Human muscle modelling from a user's perspective.

Methods for developing mathematical models representing entire human muscles are briefly reviewed, with special emphasis on aspects of modelling velocity dependence using cross-bridge dynamics, and isometric force-length properties from myofilament lengths and muscle architecture. For each of these components, mechanistic (using basic contraction mechanisms) and phenomenological ("black-box") models are available. Experiments on constant-velocity lengthening at different velocities were simulated using (a) a cross-bridge based model and (b) a Hill-based model. The Hill model was superior in its ability to predict muscle forces under different conditions with the same model parameters. Regarding force-length properties, myofilament overlap and muscle architecture did not correctly predict maximal isometric joint moments over the entire functional range of motion. The width of the force-length relationship of all contractile elements in a lower extremity model may be optimized to fit measured isometric moment-angle relationships. The resulting increase in width suggests that for some short-fibered muscles with complex architecture, the "effective" muscle fibre length is increased because muscle fibres may be partly connected in series as well as in parallel. It is concluded that a hybrid phenomenological/mechanistic muscle model is most likely to be practical (i.e. parameters can be estimated for human muscle) as well as accurate (i.e. correct forces are predicted for a wide range of conditions.

Modeling dynamic contraction of muscle using the cross-bridge theory.

During normal, voluntary movements, skeletal muscles typically contract in a highly dynamic manner; the length of the muscle and the speed of contraction change continuously. In this study, we present an approach to predict the accurate behavior of muscles for such dynamic contractions using Huxley's cross-bridge model. A numerical procedure is proposed to solye, without any assumptions, the partial differential equation that governs the attachment distribution function in Huxley's cross-bridge model. The predicted attachment distribution functions, and the corresponding force responses for shortening and stretching, were compared with those obtained using Zahalak's analytical solution and those obtained using the so-called "distribution moment model" in transient and steady-state contractions. Compared to the distribution moment model, the solutions obtained using our model are exact rather than approximate. The solutions obtained using the analytical approach and the present approach were virtually identical; however, in terms of CPU times, the present approach was 250-300 times faster than Zahalak's. From the results of this study, we concluded that the proposed solution is an exact and efficient way for solving the partial differential equation governing the cross-bridge model.

Modelling of force production in skeletal muscle undergoing stretch.

Many human movements involve eccentric contraction of muscles. Therefore, it is important that a theoretical model is able to represent the kinetic response of activated muscle during lengthening if it is to be applied to dynamic simulation of such movements. The so-called Hill and Distribution Moment models are two commonly used models of skeletal muscle. The Hill model is a phenomenological model based on experimental observations; the Distribution Moment model is based on the cross-bridge theory of muscle contraction. The ability of each of these models to predict the force-velocity relation has been considered previously; however, few attempts have been made to evaluate the force response of each model with respect to time during stretches at different velocities. The purpose of this study was to compare the predicted force-time responses of the Hill and Distribution Moment models to the actual force produced by the cat soleus during experimental iso-velocity stretches at maximal activation. Two stretch velocities were simulated: 7.2 and 400 mm s-1. Model parameters were derived from the literature where possible. In addition, model parameters were optimized to provide the best possible fit between model force predictions and experimental results at each velocity. The results of the study showed that using the Hill model, it was possible to describe qualitatively the force-time response of the muscle at both velocities of stretch using parameters derived from the literature. It was also possible to optimize a set of parameters for the Hill model to provide a quantitative description of the force-time response at each velocity. Using the Distribution Moment model, it was not possible to describe the force-time response of the muscle for both velocities using a single set of rate constants, suggesting that the cross-bridge theory, upon which the model is based, may have to be further evaluated for lengthening muscle. Further research is required to determine if the model results can be generalized to other muscles and other velocities of stretch.

The clinical biomechanics award paper 1995 Lower extremity joint loading during impact in running.

OBJECTIVE: The main purpose of this study was to estimate lower extremity joint impact loading in running and the influences of muscles on this loading. DESIGN: A 2D simulation model that included skeletal motion, muscles, and soft-tissue movement was developed in this study. BACKGROUND: Our understanding of joint impact loading has been mainly based on measurable external loading variables. Furthermore, changes in muscular forces have often been neglected, assuming that muscular activation cannot react during the period of impact, which ignores passive muscle properties. METHODS: Kinematics and ground reaction forces were collected for each of five subjects performing heel-toe running. Kinematic and inverse dynamics analyses provided the initial conditions for the simulation models. The motion of each subject was simulated for 50 ms following heelstrike. RESULTS: Motion of body segments following heelstrike reduced the rate of joint impact loading, sometimes substantially, in comparison to the ground reaction force. In addition, substantial changes in muscular forces were sometimes observed that further reduced the rates of joint loading. CONCLUSIONS: The rates of joint impact loading are reduced in comparison to the ground reaction force during normal heel-toe running. Changes in muscular forces may have a relevant effect on joint impact loading and should not be neglected in future studies. RELEVANCE: Repetitive external impact loading has resulted in degeneration of articular cartilage in animal models. However, runners, as a group, do not have a high incidence of osteoarthritis. The present study suggests that there are mechanisms available to the runner that can substantially reduce the rate of joint impact loading relative to the rate of external loading. These mechanisms may be sufficient to prevent overloading and degeneration of the joints.

