Effects of speed and distance of muscle shortening on force depression during voluntary contractions

The purpose of this study was to determine the influence of speed and distance of muscle shortening on the amount of force depression for voluntary contractions. Two experimental tests were performed. In the first test, subjects performed isometric knee extensor contractions following muscle shortening produced by isokinetic knee extensions over the range 25-50 degrees. In the second test, subjects performed isometric knee extensor contractions following muscle shortening produced by isokinetic knee extensions at two speeds: 20 and 240 degrees /s. Knee extensor moments, surface electromyographical (EMG) signals of quadriceps femoris, and interpolated twitch moments were measured during all contractions and were compared with the corresponding values obtained during purely isometric contractions. Force depression following muscle shortening for the voluntary contractions tested in this study did not depend on the distance or the speed of muscle shortening. These results are in contrast to the corresponding results in the literature obtained using artificial electrical stimulation in which force depression was always found to be directly related to the distance of shortening and inversely related to the speed of shortening. The difference in force depression as a function of the distance and speed of muscle shortening between voluntary and artificial electrical stimulation may be associated with changes in activation following the voluntary shortening contractions, whereas activation is controlled and constant in all artificial stimulation protocols.     

Muscular force production after concentric contraction

The steady-state force following active shortening does not reach the maximum isometric force associated with the final length. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this shortening-induced force depression. The muscles were pre-stimulated at fixed length, shortened and then held isometrically to give maximum post-shortening forces, before de-stimulation. The shortening magnitude was 0.18, 0.36 or 0.72mm (about 2-7% of optimal length), time of shortening was chosen as 0.03, 0.06 and 0.12s, and final length as +0.72, 0 and -0.72mm, related to optimal length. The mechanical work during active shortening was evaluated by integrating the product of force and shortening velocity over the shortening period. The results show a positive correlation between the force depression and the mechanical work, whereas the force depression was not correlated to the velocity of shortening. Depression of the passive force component was also observed following all stimulations. Experiments show that the fully stimulated redevelopment of isometric force following concentric contraction follows a time function similar to the creation of force when isometric muscle is initially stimulated. The conclusion is that the isometric force development after active shortening can be well described by an asymptotic force which is decided by the produced work, and the initial isometric time constant.     

Force depression following muscle shortening in sub-maximal voluntary contractions of human adductor pollicis

Mechanical properties of skeletal muscles are often studied for controlled, electrically induced, maximal, or supra-maximal contractions. However, many mechanical properties, such as the force-length relationship and force enhancement following active muscle stretching, are quite different for maximal and sub-maximal, or electrically induced and voluntary contractions. Force depression, the loss of force observed following active muscle shortening, has been observed and is well documented for electrically induced and maximal voluntary contractions. Since sub-maximal voluntary contractions are arguably the most important for everyday movement analysis and for biomechanical models of skeletal muscle function, it is important to study force depression properties under these conditions. Therefore, the purpose of this study was to examine force depression following sub-maximal, voluntary contractions. Sets of isometric reference and isometric-shortening-isometric test contractions at 30% of maximal voluntary effort were performed with the adductor pollicis muscle. All reference and test contractions were executed by controlling force or activation using a feedback system. Test contractions included adductor pollicis shortening over 10 degrees, 20 degrees, and 30 degrees of thumb adduction. Force depression was assessed by comparing the steady-state isometric forces (activation control) or average electromyograms (EMGs) (force control) following active muscle shortening with those obtained in the corresponding isometric reference contractions. Force was decreased by 20% and average EMG was increased by 18% in the shortening test contractions compared to the isometric reference contractions. Furthermore, force depression was increased with increasing shortening amplitudes, and the relative magnitudes of force depression were similar to those found in electrically stimulated and maximal contractions. We conclude from these results that force depression occurs in sub-maximal voluntary contractions, and that force depression may play a role in the mechanics of everyday movements, and therefore may have to be considered in biomechanical models of human movement.     

Does the speed of shortening affect steady-state force depression in cat soleus muscle?

