The effects of muscle stretching and shortening on isometric forces on the descending limb of the force-length relationship

The purpose of this study was to examine the effects of stretching and shortening on the isometric forces at different lengths on the descending limb of the force-length relationship. Cat soleus (N = 10) was stretched and shortened by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these dynamic contractions were compared to the isometric forces at the corresponding muscle lengths. We found a shift of the force-length relationship to greater force values following muscle stretching, and to smaller force values following muscle shortening. Shifts in both directions critically depended on the magnitude of stretching/shortening and the final muscle length. We confirm recent findings that the steady-state isometric force following some stretch conditions clearly exceeded the maximal isometric forces at optimum muscle length, and that force enhancement was associated with an increase in the passive force, i.e., a passive force enhancement. When the passive force enhancement was subtracted from the total force enhancement, forces following stretch were always equal to or smaller than the isometric force at optimum muscle length. Together, these findings led to the conclusions: (a). that force enhancement is composed of an "active and a "passive" component; (b). that the "passive" component of force enhancement allows for forces greater than the maximal isometric forces at the muscle's optimum length; and (c). that force enhancement and force depression are critically affected by muscle length and stretch/shortening amplitude.     

Residual force enhancement exceeds the isometric force at optimal sarcomere length for optimized stretch conditions.

Residual force enhancement (FE) following stretch of an activated muscle is a well accepted property of skeletal muscle contraction. However, the mechanism underlying FE remains unknown. A crucial assumption on which some proposed mechanisms are based is the idea that forces in the enhanced state cannot exceed the steady-state isometric force at a sarcomere length associated with optimal myofilament overlap. Although there are a number of studies in which forces in the enhanced state were compared with the corresponding isometric forces on the plateau of the force-length relationship, these studies either did not show enhanced forces above the plateau or, if they did, they lacked measurements of sarcomere lengths confirming the plateau region. Here, we revisited this question by optimizing stretch conditions and measuring the average sarcomere lengths in isolated fibers, and we found that FE exceeded the maximal isometric reference force obtained at the plateau of the force-length relationship consistently (mean+/-SD: 4.8+/-2.1%) and by up to 10%. When subtracting the passive component of FE from the total FE, the enhanced forces remained greater than the isometric plateau force (mean+/-SD: 4.3+/-2.0%). Calcium-induced increases in passive forces, known to be present in single fibers and myofibrils, are too small to account for the FE observed here. We conclude that FE cannot be explained exclusively with a stretch-induced development of sarcomere length nonuniformities, that FE in single fibers may be associated with the recruitment of additional contractile force, and that isometric steady-state forces in the enhanced state are not uniquely determined by sarcomere lengths.     

Muscular sound and force relationship during isometric contraction in man

The contracting muscle generates a low frequency sound detectable at the belly surface, ranging from 11 to 40 Hz. To study the relationship between the muscular sound and the intensity of the contraction a sound myogram (SMG) was recorded by a contact sensor from the biceps brachii of seven young healthy males performing 4-s isometric contractions from 10% to 100% of the maximal voluntary contraction (MVC), in 10% steps. Simultaneously, the electromyogram (EMG) was recorded as an index of muscle activity. SMG and EMG were integrated by conventional methods (iSMG and iEMG). The relationship between iSMG and iEMG vs MVC% is described by parabolic functions up to 80% and 100% MVC respectively. Beyond 80% MVC the iSMG decreases, being about half of its maximal value at 100% MVC. Our results indicate that the motor unit recruitment and firing rate affect the iSMG and iEMG in the same way up to 80% MVC. From 80% to 100% MVC the high motor units' discharge rate and the muscular stiffness together limit the pressure waves generated by the dimensional changes of the active fibres. The muscular sound seems to reflect the intramuscular visco-elastic characteristics and the motor unit activation pattern of a contracting muscle.     

Nonlinear force-length relationship in the ADP-induced contraction of skeletal myofibrils

The regulatory mechanism of sarcomeric activity has not been fully clarified yet because of its complex and cooperative nature, which involves both Ca²⁺ and cross-bridge binding to the thin filament. To reveal the mechanism of regulation mediated by the cross-bridges, separately from the effect of Ca²⁺, we investigated the force-sarcomere length (SL) relationship in rabbit skeletal myofibrils (a single myofibril or a thin bundle) at SL > 2.2 μm in the absence of Ca²⁺ at various levels of activation by exogenous MgADP (4-20 mM) in the presence of 1 mM MgATP. The individual SLs were measured by phase-contrast microscopy to confirm the homogeneity of the striation pattern of sarcomeres during activation. We found that at partial activation with 4-8 mM MgADP, the developed force nonlinearly depended on the length of overlap between the thick and the thin filaments; that is, contrary to the maximal activation, the maximal active force was generated at shorter overlap. Besides, the active force became larger, whereas this nonlinearity tended to weaken, with either an increase in [MgADP] or the lateral osmotic compression of the myofilament lattice induced by the addition of a macromolecular compound, dextran T-500. The model analysis, which takes into account the [MgADP]-and the lattice-spacing-dependent probability of cross-bridge formation, was successfully applied to account for the force-SL relationship observed at partial activation. These results strongly suggest that the cross-bridge works as a cooperative activator, the function of which is highly sensitive to as little as ≤1 nm changes in the lattice spacing.     

