Three-dimensional model of the feline hindlimb

ROLE OF FORELIMB MORPHOLOGY IN MUSCLE SENSORIMOTOR FUNCTIONS DURING LOCOMOTION IN THE CAT

Previous studies established strong links between morphological characteristics of mammalian hindlimb muscles and their sensorimotor functions during locomotion. Less is known about the role of forelimb morphology in motor outputs and generation of sensory signals. Here, we measured morphological characteristics of 46 forelimb muscles from 6 cats. These characteristics included muscle attachments, physiological cross-sectional area (PCSA), fascicle length, etc. We also recorded full-body mechanics and EMG activity of forelimb muscles during level overground and treadmill locomotion in 7 and 16 adult cats of either sex, respectively. We computed forelimb muscle forces along with force- and length-dependent sensory signals mapped onto corresponding cervical spinal segments. We found that patterns of computed muscle forces and afferent activities were strongly affected by the muscle's moment arm, PCSA, and fascicle length. Morphology of the shoulder muscles suggests distinct roles of the forelimbs in lateral force production and movements. Patterns of length-dependent sensory activity of muscles with long fibers (brachioradialis, extensor carpi radialis) closely matched patterns of overall forelimb length, whereas the activity pattern of biceps brachii matched forelimb orientation. We conclude that cat forelimb muscle morphology contributes substantially to locomotor function, particularly to control lateral stability and turning, rather than propulsion.

Emergence of Extreme Paw Accelerations During Cat Paw Shaking: Interactions of Spinal Central Pattern Generator, Hindlimb Mechanics and Muscle Length-Depended Feedback

Cat paw shaking is a spinal reflex for removing an irritating stimulus from paw by developing extremely high paw accelerations. Previous studies of paw shaking revealed a proximal-to-distal gradient of hindlimb segmental velocities/accelerations, as well as complex inter-joint coordination: passive motion-dependent interaction moments acting on distal segments are opposed by distal muscle moments. However, mechanisms of developing extreme paw accelerations during paw shaking remain unknown. We hypothesized that paw-shaking mechanics and muscle activity might correspond to a whip-like mechanism of energy generation and transfer along the hindlimb. We first demonstrated in experiments with five intact, adult, female cats that during paw shaking, energy generated by proximal muscle moments was transmitted to distal segments by joint forces. This energy transfer was mostly responsible for the segmental velocity/acceleration proximal-to-distal gradient. Distal muscle moments mostly absorbed energy of the distal segments. We then developed a neuromechanical model of hindlimb paw shaking comprised a half-center CPG, activating hip flexors and extensors, and passive viscoelastic distal muscles that produced length/velocity-depended force. Simulations reproduced whip-like mechanisms found experimentally: the proximal-to-distal velocity/acceleration gradient, energy transfer by joint forces and energy absorption by distal muscle moments, as well as atypical co-activation of ankle and hip flexors with knee extensors. Manipulating model parameters, including reversal of segmental inertia distal-to-proximal gradient, demonstrated important inertia contribution to developing the segmental velocity/acceleration proximal-to-distal gradient. We concluded that extreme paw accelerations during paw shaking result from interactions between a spinal CPG, hindlimb segmental inertia, and muscle length/velocity-depended feedback that tunes limb viscoelastic properties.

Three-dimensional interactive graphical model of the hindlimb muscles of the rat

Many questions in human movement sciences are addressed by exploiting the advantages of animal models. However, a 3D model of the musculoskeletal system of the frequently used rat model that includes a sufficient level of detail does not exist. Therefore, the aim of the present work was to develop an freely accessible 3D model of the rat hindlimb. Using the anatomical data of the Wistar rat (Mus norveqicus albinus) published by Green [Greene, 1935], a 3D representation of 34 muscles of the hindlimb was drawn. Two models were created, one using muscle like appearances and one using different colors. Each muscle can be viewed separately or within the context of its synergistic and antagonistic muscles. This model can serve to train new students before starting their experiments, but also for producing illustrations of experimental conditions or results. Further development of the model will be needed to equip it with the same advanced functionalities of some of the human anatomy atlases.

