Nonlinear summation of force in cat soleus muscle results primarily from stretch of the common-elastic elements

Cadence Paradox in Cycling-Part 2: Theory and Simulation of Maximal Lactate Steady State and Carbohydrate Utilization Dependent on Cycling Cadence

PURPOSE

To develop and evaluate a theory on the frequent observation that cyclists prefer cadences (RPMs) higher than those considered most economical at submaximal exercise intensities via modeling and simulation of its mathematical description.

METHODS

The theory combines the parabolic power-to-velocity (v) relationship, where v is defined by crank length, RPM-dependent ankle velocity, and gear ratio, RPM effects on the maximal lactate steady state (MLSS), and lactate-dependent carbohydrate oxidation (CHO). It was tested against recent experimental results of 12 healthy male recreational cyclists determining the v-dependent peak oxygen uptake (VO2PEAKv), MLSS (MLSSv), corresponding power output (PMLSSv), oxygen uptake at PMLSSv (VO2MLSSv), and CHOMLSSv-management at 100 versus 50 per minute, respectively. Maximum RPM (RPMMAX) attained at minimized pedal torque was measured. RPM-specific maximum sprint power output (PMAXv) was estimated at RPMs of 100 and 50, respectively.

RESULTS

Modeling identified that MLSSv and PMLSSv related to PMAXv (IPMLSSv) promote CHO and that VO2MLSSv related to VO2PEAKv inhibits CHO. It shows that cycling at higher RPM reduces IPMLSSv. It suggests that high cycling RPMs minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX.

CONCLUSIONS

The present theory-guided modeling approach is exclusively based on data routinely measured in high-performance testing. It implies a higher performance reserve above IPMLSSv at higher RPM. Cyclists may prefer high cycling RPMs because they appear to minimize differences in the reliance on CHO at MLSSv between athletes with high versus low RPMMAX.

Skeletal muscle models composed of motor units: A review

The mathematical muscle models should include several aspects of muscle structure and physiology. First, muscle force is the sum of forces of multiple motor units (MUs), which have different contractile properties and play different roles in generating muscle force. Second, whole muscle activity is an effect of net excitatory inputs to a pool of motoneurons innervating the muscle, which have different excitability, influencing MU recruitment. In this review, we compare various methods for modeling MU twitch and tetanic forces and then discuss muscle models composed of different MU types and number. We first present four different analytical functions used for twitch modeling and show limitations related to the number of twitch describing parameters. We also show that a nonlinear summation of twitches should be considered in modeling tetanic contractions. We then compare different muscle models, most of which are variations of Fuglevand's model, adopting a common drive hypothesis and the size principle. We pay attention to integrating previously developed models into a consensus model based on physiological data from in vivo experiments on the rat medial gastrocnemius muscle and its respective motoneurons. Finally, we discuss the shortcomings of existing models and potential applications for studying MU synchronization, potentiation, and fatigue.

Transitory force decrease following a sudden reduction in stimulation frequency in motor units of rat medial gastrocnemius

Effects of a sudden decrease in the stimulation frequency for motor unit force were studied in rat medial gastrocnemius. For 161 functionally isolated single motor units of three types (S, FR, FF), unfused tetanic contractions were evoked by three-phase trains of stimuli (low-high-low frequency). The course of the tetanus at the onset of the third phase of the force recording was analyzed in tetani with variable fusion degree. For 78 units within the third phase of tetanus, a transitory force decrease to a level lower than in the first phase (identical frequency), was observed. This phenomenon was more frequent for fast fatigue resistant (65.9%) than for fast fatigable and slow motor units (27.1% and 35.5%, respectively). Moreover, the force decrease was strongest for fast resistant motor units (up to 36.5%) and when contractions evoked at variable frequencies of stimulation were compared, the highest amplitudes of the studied force decrease were noted for middle-fused tetani (0.50-0.90). A new phenomenon of transitory force decrease in tetanic contractions of motor units with a decrease in stimulation frequency was found. Most probably, the phenomenon is dependent on disturbances in the force transmission by collagen surrounding active muscles fibers.

Longitudinal and transversal displacements between triceps surae muscles during locomotion of the rat

The functional consequences of differential muscle activation and contractile behavior between mechanically coupled synergists are still poorly understood. Even though synergistic muscles exert similar mechanical effects at the joint they span, differences in the anatomy, morphology and neural drive may lead to non-uniform contractile conditions. This study aimed to investigate the patterns of activation and contractile behavior of triceps surae muscles, to understand how these contribute to the relative displacement between the one-joint soleus (SO) and two-joint lateral gastrocnemius (LG) muscle bellies and their distal tendons during locomotion in the rat. In seven rats, muscle belly lengths and muscle activation during level and upslope trotting were measured by sonomicrometry crystals and electromyographic electrodes chronically implanted in the SO and LG. Length changes of muscle–tendon units (MTUs) and tendon fascicles were estimated based on joint kinematics and muscle belly lengths. Distances between implanted crystals were further used to assess longitudinal and transversal deformations of the intermuscular volume between the SO and LG. For both slope conditions, we observed differential timing of muscle activation as well as substantial differences in contraction speeds between muscle bellies (maximal relative speed 55.9 mm s−1). Muscle lengths and velocities did not differ significantly between level and upslope locomotion, only EMG amplitude of the LG was affected by slope. Relative displacements between SO and LG MTUs were found in both longitudinal and transversal directions, yielding an estimated maximal length change difference of 2.0 mm between their distal tendons. Such relative displacements may have implications for the force exchanged via intermuscular and intertendinous pathways.

