Velocity transients and viscoelastic resistance to active shortening in cat papillary muscle.

When isotonic force steps were applied to activated papillary muscles, the velocity was almost never constant. Early rapid shortening associated with the step persisted for 2-7 ms after the step ends. The early rapid shortening is attributed to lightly damped series elastic recoil and velocity transients of the contractile elements. In most steps, the subsequent velocity declines progressively with shortening, and most of the decline in velocity can be accounted for by compression of a viscoelastic element in parallel with the contractile elements. To demonstrate this, the time course of isotonic velocity was compared with a model in which the force-velocity characteristics of the contractile element were assumed to be constant, and the decline in velocity was due to increasing compression of the viscoelastic element. This model predicted the observed results except that the predicted velocities rose progressively above the measured values for steps to light loads applied late in the twitch, and fell below the velocity trace for heavy loads applied early in the twitch. These deviations would occur if rapid shortening caused deactivation late in the twitch, and if activation were rising early in the twitch. A conditioning step applied to the muscle during the rise of force depressed both isometric force and maximum velocity measured at the peak of force; isometric force was more depressed with later conditioning steps than with earlier steps, while maximum velocity was depressed by about the same extent with both early and late steps. This difference between the effects on isometric force and maximum velocity are explained by a combination of deactivation and viscoelastic load.     

A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle.

The responses of muscle to steady and stepwise shortening are simulated with a model in which actin-myosin cross-bridges cycle through two pathways distinct for the attachment-detachment kinetics and for the proportion of energy converted into work. Small step releases and steady shortening at low velocity (high load) favor the cycle implying approximately 5 nm sliding per cross-bridge interaction and approximately 100/s detachment-reattachment process; large step releases and steady shortening at high velocity (low load) favor the cycle implying approximately 10 nm sliding per cross-bridge interaction and approximately 20/s detachment-reattachment process. The model satisfactorily predicts specific mechanical properties of frog skeletal muscle, such as the rate of regeneration of the working stroke as measured by double-step release experiments and the transition to steady state during multiple step releases (staircase shortening). The rate of energy liberation under different mechanical conditions is correctly reproduced by the model. During steady shortening, the relation of energy liberation rate versus shortening speed attains a maximum (approximately 6 times the isometric rate) for shortening velocities lower than half the maximum velocity of shortening and declines for higher velocities. In addition, the model provides a clue for explaining how, in different muscle types, the higher the isometric maintenance heat, the higher the power output during steady shortening.     

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.     

Dynamic and steady state characteristics of the rabbit gastrocnemius muscle determined in series measurements

1. Within the range of the given conditions of measuring static and dynamic properties of the rabbit gastrocnemius muscle the following results were obtained: a) the dependence of the maxima of isotonic shortening upon the relative length of the muscle at constant load is linear; b) the parameters of the non-linear dependence of the passive elastic force of the muscle upon its relative length (measured in series) were identified using asymptotic regression; c) the time course of isotonic contractions (at an interval from 0 to 0.3 s after the beginning of stimulation) could be satisfactorily approximated by responses of a linear system to a step-function; d) the time course of isometric contractions (at an interval from 0 to 0.3 s after the beginning of stimulation) could be closely approximated by responses of a linear system to a step-function. 2. The time constants of isotonic and isometric contractions were determined as the parameters of the corresponding linear systems. 3. The maximum rates of the isometric and isotonic contractions were determined as maxima of the first derivatives of the responses of the corresponding models. 4. The experimental set-up made it possible to compare the values of the parameters concomitantly followed at various muscle lengths and at various loads.     

A simple Hill element-nonlinear spring model of muscle contraction biomechanics

The purpose of this study was to develop a model to predict the mechanical response of muscles during isometric tetanic, afterloaded isotonic and isovelocity shortening contractions. Two versions of the model were developed. Both incorporated a contractile element that obeyed a Hill force-velocity relationship and a series elastic element. In a quadratic spring version, the series elastic element force was represented as proportional to the square of the stretch; in a cubic spring version, it was represented as proportional to the cube of the stretch. Both versions provided closed-form equations for response predictions that involved four independent parameters. Once the four parameters were chosen, each of these responses could be predicted. Model validity was established by comparing predicted and observed responses in slow and fast hindlimb muscles of rodents. Significant model-predicted responses seldom differed by more than 15% from experimental values. The model can provide insights into how changes in individual properties affect the overall mechanical behavior of muscles in a variety of circumstances and reduce the need for collection of experimental data.     