The expression of the skeletal muscle force-length relationship in vivo: A simulation study

The force-length relationship is one of the most important mechanical characteristics of skeletal muscle in humans and animals. For a physiologically realistic joint range of motion and therefore range of muscle fibre lengths only part of the force-length curve may be used in vivo, i.e. only a section of the force-length curve is expressed. A generalised model of a mono-articular muscle-tendon complex was used to examine the effect of various muscle architecture parameters on the expressed section of the force-length relationship for a 90° joint range of motion. The parameters investigated were: the ratio of tendon resting length to muscle fibre optimum length (L_TR:L_F·OPT) (varied from 0.5 to 11.5), the ratio of muscle fibre optimum length to average moment arm (L_F·OPT:r) (varied from 0.5 to 5), the normalised tendon strain at maximum isometric force (c) (varied from 0 to 0.08), the muscle fibre pennation angle (θ) (varied from 0° to 45°) and the joint angle at which the optimum muscle fibre length occurred (φ). The range of values chosen for each parameter was based on values reported in the literature for five human mono-articular muscles with different functional roles. The ratios L_TR:L_F·OPT and L_F·OPT:r were important in determining the amount of variability in the expressed section of the force-length relationship. The modelled muscle operated over only one limb at intermediate values of these two ratios (L_TR:L_F·OPT=5; L_F·OPT:r=3), whether this was the ascending or descending limb was determined by the precise values of the other parameters. It was concluded that inter-individual variability in the expressed section of the force-length relationship is possible, particularly for muscles with intermediate values of L_TR:L_F·OPT and L_F·OPT:r such as the brachialis and vastus lateralis. Understanding the potential for inter-individual variability in the expressed section is important when using muscle models to simulate movement.     

The force-length relationship of a muscle-tendon complex: experimental results and model calculations

Models are useful when studying how architectural and physiological properties of muscle-tendon complexes are related to function, because they allow for the simulation of the behaviour of such complexes during natural movements. In the construction of these models, evaluation of their accuracy is an important step. In the present study, a model was constructed to calculate the isometric force-length relationship of the rat extensor digitorum longus muscle-tendon complex. The model is based on the assumption that a muscle-tendon complex is a collection of independent units, each consisting of a muscle fibre in series with a tendon fibre. By intention, values for model parameters were derived indirectly, using only the measured maximal isometric tetanic force, the distance between origin and insertion at which it occurred (optimum lOI) and an estimate of muscle fibre optimal length. The accuracy of the calculated force-length relationship was subsequently evaluated by comparing it to the relationship measured in isometric tetanic contractions of a real complex in the rat. When the length of distal muscle fibres, measured during isometric contraction at optimal lOI of the whole complex, was used as an estimate for muscle fibre optimal length of all muscle fibre-tendon fibre units in the model, the calculated relationship was too narrow. That is, both on the ascending limb and on the descending limb the calculated tetanic force was lower than the measured tetanic force.(ABSTRACT TRUNCATED AT 250 WORDS)     

Role of signal-dependent noise during maintenance of isometric force

The assumption that signal-dependent noise during isometric force production controls the stabilization of voluntary isometric force is considered. To verify the assumption the trajectory of isometric force is decomposed into voluntary and involuntary components and the mathematical model describing the relationship between them is developed. It is shown that the integral of an involuntary component (signal-dependent noise) plays the role of the controlling parameter realizing the stabilization of a voluntary component. The stabilization is carried out both in the absence and in the presence of visual feedback. Changes of experimental conditions are accompanied by essential changes in the amplitude of the involuntary component oscillations.     