It has been stated repeatedly for the past 50 years that the steady-state force depression following shortening of an activated muscle depends on the speed of shortening. However, these statements were based on results from experiments in which muscles were shortened at different speeds but identical activation levels. Therefore, the force during shortening was changed in accordance with the force-velocity relationship of muscles: that is, increasing speeds of shortening were associated with decreasing forces, and vice versa. Consequently, it is not possible at present to distinguish whether force depression is caused by the changes in speed, as frequently stated, or the associated changes in force, or both. The purpose of this study was to test if force depression depends on the speed of shortening. We hypothesized that force depression was dependent on the force but not the speed of contraction. Our prediction is that the amount of force depression after shortening contractions at different speeds could be similar if the force during contraction was controlled at a similar level. Cat soleus muscles (n=7) were shortened by 9 or 12 mm at speeds of 3, 9, and 27 mm/s, first with a constant activation during shortening (30Hz), then with activation levels that were reduced (<30Hz) for the slow speeds (3 and 9 mm/s) to approximate the shortening forces of the fast speed contractions (27 mm/s). If done properly, force depression could be precisely matched at the three different speeds, indicating that force depression was related to the force during the shortening contraction but not to the speed. However, in order to match force depression, the forces during shortening had to be systematically greater for the slow compared to the fast speeds of shortening, suggesting that force depression also depends on the level of activation, as force depression at constant activation levels can only be matched if the force during shortening, evaluated by the mechanical work, is identical. Therefore, we conclude that force depression depends on the force and activation level during shortening, but does not depend on the speed of shortening as has been assumed for half a century. These results support, but do not prove, the current hypothesis that force depression is caused by a stress-related cross-bridge inhibition in the actin-myosin overlap zone that is newly formed during muscle shortening.     

Mechanical work as predictor of force enhancement and force depression

The steady-state force following active muscle shortening or stretch differs from the maximum isometric force associated with the final length. This phenomenon proves that the isometric force production is not only dependent on current muscle length and length time derivative, but depends on the preceding contraction history. Isolated extensor digitorum longus and soleus muscles from mice (NMRI strain) were used to investigate the force produced by a muscle, and some parameters hypothetically influencing this history-dependent force modification. The muscles were pre-stimulated at a fixed length, then different stretch/shortening episodes were introduced, whereafter changes of the active force were recorded while the muscles were held isometrically to approach a steady-state force before de-stimulation. The mechanical work during active stretch and shortening was evaluated by integrating the product of force and ramp velocity over the length-varying period. The results show a negative linear correlation between the force modification and the mechanical work produced on or by the muscle, continuous between shortening and stretch. A corresponding modification of the passive force component following each stimulation was also observed. The conclusion is that the isometric force attained after stretch or shortening is well described by an asymptotic force which is determined by the mechanical work.     

Force recovery after activated shortening in whole skeletal muscle: transient and steady-state aspects of force depression.

The depression of isometric force after active shortening is a well-accepted characteristic of skeletal muscle, yet its mechanisms remain unknown. Although traditionally analyzed at steady state, transient phenomena caused, at least in part, by cross-bridge kinetics may provide novel insight into the mechanisms associated with force depression (FD). To identify the transient aspects of FD and its relation to shortening speed, shortening amplitude, and muscle mechanical work, in situ experiments were conducted in soleus muscle-tendon units of anesthetized cats. The period immediately after shortening, in which force recovers toward steady state, was fit by using an exponential recovery function (R2 > 0.99). Statistical analyses revealed that steady-state FD (FD(ss)) increased with shortening amplitude and mechanical work. This FD(ss) increase was always accompanied by a significant decrease in force recovery rate. Furthermore, a significant reduction in stiffness was observed after all activated shortenings, presumably because of a reduced proportion of attached cross bridges. These results were interpreted with respect to the two most prominent proposed mechanisms of force depression: sarcomere length nonuniformity theory (7, 32) and a stress-induced inhibition of cross-bridge binding in the newly formed actin-myosin overlap zone (14, 28). We hypothesized that the latter could describe both steady-state and transient aspects of FD using a single scalar variable, the mechanical work done during shortening. As either excursion (overlap) or force (stress) is increased, mechanical work increases, and cross-bridge attachment would become more inhibited, as supported by this study in which an increase in mechanical work resulted in a slower recovery to a more depressed steady-state force.     