Mechanics of cardiac muscle, based on Huxley's model: Mathematical simulation of isometric contraction

Hill's three-component model (Maxwell model) is used to represent the mechanical property of cardiac muscle. The parallel and series elastic elements of the fibres are described according to their non-linear exponential function; and Huxley's sliding-filaments model, together with the activating role of calcium, is applied to the contractile element.

With this composite model, the following responses can be simulated mathematically: isometric twitch at various muscle lengths, tension-length relationships; isometric contraction during quick stretch; and the Bowditch Treppe and tension velocity relationships of the contractile element.     

Heat changes during transient tension responses to small releases in active frog muscle.

Tension and heat production were measured in frog sartorius muscles in response to small shortening ramps (releases) at high and moderate speed. Transient tension responses to fast releases (0.1 to 0.4 mm in 1 or 4 ms) were similar to the tension transients length-clamped single fibers. Tension time courses during releases at 25 mm/s were like fiber responses calculated from the first two phases of the step responses (Ford et al., 1977). We conclude that similar crossbridge transitions produce tension transients observed in whole muscles and single fibers. Heat was absorbed during rapid tension recovery after fast releases and during the later part of releases at 25 mm/s. Variation of heat absorption with release size was compared with that of crossbridge movement predicted by the Huxley-Simmons hypothesis of force generation (Huxley and Simmons, 1971). Agreement between the two supports the conclusion that heat is absorbed by the crossbridge transitions responsible for rapid tension recovery after release. The results indicate that the entropy change of these transitions is positive.     

Tension responses of frog skeletal muscle to ramp and step length changes

Tension responses to ramp shortening of varying speed in whole muscle or single fibres from the plateau of an isometric tetanus, revealed at least two distinct phases. There was a fast initial drop in tension followed by a change of slope and a definite inflexion on the tension record. As the velocity of the imposed length change was increased, the inflexion point appeared at a lower tension. Similar inflexions were not observed during ramp releases to an elastic band or a segment of semitendinosus tendon. The tension records obtained with moderately fast ramp length changes to contracting muscle reflect the T1 and T2 phases of the tension transients.     

High ionic strength and low pH detain activated skinned rabbit skeletal muscle crossbridges in a low force state

The effects of varying pH and ionic strength on the force-velocity relations and tension transients of skinned rabbit skeletal muscle were studied at 1-2 degrees C. Both decreasing pH from 7.35 to 6.35 and raising ionic strength from 125 to 360 mM reduced isometric force by about half and decreased sarcomere stiffness by about one-fourth, so that the stiffness/force ratio was increased by half. Lowering pH also decreased maximum shortening velocity by approximately 29%, while increasing ionic strength had little effect on velocity. These effects on velocity were correlated with asymmetrical effects on stiffness. The increase in the stiffness/force ratio with both interventions was manifest as a greater relative force change associated with a sarcomere length step. This force difference persisted for a variable time after the step. At the high ionic strength the force difference was long- lasting after stretches but relaxed quickly after releases, suggesting that the structures responsible would not impose much resistance to steady-state shortening. The opposite was found in the low pH experiments. The force difference relaxed quickly after stretches but persisted for a long time after releases. Furthermore, this force difference reached a constant value of approximately 8% of isometric force with intermediate sizes of release, and was not increased with larger releases. This value was almost identical to the value of an internal load that would be sufficient to account for the reduction in maximum velocity seen at the low pH. The results are interpreted as showing that both low pH and high ionic strength inhibit the movement of crossbridges into the force-generating parts of their cycle after they have attached to the actin filaments, with very few other effects on the cycle. The two interventions are different, however, in that detained bridges can be detached readily by shortening when the detention is caused by high ionic strength but not when it is caused by low pH.     