Transducer and base compliance alter the in situ 6 dof force measured from muscle during an isometric contraction in a multi-joint limb

Although musculoskeletal models are commonly used, validating the muscle actions predicted by such models is often difficult. In situ isometric measurements are a possible solution. The base of the skeleton is immobilized and the endpoint of the limb is rigidly attached to a 6-axis force transducer. Individual muscles are stimulated and the resulting forces and moments recorded. Such analyses generally assume idealized conditions. In this study we have developed an analysis taking into account the compliances due to imperfect fixation of the skeleton, imperfect attachment of the force transducer, and extra degrees of freedom (dof) in the joints that sometimes become necessary in fixed end contractions. We use simulations of the rat hindlimb to illustrate the consequences of such compliances. We show that when the limb is overconstrained, i.e., when there are fewer dof within the limb than are restrained by the skeletal fixation, the compliances of the skeletal fixation and of the transducer attachment can significantly affect measured forces and moments. When the limb dofs and restrained dofs are matched, however, the measured forces and moments are independent of these compliances. We also show that this framework can be used to model limb dofs, so that rather than simply omitting dofs in which a limb does not move (e.g., abduction at the knee), the limited motion of the limb in these dofs can be more realistically modeled as a very low compliance. Finally, we discuss the practical implications of these results to experimental measurements of muscle actions.     

Four-component power spectral density model of steady-state isometric force

The aim of this study was to develop and evaluate a model based upon four identified characteristics of the power spectral density associated with isometric force at a range of constant force levels (5–95% maximum voluntary contraction). The characteristics modeled were: (1) a low-frequency resonant peak located at about 1 Hz; (2) a region of 1/f-like fractional Gaussian noise (fGn); (3) the resonant peak in the 8–12 Hz region on the PSD; and (4) Gaussian white noise resulting from a combination of neural as well as equipment noise. When superimposed, these components were used in a direct fit to the isometric force data to generate a linear predictor that resulted in residual values on the order of the white noise present in the original force time series.     

In vivo muscular force analysis during the isometric flexion on a monkey's elbow

An experimental method has been developed to analyse muscular forces and torques in vivo during isometric flexion of the elbow in small monkeys (Macaca fascicularis). A mini-transducer was built with a view to measure forces in situ, without cutting tendons. The positions of tendon insertions were measured on anatomical parts, then integrated in a series of calculations aiming of deducing the lever arms of forces to be included in a torque equilibrium relationship. Muscle activity of the three main flexors was measured for five angles of isometric flexion between 70 degrees and 110 degrees, 0 degrees corresponding to the full extended forearm. The analysed signals were selected using physiological and biomechanical criteria. Then, results corresponding to force participation, and torque participations, were worked out; they are presented and discussed in the present paper.     

The effect of finger extensor mechanism on the flexor force during isometric tasks.

The role of the intrinsic finger flexor muscles was investigated during finger flexion tasks. A suspension system was used to measure isometric finger forces when the point of force application varied along fingers in a distal-proximal direction. Two biomechanical models, with consideration of extensor mechanism Extensor Mechanism Model (EMM) and without consideration of extensor mechanism Flexor Model (FM), were used to calculate forces of extrinsic and intrinsic finger flexors. When the point of force application was at the distal phalanx, the extrinsic flexor muscles flexor digitorum profundus, FDP, and flexor digitorum superficialis, FDS, accounted for over 80% of the summed force of all flexors, and therefore were the major contributors to the joint flexion at the distal interphalangeal (DIP), proximal interphalangeal (PIP), and metacarpophalangeal (MCP) joints. When the point of force application was at the DIP joint, the FDS accounted for more than 70% of the total force of all flexors, and was the major contributor to the PIP and MCP joint flexion. When the force of application was at the PIP joint, the intrinsic muscle group was the major contributor for MCP flexion, accounting for more than 70% of the combined force of all flexors. The results suggest that the effects of the extensor mechanism on the flexors are relatively small when the location of force application is distal to the PIP joint. When the external force is applied proximally to the PIP joint, the extensor mechanism has large influence on force production of all flexors. The current study provides an experimental protocol and biomechanical models that allow estimation of the effects of extensor mechanism on both the extrinsic and intrinsic flexors in various loading conditions, as well as differentiating the contribution of the intrinsic and extrinsic finger flexors during isometric flexion.     

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.     

The minimum number of contractions required to examine the EMG amplitude versus isometric force relationship for the vastus lateralis and vastus medialis

Studies have demonstrated that the electromyographic (EMG) amplitude versus submaximal isometric force relationship is relatively linear. The purpose of this investigation was to determine the minimum number of contractions required to study this relationship. Eighteen men (mean age = 23 years) performed isometric contractions of the leg extensors at 10–90% of the maximum voluntary contraction (MVC) in 10% increments while surface EMG signals were detected from the vastus lateralis and vastus medialis. Linear regression was used to determine the coefficient of determination, slope coefficient, and y-intercept for each muscle and force combination with successively higher levels included in the model (i.e., 10–30%, … 10–90% MVC). For the slope coefficients, there was a main effect for force combination (P < .001). The pairwise comparisons showed there was no difference from 10–60% through 10–90% MVC. For the y-intercepts, there were main effects for both muscle (vastus lateralis [4.3 μV RMS] > vastus medialis [−3.7 μV RMS]; P = .034) and force combination (P < .001), with similar values shown from 10–50% through 10–90% MVC. The linearity of the absolute EMG amplitude versus isometric force relationship for the vastus lateralis and vastus medialis suggests that investigators may exclude high force contractions from their testing protocol.     