Morphometric properties and innervation of muscle compartments in rat medial gastrocnemius

The rat medial gastrocnemius (MG) muscle is composed of the proximal and distal compartments. In this study, morphometric properties of the compartments and their muscle fibres at five levels of the muscle length and the innervation pattern of these compartments from lumbar segments were investigated. The size and number of muscle fibres in the compartments were different. The proximal compartment at the largest cross section (25% of the muscle length) had 34% smaller cross-sectional area but contained a slightly higher number of muscle fibres (max. 5521 vs. 5360) in comparison to data for the distal compartment which had the largest cross-sectional area at 40% of the muscle length. The muscle fibre diameters revealed a clear tendency within both compartments to increase along the muscle (from the knee to the Achilles tendon) up to 46.9 μm in the proximal compartment and 58.4 μm in the distal one. The maximal tetanic and single twitch force evoked by stimulation of L4, L5, and L6 ventral roots in whole muscle and compartments were measured. The MG was innervated from L4 and L5, only L5, or L5 and L6 segments. The proximal compartment was innervated by axons from L5 or L5 and L4, and the distal one from L5, L5 and L6, or L5 and L4 segments. The forces produced by the compartments summed non-linearly. The tetanic forces of the proximal and distal compartments amounted to 2.24 and 4.86 N, respectively, and their algebraic sums were 11% higher than the whole muscle force (6.37 N).

Additional in-series compliance reduces muscle force summation and alters the time course of force relaxation during fixed-end contractions

There are high mechanical demands placed on skeletal muscles in movements requiring rapid acceleration of the body or its limbs. Tendons are responsible for transmitting muscle forces, but, because of their elasticity, can manipulate the mechanics of the internal contractile apparatus. Shortening of the contractile apparatus against the stretch of tendon affects force generation according to known mechanical properties; however, the extent to which differences in tendon compliance alter force development in response to a burst of electrical impulses is unclear. To establish the influence of series compliance on force summation, we studied electrically evoked doublet contractions in the cane toad peroneus muscle in the presence and absence of a compliant artificial tendon. Additional series compliance reduced tetanic force by two-thirds, a finding predicted based on the force-length property of skeletal muscle. Doublet force and force-time integral expressed relative to the twitch were also reduced by additional series compliance. Active shortening over a larger range of the ascending limb of the force-length curve and at a higher velocity, leading to a progressive reduction in force-generating potential, could be responsible. Muscle-tendon interaction may also explain the accelerated time course of force relaxation in the presence of additional compliance. Our findings suggest that a compliant tendon limits force summation under constant-length conditions. However, high series compliance can be mechanically advantageous when a muscle-tendon unit is actively stretched, permitting muscle fibres to generate force almost isometrically, as shown during stretch-shorten cycles in locomotor activities. Restricting active shortening would likely favour rapid force development.

A lumped stiffness model of intermuscular and extramuscular myofascial pathways of force transmission

Mechanical behavior of skeletal muscles is commonly modeled under the assumption of mechanical independence between individual muscles within a muscle group. Epimuscular myofascial force transmission via the connective tissue network surrounding a muscle challenges this assumption as it alters the force distributed to the tendons of individual muscles. This study aimed to derive a lumped estimate of stiffness of the intermuscular and extramuscular connective tissues and to assess changes in such stiffness in response to a manipulation of the interface between adjacent muscles. Based on in situ measurements of force transmission in the rat plantar flexors, before and after resection of their connective tissue network, a nonlinear estimate of epimuscular myofascial stiffness was quantified and included in a multi-muscle model with lumped parameters which allows for force transmission depending on the relative position between the muscles in the group. Such stiffness estimate was assessed for a group with normal intermuscular connective tissues and for a group with increased connectivity, mimicking scar tissue development. The model was able to successfully predict the amount of epimuscular force transmission for different experimental conditions than those used to obtain the model parameters. The proposed nonlinear stiffness estimates of epimuscular pathways could be integrated in larger musculoskeletal models, to provide more accurate predictions of force when effects of mechanical interaction or altered epimuscular connections, e.g. after surgery or injury, are substantial.

