Estimation of musculotendon kinematics in large musculoskeletal models using multidimensional B-splines

We present a robust and computationally inexpensive method to estimate the lengths and three-dimensional moment arms for a large number of musculotendon actuators of the human lower limb. Using a musculoskeletal model of the lower extremity, a set of values was established for the length of each musculotendon actuator for different lower limb generalized coordinates (joint angles). A multidimensional spline function was then used to fit these data. Muscle moment arms were obtained by differentiating the musculotendon length spline function with respect to the generalized coordinate of interest. This new method was then compared to a previously used polynomial regression method. Compared to the polynomial regression method, the multidimensional spline method produced lower errors for estimating musculotendon lengths and moment arms throughout the whole generalized coordinate workspace. The fitting accuracy was also less affected by the number of dependent degrees of freedom and by the amount of experimental data available. The spline method only required information on musculotendon lengths to estimate both musculotendon lengths and moment arms, thus relaxing data input requirements, whereas the polynomial regression requires different equations to be used for both musculotendon lengths and moment arms. Finally, we used the spline method in conjunction with an electromyography driven musculoskeletal model to estimate muscle forces under different contractile conditions, which showed that the method is suitable for the integration into large scale neuromusculoskeletal models.     

Computational modelling of muscle fibre operating ranges in the hindlimb of a small ground bird (Eudromia elegans), with implications for modelling locomotion in extinct species

The arrangement and physiology of muscle fibres can strongly influence musculoskeletal function and whole-organismal performance. However, experimental investigation of muscle function during in vivo activity is typically limited to relatively few muscles in a given system. Computational models and simulations of the musculoskeletal system can partly overcome these limitations, by exploring the dynamics of muscles, tendons and other tissues in a robust and quantitative fashion. Here, a high-fidelity, 26-degree-of-freedom musculoskeletal model was developed of the hindlimb of a small ground bird, the elegant-crested tinamou (Eudromia elegans, ~550 g), including all the major muscles of the limb (36 actuators per leg). The model was integrated with biplanar fluoroscopy (XROMM) and forceplate data for walking and running, where dynamic optimization was used to estimate muscle excitations and fibre length changes throughout both gaits. Following this, a series of static simulations over the total range of physiological limb postures were performed, to circumscribe the bounds of possible variation in fibre length. During gait, fibre lengths for all muscles remained between 0.5 to 1.21 times optimal fibre length, but operated mostly on the ascending limb and plateau of the active force-length curve, a result that parallels previous experimental findings for birds, humans and other species. However, the ranges of fibre length varied considerably among individual muscles, especially when considered across the total possible range of joint excursion. Net length change of muscle–tendon units was mostly less than optimal fibre length, sometimes markedly so, suggesting that approaches that use muscle–tendon length change to estimate optimal fibre length in extinct species are likely underestimating this important parameter for many muscles. The results of this study clarify and broaden understanding of muscle function in extant animals, and can help refine approaches used to study extinct species.     

Are Subject-Specific Musculoskeletal Models Robust to the Uncertainties in Parameter Identification?

Subject-specific musculoskeletal modeling can be applied to study musculoskeletal disorders, allowing inclusion of personalized anatomy and properties. Independent of the tools used for model creation, there are unavoidable uncertainties associated with parameter identification, whose effect on model predictions is still not fully understood. The aim of the present study was to analyze the sensitivity of subject-specific model predictions (i.e., joint angles, joint moments, muscle and joint contact forces) during walking to the uncertainties in the identification of body landmark positions, maximum muscle tension and musculotendon geometry. To this aim, we created an MRI-based musculoskeletal model of the lower limbs, defined as a 7-segment, 10-degree-of-freedom articulated linkage, actuated by 84 musculotendon units. We then performed a Monte-Carlo probabilistic analysis perturbing model parameters according to their uncertainty, and solving a typical inverse dynamics and static optimization problem using 500 models that included the different sets of perturbed variable values. Model creation and gait simulations were performed by using freely available software that we developed to standardize the process of model creation, integrate with OpenSim and create probabilistic simulations of movement. The uncertainties in input variables had a moderate effect on model predictions, as muscle and joint contact forces showed maximum standard deviation of 0.3 times body-weight and maximum range of 2.1 times body-weight. In addition, the output variables significantly correlated with few input variables (up to 7 out of 312) across the gait cycle, including the geometry definition of larger muscles and the maximum muscle tension in limited gait portions. Although we found subject-specific models not markedly sensitive to parameter identification, researchers should be aware of the model precision in relation to the intended application. In fact, force predictions could be affected by an uncertainty in the same order of magnitude of its value, although this condition has low probability to occur.     

