaphragm is, however, just as important for adequate ventilation. In this study we have examined in vitro the contractile properties of the rat diaphragm under afterloaded isotonic conditions and the effect of fatigue on the ability of the diaphragm to shorten. Shortening of the muscle strips was found to depend on size of afterload, frequency of stimulation, duration of stimulation, and initial length of the muscle. The afterloaded isotonic length-tension relationship coincided with the relationship between length and active isometric tension only for relatively small afterloads. Fatigue of the muscle strips, induced by isometric or afterloaded isotonic contractions, was associated with a decline in the extent of shortening as well as a decrease in active isometric tension. Ability to shorten and ability to develop isometric tension did not decrease to the same extent under all conditions. We conclude that active shortening, as well as active isometric tension, is decreased by muscular fatigue and that changes in these properties can be different depending on experimental conditions. The results suggest that the definition of diaphragmatic fatigue should be expanded to include the ability of the muscle to shorten by an appropriate amount. The results also suggest that measurement of isometric performance may not provide a complete estimate of the overall performance of the fatigued diaphragm.     

Power fatigue of the rat diaphragm muscle.

We hypothesized that decrements in maximum power output (W(max)) of the rat diaphragm (Dia) muscle with repetitive activation are due to a disproportionate reduction in force (force fatigue) compared with a slowing of shortening velocity (velocity fatigue). Segments of midcostal Dia muscle were mounted in vitro (26 degrees C) and stimulated directly at 75 Hz in 400-ms-duration trains repeated each second (duty cycle = 0.4) for 120 s. A novel technique was used to monitor instantaneous reductions in maximum specific force (P(o)) and W(max) during fatigue. During each stimulus train, activation was isometric for the initial 360 ms during which P(o) was measured; the muscle was then allowed to shorten at a constant velocity (30% V(max)) for the final 40 ms, and W(max) was determined. Compared with initial values, after 120 s of repetitive activation, P(o) and W(max) decreased by 75 and 73%, respectively. Maximum shortening velocity was measured in two ways: by extrapolation of the force-velocity relationship (V(max)) and using the slack test [maximum unloaded shortening velocity (V(o))]. After 120 s of repetitive activation, V(max) slowed by 44%, whereas V(o) slowed by 22%. Thus the decrease in W(max) with repetitive activation was dominated by force fatigue, with velocity fatigue playing a secondary role. On the basis of a greater slowing of V(max) vs. V(o), we also conclude that force and power fatigue cannot be attributed simply to the total inactivation of the most fatigable fiber types.     

The effect of shortening history on isometric and dynamic muscle function

Despite numerous reports on isometric force depression, few reports have quantified force depression during active muscle shortening (dynamic force depression). The purpose of this investigation was to determine the influence of shortening history on isometric force following active shortening, force during isokinetic shortening, and velocity during isotonic shortening. The soleus muscles of four cats were subjected to a series of isokinetic contractions at three shortening velocities and isotonic contractions under three loads. Muscle excursions initiated from three different muscle lengths but terminated at a constant length. Isometric force produced subsequent to active shortening, and force or shortening velocity produced at a specific muscle length during shortening, were compared across all three conditions. Results indicated that shortening history altered isometric force by up to 5%, force during isokinetic shortening up to 30% and shortening velocity during isotonic contractions by up to 63%. Furthermore, there was a load by excursion interaction during isotonic contractions such that excursion had the most influence on shortening velocity when the loads were the greatest. There was not a velocity by excursion interaction during isokinetic contractions. Isokinetic and isotonic power–velocity relationships displayed a downward shift in power as excursions increased. Thus, to discuss force depression based on differences in isometric force subsequent to active shortening may underestimate its importance during dynamic contractions. The presence of dynamic force depression should be realized in sport performance, motor control modeling and when controlling paralyzed limbs through artificial stimulation.     

The measurement of force/velocity relationships of fresh and fatigued human adductor pollicis muscle

The purpose of the study was to obtain force/velocity relationships for electrically stimulated (80 Hz) human adductor pollicis muscle (n = 6) and to quantify the effects of fatigue. There are two major problems of studying human muscle in situ; the first is the contribution of the series elastic component, and the second is a loss of force consequent upon the extent of loaded shortening. These problems were tackled in two ways. Records obtained from isokinetic releases from maximal isometric tetani showed a late linear phase of force decline, and this was extrapolated back to the time of release to obtain measures of instantaneous force. This method gave usable data up to velocities of shortening equivalent to approximately one-third of maximal velocity. An alternative procedure (short activation, SA) allowed the muscle to begin shortening when isometric force reached a value that could be sustained during shortening (essentially an isotonic protocol). At low velocities both protocols gave very similar data (r2 = 0.96), but for high velocities only the SA procedure could be used. Results obtained using the SA protocol in fresh muscle were compared to those for muscle that had been fatigued by 25 s of ischaemic isometric contractions, induced by electrical stimulation at the ulnar nerve. Fatigue resulted in a decrease of isometric force [to 69 (3)%], an increase in half-relaxation time [to 431 (10)%], and decreases in maximal shortening velocity [to 77 (8)%] and power [to 42 (5)%]. These are the first data for human skeletal muscle to show convincingly that during acute fatigue, power is reduced as a consequence of both the loss of force and slowing of the contractile speed.     