Summation of slow motor unit forces at constant and variable interpulse intervals in rat soleus muscle

Effects of the summation of forces generated by functionally isolated slow-twitch motor units (MU) of the rat soleus muscle were examined in this study. Initially, the twitch, fused tetanic and unfused tetanic contractions evoked by trains of stimuli at variable interpulse intervals were recorded for each MU. Then, two, three or four MUs were co-activated, and the recorded forces were compared to the algebraic sum of the forces of individual MUs. The mean cumulative force of twitches and the mean cumulative force of fused tetani were not statistically different from the respective algebraic sums of forces, which revealed a high degree of linearity in the summation. However, relaxation of the recorded tetanic contractions (either fused or unfused) was faster than that predicted by the linear summation of individual contractions. Moreover, for twitch and tetanic contractions, a tendency to shorten relaxation with an increasing number of co-active MUs was noted. The results indicate that forces of rat soleus slow MUs sum up more linearly than in the respective cat muscle as well as more linearly than for fast MUs in the medial gastrocnemius muscle.

Effects of series elastic compliance on muscle force summation and the rate of force rise

Compliant tendons permit mechanically unfavourable fascicle dynamics during fixed-end contractions. The purpose of this study was to reduce the effective compliance of tendon and investigate how small reductions in active shortening affect twitch kinetics and contractile performance in response to a second stimulus. The series elastic element (SEE) of the human triceps surae (N=15) was effectively stiffened by applying a 55 ms rotation to the ankle, through a range of 5°, at the onset of twitch and doublet [interstimulus interval (ISI) of 80 ms] stimulation. Ultrasonography was employed to quantify lateral gastrocnemius and soleus fascicle lengths. Rotation increased twitch torque (40-75%), rate of torque development (RTD, 124-154%) and torque-time integral (TTI, 70-110%) relative to constant-length contractions at the initial and final joint positions, yet caused only modest reductions in shortening amplitude and velocity. The torque contribution of the second pulse increased when stimulation was preceded by rotation, a finding unable to be explained on the basis of fascicle length or SEE stiffness during contraction post-rotation. A further increase in torque contribution was not demonstrated, nor an increase in doublet TTI, when the second pulse was delivered during rotation and shortly after the initial pulse (ISI of 10 ms). The depressant effect of active shortening on subsequent torque generation suggests that compliant tendons, by affording large length changes, may limit torque summation. Our findings indicate that changes in tendon compliance shown to occur in response to resistance training or unloading are likely sufficient to considerably alter contractile performance, particularly maximal RTD.

Significant mechanical interactions at physiological lengths and relative positions of rat plantar flexors

In situ studies involving supraphysiological muscle lengths and relative positions have shown that connective tissue linkages connecting adjacent muscles can transmit substantial forces, but the physiological significance is still subject to debate. The present study investigates effects of such epimuscular myofascial force transmission in the rat calf muscles. Unlike previous approaches, we quantified the mechanical interaction between the soleus (SO) and the lateral gastrocnemius and plantaris complex (LG+PL) applying a set of muscle lengths and relative positions corresponding to the range of knee and ankle angles occurring during normal movements. In nine deeply anesthetized Wistar rats, the superficial posterior crural compartment was exposed, and distal and proximal tendons of LG+PL and the distal SO tendon were severed and connected to force transducers. The target muscles were excited simultaneously. We found that SO active and passive tendon force was substantially affected by proximally lengthening of LG+PL mimicking knee extension (10% and 0.8% of maximal active SO force, respectively; P < 0.05). Moreover, SO relative position significantly changed the LG+PL length-force relationship, resulting in nonunique values for passive slack-length and optimum-length estimates. We conclude that also, for physiological muscle conditions, isometric force of rat triceps surae muscles is determined by its muscle-tendon unit length as well as by the length and relative position of its synergists. This has implications for understanding the neuromechanics of skeletal muscle in normal and pathological conditions, as well as for studies relying on the assumption that muscles act as independent force actuators.

Three-dimensional ankle moments and nonlinear summation of rat triceps surae muscles

The Achilles tendon and epimuscular connective tissues mechanically link the triceps surae muscles. These pathways may cause joint moments exerted by each muscle individually not to sum linearly, both in magnitude and direction. The aims were (i) to assess effects of sagittal plane ankle angle (varied between 150° and 70°) on isometric ankle moments, in both magnitude and direction, exerted by active rat triceps surae muscles, (ii) to assess ankle moment summation between those muscles for a range of ankle angles and (iii) to assess effects of sagittal plane ankle angle and muscle activation on Achilles tendon length. At each ankle angle, soleus (SO) and gastrocnemius (GA) muscles were first excited separately to assess ankle-angle moment characteristics and subsequently both muscles were excited simultaneously to investigate moment summation. The magnitude of ankle moment exerted by SO and GA, the SO direction in the transverse and sagittal planes, and the GA direction in the transverse plane were significantly affected by ankle angle. SO moment direction in the frontal and sagittal planes were significantly different from that of GA. Nonlinear magnitude summation varied between 0.6±2.9% and −3.6±2.9%, while the nonlinear direction summation varied between 0.3±0.4° and −0.4±0.7° in the transverse plane, between 0.5±0.4° and 0.1±0.4° in the frontal plane, and between 3.0±7.9° and 0.3±2.3° in the sagittal plane. Changes in tendon length caused by SO contraction were significantly lower than those during contraction of GA and GA+SO simultaneously. Thus, moments exerted by GA and SO sum nonlinearly both in the magnitude and direction. The limited degree of nonlinear summation may be explained by different mechanisms acting in opposite directions.