The effects of electromyography-assisted modelling in estimating musculotendon forces during gait in children with cerebral palsy

Neuro-musculoskeletal modelling can provide insight into the aberrant muscle function during walking in those suffering cerebral palsy (CP). However, such modelling employs optimization to estimate muscle activation that may not account for disturbed motor control and muscle weakness in CP. This study evaluated different forms of neuro-musculoskeletal model personalization and optimization to estimate musculotendon forces during gait of nine children with CP (GMFCS I-II) and nine typically developing (TD) children. Data collection included 3D-kinematics, ground reaction forces, and electromyography (EMG) of eight lower limb muscles. Four different optimization methods estimated muscle activation and musculotendon forces of a scaled-generic musculoskeletal model for each child walking, i.e. (i) static optimization that minimized summed-excitation squared; (ii) static optimization with maximum isometric muscle forces scaled to body mass; (iii) an EMG-assisted approach using optimization to minimize summed-excitation squared while reducing tracking errors of experimental EMG-linear envelopes and joint moments; and (iv) EMG-assisted with musculotendon model parameters first personalized by calibration. Both static optimization approaches showed a relatively low model performance compared to EMG envelopes. EMG-assisted approaches performed much better, especially in CP, with only a minor mismatch in joint moments. Calibration did not affect model performance significantly, however it did affect musculotendon forces, especially in CP. A model more consistent with experimental measures is more likely to yield more physiologically representative results. Therefore, this study highlights the importance of calibrated EMG-assisted modelling when estimating musculotendon forces in TD children and even more so in children with CP.     

Musculotendon lengths and moment arms for a three-dimensional upper-extremity model

Generating muscle-driven forward dynamics simulations of human movement using detailed musculoskeletal models can be computationally expensive. This is due in part to the time required to calculate musculotendon geometry (e.g., musculotendon lengths and moment arms), which is necessary to determine and apply individual musculotendon forces during the simulation. Modeling upper-extremity musculotendon geometry can be especially challenging due to the large number of multi-articular muscles and complex muscle paths. To accurately represent this geometry, wrapping surface algorithms and/or other computationally expensive techniques (e.g., phantom segments) are used. This paper provides a set of computationally efficient polynomial regression equations that estimate musculotendon length and moment arms for thirty-two (32) upper-extremity musculotendon actuators representing the major muscles crossing the shoulder, elbow and wrist joints. Equations were developed using a least squares fitting technique based on geometry values obtained from a validated public-domain upper-extremity musculoskeletal model that used wrapping surface elements (Holzbaur et al., 2005). In general, the regression equations fit well the original model values, with an average root mean square difference for all musculotendon actuators over the represented joint space of 0.39 mm (1.1% of peak value). In addition, the equations reduced the computational time required to simulate a representative upper-extremity movement (i.e., wheelchair propulsion) by more than two orders of magnitude (315 versus 2.3 s). Thus, these equations can assist in generating computationally efficient forward dynamics simulations of a wide range of upper-extremity movements.     

Evaluation of different analytical methods for subject-specific scaling of musculotendon parameters

Musculoskeletal models are often used to estimate internal muscle forces and the effects of those forces on the development of human movement. The Hill-type muscle model is an important component of many of these models, yet it requires specific knowledge of several muscle and tendon properties. These include the optimal muscle fibre length, the length at which the muscle can generate maximum force, and the tendon slack length, the length at which the tendon starts to generate a resistive force to stretch. Both of these parameters greatly influence the force-generating behaviour of a musculotendon unit and vary with the size of the person. However, these are difficult to measure directly and are often estimated using the results of cadaver studies, which do not account for differences in subject size. This paper examined several different techniques that can be used to scale the optimal muscle fibre length and tendon slack length of a musculotendon unit according to subject size. The techniques were divided into three categories corresponding to linear scaling, scaling by maintaining a constant tendon slack length throughout the range of joint motion, and scaling by maintaining muscle operating range throughout the range of joint motion. We suggest that a good rationale for scaling muscle properties should be to maintain the same force-generating characteristics of a musculotendon unit for all subjects, which is best achieved by scaling that preserves the muscle operating range when the muscle is maximally activated.     