Force depression decays during shortening in the medial gastrocnemius of the rat

Force depression due to shortening of activated skeletal muscles has previously been described to be long lasting during isometric contractions following the shortening. In the present study, using the medial gastrocnemius of the rat, effects of force depression have been made apparent during shortening by computationally partially compensating for the direct effect of shortening velocity due to the tension–velocity relation. Evidence was found for the decay and complete disappearance of force depression already during continuation of the shortening contraction to short muscle lengths.     

Changes in fascicle lengths and pennation angles do not contribute to residual force enhancement/depression in voluntary contractions

Force enhancement following muscle stretching and force depression following muscle shortening are well-accepted properties of skeletal muscle contraction. However, the factors contributing to force enhancement/depression remain a matter of debate. In addition to factors on the fiber or sarcomere level, fiber length and angle of pennation affect the force during voluntary isometric contractions in whole muscles. Therefore, we hypothesized that differences in fiber lengths and angles of pennation between force-enhanced/depressed and reference states may contribute to force enhancement/depression during voluntary contractions. The purpose of this study was to test this hypothesis. Twelve subjects participated in this study, and force enhancement/depression was measured in human tibialis anterior. Fiber lengths and angles of pennation were quantified using ultrasound imaging. Neither fiber lengths nor angles of pennation were found to differ between the isometric reference contractions and any of the force-enhanced or force-depressed conditions. Therefore, we rejected our hypothesis and concluded that differences in fiber lengths or angles of pennation do not contribute to the observed force enhancement/depression in human tibialis anterior, and speculate that this result is likely true for other muscles too.     

History-dependent properties of skeletal muscle myofibrils contracting along the ascending limb of the force–length relationship

There is a history dependence of skeletal muscle contraction: stretching activated muscles induces a long-lasting force enhancement, while shortening activated muscles induces a long-lasting force depression. These history-dependent properties cannot be explained by the current model of muscle contraction, and its mechanism is unknown. The purposes of this study were (i) to evaluate if force enhancement and force depression are present at short lengths (the ascending limb of the force–length (FL) relationship), (ii) to evaluate if the history-dependent properties are associated with sarcomere length (SL) non-uniformity and (iii) to determine the effects of cross-bridge (de)activation on force depression. Rabbit psoas myofibrils were isolated and attached between two microneedles for force measurements. Images of the myofibrils were projected onto a linear photodiode array for measurements of SL. Myofibrils were activated by either Ca²⁺ or MgADP; the latter induces cross-bridge attachment to actin independently of Ca²⁺. Activated myofibrils were subjected to three stretches or shortenings (approx. 4% SL at approx. 0.07 µm s⁻¹ sarcomere⁻¹) along the ascending limb of the FL relationship separated by periods (approx. 5 s) of isometric contraction. Force after stretch was higher than force after shortening at similar SLs. The differences in force could not be explained by SL non-uniformity. The FL relationship produced by Ca²⁺- and MgADP-activated myofibrils were similar in stretch experiments, but after shortening MgADP activation produced forces that were higher than Ca²⁺ activation. Since MgADP induces the formation of strongly bound cross-bridges, this result suggests that force depression following shortening is associated with cross-bridge deactivation.     

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.     