Effect of denervation on ATP consumption rate of diaphragm muscle fibers.

Denervation (DNV) of rat diaphragm muscle (DIAm) decreases myosin heavy chain (MHC) content in fibers expressing MHC(2X) isoform but not in fibers expressing MHC(slow) and MHC(2A). Since MHC is the site of ATP hydrolysis during muscle contraction, we hypothesized that ATP consumption rate during maximum isometric activation (ATP(iso)) is reduced following unilateral DIAm DNV and that this effect is most pronounced in fibers expressing MHC(2X). In single-type-identified, permeabilized DIAm fibers, ATP(iso) was measured using NADH-linked fluorometry. The maximum velocity of the actomyosin ATPase reaction (V(max) ATPase) was determined using quantitative histochemistry. The effect of DNV on maximum unloaded shortening velocity (V(o)) and cross-bridge cycling rate [estimated from the rate constant for force redevelopment (k(TR)) following quick release and restretch] was also examined. Two weeks after DNV, ATP(iso) was significantly reduced in fibers expressing MHC(2X), but unaffected in fibers expressing MHC(slow) and MHC(2A). This effect of DNV on fibers expressing MHC(2X) persisted even after normalization for DNV-induced reduction in MHC content. With DNV, V(o) and k(TR) were slowed in fibers expressing MHC(2X), consistent with the effect on ATP(iso). The difference between V(max) ATPase and ATP(iso) reflects reserve capacity for ATP consumption, which was reduced across all fibers following DNV; however, this effect was most pronounced in fibers expressing MHC(2X). DNV-induced reductions in ATP(iso) and V(max) ATPase of fibers expressing MHC(2X) reflect the underlying decrease in MHC content, while reduction in ATP(iso) also reflects a slowing of cross-bridge cycling rate.     

Strain-dependent cross-bridge cycle for muscle. II. Steady-state behavior.

Quantitative predictions of steady-state muscle properties from the strain-dependent cross-bridge for muscle are presented. With a stiffness of 5.4 x 10(-4) N/m per head, a throw distance of 11 nm, and three allowed actin sites/head, isometric properties and their dependence on phosphate and nucleotide levels are well described if the tension-generating step occurs before phosphate release. At very low ATP levels, rigorlike states with negative strain are predicted. The rate-limiting step for cycling and ATP consumption is strain-blocked ADP release for isometric and slowly shortening muscle. Under rapid shortening, ATP hydrolysis on detached heads is the rate-limiting step, and the ratio of bound ATP to bound ADP.Pi increases by a factor of 7. At large positive strains, bound heads must be forcibly detached from actin to account for tension in rapid extension, but forced detachment in shortening has no effect without destroying isometric attached states. Strain-blocked phosphate release as proposed produces modest inhibition of the ATPase rate under rapid shortening, sufficient to give a maximum for one actin site per helix turn. Alternative cross-bridge models are discussed in the light of these predictions.     

Mechanical control of the rising phase of contraction of frog skeletal and cardiac muscle

The effect of shortening on contractile activity was studied in experiments in which shortening during the rising phase of an isotonic contraction was suddenly stopped. At the same muscle length and the same time after stimulation the rise in tension was much faster, if preceded by shortening, than during an isometric contraction, demonstrating an increase in contractile activity. In this experiment the rate of tension rise determined in various phases of contraction was proportional to the rate of isotonic shortening at the same time after stimulation. Therefore, the time course of the isotonic rising phase could be derived from the tension rise after shortening. The rate of isotonic shortening was found to be unrelated to the tension generated at various lengths and to correspond closely to the activation process induced by shortening. The length response explains differences between isotonic and isometric contractions with regard to energy release (Fenn effect) and time relations. These results extend previous work which showed that shortening during later phases of a twitch prolongs, while lengthening abbreviates contraction. Thus the length responses, which have been called shortening activation and lengthening deactivation, control activity throughout an isotonic twitch.     

Relative shortening velocity in locomotor muscles: turkey ankle extensors operate at low V/V(max)

The force-velocity properties of skeletal muscle have an important influence on locomotor performance. All skeletal muscles produce less force the faster they shorten and typically develop maximal power at velocities of approximately 30% of maximum shortening velocity (V(max)). We used direct measurements of muscle mechanical function in two ankle extensor muscles of wild turkeys to test the hypothesis that during level running muscles operate at velocities that favor force rather than power. Sonomicrometer measurements of muscle length, tendon strain-gauge measurements of muscle force, and bipolar electromyographs were taken as animals ran over a range of speeds and inclines. These measurements were integrated with previously measured values of muscle V(max) for these muscles to calculate relative shortening velocity (V/V(max)). At all speeds for level running the V/V(max) values of the lateral gastrocnemius and the peroneus longus were low (<0.05), corresponding to the region of the force-velocity relationship where the muscles were capable of producing 90% of peak isometric force but only 35% of peak isotonic power. V/V(max) increased in response to the demand for mechanical power with increases in running incline and decreased to negative values to absorb energy during downhill running. Measurements of integrated electromyograph activity indicated that the volume of muscle required to produce a given force increased from level to uphill running. This observation is consistent with the idea that V/V(max) is an important determinant of locomotor cost because it affects the volume of muscle that must be recruited to support body weight.     