Effect of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit

Findings from animal experiments are sometimes contradictory to the idea that the tendon structure is a simple elastic spring in series with muscle fibers, and suggest influence of muscle contraction on the tendon mechanical properties. The purpose of the present study was to investigate the influence of muscle contraction levels on the force-length relationship of the human Achilles tendon during lengthening of the triceps surae muscle-tendon unit. For seven subjects, ankle dorsiflexion was performed without (passive condition) and with contraction of plantar flexor muscles (eccentric conditions, at 3 contraction levels) on an isokinetic dynamometer. Deformation of the Achilles tendon during each trial was measured using ultrasonography. The Achilles tendon force corresponding to the tendon elongation of 10mm in the passive condition was significantly smaller than those in the eccentric conditions (p<0.05 or p<0.01). Within the eccentric conditions, the Achilles tendon force corresponding to the tendon elongation of 10mm was significantly greater in the maximal contraction level than those in submaximal eccentric conditions (p<0.05 or p<0.01). In addition, the tendon stiffness was greater in higher contraction levels (p<0.05 or p<0.01). Present results suggest that the human tendon structure is not a simple elastic spring in series with muscle fibers.     

Effects of palmatine on isometric force and intracellular calcium levels of arterial smooth muscle

The effects of palmatine on isometric force and intracellular free calcium levels ([Ca2+]i) were determined in isolated rat arterial strips. Palmatine dose-dependently relaxed the contractile responses stimulated by phenylephrine (PE) in aortic strips. In contrast, it only partially relaxed aortic strips contracted by 51 mM KCl. Pretreatment with palmatine shifted the dose-response curves of PE both rightwards and downwards in a dose-dependent manner. When Ca2+-free solution and re-addition of Ca2+ were applied to assess PE-induced phasic and tonic contractions, palmatine was found to be effective in inhibiting both contractions. The effects of palmatine on intracellular calcium levels were measured with the bioluminescent calcium indicator aequorin in rat tail artery strips. Palmatine caused a concomitant, dose-dependent decrease in PE-activated isometric force and [Ca2+]i, resulting in small changes in the [Ca2+]i-force relationship. These results suggest that vasodilatory effect of palmatine was mediated by reducing [Ca2+]i as well as affecting [Ca2+]i sensitivity of the contractile apparatus. Palmatine-induced [Ca2+]i decreases appeared to involve decreases in both Ca2+ release from intracellular stores and Ca2+ influx through calcium channels.     

Measurement of the isometric dorsiflexion and plantar flexion force in the ankle joint]

This article describes an easy to use test equipment for measuring the isometric force in the ankle joints in dorsiflexion and plantar flexion. The combination of the test equipment for measuring the voluntary maximal isometric muscle force in the ankle joint, the surface electromyograms and the motion analysis of the measured leg allow an objective comparison of the strength of the muscular force between the left and right leg. It might be also used as a control setup during rehabilitation after surgical treatment or injuries.     

Influence of bite force on jaw muscle activity ratios in subject-controlled unilateral isometric biting

Ratios of muscle activities in unilateral isometric biting are assumed to provide information on strategies of muscle activation independently from bite force. If valid, this assumption would facilitate experiments as it would justify subject-control instead of transducer-based force control in biting studies. As force independence of ratios is controversial, we tested whether activity ratios are associated with bite force and whether this could affect findings based on subject-controlled force. In 52 subjects, bite force and bilateral masseter and temporalis electromyograms were recorded during unilateral biting on a transducer with varying force levels and with uniform subject-controlled force. Working/balancing and temporalis/masseter ratios of activity peaks were related to bite force peaks. Activity ratios were significantly but weakly correlated with the bite force. The subject-controlled force varied within ±25% around the prescribed force in 95% of all bites. This scatter could cause a variation of group mean activity ratios of at most ±6% because of the weak correlation between bite force and ratios. As this small variation is negligible in most cases, subject-control of bite force can be considered an appropriate method to obtain group means of relative muscle activation in particular when force control with transducers is not feasible.     

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.