Impact of ankle foot orthosis stiffness on Achilles tendon and gastrocnemius function during unimpaired gait

Ankle foot orthoses (AFOs) are designed to improve gait for individuals with neuromuscular conditions and have also been used to reduce energy costs of walking for unimpaired individuals. AFOs influence joint motion and metabolic cost, but how they impact muscle function remains unclear. This study investigated the impact of different stiffness AFOs on medial gastrocnemius muscle (MG) and Achilles tendon (AT) function during two walking speeds. We performed gait analyses for eight unimpaired individuals. Each individual walked at slow and very slow speeds with a 3D printed AFO with no resistance (free hinge condition) and four levels of ankle dorsiflexion stiffness: 0.25 Nm/°, 1 Nm/°, 2 Nm/°, and 3.7 Nm/°. Motion capture, ultrasound, and musculoskeletal modeling were used to quantify MG and AT lengths with each AFO condition. Increasing AFO stiffness increased peak AFO dorsiflexion moment with decreased peak knee extension and peak ankle dorsiflexion angles. Overall musculotendon length and peak AT length decreased, while peak MG length increased with increasing AFO stiffness. Peak MG activity, length, and velocity significantly decreased with slower walking speed. This study provides experimental evidence of the impact of AFO stiffness and walking speed on joint kinematics and musculotendon function. These methods can provide insight to improve AFO designs and optimize musculotendon function for rehabilitation, performance, or other goals.     

Optimal muscle fascicle length and tendon stiffness for maximising gastrocnemius efficiency during human walking and running

Muscles generate force to resist gravitational and inertial forces and/or to undertake work, e.g. on the centre of mass. A trade-off in muscle architecture exists in muscles that do both; the fibres should be as short as possible to minimise activation cost but long enough to maintain an appropriate shortening velocity. Energetic cost is also influenced by tendon compliance which modulates the timecourse of muscle mechanical work. Here we use a Hill-type muscle model of the human medial gastrocnemius to determine the muscle fascicle length and Achilles tendon compliance that maximise efficiency during the stance phase of walking (1.2 m/s) and running (3.2 and 3.9 m/s). A broad range of muscle fascicle lengths (ranging from 45 to 70 mm) and tendon stiffness values (150-500 N/mm) can achieve close to optimal efficiency at each speed of locomotion; however, efficient walking requires shorter muscle fascicles and a more compliant tendon than running. The values that maximise efficiency are within the range measured in normal populations. A non-linear toe-region region of the tendon force-length properties may further influence the optimal values, requiring a stiffer tendon with slightly longer muscle fascicles; however, it does not alter the main results. We conclude that muscle fibre length and tendon compliance combinations may be tuned to maximise efficiency under a given gait condition. Efficiency is maximised when the required volume of muscle is minimised, which may also help reduce limb inertia and basal metabolic costs.     

Comparison of global and joint-to-joint methods for estimating the hip joint load and the muscle forces during walking

A three-dimensional musculoskeletal model of the lower limb was developed to study the influence of biarticular muscles on the muscle force distribution and joint loads during walking. A complete walking cycle was recorded for 9 healthy subjects using the standard optoelectronic motion tracking system. Ground contact forces were also measured using a 6-axes force plate. Inverse dynamics was used to compute net joint reactions (forces and torques) in the lower limb. A static optimization method was then used to estimate muscle forces. Two different approaches were used: in the first one named global method, the biarticular muscles exerted a torque on the two joints they spanned at the same time, and in the second one called joint-by-joint method, these biarticular muscles were divided into two mono-articular muscles with geometrical (insertion, origin, via points) and physiological properties remained unchanged. The hip joint load during the gait cycle was then calculated taking into account the effect of muscle contractions. The two approaches resulted in different muscle force repartition: the biarticular muscles were favoured over any set of single-joint muscles with the same physiological function when using the global method. While the two approaches yielded only little difference in the resultant hip load, the examination of muscle power showed that biarticular muscles could produce positive work at one joint and negative work at the other, transferring energy between body segments and thus decreasing the metabolic cost of movement.     