Shortening induced effects on force (re)development in pig urinary smooth muscle

INTRODUCTION: When muscle is allowed to shorten during an active contraction, the maximum force that redevelops after shortening is smaller than the isometric force at the same muscle length without prior shortening. We studied the course of force redevelopment after shortening in smooth muscle to unravel the mechanism responsible for this deactivation. METHOD: In a first series of measurements the shortening velocity was varied resulting in different shortening amplitudes. In a second series, the duration of stimulation before shortening (shortening delay) was varied. In a third series, the stimulation was interrupted for a certain duration immediately after shortening. Force, muscle length and stimulation were continuously recorded. Time constants were calculated to describe the rate of force development before and after shortening. RESULTS: With increasing shortening amplitude and with increasing shortening delay, force redevelopment decreased. Redevelopment increased with an increase in the interruption time. After stimulus interruption force redeveloped mono-exponentially with a time constant similar to that of isometric contractions (approximately 3s). Without the interruption of stimulation, the redevelopment of force immediately after shortening was best described by two time constants; one similar to and one about 3-5 times faster than the isometric time constant. DISCUSSION: Force (re)development is caused by a cascade of events leading to the cycling of cross-bridges. In smooth muscle, isometric force development is described by a time constant of about 3s. Force redevelopment immediately after shortening involves a second process which takes place at a faster rate (time constant about 1s). We assume that this process is faster due to the immediate availability of cytoplasmic calcium released during active shortening. Deactivation presumably is caused by disorganization of filaments during shortening.     

A phenomenological model and validation of shortening-induced force depression during muscle contractions

History-dependent effects on muscle force development following active changes in length have been measured in a number of experimental studies. However, few muscle models have included these properties or examined their impact on force and power output in dynamic cyclic movements. The goal of this study was to develop and validate a modified Hill-type muscle model that includes shortening-induced force depression and assess its influence on locomotor performance. The magnitude of force depression was defined by empirical relationships based on muscle mechanical work. To validate the model, simulations incorporating force depression were developed to emulate single muscle in situ and whole muscle group leg extension experiments. There was excellent agreement between simulation and experimental values, with in situ force patterns closely matching the experimental data (average RMS error <1.5 N) and force depression in the simulated leg extension exercise being similar in magnitude to experimental values (6.0% vs. 6.5%, respectively). To examine the influence of force depression on locomotor performance, simulations of maximum power pedaling with and without force depression were generated. Force depression decreased maximum crank power by 20–40%, depending on the relationship between force depression and muscle work used. These results indicate that force depression has the potential to substantially influence muscle power output in dynamic cyclic movements. However, to fully understand the impact of this phenomenon on human movement, more research is needed to characterize the relationship between force depression and mechanical work in large muscles with different morphologies.     

Effects of cyclic changes in muscle length on force production in in-situ cat soleus.

Muscle shortening and stretch are associated with force depression and force enhancement, respectively. Previously, we have investigated the effect of combined dynamic contractions (i.e. a single shortening-stretch and stretch-shortening cycle) on force production (Herzog and Leonard, 2000). In order to investigate the relationship between force depression and force enhancement systematically, we studied the effects of a single as well as multiple stretch-shortening and shortening-stretch cycles on the ascending limb of the force-length relationship. Furthermore, by systematically varying the speed and magnitude of stretch preceding shortening and the speed and magnitude of shortening preceding stretch, we investigated the influence of these varying contractile conditions on force depression and force enhancement, respectively. Test contractions were performed on cat soleus (n=6) by electrical stimulation using four conceptually different protocols containing a single or repeated stretch-shortening and shortening-stretch cycles. The results of this study showed that: (1) force depression was not influenced by stretch preceding shortening independent of the speed and amount of stretch; (2) force enhancement was influenced in a dose-dependent manner by the amount of shortening preceding stretch but was not affected by the speed of shortening; (3) repeated stretch-shortening (shortening-stretch) cycles showed cumulative effects; (4) the number of shortening steps over a given distance did not influence the amount of force depression. The findings of this study support the idea that the mechanism of force depression associated with muscle shortening is different from that of force enhancement associated with muscle stretch. Furthermore, they support and extend our previous findings that stretch-shortening and shortening-stretch cycles are not commutative.     

Force depression in human quadriceps femoris following voluntary shortening contractions.