Direct Validation of Model-Predicted Muscle Forces in the Cat Hindlimb During Locomotion

Various methods are available for simulating the movement patterns of musculoskeletal systems and determining individual muscle forces, but the results obtained from these methods have not been rigorously validated against experiment. The aim of this study was to compare model predictions of muscle force derived for a cat hindlimb during locomotion against direct measurements of muscle force obtained in vivo. The cat hindlimb was represented as a 5-segment, 13-degrees-of-freedom (DOF), articulated linkage actuated by 25 Hill-type muscle-tendon units (MTUs). Individual muscle forces were determined by combining gait data with two widely used computational methods-static optimization and computed muscle control (CMC)-available in opensim, an open-source musculoskeletal modeling and simulation environment. The forces developed by the soleus, medial gastrocnemius (MG), and tibialis anterior muscles during free locomotion were measured using buckle transducers attached to the tendons. Muscle electromyographic activity and MTU length changes were also measured and compared against the corresponding data predicted by the model. Model-predicted muscle forces, activation levels, and MTU length changes were consistent with the corresponding quantities obtained from experiment. The calculated values of muscle force obtained from static optimization agreed more closely with experiment than those derived from CMC.

Effects of treadmill running and limb immobilization on knee cartilage degeneration and locomotor joint kinematics in rats following knee meniscal transection

OBJECTIVE

This study examined the effects of reduced and elevated weight bearing on post-traumatic osteoarthritis (PTOA) development, locomotor joint kinematics, and degree of voluntary activity in rats following medial meniscal transection (MMT).

DESIGN

Twenty-one adult rats were subjected to MMT surgery of the left hindlimb and then assigned to one of three groups: (1) regular (i.e., no intervention), (2) hindlimb immobilization, or (3) treadmill running. Sham surgery was performed in four additional rats. Voluntary wheel run time/distance was measured, and 3D hindlimb kinematics were quantified during treadmill locomotion using biplanar radiography. Rats were euthanized 8 weeks after MMT or sham surgery, and the microstructure of the tibial cartilage and subchondral bone was quantified using contrast enhanced micro-CT.

RESULTS

All three MMT groups showed signs of PTOA (full-thickness lesions and/or increased cartilage volume) compared to the sham group, however the regular and treadmill-running groups had greater osteophyte formation than the immobilization group. For the immobilization group, increased volume was only observed in the anterior region of the cartilage. The treadmill-running group demonstrated a greater knee varus angle at mid-stance than the sham group, while the immobilization group demonstrated greater reduction in voluntary running than all the other groups at 2 weeks post-surgery.

CONCLUSIONS

Elevated weight-bearing via treadmill running at a slow/moderate speed did not accelerate PTOA in MMT rats when compared to regular weight-bearing. Reduced weight-bearing via immobilization may attenuate overall PTOA but still resulted in regional cartilage degeneration. Overall, there were minimal differences in hindlimb kinematics and voluntary running between MMT and sham rats.

A three dimensional multiplane kinematic model for bilateral hind limb gait analysis in cats

Background

Kinematic gait analysis is an important noninvasive technique used for quantitative evaluation and description of locomotion and other movements in healthy and injured populations. Three dimensional (3D) kinematic analysis offers additional outcome measures including internal-external rotation not characterized using sagittal plane (2D) analysis techniques.

Methods

The objectives of this study were to 1) develop and evaluate a 3D hind limb multiplane kinematic model for gait analysis in cats using joint coordinate systems, 2) implement and compare two 3D stifle (knee) prediction techniques, and 3) compare flexion-extension determined using the multiplane model to a sagittal plane model. Walking gait was recorded in 3 female adult cats (age = 2.9 years, weight = 3.5 ± 0.2 kg). Kinematic outcomes included flexion-extension, internal-external rotation, and abduction-adduction of the hip, stifle, and tarsal (ankle) joints.

Results

Each multiplane stifle prediction technique yielded similar findings. Joint angles determined using markers placed on skin above bony landmarks in vivo were similar to joint angles determined using a feline hind limb skeleton in which markers were placed directly on landmarks ex vivo. Differences in hip, stifle, and tarsal joint flexion-extension were demonstrated when comparing the multiplane model to the sagittal plane model.

Conclusions

This multiplane cat kinematic model can predict joint rotational kinematics as a tool that can quantify frontal, transverse, and sagittal plane motion. This model has multiple advantages given its ability to characterize joint internal-external rotation and abduction-adduction. A further, important benefit is greater accuracy in representing joint flexion-extension movements.