Transfer of movement between calcaneus and tibia in vitro.

Excessive foot eversion and/or abnormal tibial rotation have been associated with knee injuries. The mechanical coupling of leg and foot, which may be related to the aetiology of knee injuries, is still not well understood. The goal of this study was to determine in vitro, as a function of loading and flexion position of the foot, the movement transfer from calcaneal eversion-inversion to tibial rotation and vice versa occurring in the ankle-joint complex. A lower leg holding and loading device with 6 degrees of freedom was used in the investigation. Fourteen fresh-frozen, foot-leg specimens were tested. The movement transfer from calcaneus to tibia and vice versa differed significantly between the specimens. The transferred movement was not the same for all input modes. Specifically, calcaneal eversion resulted in significant internal tibial rotation; however, internal tibial rotation did not induce any calcaneal eversion. Vertical loading of the tibia and foot flexion position had a major influence on this movement transfer. The amount of calcaneal eversion transferred to internal tibial rotation depends on the individual mechanical coupling at the ankle-joint complex. Therefore excessive pronation, in running for instance, is only critical for high knee loading when coupled with a high movement transfer in the ankle-joint complex. The interindividual differences may also signal difficulties for prosthesis design in total ankle-joint replacement and for the design of shoe orthotics.

Influence of selective arthrodesis on the movement transfer between calcaneus and tibia in vitro.

Arthrodeses of foot and ankle are well established, accepted, and practical methods for treatment of painful joint degeneration, foot deformity, and instability. Consecutive changes in gait and over-use injuries have been explained by the created lever arms and the overall compensatory motion in the neighbouring joints, rather than by changes in the mechanical coupling of foot and tibia. Thus the purpose of this study was to quantify the change of movement transferred from calcaneus to tibia, and vice versa, for selective joint fusions (ankle, subtalar, and talonavicular joints) under different flexion and loading conditions. In six fresh cadaveric foot-leg specimens, transfer of rotational movement between calcaneus and tibia occurred in all arthrodesis conditions. Fusion of the subtalar joint, which is commonly believed to be crucial in the transfer of rotational movement in the ankle joint complex, decreased the movement transfer from calcaneal inversion to external tibial rotation about 71.8% and, vice versa, from external tibial rotation to calcaneal inversion about 35.8%. However, the movement transfer did not change when calcaneal eversion and internal tibial rotation were the input movements. The ankle (talocrural) joint must have more than 1 degree of freedom, since significant movement transfer still occurred when the subtalar joint was fused. It could be that other structures such as ligaments also play an important role in transferring movement. Consequently it may be difficult to predict the effect of a planned arthrodesis since the resulting restriction of motion and movement transfer may be substantially determined by the integrity of the surrounding soft tissue, especially the ligaments.

Application of the joint coordinate system to three-dimensional joint attitude and movement representation: a standardization proposal.

The selection of an appropriate and/or standardized method for representing 3-D joint attitude and motion is a topic of popular debate in the field of biomechanics. The joint coordinate system (JCS) is one method that has seen considerable use in the literature. The JCS consists of an axis fixed in the proximal segment, an axis fixed in the distal segment, and a "floating" axis. There has not been general agreement in the literature on how to select the body fixed axes of the JCS. The purpose of this paper is to propose a single definition of the body fixed axes of the JCS. The two most commonly used sets of body fixed axes are compared and the differences between them quantified. These differences are shown to be relevant in terms of practical applications of the JCS. Argumentation is provided to support a proposal for a standardized selection of body fixed axes of the JCS consisting of the axis ê1 embedded in the proximal segment and chosen to represent flexion-extension, the "floating" axis ê2 chosen to represent ad-abduction, and the axis ê3 embedded in the distal segment and chosen to represent axial rotation of that segment. The algorithms for the JCS are then documented using generalized terminology.

Effects of arch height of the foot on angular motion of the lower extremities in running.

It has been suggested that a relationship exists between the height of the medial longitudinal arch of the foot and athletic injuries to the lower extremities. However, the functional significance of arch height in relation to injury is not well understood. The purpose of this study was to determine the influence of arch height on kinematic variables of the lower extremities that have been associated with the incidence of injury in running in an attempt to gain some insight into a functional relationship between arch height and injury. The three-dimensional kinematics of the lower extremities were measured during running for 30 subjects using high-speed video cameras. A joint coordinate system was used to calculate the three-dimensional orientation of the ankle joint complex for a single stance phase. Simple, linear regression analyses showed that arch height does not influence either maximal eversion movement or maximal internal leg rotation during running stance. However, assuming that knee pain in running can result from the transfer of foot eversion to internal rotation of the tibia, a functional relationship between arch height and injury may exist in that the transfer of foot eversion to internal leg rotation was found to increase significantly with increasing arch height. A substantial (27%), yet incomplete, amount of the variation in the transfer of movement between subjects was explained by arch height, indicating that there must be factors other than arch height that influence the kinematic coupling at the ankle joint complex. Additionally, the transfer of movement is only one factor of many associated with the etiology of knee pain in running.(ABSTRACT TRUNCATED AT 250 WORDS)