Active state of muscle in iodoacetate rigor

Frog sartorius muscles, equilibrated to 2 x 10(-4)M iodoacetic acid-Ringer's solution and activated by a series of twitches or a long tetanus, perform a rigor response consisting in general of a contractile change which plateaus and is then automatically reversed. Isotonic rigor shortening obeys a force-velocity relation which, with certain differences in value of the constants, accords with Hill's equation for this relation. Changes in rigidity during either isotonic or isometric rigor response show that the capacity of the rigor muscle to bear a load increases more abruptly than the corresponding onset of the ordinarily recorded response, briefly plateaus, and then decays. A quick release of about 1 mm. applied at any instant of isometric rigor output causes the tension to drop instantaneously to zero and then redevelop, the rate of redevelopment varying as does the intensity of the load-bearing capacity. These results demonstrate that rigor mechanical responses result from interaction of a passive, undamped series elastic component, and a contractile component with active state properties like those of normal contraction. Adenosinetriphosphate is known to break down in association with development of the rigor active state. This is discussed in relation to the apparent absence of ATP splitting in normal activation of the contractile component.     

Characterization of cross-bridge elasticity and kinetics of cross-bridge cycling during force development in single smooth muscle cells

Force development in smooth muscle, as in skeletal muscle, is believed to reflect recruitment of force-generating myosin cross-bridges. However, little is known about the events underlying cross-bridge recruitment as the muscle cell approaches peak isometric force and then enters a period of tension maintenance. In the present studies on single smooth muscle cells isolated from the toad (Bufo marinus) stomach muscularis, active muscle stiffness, calculated from the force response to small sinusoidal length changes (0.5% cell length, 250 Hz), was utilized to estimate the relative number of attached cross-bridges. By comparing stiffness during initial force development to stiffness during force redevelopment immediately after a quick release imposed at peak force, we propose that the instantaneous active stiffness of the cell reflects both a linearly elastic cross-bridge element having 1.5 times the compliance of the cross-bridge in frog skeletal muscle and a series elastic component having an exponential length-force relationship. At the onset of force development, the ratio of stiffness to force was 2.5 times greater than at peak isometric force. These data suggest that, upon activation, cross-bridges attach in at least two states (i.e., low-force-producing and high-force-producing) and redistribute to a steady state distribution at peak isometric force. The possibility that the cross-bridge cycling rate was modulated with time was also investigated by analyzing the time course of tension recovery to small, rapid step length changes (0.5% cell length in 2.5 ms) imposed during initial force development, at peak force, and after 15 s of tension maintenance. The rate of tension recovery slowed continuously throughout force development following activation and slowed further as force was maintained. Our results suggest that the kinetics of force production in smooth muscle may involve a redistribution of cross-bridge populations between two attached states and that the average cycling rate of these cross-bridges becomes slower with time during contraction.     

Influence of muscle shortening on the geometry of gastrocnemius medialis muscle of the rat

For static and dynamic conditions muscle geometry of the musculus gastrocnemius medialis of the rat was compared at different muscle lengths. The dynamic conditions differed with respect to isokinetic shortening velocity (25, 50 and 75 mm/s) of the muscle-tendon complex and in constancy of force (isotonic) and velocity (isokinetic) during shortening. Muscle geometry was characterized by fibre length and angle as well as aponeurosis length and angle. At high isokinetic shortening velocities (50 and 75 mm/s) small differences in geometry were found with respect to isometric conditions: aponeurosis lengths differed maximally by -2%, fibre length only showed a significant increase (+3.2%) at the highest shortening velocity. The isotonic condition only yielded significant differences of fibre angle (-4.5%) in comparison with isometric conditions. No significant differences of muscle geometry were found when comparing isotonic with isokinetic conditions of similar shortening velocity. The small differences of geometry between isometric and dynamic conditions are presumably due to the lower muscle force in the dynamic condition and the elastic behaviour of the aponeurosis. It is concluded that, unless very high velocities of shortening are used, the relationship between muscle geometry and muscle length in the isometric condition may be used to describe muscle geometry in the dynamic condition.     

Effects of elastic loading on porcine trachealis muscle mechanics

To shorten in vivo, airway smooth muscle must overcome an elastic load provided by cartilage and lung parenchyma. We examined the effects of linear elastic loads (0.2-80 g/cm) on the active changes in porcine trachealis muscle length and tension in response to electrical field stimulation in vitro. Increasing elastic loads produced an exponential decrease in the shortening and velocity of shortening while causing an increase in tension generation of muscle strips stimulated by electrical field stimulation. Shortening was decreased by 50% at a load of 8 g/cm. At small elastic loads (less than or equal to 1 g/cm) contractile responses approximated isotonic responses (shortening approximately 60% of starting length), whereas at large loads (20 g/cm) responses approximated isometric responses with minimal shortening (20%). We conclude that elastic loading significantly alters the mechanical properties of airway smooth muscle in vitro, effects that are likely relevant to the loads against which the smooth muscle must contract in vivo.     