Musculoskeletal geometry accounts for apparent extrinsic representation of paw position in dorsal spinocerebellar tract

Proprioception, the sense of limb position and motion, arises from individual muscle receptors. An important question is how and where in the neuroaxis our high level "extrinsic" sense of limb movement originates. In the 1990s, a series of papers detailed the properties of neurons in the dorsal spinocerebellar tract (DSCT) of the cat. Despite their direct projections from sensory receptors, it appeared that half of these neurons had consistent, high-level tuning to paw position rather than to joint angles (or muscle lengths). These results suggested that many DSCT neurons compute paw position from lower level sensory information. We examined the contribution of musculoskeletal geometry to this apparent extrinsic representation by simulating a three-joint hindlimb with mono- and biarticular muscles, each providing a muscle spindlelike signal, modulated by the muscle length. We simulated neurons driven by randomly weighted combinations of these signals and moved the paw to different positions under two joint-covariance conditions similar to the original experiments. Our results paralleled those experiments in a number of respects: 1) Many neurons were tuned to paw position relative to the hip under both conditions. 2) The distribution of tuning was strongly bimodal, with most neurons driven by whole-leg flexion or extension. 3) The change in tuning between conditions clustered around zero (median absolute change ~20°). These results indicate that, at least for these constraint conditions, extrinsic-like representation can be achieved simply through musculoskeletal geometry and convergent muscle length inputs. Consequently, they suggest a reinterpretation of the earlier results may be required.NEW & NOTEWORTHY A classic experiment concluding that many dorsal spinocerebellar tract neurons encode paw position rather than joint angles has been cited by many studies as evidence for high-level computation occurring within a single synapse of the sensors. However, our study provides evidence that such a computation is not required to explain the results. Using simulation, we replicated many of the original results with purely random connectivity, suggesting that a reinterpretation of the classic experiment is needed.

Muscle moment arms and sensitivity analysis of a mouse hindlimb musculoskeletal model

Musculoskeletal modelling has become a valuable tool with which to understand how neural, muscular, skeletal and other tissues are integrated to produce movement. Most musculoskeletal modelling work has to date focused on humans or their close relatives, with few examples of quadrupedal animal limb models. A musculoskeletal model of the mouse hindlimb could have broad utility for questions in medicine, genetics, locomotion and neuroscience. This is due to this species’ position as a premier model of human disease, having an array of genetic tools for manipulation of the animal in vivo, and being a small quadruped, a category for which few models exist. Here, the methods used to develop the first three‐dimensional (3D) model of a mouse hindlimb and pelvis are described. The model, which represents bones, joints and 39 musculotendon units, was created through a combination of previously gathered muscle architecture data from microdissections, contrast‐enhanced micro‐computed tomography (CT) scanning and digital segmentation. The model allowed muscle moment arms as well as muscle forces to be estimated for each musculotendon unit throughout a range of joint rotations. Moment arm analysis supported the reliability of musculotendon unit placement within the model, and comparison to a previously published rat hindlimb model further supported the model's reliability. A sensitivity analysis performed on both the force‐generating parameters and muscle's attachment points of the model indicated that the maximal isometric muscle moment is generally most sensitive to changes in either tendon slack length or the coordinates of insertion, although the degree to which the moment is affected depends on several factors. This model represents the first step in the creation of a fully dynamic 3D computer model of the mouse hindlimb and pelvis that has application to neuromuscular disease, comparative biomechanics and the neuromechanical basis of movement. Capturing the morphology and dynamics of the limb, it enables future dissection of the complex interactions between the nervous and musculoskeletal systems as well as the environment.

Musculoskeletal modelling in dogs: challenges and future perspectives

Musculoskeletal models have proven to be a valuable tool in human orthopaedics research. Recently, veterinary research started taking an interest in the computer modelling approach to understand the forces acting upon the canine musculoskeletal system. While many of the methods employed in human musculoskeletal models can applied to canine musculoskeletal models, not all techniques are applicable. This review summarizes the important parameters necessary for modelling, as well as the techniques employed in human musculoskeletal models and the limitations in transferring techniques to canine modelling research. The major challenges in future canine modelling research are likely to centre around devising alternative techniques for obtaining maximal voluntary contractions, as well as finding scaling factors to adapt a generalized canine musculoskeletal model to represent specific breeds and subjects.