The effect of fast and slow motor unit activation on whole-muscle mechanical performance: the size principle may not pose a mechanical paradox

The output of skeletal muscle can be varied by selectively recruiting different motor units. However, our knowledge of muscle function is largely derived from muscle in which all motor units are activated. This discrepancy may limit our understanding of in vivo muscle function. Hence, this study aimed to characterize the mechanical properties of muscle with different motor unit activation. We determined the isometric properties and isotonic force-velocity relationship of rat plantaris muscles in situ with all of the muscle active, 30% of the muscle containing predominately slower motor units active or 20% of the muscle containing predominately faster motor units active. There was a significant effect of active motor unit type on isometric force rise time (p < 0.001) and the force-velocity relationship (p < 0.001). Surprisingly, force rise time was longer and maximum shortening velocity higher when all motor units were active than when either fast or slow motor units were selectively activated. We propose this is due to the greater relative effects of factors such as series compliance and muscle resistance to shortening during sub-maximal contractions. The findings presented here suggest that recruitment according to the size principle, where slow motor units are activated first and faster ones recruited as demand increases, may not pose a mechanical paradox, as has been previously suggested.

Motor unit

Movement is accomplished by the controlled activation of motor unit populations. Our understanding of motor unit physiology has been derived from experimental work on the properties of single motor units and from computational studies that have integrated the experimental observations into the function of motor unit populations. The article provides brief descriptions of motor unit anatomy and muscle unit properties, with more substantial reviews of motoneuron properties, motor unit recruitment and rate modulation when humans perform voluntary contractions, and the function of an entire motor unit pool. The article emphasizes the advances in knowledge on the cellular and molecular mechanisms underlying the neuromodulation of motoneuron activity and attempts to explain the discharge characteristics of human motor units in terms of these principles. A major finding from this work has been the critical role of descending pathways from the brainstem in modulating the properties and activity of spinal motoneurons. Progress has been substantial, but significant gaps in knowledge remain.

Non-invasive method for selection of electrodes and stimulus parameters for FES applications with intrafascicular arrays

High-channel-count intrafascicular electrode arrays provide comprehensive and selective access to the peripheral nervous system. One practical difficulty in using several electrode arrays to evoke coordinated movements in paralyzed limbs is the identification of the appropriate stimulation channels and stimulus parameters to evoke desired movements. Here we present the use of a six degree-of-freedom load cell placed under the foot of a feline to characterize the muscle activation produced by three 100-electrode Utah Slanted Electrode Arrays (USEAs) implanted into the femoral nerves, sciatic nerves, and muscular branches of the sciatic nerves of three cats. Intramuscular stimulation was used to identify the endpoint force directions produced by 15 muscles of the hind limb, and these directions were used to classify the forces produced by each intrafascicular USEA electrode as flexion or extension. For 451 USEA electrodes, stimulus intensities for threshold and saturation muscle forces were identified, and the 3D direction and linearity of the force recruitment curves were determined. Further, motor unit excitation independence for 198 electrode pairs was measured using the refractory technique. This study demonstrates the utility of 3D endpoint force monitoring as a simple and non-invasive metric for characterizing the muscle-activation properties of hundreds of implanted peripheral nerve electrodes, allowing for electrode and parameter selection for neuroprosthetic applications.

Multiple-input single-output closed-loop isometric force control using asynchronous intrafascicular multi-electrode stimulation

Although asynchronous intrafascicular multi-electrode stimulation (IFMS) can evoke fatigue-resistant muscle force, a priori determination of the necessary stimulation parameters for precise force production is not possible. This paper presents a proportionally-modulated, multiple-input single-output (MISO) controller that was designed and experimentally validated for real-time, closed-loop force-feedback control of asynchronous IFMS. Experiments were conducted on anesthetized felines with a Utah Slanted Electrode Array implanted in the sciatic nerve, either acutely or chronically ( n = 1 for each). Isometric forces were evoked in plantar-flexor muscles, and target forces consisted of up to 7 min of step, sinusoidal, and more complex time-varying trajectories. The controller was successful in evoking steps in force with time-to-peak of less than 0.45 s, steady-state ripple of less than 7% of the mean steady-state force, and near-zero steady-state error even in the presence of muscle fatigue, but with transient overshoot of near 20%. The controller was also successful in evoking target sinusoidal and complex time-varying force trajectories with amplitude error of less than 0.5 N and time delay of approximately 300 ms. This MISO control strategy can potentially be used to develop closed-loop asynchronous IFMS controllers for a wide variety of multi-electrode stimulation applications to restore lost motor function.