Influence of viscosity on myocardium mechanical activity: a mathematical model

We have previously proposed and validated a mathematical model of myocardium contraction-relaxation cycle based on current knowledge of regulatory role of Ca2+ and cross-bridge kinetics in cardiac cell. That model did not include viscous elements. Here we propose a modification of the model, in which two viscous elements are added, one in parallel to the contractile element, and one more in parallel to the series elastic element. The modified model allowed us to simulate and explain some subtle experimental data on relaxation velocity in isotonic twitches and on a mismatch between the time course of sarcomere shortening/lengthening and the time course of active force generation in isometric twitches. Model results were compared with experimental data obtained from 28 rat LV papillary muscles contracting and relaxing against various loads. Additional model analysis suggested contribution of viscosity to main inotropic and lusitropic characteristics of myocardium performance.     

The biphasic force-velocity relationship in whole rat skeletal muscle in situ.

Edman has reported that the force-velocity relationship (FVR) departs from Hill's classic hyperbola near 0.80 of measured isometric force (J Physiol 404: 301-321, 1988). The purpose of this study was to investigate the biphasic nature of the FVR in the rested state and after some recovery from fatigue in the rat medial gastrocnemius muscle in situ. Force-velocity characteristics were determined before and during recovery from fatigue induced by intermittent stimulation at 170 Hz for 100 ms each second for 6 min. Force-velocity data were obtained for isotonic contractions with 100 ms of 200-Hz stimulation, including several measurements with loads above 0.80 of measured isometric force. The force-velocity data obtained in this study were fit well by a double-hyperbolic equation. A departure from Hill's classic hyperbola was found at 0.88+/-0.01 of measured isometric force, which is higher than the approximately 0.80 reported by Edman et al. for isolated frog fibers. After 45 min of recovery, maximum shortening velocity was 86+/-2% of prefatigue, but neither curvature nor predicted isometric force was significantly different from prefatigue. The location of the departure from Hill's classic hyperbola was not different after this recovery from the fatiguing contractions. Including an isometric point in the data set will not yield the same values for maximal velocity and the degree of curvature as would be obtained using the double hyperbola approach. Data up to 0.88 of measured isometric force can be used to fit data to the Hill equation.     

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.     

Fatigue and recovery of power and isometric torque following isotonic knee extensions.

The purpose of this study was to assess fatigue and recovery of isotonic power and isometric contractile properties after a series of maximal isotonic contractions. Using a Biodex dynamometer, 13 men [26 yr (SD 3)] performed isotonic [50% of isometric maximal voluntary contraction (MVC) every 1.2 s through 75 degrees range of motion] single-limb knee extensions at the fastest velocity they could achieve until velocity was reduced by 35%. Time to task failure was 38 s, and, compared with baseline, power declined by approximately 42% [741.0 (SD 106.0) vs. 426.5 W (SD 60.3) at task failure], and MVC declined by approximately 26% [267.3 (SD 42.5) vs. 198.4 N.m (SD 45.7) at task failure]. Power recovered by 5 min, whereas MVC did not recover, and at 10 min was only approximately 85% of baseline. Isometric MVC motor unit activation was approximately 95% at rest and was unchanged at task failure (approximately 96%), but a small amount of failure was apparent between 1.5 and 10 min of recovery (approximately 87 to approximately 91%). Half relaxation time measured from a 50-Hz isometric tetanus was significantly prolonged by approximately 33% immediately after task failure but recovered by 1.5 min. A decline in the 10- to 50-Hz ratio of the evoked isometric contractions was observed at 5 and 10 min of recovery, which suggests excitation-contraction coupling impairment. Changes in velocity and half relaxation time during the protocol were strongly and negatively correlated (r = -0.85). Thus mainly peripheral mechanisms were implicated in the substantial depression but relatively fast recovery of isotonic power. Furthermore, isometric muscle contractile properties were related to some, but not all, changes in isotonic function.     