Suboptimal Muscle Synergy Activation Patterns Generalize their Motor Function across Postures

We used a musculoskeletal model to investigate the possible biomechanical and neural bases of using consistent muscle synergy patterns to produce functional motor outputs across different biomechanical conditions, which we define as generalizability. Experimental studies in cats demonstrate that the same muscle synergies are used during reactive postural responses at widely varying configurations, producing similarly-oriented endpoint force vectors with respect to the limb axis. However, whether generalizability across postures arises due to similar biomechanical properties or to neural selection of a particular muscle activation pattern has not been explicitly tested. Here, we used a detailed cat hindlimb model to explore the set of feasible muscle activation patterns that produce experimental synergy force vectors at a target posture, and tested their generalizability by applying them to different test postures. We used three methods to select candidate muscle activation patterns: (1) randomly-selected feasible muscle activation patterns, (2) optimal muscle activation patterns minimizing muscle effort at a given posture, and (3) generalizable muscle activation patterns that explicitly minimized deviations from experimentally-identified synergy force vectors across all postures. Generalizability was measured by the deviation between the simulated force direction of the candidate muscle activation pattern and the experimental synergy force vectors at the test postures. Force angle deviations were the greatest for the randomly selected feasible muscle activation patterns (e.g., >100°), intermediate for effort-wise optimal muscle activation patterns (e.g., ~20°), and smallest for generalizable muscle activation patterns (e.g., <5°). Generalizable muscle activation patterns were suboptimal in terms of effort, often exceeding 50% of the maximum possible effort (cf. ~5% in minimum-effort muscle activation patterns). The feasible muscle activation ranges of individual muscles associated with producing a specific synergy force vector was reduced by ~45% when generalizability requirements were imposed. Muscles recruited in the generalizable muscle activation patterns had less sensitive torque-producing characteristics to changes in postures. We conclude that generalization of function across postures does not arise from limb biomechanics or a single optimality criterion. Muscle synergies may reflect acquired motor solutions globally tuned for generalizability across biomechanical contexts, facilitating rapid motor adaptation.

Musculoskeletal modelling of an ostrich (Struthio camelus) pelvic limb: influence of limb orientation on muscular capacity during locomotion

We developed a three-dimensional, biomechanical computer model of the 36 major pelvic limb muscle groups in an ostrich (Struthio camelus) to investigate muscle function in this, the largest of extant birds and model organism for many studies of locomotor mechanics, body size, anatomy and evolution. Combined with experimental data, we use this model to test two main hypotheses. We first query whether ostriches use limb orientations (joint angles) that optimize the moment-generating capacities of their muscles during walking or running. Next, we test whether ostriches use limb orientations at mid-stance that keep their extensor muscles near maximal, and flexor muscles near minimal, moment arms. Our two hypotheses relate to the control priorities that a large bipedal animal might evolve under biomechanical constraints to achieve more effective static weight support. We find that ostriches do not use limb orientations to optimize the moment-generating capacities or moment arms of their muscles. We infer that dynamic properties of muscles or tendons might be better candidates for locomotor optimization. Regardless, general principles explaining why species choose particular joint orientations during locomotion are lacking, raising the question of whether such general principles exist or if clades evolve different patterns (e.g., weighting of muscle force-length or force-velocity properties in selecting postures). This leaves theoretical studies of muscle moment arms estimated for extinct animals at an impasse until studies of extant taxa answer these questions. Finally, we compare our model's results against those of two prior studies of ostrich limb muscle moment arms, finding general agreement for many muscles. Some flexor and extensor muscles exhibit self-stabilization patterns (posture-dependent switches between flexor/extensor action) that ostriches may use to coordinate their locomotion. However, some conspicuous areas of disagreement in our results illustrate some cautionary principles. Importantly, tendon-travel empirical measurements of muscle moment arms must be carefully designed to preserve 3D muscle geometry lest their accuracy suffer relative to that of anatomically realistic models. The dearth of accurate experimental measurements of 3D moment arms of muscles in birds leaves uncertainty regarding the relative accuracy of different modelling or experimental datasets such as in ostriches. Our model, however, provides a comprehensive set of 3D estimates of muscle actions in ostriches for the first time, emphasizing that avian limb mechanics are highly three-dimensional and complex, and how no muscles act purely in the sagittal plane. A comparative synthesis of experiments and models such as ours could provide powerful synthesis into how anatomy, mechanics and control interact during locomotion and how these interactions evolve. Such a framework could remove obstacles impeding the analysis of muscle function in extinct taxa.