Force transmission between synergistic skeletal muscles through connective tissue linkages

The classic view of skeletal muscle is that force is generated within its muscle fibers and then directly transmitted in-series, usually via tendon, onto the skeleton. In contrast, recent results suggest that muscles are mechanically connected to surrounding structures and cannot be considered as independent actuators. This article will review experiments on mechanical interactions between muscles mediated by such epimuscular myofascial force transmission in physiological and pathological muscle conditions. In a reduced preparation, involving supraphysiological muscle conditions, it is shown that connective tissues surrounding muscles are capable of transmitting substantial force. In more physiologically relevant conditions of intact muscles, however, it appears that the role of this myofascial pathway is small. In addition, it is hypothesized that connective tissues can serve as a safety net for traumatic events in muscle or tendon. Future studies are needed to investigate the importance of intermuscular force transmission during movement in health and disease.

Summation of motor unit forces in rat medial gastrocnemius muscle

The summation of contractile forces of motor units (MUs) was analyzed by comparing the recorded force during parallel stimulation of two and four individual MUs or four groups of MUs to the algebraic sum of their individual forces. Contractions of functionally-isolated single MUs of the medial gastrocnemius muscle were evoked by electrical stimulation of thin filaments of the split L5 or L4 ventral roots of spinal nerves. Additionally, contractions of large groups of MUs were evoked by stimuli delivered to four parts of the divided L5 ventral root. Single twitches, 40Hz unfused tetani, and 150Hz fused maximum tetani were recorded. In these experimental situations the summation was more effective for unfused tetani than for twitches or maximum tetani. The results obtained for pairs of MUs were highly variable (more- or less-than-linear summation), but coactivation of more units led to progressively weaker effects of summation, which were usually less-than-linear in comparison to the algebraic sums of the individual forces. The variability of the results highlights the importance of the structure of the muscle and the architecture of its MUs. Moreover, the simultaneous activity of fast and slow MUs was considerably more effective than that of two fast units.

Distinct muscle fascicle length changes in feline medial gastrocnemius and soleus muscles during slope walking

On the basis of differences in physiology, e.g., histochemical properties and spindle density, and the structural design of the cat soleus (SO) and medial gastrocnemius (MG) muscles, we hypothesized that 1) fascicle length changes during overground walking would be both muscle and slope dependent, which would have implications for the muscles' force output as well as sensory function, and that 2) muscle-tendon unit (MTU) and fascicle length changes would be different, in which case MTU length could not be used as an indicator of muscle spindle strain. To test these hypotheses, we quantified muscle fascicle length changes and compared them with length changes of the whole MTU in the SO and MG during overground walking at various slopes (0, +/- 25, +/- 50, +75, and +100%). The SO and MG were surgically instrumented with sonomicrometry crystals and fine-wire electromyogram electrodes to measure changes in muscle fascicle length and muscle activity, respectively. MTU lengths were calculated using recorded ankle and knee joint angles and a geometric model of the hindlimb. The resultant joint moments were calculated using inverse dynamics analysis to infer muscle loading. It was found that although MTU length and velocity profiles of the SO and MG appeared similar, length changes and velocities of muscle fascicles were substantially different between the two muscles. Fascicle length changes of both SO and MG were significantly affected by slope intensity acting eccentrically in downslope walking (-25 to -50%) and concentrically in upslope walking (+25 to +100%). The differences in MTU and fascicle behaviors in both the SO and MG muscles during slope walking were explained by the three distinct features of these muscles: 1) the number of joints spanned, 2) the pennation angle, and 3) the in-series elastic component. It was further suggested that the potential role of length feedback from muscle spindles is both task and muscle dependent.

Are skeletal muscles independent actuators? Force transmission from soleus muscle in the cat

It is unclear if skeletal muscles act mechanically as independent actuators. The purpose of the present study was to investigate force transmission from soleus (SO) muscle for physiological lengths as well as relative positions in the intact cat hindlimb. We hypothesized that force transmission from SO fibers will be affected by length changes of its two-joint synergists. Ankle plantar flexor moment on excitation of the SO was measured for various knee angles (70–140°). This involved substantial length changes of gastrocnemius and plantaris muscles. Ankle angle was kept constant (80°-90°). However, SO ankle moment was not significantly affected by changes in knee angle; neither were half-relaxation time and the maximal rate of relaxation ( P > 0.05). Following tenotomy, SO ankle moment decreased substantially (55 ± 16%) but did not reach zero, indicating force transmission via connective tissues to the Achilles tendon (i.e., epimuscular myofascial force transmission). During contraction SO muscle shortened to a much greater extent than in the intact case (16.0 ± 0.6 vs. 1.0 ± 0.1 mm), which resulted in a major position shift relative to its synergists. If the SO was moved back to its position corresponding to the intact condition, SO ankle moment approached zero, and most muscle force was exerted at the distal SO tendon. Our results also suggested that in vivo the lumped intact tissues linking SO to its synergists are slack or are operating on the toe region of the stress-strain curve. Thus, within the experimental conditions of the present study, the intact cat soleus muscle appears to act mechanically as an independent actuator.