A musculoskeletal model of the human lower extremity: the effect of muscle, tendon, and moment arm on the moment-angle relationship of musculotendon actuators at the hip, knee, and ankle

We have developed a musculoskeletal model of the human lower extremity for computer simulation studies of musculotendon function and muscle coordination during movement. This model incorporates the salient features of muscle and tendon, specifies the musculoskeletal geometry and musculotendon parameters of 18 musculotendon actuators, and defines the active isometric moment of these actuators about the hip, knee, and ankle joints in the sagittal plane. We found that tendon slack length, optimal muscle-fiber length, and moment arm are different for each actuator, thus each actuator develops peak isometric moment at a different joint angle. The joint angle where an actuator produces peak moment does not necessarily coincide with the joint angle where: (1) muscle force peaks, (2) moment arm peaks, or (3) the in vivo moment developed by maximum voluntary contractions peaks. We conclude that when tendon is neglected in analyses of musculotendon force or moment about joints, erroneous predictions of human musculotendon function may be stated, not only in static situations as studied here, but during movement as well.     

In vivo behaviour of human muscle tendon during walking

In the present study we investigated in vivo length changes in the fascicles and tendon of the human gastrocnemius medialis (GM) muscle during walking. The experimental protocol involved real-time ultrasound scanning of the GM muscle, recording of the electrical activity of the muscle, measurement of knee- and ankle-joint rotations, and measurement of ground reaction forces in six men during walking at 3 km h(-1) on a treadmill. Fascicular lengths were measured from the sonographs recorded. Musculotendon complex length changes were estimated from anatomical and joint kinematic data. Tendon length changes were obtained combining the musculotendon complex and fascicular length-change data. The fascicles followed a different length-change pattern from those of the musculotendon complex and tendon throughout the step cycle. Two important features emerged: (i) the muscle contracted near-isometrically in the stance phase, with the fascicles operating at ca. 50 mm; and (ii) the tendon stretched by ca. 7 mm during single support, and recoiled in push-off. The behaviour of the muscle in our experiment indicates consumption of minimal metabolic energy for eliciting the contractile forces required to support and displace the body. On the other hand, the spring-like behaviour of the tendon indicates storage and release of elastic-strain energy. Either of the two mechanisms would favour locomotor economy     

Effects of step length and step frequency on lower-limb muscle function in human gait

The aim of this study was to quantify the effects of step length and step frequency on lower-limb muscle function in walking. Three-dimensional gait data were used in conjunction with musculoskeletal modeling techniques to evaluate muscle function over a range of walking speeds using prescribed combinations of step length and step frequency. The body was modeled as a 10-segment, 21-degree-of-freedom skeleton actuated by 54 muscle-tendon units. Lower-limb muscle forces were calculated using inverse dynamics and static optimization. We found that five muscles – GMAX, GMED, VAS, GAS, and SOL – dominated vertical support and forward progression independent of changes made to either step length or step frequency, and that, overall, changes in step length had a greater influence on lower-limb joint motion, net joint moments and muscle function than step frequency. Peak forces developed by the uniarticular hip and knee extensors, as well as the normalized fiber lengths at which these muscles developed their peak forces, correlated more closely with changes in step length than step frequency. Increasing step length resulted in larger contributions from the hip and knee extensors and smaller contributions from gravitational forces (limb posture) to vertical support. These results provide insight into why older people with weak hip and knee extensors walk more slowly by reducing step length rather than step frequency and also help to identify the key muscle groups that ought to be targeted in exercise programs designed to improve gait biomechanics in older adults.     