The purpose of this study was to investigate whether the isometric muscle force, redeveloped following maximal-effort voluntary shortening contractions in human skeletal muscle, is smaller than the purely isometric muscle force at the corresponding length. Isometric knee extensor moments, surface electromyographic (EMG) signals of quadriceps femoris, and interpolated twitch moments (ITMs) were measured while 10 subjects performed purely isometric knee extensor contractions at a 60 degrees knee angle and isometric knee extensor contractions at a 60 degrees knee angle preceded by maximal-effort voluntary shortening of the quadriceps muscles. It was found that the knee extensor moments were significantly decreased for the isometric-shortening-isometric contractions compared with the isometric contractions for the group as a whole, whereas the corresponding EMG and ITM values were the same. This study is the first to demonstrate force depression following muscle shortening for voluntary contractions. We concluded that force depression following muscle shortening is an actual property of skeletal muscle rather than a stimulation artifact and that force depression during voluntary contraction is not accompanied by systematic changes in muscle activation as evaluated by EMG and ITM.     

The history dependence of force production in mammalian skeletal muscle following stretch-shortening and shortening-stretch cycles

The purpose of this study was to determine the history dependence of force production during and following stretch-shortening and shortening-stretch cycles in mammalian skeletal muscle. Thirty-three different isometric, stretch, shortening, stretch-shortening and shortening-stretch experiments were preformed in cat soleus (n=8) using previously established methods. Stretch-shortening and shortening-stretch cycles are not commutative with respect to the isometric forces following the length changes. Whereas force depression following shortening is virtually unaffected by previous stretching of the muscle, force enhancement following stretch depends in a dose-dependent manner on the amount of muscle shortening preceding the stretch. The history dependence of isometric force following shortening-stretch cycles can conveniently be modelled using an elastic (compressive and tensile) element that engages at the length of muscle activation. Such an "elastic" mechanism has been proposed by Edman and Tsuchiya (1996) (Edman, K.A. P., Tsuchiya, T., 1996. Strain of passive elements during force enhancement by stretch in frog mucle fibres. Journal of Physiology 490. 1, 191-205) based on experimental observations, and has been implemented theoretically in a rheological model of muscle (Forcinito et al., 1997) (Forcinito, M., Epstein, M., Herzog, W., 1997. Theoretical considerations on myofibril stiffness. Biophysics Journal 72, 1278-1286). The history dependence of isometric force following stretch-shortening cycles appears independent of the stretch preceding the shortening, except perhaps, if stretching occurs at very high speeds (i.e. 6-10 times fibre length per second). The results of this study are hard to reconcile with the two major mechanisms associated with history dependence of force production: sarcomere length non-uniformity (Edman et al., 1993) and stress-induced cross-bridge inhibition (Maréchal and Plaghki, 1979) (Maréchal, G., Plaghki, L., 1979. The deficit of the isometric tetanic tension redeveloped after a relase of frog muscle at a constant velocity. Journal of General Physiology 73, 453-467). It appears that studying the history dependence of force production under more functionally relevant conditions than has been done to date may provide new information that contributes to our understanding of possible mechanisms associated with force depression and force enhancement following muscular length changes.     

Shortening-induced depression of voluntary force in unfatigued and fatigued human adductor pollicis muscle.

The goals of this study were to investigate adductor pollicis muscle (n = 7) force depression after maximal electrically stimulated and voluntarily activated isovelocity (19 and 306 degrees /s) shortening contractions and the effects of fatigue. After shortening contractions, redeveloped isometric force was significantly (P < 0.05) depressed relative to isometric force obtained without preceding shortening. For voluntarily and electrically stimulated contractions, relative force deficits respectively were (means +/- SE) 25.0 +/- 3.5 and 26.6 +/- 1.9% (19 degrees /s), 7.8 +/- 2.2 and 11.5 +/- 0.6% (306 degrees /s), and 23.9 +/- 4.4 and 31.6 +/- 4.7% (19 degrees /s fatigued). The relative force deficit was significantly smaller after fast compared with slow shortening contractions, whereas activation manner and fatigue did not significantly affect the deficit. It was concluded that in unfatigued and fatigued muscle the velocity-dependent relative force deficit was similar with maximal voluntary activation and electrical stimulation. These findings have important implications for experimental studies of force-velocity relationships. Moreover, if not accounted for in muscle models, they will contribute to differences observed between the predicted and the actually measured performance during in vivo locomotion.     