Prediction of summation in incompletely fused tetanic contractions of rat muscle

Summation is the accumulating contractile force resulting from sequential activations applied to a muscle without sufficient interval to permit complete relaxation. The purpose of this study was to evaluate summation in the rat medial gastrocnemius muscle, and to determine if the contractile responses during summation could be predicted from the relationship between force and activation pattern. In the first part of this study, the consistency of summation in the rat gastrocnemius muscle was assessed and prediction equations were derived. The second part compared predicted summation with actual contractions obtained in a new set experiments. Summation was assessed by calculation of the contractile response, per stimulation, for up to five stimulating pulses at these frequencies: 20, 40, 60 and 80Hz. This was done by subtraction of the force transient for j-1 pulses of stimulation (where j=1-5 pulses) from the force response with j pulses of stimulation. Each of these force differences was evaluated for peak rate of force development, contraction time and half-relaxation time. Contraction and half-relaxation times changed by only a small magnitude from values obtained for the twitch. Peak rate of force development was proportional to the active force for all force transients obtained by subtraction. The force per activation increased from the first to the fifth stimulus, and was dependent on interpulse delay. In the second series of experiments, the predicted force was related to the actual force for brief tetanic contractions at 40, 50 and 60Hz (r(2)=0.875). These experiments demonstrate that the force response to sequential activations is consistent and predictable. Summation can be predicted, knowing only the amplitude of the twitch contraction and the relationship between delay and force for each activating stimulus.

Extra force from asynchronous stimulation of cat soleus muscle results from minimizing the stretch of the common elastic elements

Rack and Westbury showed that low-frequency asynchronous stimulation of a muscle produces greater force compared with synchronous stimulation. This study tested the hypothesis that the difference results from the dynamic stretch of the common elastic elements. In eight anesthetized cats, the soleus was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into four bundles so each innervated approximately 1/4 of the soleus. The elasticity shared by each part of the muscle was estimated and the servomechanism programmed to compensate for its stretch. At each test frequency (5, 7.5, and 10 Hz), the muscle was stimulated by asynchronous stimulation, synchronous stimulation, summation of force with each part stimulated individually, and summation with each part stimulated individually and the servomechanism mimicking tendon stretch during asynchronous stimulation. Muscle length was isometric except for the last protocol. The observed differences were small. The greatest difference occurred during stimulation at 5 Hz with muscle length on the ascending limb of the length-tension curve. Here, the average forces, normalized by asynchronous force, were asynchronous, 100%; synchronous, 73%; summation, 110%; and summation with stretch compensation, 98%. The results support the hypothesis and suggest that the common elasticity can be used to predict force gains from asynchronous stimulation.

Myofascial force transmission in dynamic muscle conditions: effects of dynamic shortening of a single head of multi-tendoned rat extensor digitorum longus muscle

This study investigated the effects of myofascial force transmission during dynamic shortening of head III of rat extensor digitorum longus muscle (EDL III). The anterior crural compartment was left intact. Force was measured simultaneously at the distal EDL III tendon, the proximal EDL tendon and the distal tendons of tibialis anterior and extensor hallucis longus muscles (TA + EHL). Two types of distal shortening of EDL III were studied: (1) sinusoidal shortening (2 mm) and (2) isokinetic shortening (8 mm). Sinusoidal shortening of EDL III caused a decrease in force exerted at the distal tendon of EDL III: from 0.58 (0.08) N to 0.26 (0.04) N. In contrast, hardly any changes in proximal EDL force and distal TA+EHL force were found. Maximal concentric force exerted at the distal tendon of EDL III was higher than maximal isometric force expected on the basis of the physiological cross-sectional area of EDL III muscle fibers (Maas et al. 2003). Therefore, a substantial fraction of this force must originate from sources other than muscle fibers of EDL III. Isokinetic shortening of EDL III caused high changes in EDL III force from 0.97 (0.15) N to zero. In contrast, changes in proximal EDL force were much smaller: from 2.44 (0.25) N to 1.99 (0.19) N. No effects on TA + EHL force could be shown. These results are explained in terms of force transmission between the muscle belly of EDL III and adjacent tissues. Thus, also in dynamic muscle conditions, muscle fiber force is transmitted via myofascial pathways.

Summation of Motor Unit Force in Passive and Active Muscle

Nonlinear summation of force has been observed between motor units. The complex structure of muscle suggests many reasons why this could happen. When large portions of the muscle are active, however, the nonlinearities are small, and generally explained by stretch of the common elasticity. This suggests that the type of nonlinearity observed between motor units may not be physiologically significant.