Knee muscle forces during walking and running in patellofemoral pain patients and pain-free controls

One proposed mechanism of patellofemoral pain, increased stress in the joint, is dependent on forces generated by the quadriceps muscles. Describing causal relationships between muscle forces, tissue stresses, and pain is difficult due to the inability to directly measure these variables in vivo. The purpose of this study was to estimate quadriceps forces during walking and running in a group of male and female patients with patellofemoral pain (n=27, 16 female; 11 male) and compare these to pain-free controls (n=16, 8 female; 8 male). Subjects walked and ran at self-selected speeds in a gait laboratory. Lower limb kinematics and electromyography (EMG) data were input to an EMG-driven musculoskeletal model of the knee, which was scaled and calibrated to each individual to estimate forces in 10 muscles surrounding the joint. Compared to controls, the patellofemoral pain group had greater co-contraction of quadriceps and hamstrings (p=0.025) and greater normalized muscle forces during walking, even though the net knee moment was similar between groups. Muscle forces during running were similar between groups, but the net knee extension moment was less in the patellofemoral pain group compared to controls. Females displayed 30–50% greater normalized hamstring and gastrocnemius muscle forces during both walking and running compared to males (p<0.05). These results suggest that some patellofemoral pain patients might experience greater joint contact forces and joint stresses than pain-free subjects. The muscle force data are available as supplementary material.     

Approximating complex musculoskeletal biomechanics using multidimensional autogenerating polynomials

Computational models of the musculoskeletal system are scientific tools used to study human movement, quantify the effects of injury and disease, plan surgical interventions, or control realistic high-dimensional articulated prosthetic limbs. If the models are sufficiently accurate, they may embed complex relationships within the sensorimotor system. These potential benefits are limited by the challenge of implementing fast and accurate musculoskeletal computations. A typical hand muscle spans over 3 degrees of freedom (DOF), wrapping over complex geometrical constraints that change its moment arms and lead to complex posture-dependent variation in torque generation. Here, we report a method to accurately and efficiently calculate musculotendon length and moment arms across all physiological postures of the forearm muscles that actuate the hand and wrist. Then, we use this model to test the hypothesis that the functional similarities of muscle actions are embedded in muscle structure. The posture dependent muscle geometry, moment arms and lengths of modeled muscles were captured using autogenerating polynomials that expanded their optimal selection of terms using information measurements. The iterative process approximated 33 musculotendon actuators, each spanning up to 6 DOFs in an 18 DOF model of the human arm and hand, defined over the full physiological range of motion. Using these polynomials, the entire forearm anatomy could be computed in <10 μs, which is far better than what is required for real-time performance, and with low errors in moment arms (below 5%) and lengths (below 0.4%). Moreover, we demonstrate that the number of elements in these autogenerating polynomials does not increase exponentially with increasing muscle complexity; complexity increases linearly instead. Dimensionality reduction using the polynomial terms alone resulted in clusters comprised of muscles with similar functions, indicating the high accuracy of approximating models. We propose that this novel method of describing musculoskeletal biomechanics might further improve the applications of detailed and scalable models to describe human movement.     

Contribution of mono- and biarticular muscles to extending knee joint moments in runners and cyclists.

Motor actions are governed by coordinated activation of mono- and biarticular muscles. This study considered differences in mono- and biarticular knee extensors between runners and cyclists in the context of adaptations to task-specific movement requirements. Two hypotheses were tested: 1) the length-at-use hypothesis, which is that muscle adapts to have it operate around optimal length; and 2) the contraction-mode hypothesis, which is that eccentrically active muscles prefer to operate on the ascending limb of the length-force curve. Ten runners and ten cyclists performed maximal, isometric knee extensions on a dynamometer at five knee and four hip joint angles. This approach allowed the separation of the contribution of mono- and biarticular extensors. Three major differences occurred: 1) compared with runners, monoarticular extensors of cyclists reach optimal length at larger muscle length; 2) in runners, optimal length of the biarticular extensor is shifted to larger lengths; and 3) the moment generated by monoarticular extensor was larger in cyclists. Mono- and biarticular extensors respond to different adaptation triggers in runners and cyclists. Monoarticular muscles seem to adapt to the length-at-use, whereas biarticular muscles were found to be sensitive to the contraction-mode hypothesis.     