Motoneuron intrinsic properties, but not their receptive fields, recover in chronic spinal injury

Proper movement execution relies on precise input processing by spinal motoneurons (MNs). Spinal MNs are activated by limb joint rotations. Typically, their movement-related receptive fields (MRRFs) are sharply focused and joint-specific. After acute spinal transection MRRFs become wide, but their manifestation is not apparent, as intrinsic excitability, primarily resulting from the loss of persistent inward currents (PICs), dramatically decreases. PICs undergo a remarkable recovery with time after injury. Here we investigate whether MRRFs undergo a recovery that parallels that of the PIC. Using the chronic spinal cat in acute terminal decerebrate preparations, we found that MRRFs remain expanded 1 month after spinal transaction, whereas PICs recovered to >80% of their preinjury amplitudes. These recovered PICs substantially amplified the expanded inputs underlying the MRRFs. As a result, we show that single joint rotations lead to the activation of muscles across the entire limb. These results provide a potential mechanism for the propagation of spasms throughout the limb.

The mechanical actions of muscles predict the direction of muscle activation during postural perturbations in the cat hindlimb

Humans and cats respond to balance challenges, delivered via horizontal support surface perturbations, with directionally selective muscle recruitment and constrained ground reaction forces. It has been suggested that this postural strategy arises from an interaction of limb biomechanics and proprioceptive networks in the spinal cord. A critical experimental validation of this hypothesis is to test the prediction that the principal directions of muscular activation oppose the directions responding muscles exert their forces on the environment. Therefore, our objective was to quantify the endpoint forces of a diverse set of cat hindlimb muscles and compare them with the directionally sensitive muscle activation patterns generated in the intact and decerebrate cat. We hypothesized that muscles are activated based on their mechanical advantage. Our primary expectation was that the principal direction of muscle activation during postural perturbations will be directed oppositely (180°) from the muscle endpoint ground reaction force. We found that muscle activation during postural perturbations was indeed directed oppositely to the endpoint reaction forces of that muscle. These observations indicate that muscle recruitment during balance challenges is driven, at least in part, by limb architecture. This suggests that sensory sources that provide feedback about the mechanical environment of the limb are likely important to appropriate and effective responses during balance challenges. Finally, we extended the analysis to three dimensions and different stance widths, laying the groundwork for a more comprehensive study of postural regulation than was possible with measurements confined to the horizontal plane and a single stance configuration.

Contributions of phase resetting and interlimb coordination to the adaptive control of hindlimb obstacle avoidance during locomotion in rats: a simulation study

Obstacle avoidance during locomotion is essential for safe, smooth locomotion. Physiological studies regarding muscle synergy have shown that the combination of a small number of basic patterns produces the large part of muscle activities during locomotion and the addition of another pattern explains muscle activities for obstacle avoidance. Furthermore, central pattern generators in the spinal cord are thought to manage the timing to produce such basic patterns. In the present study, we investigated sensory-motor coordination for obstacle avoidance by the hindlimbs of the rat using a neuromusculoskeletal model. We constructed the musculoskeletal part of the model based on empirical anatomical data of the rat and the nervous system model based on the aforementioned physiological findings of central pattern generators and muscle synergy. To verify the dynamic simulation by the constructed model, we compared the simulation results with kinematic and electromyographic data measured during actual locomotion in rats. In addition, we incorporated sensory regulation models based on physiological evidence of phase resetting and interlimb coordination and examined their functional roles in stepping over an obstacle during locomotion. Our results show that the phase regulation based on interlimb coordination contributes to stepping over a higher obstacle and that based on phase resetting contributes to quick recovery after stepping over the obstacle. These results suggest the importance of sensory regulation in generating successful obstacle avoidance during locomotion.

Defining feasible bounds on muscle activation in a redundant biomechanical task: practical implications of redundancy

Measured muscle activation patterns often vary significantly from musculoskeletal model predictions that use optimization to resolve redundancy. Although experimental muscle activity exhibits both inter- and intra-subject variability we lack adequate tools to quantify the biomechanical latitude that the nervous system has when selecting muscle activation patterns. Here, we identified feasible ranges of individual muscle activity during force production in a musculoskeletal model to quantify the degree to which biomechanical redundancy allows for variability in muscle activation patterns. In a detailed cat hindlimb model matched to the posture of three cats, we identified the lower and upper bounds on muscle activity in each of 31 muscles during static endpoint force production across different force directions and magnitudes. Feasible ranges of muscle activation were relatively unconstrained across force magnitudes such that only a few (0-13%) muscles were found to be truly "necessary" (e.g. exhibited non-zero lower bounds) at physiological force ranges. Most of the muscles were "optional", having zero lower bounds, and frequently had "maximal" upper bounds as well. Moreover, "optional" muscles were never selected by optimization methods that either minimized muscle stress, or that scaled the pattern required for maximum force generation. Therefore, biomechanical constraints were generally insufficient to restrict or specify muscle activation levels for producing a force in a given direction, and many muscle patterns exist that could deviate substantially from one another but still achieve the task. Our approach could be extended to identify the feasible limits of variability in muscle activation patterns in dynamic tasks such as walking.