The influence of fatigue on damage from eccentric contractions in the gastrocnemius muscle of the cat

Eccentric exercise is unique in that it can lead to muscle damage and soreness. Concentric exercise is not accompanied by evidence of damage. There are reports in the literature that muscle fatigue is a factor determining the amount of damage from eccentric exercise. Our theory for the damage process predicts that susceptibility for damage is independent of fatigue. Experiments were carried out to test this prediction as well as to seek other evidence in support of our theory. Comparisons were made between the effects of eccentric and concentric contractions. The nerve supply to the medial gastrocnemius muscle of the anaesthetized cat was divided into three equal portions in terms of the tension they generated. In the first experiment a muscle portion was fatigued by giving it 200 shortening contractions over 12 mm at a shortening speed of 50 mm s(-1). This led to a mean fall in isometric tension (37 +/- 4%) without a significant shift in the optimum length for peak active tension. Giving the fatigued muscle 10 eccentric contractions, active stretches over 6 mm at 50 mm s(-1), beginning from the muscle's optimum length led to a further fall in tension (11% +/- 7%) and a significant shift in optimum length (3.7 mm +/- 0.6 mm) in the direction of longer muscle lengths. The shift in optimum was taken as an indicator of muscle damage. This shift was not significantly different from that seen after eccentric contractions carried out on an unfatigued muscle. After a series of eccentric or concentric contractions, tension at the end of a ramp shortening of 6 mm at 10 mm s(-1) fell more than isometric tension, and by near equal amounts for the two kinds of contractions. In an unfatigued muscle, if tension was altered by changing the rate of stimulation, the fall in shortening tension was greater than after either concentric or eccentric contractions. These observations were seen to be consistent with predictions of the proposed mechanism for the damage process.

Mechanical properties of rat soleus aponeurosis and tendon during variable recruitment in situ

The in vitro mechanical properties of tendons are well described, whereas little data exist for conditions mimicking those found in vivo. Descriptions of the in situ mechanical properties of aponeuroses are more common, but the results are variable. Our goal was to examine the mechanical properties of these tissues under conditions mimicking the in vivo state. Tissue strains were measured in the rat (Rattus norvegicus) soleus muscle directly from the spacing of metal markers implanted within the tissues of interest using an X-ray video microscope. Strains were measured for the tendon and three regions (proximal, middle and distal) of the aponeurosis. Muscle stimulation was accomplished through isolated ventral rootlets, allowing force to be graded in seven repeatable increments independent of muscle-tendon unit length. Peak strains (during maximal tetanic contraction at optimum length; P(o)) were approximately 5% in tendon and approximately 12% in all regions of the aponeurosis. At forces above 50% of P(o), tissue stiffness was nearly constant in all regions, and a pronounced toe region was observed only at forces below approximately 25% of P(o). Stiffness increased in all regions as the muscle-tendon unit was lengthened. These results suggest that using mechanical properties measured ex vivo or during single contractile events in situ to estimate the in vivo behavior of tendon and aponeurosis may lead to errors in estimating the distribution of strain among the contractile and series elastic elements of the muscle.

Intrinsic properties and reflex compensation in reinnervated triceps surae muscles of the cat: effect of activation level

The manner in which activation levels influence intrinsic muscular properties and contributions of the stretch reflex were studied in homogeneous soleus (SOL) and heterogeneous gastrocnemius (G) muscles in the decerebrate cat. Intrinsic mechanical properties were represented by the initial stiffness of the muscle, measured prior to reflex action, and by the tendency of the muscle to yield during stretch in the absence of the stretch reflex. Stiffness regulation by the stretch reflex was evaluated by measuring the extent to which reflex action reduces yielding and the extent to which stiffness depends on background force. Intrinsic mechanical properties were measured in muscles deprived of effective autogenic reflexes using the method of muscular reinnervation. Reinnervated muscles were recruited to force levels comparable to those achieved during natural locomotion. As force declined during crossed-extension reflexes in reinnervated and intact muscles, initial stiffness declined according to similar convex trajectories. The data did not support the hypothesis that, for a given force level, initial stiffness is greatest in populations of predominantly type I motor units. Incremental stiffness (Deltaf/Deltal) of both G and SOL increased in the presence of the stretch reflex. Yielding of SOL (ratio of incremental to initial stiffness) substantially decreased in the presence of the stretch reflex over the full range of forces. In reflexive G, yielding significantly decreased for low to intermediate forces, whereas at higher forces, yielding was similar irrespective of the presence or absence of the stretch reflex. The stretch reflex regulates stiffness in both homogeneous and heterogeneous muscles.