Architectural properties of distal forelimb muscles in horses,Equus caballus

Articular injuries in athletic horses are associated with large forces from ground impact and from muscular contraction. To accurately and noninvasively predict muscle and joint contact forces, a detailed model of musculoskeletal geometry and muscle architecture is required. Moreover, muscle architectural data can increase our understanding of the relationship between muscle structure and function in the equine distal forelimb. Muscle architectural data were collected from seven limbs obtained from five thoroughbred and thoroughbred-cross horses. Muscle belly rest length, tendon rest length, muscle volume, muscle fiber length, and pennation angle were measured for nine distal forelimb muscles. Physiological cross-sectional area (PCSA) was determined from muscle volume and muscle fiber length. The superficial and deep digital flexor muscles displayed markedly different muscle volumes (227 and 656 cm3, respectively), but their PCSAs were very similar due to a significant difference in muscle fiber length (i.e., the superficial digital flexor muscle had very short fibers, while those of the deep digital flexor muscle were relatively long). The ulnaris lateralis and flexor carpi ulnaris muscles had short fibers (17.4 and 18.3 mm, respectively). These actuators were strong (peak isometric force, Fmax=5,814 and 4,017 N, respectively) and stiff (tendon rest length to muscle fiber length, LT:LMF=5.3 and 2.1, respectively), and are probably well adapted to stabilizing the carpus during the stance phase of gait. In contrast, the flexor carpi radialis muscle displayed long fibers (89.7 mm), low peak isometric force (Fmax=555 N), and high stiffness (LT:LMF=1.6). Due to its long fibers and low Fmax, flexor carpi radialis appears to be better adapted to flexion and extension of the limb during the swing phase of gait than to stabilization of the carpus during stance. Including muscle architectural parameters in a musculoskeletal model of the equine distal forelimb may lead to more realistic estimates not only of the magnitudes of muscle forces, but also of the distribution of forces among the muscles crossing any given joint.     

In vivo operational fascicle lengths of vastus lateralis during sub-maximal and maximal cycling

Instantaneous contractile characteristics of skeletal muscle, during movement tasks, can be determined and related to steady state mechanical properties such as the force–length relationship with the use of ultrasound imaging. A previous investigation into the contractile characteristics of the vastus lateralis (VL) during cycling has shown that fascicles operate on the “weak” descending limb of the force–length relationship, thus not taking advantage of the “strong” plateau region. The purpose of this study was to investigate if VL fascicle lengths change from sub-maximal to maximal cycling conditions, and if maximal cycling results in VL fascicle lengths which operate across the plateau of the force–length relationship. Fifteen healthy male subjects (age 20.9±1.8 yr, wt. 67.0±6.3 kg, ht. 176.7±7.2 cm) were tested to establish the maximal force–length relationship for the VL through ten maximal isometric contractions at various knee angles. Subjects then cycled on an SRM cycle ergometer at cadences of 50 and 80 revolutions per minute at 100 W, 250 W, and maximal effort. Fascicle lengths were determined at crank angles of 0, 90, and 180°. Fascicles operated at or near the plateau of the maximal force–length relationship for maximal cycling, while operating on the descending limb during sub-maximal conditions for both cadences. However, when comparing the fascicle operating range for the sub-maximal cycling conditions to the corresponding sub-maximal force–length relationships, the VL now also operated across the plateau region. We concluded from these results that regardless of cycling effort, the VL operated through the ideal plateau region of the corresponding force–length relationship, hence always working optimally. We hypothesize that this phenomenon is due to the coupling of series elastic compliance and length dependent calcium sensitivity in the VL.     

The effects of Achilles tendon compliance on triceps surae mechanics and energetics in walking

Achilles tendon (AT) compliance can affect the generation and transmission of triceps surae muscle forces, and thus has important biomechanical consequences for walking performance. However, the uniarticular soleus (SOL) and the biarticular (GAS) function differently during walking, with in vivo evidence suggesting that their associated fascicles and tendinous structures exhibit unique kinematics during walking. Given the strong association between muscle fiber length, velocity and force production, we conjectured that SOL and GAS mechanics and energetic behavior would respond differently to altered AT compliance. To test this, we characterized GAS and SOL muscle and tendon mechanics and energetics due to systematic changes in tendon compliance using musculoskeletal simulations of walking. Increased tendon compliance enlarged GAS and SOL tendon excursions, shortened fiber operation lengths and affected muscle excitation patterns. For both muscles, an optimal tendon compliance (tendon strains of approximately 5% with maximum isometric force) existed that minimized metabolic energy consumption. However, GAS muscle-tendon mechanics and energetics were significantly more sensitive to changes in tendon compliance than were those for SOL. In addition, GAS was not able to return stored tendon energy during push-off as effectively as SOL, particularly for larger values of tendon compliance. These fundamental differences between GAS and SOL sensitivity to altered tendon compliance seem to arise from the biarticular nature of GAS. These insights are potentially important for understanding the functional consequences of altered Achilles tendon compliance due to aging, injury, or disease.     