The latch-bridge hypothesis of smooth muscle contraction

In contrast to striated muscle, both normalized force and shortening velocities are regulated functions of cross-bridge phosphorylation in smooth muscle. Physiologically this is manifested as relatively fast rates of contraction associated with transiently high levels of cross-bridge phosphorylation. In sustained contractions, Ca2+, cross-bridge phosphorylation, and ATP consumption rates fall, a phenomenon termed "latch". This review focuses on the Hai and Murphy (1988a) model that predicted the highly non-linear dependence of force on phosphorylation and a directly proportional dependence of shortening velocity on phosphorylation. This model hypothesized that (i) cross-bridge phosphorylation was obligatory for cross-bridge attachment, but also that (ii) dephosphorylation of an attached cross-bridge reduced its detachment rate. The resulting variety of cross-bridge cycles as predicted by the model could explain the observed dependencies of force and velocity on cross-bridge phosphorylation. New evidence supports modifications for more general applicability. First, myosin light chain phosphatase activity is regulated. Activation of myosin phosphatase is best demonstrated with inhibitory regulatory mechanisms acting via nitric oxide. The second modification of the model incorporates cooperativity in cross-bridge attachment to predict improved data on the dependence of force on phosphorylation. The molecular basis for cooperativity is unknown, but may involve thin filament proteins absent in striated muscle.     

Strain-dependent modulation of phosphate transients in rabbit skeletal muscle fibers.

When inorganic phosphate (Pi) is photogenerated from caged Pi during isometric contractions of glycerinated rabbit psoas muscle fibers, the released Pi binds to cross-bridges and reverses the working stroke of cross-bridges. The consequent force decline, the Pi-transient, is exponential and probes the kinetics of the power-stroke and Pi release. During muscle shortening, the fraction of attached cross-bridges and the average strain on them decreases (Ford, L. E., A.F. Huxley, and R.M. Simmons, 1977. Tension responses to sudden length change in stimulated frog muscle fibers near slack length. J. Physiol. (Lond.). 269:441-515; Ford, L. E., A. F. Huxley, and R.M. Simmons, 1985. Tension transients during steady state shortening of frog muscle fibers. J. Physiol. (Lond.). 361:131-150. To learn to what extent the Pi transient is strain dependent, muscle fibers were activated and shortened or lengthened at a fixed velocity during the photogeneration of Pi. The Pi transients observed during changes in muscle length showed three primary characteristics: 1) during shortening the Pi transient rate, Kpi, increased and its amplitude decreased with shortening velocity; Kpi increased linearly with velocity to > 110 s-1 at 0.3 muscle lengths per second (ML/s). 2) At a specific shortening velocity, increases in [Pi] produce increases in Kpi that are nonlinear with [Pi] and approach an asymptote. 3) During forced lengthening Kpi and the amplitude of the Pi transient are little different from the isometric contractions. These data can be approximated by a strain-dependent three-state cross-bridge model. The results show that the power stroke's rate is strain-dependent, and are consistent with biochemical studies indicating that the rate-limiting step at low strains is a transition from a weakly to a strongly bound cross-bridge state.     

Are the maximum shortening velocity and the shape parameter in a Hill-type model of whole muscle related to activation?

Mathematical models of the inter-relationship of muscle force, velocity, and activation are useful in forward dynamic simulations of human movement tasks. The objective of this work was to determine whether the parameters (maximum shortening velocity V(max) and shape parameter k) of a Hill-type muscle model, interrelating muscle force, velocity, and activation, are themselves dependent on the activation. To fulfill this objective, surface EMG signals from four muscles, as well as the kinematics and kinetics of the arm, were recorded from 14 subjects who performed rapid-release elbow extension tasks at 25%, 50%, 75%, and 100% activation (MVC). The experimental elbow flexion angle was tracked by a forward dynamic simulation of the task in which V(max) and k of the triceps brachii were varied at each activation level to minimize the difference between the simulated and experimental elbow flexion angle. Because a preliminary analysis demonstrated no dependency of k on activation, additional simulations were performed with constant k values of 0.15, 0.20, and 0.25. The optimized values of V(max) normalized to the average value within a subject were then regressed onto the activation. Normalized V(max) depended significantly on the activation (p<0.001) for all values of k. Furthermore, the estimated V(max) values were not sensitive to the selected k value. The results support the use of Hill-type models in which V(max) depends on activation in forward dynamic simulations modeling muscles with mixed fiber-type composition recruited in the range of 25-100% activation. The use of more accurate models will lend greater confidence to the results of forward dynamic simulations.