Practical limits on muscle synergy identification by non-negative matrix factorization in systems with mechanical constraints

Statistical decomposition, including non-negative matrix factorization (NMF), is a convenient tool for identifying patterns of structured variability within behavioral motor programs, but it is unclear how the resolved factors relate to actual neural structures. Factors can be extracted from a uniformly sampled, low-dimension command space. In practical application, the command space is limited, either to those activations that perform some task(s) successfully or to activations induced in response to specific perturbations. NMF was applied to muscle activation patterns synthesized from low dimensional, synergy-like control modules mimicking simple task performance or feedback activation from proprioceptive signals. In the task-constrained paradigm, the accuracy of control module recovery was highly dependent on the sampled volume of control space, such that sampling even 50% of control space produced a substantial degradation in factor accuracy. In the feedback paradigm, NMF was not capable of extracting more than four control modules, even in a mechanical model with seven internal degrees of freedom. Reduced access to the low-dimensional control space imposed by physical constraints may result in substantial distortion of an existing low dimensional controller, such that neither the dimensionality nor the composition of the recovered/extracted factors match the original controller.

Optimization of muscle activity for task-level goals predicts complex changes in limb forces across biomechanical contexts

Optimality principles have been proposed as a general framework for understanding motor control in animals and humans largely based on their ability to predict general features movement in idealized motor tasks. However, generalizing these concepts past proof-of-principle to understand the neuromechanical transformation from task-level control to detailed execution-level muscle activity and forces during behaviorally-relevant motor tasks has proved difficult. In an unrestrained balance task in cats, we demonstrate that achieving task-level constraints center of mass forces and moments while minimizing control effort predicts detailed patterns of muscle activity and ground reaction forces in an anatomically-realistic musculoskeletal model. Whereas optimization is typically used to resolve redundancy at a single level of the motor hierarchy, we simultaneously resolved redundancy across both muscles and limbs and directly compared predictions to experimental measures across multiple perturbation directions that elicit different intra- and interlimb coordination patterns. Further, although some candidate task-level variables and cost functions generated indistinguishable predictions in a single biomechanical context, we identified a common optimization framework that could predict up to 48 experimental conditions per animal (n = 3) across both perturbation directions and different biomechanical contexts created by altering animals' postural configuration. Predictions were further improved by imposing experimentally-derived muscle synergy constraints, suggesting additional task variables or costs that may be relevant to the neural control of balance. These results suggested that reduced-dimension neural control mechanisms such as muscle synergies can achieve similar kinetics to the optimal solution, but with increased control effort (≈2×) compared to individual muscle control. Our results are consistent with the idea that hierarchical, task-level neural control mechanisms previously associated with voluntary tasks may also be used in automatic brainstem-mediated pathways for balance.

Patterns of spinal sensory-motor connectivity prescribed by a dorsoventral positional template

Sensory-motor circuits in the spinal cord are constructed with a fine specificity that coordinates motor behavior, but the mechanisms that direct sensory connections with their motor neuron partners remain unclear. The dorsoventral settling position of motor pools in the spinal cord is known to match the distal-to-proximal position of their muscle targets in the limb, but the significance of invariant motor neuron positioning is unknown. An analysis of sensory-motor connectivity patterns in FoxP1 mutant mice, where motor neuron position has been scrambled, shows that the final pattern of sensory-motor connections is initiated by the projection of sensory axons to discrete dorsoventral domains of the spinal cord without regard for motor neuron subtype or, indeed, the presence of motor neurons. By implication, the clustering and dorsoventral settling position of motor neuron pools serve as a determinant of the pattern of sensory input specificity and thus motor coordination.