A Neuro-Mechanical Model of a Single Leg Joint Highlighting the Basic Physiological Role of Fast and Slow Muscle Fibres of an Insect Muscle System

In legged animals, the muscle system has a dual function: to produce forces and torques necessary to move the limbs in a systematic way, and to maintain the body in a static position. These two functions are performed by the contribution of specialized motor units, i.e. motoneurons driving sets of specialized muscle fibres. With reference to their overall contraction and metabolic properties they are called fast and slow muscle fibres and can be found ubiquitously in skeletal muscles. Both fibre types are active during stepping, but only the slow ones maintain the posture of the body. From these findings, the general hypothesis on a functional segregation between both fibre types and their neuronal control has arisen. Earlier muscle models did not fully take this aspect into account. They either focused on certain aspects of muscular function or were developed to describe specific behaviours only. By contrast, our neuro-mechanical model is more general as it allows functionally to differentiate between static and dynamic aspects of movement control. It does so by including both muscle fibre types and separate motoneuron drives. Our model helps to gain a deeper insight into how the nervous system might combine neuronal control of locomotion and posture. It predicts that (1) positioning the leg at a specific retraction angle in steady state is most likely due to the extent of recruitment of slow muscle fibres and not to the force developed in the individual fibres of the antagonistic muscles; (2) the fast muscle fibres of antagonistic muscles contract alternately during stepping, while co-contraction of the slow muscle fibres takes place during steady state; (3) there are several possible ways of transition between movement and steady state of the leg achieved by varying the time course of recruitment of the fibres in the participating muscles.     

Force enhancement above the initial isometric force on the descending limb of the force-length relationship

Edman et al. (J. General Physiol. 80 (1982) 769) observed in single fibres of frog that the steady-state forces following active fibre stretch were greater than the purely isometric force obtained at the length from which the stretch was initiated. Operating on the descending limb of the force-length relationship, such a result can only be explained within the framework of the sarcomere length non-uniformity theory, if some fibre segments shortened during the fibre stretch. However, such a result was not found, leaving Edman's observation unexplained. Force enhancement above the initial isometric force has not been investigated systematically in whole muscle, and therefore it is not known whether this property is also part of whole muscle mechanics. The purpose of this study was to test if the steady-state forces following active stretch of cat semitendinosus were greater than the corresponding purely isometric forces at the muscle length from which the stretch was started. Cat semitendinosus was stretched by various amounts on the descending limb of the force-length relationship, and the steady-state forces following these stretches were compared to the corresponding isometric forces at the initial and final muscle lengths. In 109 of 131 tests, the steady-state forces following stretching were greater than the isometric forces at the initial muscle lengths. Force enhancement increased with increasing amounts of stretching, and force enhancement above the initial isometric force was more likely to occur following stretches of great compared to small amplitude. Passive forces following active muscle stretching were often significantly greater than the passive forces at the same muscle length following an isometric contraction or a passive stretching of the muscle. This observation was made consistently at the longest muscle lengths tested. It appears, therefore, that there is a passive force that accounts for part of the force enhancement above the isometric force at the initial muscle length, and that provides increased passive force when a muscle is actively, rather than passively, stretched at long muscle lengths. We conclude that cat semitendinosus demonstrates steady-state force enhancement above the corresponding purely isometric force at the initial muscle length on the descending limb of the force-length relationship for many contractile conditions, and that a unique, and so far undetected, passive, parallel element contributes to this force enhancement, particularly at long muscle lengths where muscle is assumed to be most vulnerable to injuries associated with sarcomere length instability.