Modelling concentric contraction of muscle using an improved cross-bridge model.

Despite its overwhelming acceptance in muscle research, the cross-bridge theory does not account for all phenomena observed during muscular contractions. A phenomenon which has received much attention in the biomechanics literature, but has evaded convincing explanation and is not accounted for in the formulation of the classic cross-bridge theory, is the persistent aftereffects of muscular length changes on force production. For example, following muscle shortening, the isometric force of a muscle is depressed for a long time period ( > 5 s) compared to the corresponding isometric force following no length change. In the present study, the classic cross-bridge model was modified in two ways in an attempt to account for the force depressions following muscle shortening. First, the steady-state force depressions following shortening were described by a single scalar variable: the work performed by the muscle during shortening; and second, the dynamic, history-dependent cross-bridge properties were described using a fading memory function. The proposed model was developed and tested for shortening of the cat soleus at constant speeds ranging from 4 to 32 mm/s, for shortening at changing speeds, and for shortening of different magnitudes ranging from 2 to 10 mm. The history-dependent forces during shortening and the steady-state force depressions following shortening were well captured with the modified cross-bridge model. The present model contains two mathematically simple adaptations to the classic cross-bridge model, and is the first such model to account for the long-lasting force depressions following muscle shortening using a single scalar variable.     

Residual force depression is not abolished following a quick shortening step

Residual force depression is long lasting, but can be abolished instantaneously when a muscle is deactivated just long enough for force to drop to zero. According to the "cross-bridge inhibition theory" of force depression, this result is predicted as the release of stress on actin during deactivation restores the angular distortion of the actin binding sites, thereby establishing conditions identical to those of a purely isometric contraction. According to this theory, force depression should also be abolished if stress on actin is released through a quick shortening step. For slow (4.5mm/s) shortening of cat soleus (n=8), force depression was achieved in all muscles and averaged 5.3% (+/-1.9%) and 5.8% (+/-1.3%) for 9 and 18 mm shortening amplitudes. Following quick shortening (200 mm/s) of 18 mm, there was no statistically significant force depression. However, when slow shortening (4.5mm/s for 9 mm) was followed by quick shortening (200 mm/s for 9 mm) after delays of 0, 1, and 2s, there was a small but significant force depression in all cases averaging 3.2%, 3.7%, and 4.2%, respectively. We conclude from these results that a small amount of force depression persists following stress release caused by quick shortening, and therefore that the cross-bridge inhibition theory cannot be the sole cause of force depression.     

Energy balance studies in frog skeletal muscles shortening at one-half maximal velocity

High-energy phosphate metabolism and energy liberated as heat and work were measured in 3-s tetani of frog sartorius muscle at 0 degree C. Two contraction periods were studied: (a) a 0.35-s period of shortening near half-maximum velocity beginning after 2 s of isometric stimulation, and (b) a 0.65-s isometric period immediately following the shortening. There were no significant changes in levels of ATP, ADP, or AMP in the two contraction periods. The observed changes in inorganic phosphate and creatine levels indicated that the only significant reaction occurring was phosphocreatine splitting. The mean rate of high-energy phosphate splitting during the shortening, 1.60 +/- 0.23 mumol X g-1 X s-1 (n = 24), was about fivefold higher than that in the 1-s period in the isometric tetanus, 0.32 +/- 0.11 mumol X g-1 X s- 1 (n = 17), observed in our previous study. The mean rate in the post- shortening period, 0.46 +/- 0.13 mumol X g-1 X s-1 (n = 17), was not significantly different from that in the 1-s period in the isometric tetanus. A large amount of heat plus work was produced during the shortening period, and this could be accounted for by simultaneous chemical changes. In the post-shortening period, the observed enthalpy was also accounted for by simultaneous chemical reactions. Thus, the present result is in sharp contrast to that obtained from a similar study performed at a shortening at Vmax, where an enthalpy excess was produced during shortening and an enthalpy deficit was produced during the period following the shortening.