Slowing of velocity during isotonic shortening in single isolated smooth muscle cells. Evidence for an internal load

In single smooth muscle cells, shortening velocity slows continuously during the course of an isotonic (fixed force) contraction (Warshaw, D.M. 1987. J. Gen. Physiol. 89:771-789). To distinguish among several possible explanations for this slowing, single smooth muscle cells were isolated from the gastric muscularis of the toad (Bufo marinus) and attached to an ultrasensitive force transducer and a length displacement device. Cells were stimulated electrically and produced maximum stress of 144 mN/mm2. Cell force was then reduced to and maintained at preset fractions of maximum, and cell shortening was allowed to occur. Cell stiffness, a measure of relative numbers of attached crossbridges, was measured during isotonic shortening by imposing 50-Hz sinusoidal force oscillations. Continuous slowing of shortening velocity was observed during isotonic shortening at all force levels. This slowing was not related to the time after the onset of stimulation or due to reduced isometric force generating capacity. Stiffness did not change significantly over the course of an isotonic shortening response, suggesting that the observed slowing was not the result of reduced numbers of cycling crossbridges. Furthermore, isotonic shortening velocity was better described as a function of the extent of shortening than as a function of the time after the onset of the release. Therefore, we propose that slowing during isotonic shortening in single isolated smooth muscle cells is the result of an internal load that opposes shortening and increases as cell length decreases.     

Isotonic contraction of skinned muscle fibers on a slow time base: effects of ionic strength and calcium

The force development by calcium-activated skinned frog skeletal muscle fibers and the motion on a slow time base after a quick decrease in load were studied at 0-1 degrees C as a function of the ionic strength and the degree of activation. The ionic strength was varied between 50 and 190 mM by adding appropriate concentrations of KCl to the bathing solution. Under these conditions, the fibers could be maximally activated for several cycles at low ionic strength without developing residual tension. We found that the steady isometric force in fully activated fibers linearly decreased when the KCl concentration was increased from 0 to 140 mM. The steady isotonic motion at a given relative load in fully activated fibers was almost the same at KCl concentration greater than or equal to 50 mM. In 0 and 20 mM KCl, the isotonic velocity decreased continuously for more than 300 ms. At a given relative load, the initial velocity of the motion in 0 and 20 mM KCl was about 0.6 and 0.9 times, respectively, that in 140 mM KCl. The initial velocity decreased further when residual tension developed; this observation provides additional evidence that residual tension may reflect the presence of an internal load. The effect of calcium on the motion was examined at 70 mM KCl. In this solution, the motion during the velocity transient at a given relative load appeared to be the same at different levels of activation. The speed of the subsequent motion was almost steady at high calcium levels but decreased continuously in low calcium levels. These results support the idea that at low ionic strength the response of the fiber to calcium is switch-like, but that other factors also affect the contraction mechanism under these conditions.     

Active and passive components in the length-dependent stiffness of tracheal smooth muscle during isotonic shortening.

Contraction of smooth muscle tissue involves interactions between active and passive structures within the cells and in the extracellular matrix. This study focused on a defined mechanical behavior (shortening-dependent stiffness) of canine tracheal smooth muscle tissues to evaluate active and passive contributions to tissue behavior. Two approaches were used. In one, mechanical measurements were made over a range of temperatures to identify those functions whose temperature sensitivity (Q(10)) identified them as either active or passive. Isotonic shortening velocity and rate of isometric force development had high Q(10) values (2.54 and 2.13, respectively); isometric stiffness showed Q(10) values near unity. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged by temperature. In the other approach, muscle contractility was reduced by applying a sudden shortening step during the rise of isometric tension. Control contractions began with the muscle at the stepped length so that properties were measured over comparable length ranges. Under isometric conditions, redeveloped isometric force was reduced, but the ratio between force and stiffness did not change. Under isotonic conditions beginning during force redevelopment at the stepped length, initial shortening velocity and the extent of shortening were reduced, whereas the rate of relaxation was increased. The shape of the curve relating stiffness to isotonic shortening lengths was unchanged, despite the step-induced changes in muscle contractility. Both sets of findings were analyzed in the context of a quasi-structural model describing the shortening-dependent stiffness of lightly loaded tracheal muscle strips.