Rises in whole muscle passive tension of mammalian muscle after eccentric contractions at different lengths

This is a report of experiments carried out on the medial gastrocnemius muscle of the anesthetized cat, investigating the effects of eccentric contractions carried out at different muscle lengths on the passive and active length-tension relationships. In one series of experiments, the motor supply to the muscle was divided into three approximately equal parts; in the other, whole muscles were used. Fifty eccentric contractions were carried out over different regions of the active length-tension curve for each partial or whole muscle. Active and passive length-tension curves were measured before and after the eccentric contractions. When eccentric contractions were carried out at longer lengths, there was a larger shift of the optimum length for active tension in the direction of longer muscle lengths and a larger fall in peak isometric tension. Passive tension was higher immediately after the eccentric contractions, and if the muscle was left undisturbed for 40 min, it increased further to higher values, particularly after contractions at longer lengths. A series of 20 passive stretches of the same speed and amplitude and covering the same length range as the active stretches, reduced the passive tension which redeveloped over a subsequent 40-min period. It is hypothesized that there are two factors influencing the level of passive tension in a muscle after a series of eccentric contractions. One is injury contractures in damaged muscle fibers tending to raise passive tension; the other is the presence of disrupted sarcomeres in series with still-functioning sarcomeres tending to reduce it.

Nonlinear summation of force in cat tibialis anterior: a muscle with intrafascicularly terminating fibers

The complex connective tissue structure of muscle and tendon suggests that forces from two parts of a muscle may not summate linearly, particularly in muscles with intrafasciculary terminating fibers, such as cat tibialis anterior (TA). In four anesthetized cats, the TA was attached to a servomechanism to control muscle length and record force. The ventral roots were divided into two bundles, each innervating about half the TA, so the two parts could be stimulated alone or together. Nonlinear summation of force (F(nl)) was measured during isometric contractions. F(nl) was small and negative, indicating less than linear summation of the parts, which is consistent with the predicted F(nl) of muscle fibers connected in series. F(nl) was more significant when smaller parts of the muscle were tested (21.8 vs. 8% for whole muscle). These data were fit to a model where both parts of the muscle were assumed to stretch a common elasticity. Compensatory movements of the servomechanism showed the common elasticity is very stiff, and the model cannot account for F(nl) in cat TA.

Summation of forces from multiple motor units in the cat soleus muscle

Nearly all muscle models and most motor control concepts assume that forces from individual muscle fibers and motor units sum in an additive manner once effects of in-series tendon compliance are taken into account. Due to the numerous mechanical linkages between individual fibers, though, it is unclear whether this assumption is warranted. This work examined motor unit force summation over a wide range of muscle forces in the cat soleus. Nonadditive summation implies a nonlinear summation of motor unit forces. Summation nonlinearities were quantified during interactions of 10 individual motor units and 4 motor unit bundles containing approximately 10 units each. These protocols allowed motor unit force summation to be examined from approximately 0 to 25% of tetanic muscle force. Nonlinear summation was assessed by comparing the actual forces to the algebraic sum of individual units and bundles stimulated in isolation. Superadditive summation meant that the actual force exceeded the algebraic sum, whereas subadditive summation meant that the actual force was smaller than the algebraic sum. Experiments tested the hypothesis that superadditive summation occurs at low force levels when few motor units are recruited, whereas subadditive summation prevails above 10% of tetanic force. Results were consistent with this hypothesis. As in previous studies, nonlinear summation in the soleus was modest, but a clear transition from predominately superadditive to predominantly subadditive summation occurred in the range of 6-8% of tetanic force. The largest nonlinearities were transient and appeared at the onset of recruitment and derecruitment of groups of motor units. The results are discussed in terms of the mechanical properties of the connective tissue forming the tendon and linking muscle fibers.

Whole muscle length-tension properties vary with recruitment and rate modulation in areflexive cat soleus

The length-tension relationship is a fundamental property of muscle. In its classic form, which is used in muscle models incorporated into studies of motor control, the length-tension relationship is measured during maximal activation via tetanic electrical stimulation in whole muscles or during high intracellular calcium levels in single muscle fibers. In this study, we measured the length-tension relationship of the cat soleus muscle during different levels of natural activation consisting of recruitment and rate modulation of motor units generated by the crossed extension reflex. The ipsilateral dorsal roots were cut to eliminate sensory feedback from the soleus. Length-tension was measured by large shortening steps that transiently allowed force to drop to zero. Force then recovered to a new steady value as the shorter length was maintained for several seconds. The effects of various levels of crossed extension activation on length-tension were compared with direct electrical stimulation of the muscle at 5, 10, 20, and 100 Hz. At all levels of crossed extension, the slope of the length-tension function was much steeper than the slope for tetanic stimulation at 100 Hz. Most slopes for crossed extension fell between the slopes seen with electrical stimulation at 10 and 20 Hz. There was a modest overall tendency for slope to decrease with the level of crossed extension activation. Because much of the normal movement repertoire requires submaximal activation, muscle models based on the tetanic length tension relationship will greatly underestimate the contribution of this relationship to force modulation at different muscle lengths.