Estimation of musculoskeletal models from in situ measurements of muscle action in the rat hindlimb

Musculoskeletal models are often created by making detailed anatomical measurements of muscle properties. These measurements can then be used to determine the parameters of canonical models of muscle action. We describe here a complementary approach for developing and validating muscle models, using in situ measurements of muscle actions. We characterized the actions of two rat hindlimb muscles: the gracilis posticus (GRp) and the posterior head of biceps femoris (BFp; excluding the anterior head with vertebral origin). The GRp is a relatively simple muscle, with a circumscribed origin and insertion. The BFp is more complex, with an insertion distributed along the tibia. We measured the six-dimensional isometric forces and moments at the ankle evoked from stimulating each muscle at a range of limb configurations. The variation of forces and moments across the workspace provides a succinct characterization of muscle action. We then used this data to create a simple muscle model with a single point insertion and origin. The model parameters were optimized to best explain the observed force-moment data. This model explained the relatively simple muscle, GRp, very well (R(2)>0.85). Surprisingly, this simple model was also able to explain the action of the BFp, despite its greater complexity (R(2)>0.84). We then compared the actions observed here with those predicted using recently published anatomical measurements. Although the forces and moments predicted for the GRp were very similar to those observed here, the predictions for the BFp differed. These results show the potential utility of the approach described here for the development and refinement of musculoskeletal models based on in situ measurements of muscle actions.

Short-term motor compensations to denervation of feline soleus and lateral gastrocnemius result in preservation of ankle mechanical output during locomotion

Denervation of selected ankle extensors in animals results in locomotor changes. These changes have been suggested to permit preservation of global kinematic characteristics of the hindlimb during stance. The peak ankle joint moment is also preserved immediately after denervation of several ankle extensors in the cat, suggesting that the animal's response to peripheral nerve injury may also be aimed at preserving ankle mechanical output. We tested this hypothesis by comparing joint moments and power patterns during walking before and after denervation of soleus and lateral gastrocnemius muscles. Hindlimb kinematics, ground reaction forces and electromyographic activity of selected muscles were recorded during level, downslope (-50%) and upslope (50%) walking before and 1-3 weeks after nerve denervation. Denervation resulted in increased activity of the intact medial gastrocnemius and plantaris muscles, greater ankle dorsiflexion, smaller knee flexion, and the preservation of the peak ankle moment during stance. Surprisingly, ankle positive power generated in the propulsion phase of stance was increased (up to 50%) after denervation in all walking conditions (p < 0.05). The obtained results suggest that the short-term motor compensation to denervation of lateral gastrocnemius and soleus muscles may allow for preservation of mechanical output at the ankle. The additional mechanical energy generated at the ankle during propulsion can result, in part, from increased activity of intact synergists, the use of passive tissues around the ankle and by the tendon action of ankle two-joint muscles and crural fascia.

Directional constraint of endpoint force emerges from hindlimb anatomy

Postural control requires the coordination of force production at the limb endpoints to apply an appropriate force to the body. Subjected to horizontal plane perturbations, quadruped limbs stereotypically produce force constrained along a line that passes near the center of mass. This phenomenon, referred to as the force constraint strategy, may reflect mechanical constraints on the limb or body, a specific neural control strategy or an interaction among neural controls and mechanical constraints. We used a neuromuscular model of the cat hindlimb to test the hypothesis that the anatomical constraints restrict the mechanical action of individual muscles during stance and constrain the response to perturbations to a line independent of perturbation direction. In a linearized neuromuscular model of the cat hindlimb, muscle lengthening directions were highly conserved across 10,000 different muscle activation patterns, each of which produced an identical, stance-like endpoint force. These lengthening directions were closely aligned with the sagittal plane and reveal an anatomical structure for directionally constrained force responses. Each of the 10,000 activation patterns was predicted to produce stable stance based on Lyapunov stability analysis. In forward simulations of the nonlinear, seven degree of freedom model under the action of 200 random muscle activation patterns, displacement of the endpoint from its equilibrium position produced restoring forces, which were also biased toward the sagittal plane. The single exception was an activation pattern based on minimum muscle stress optimization, which produced destabilizing force responses in some perturbation directions. The sagittal force constraint increased during simulations as the system shifted from an inertial response during the acceleration phase to a viscoelastic response as peak velocity was obtained. These results qualitatively match similar experimental observations and suggest that the force constraint phenomenon may result from the anatomical arrangement of the limb.

The Influence of Modeling Separate Neuromuscular Compartments on the Force and Moment Generating Capacities of Muscles of the Feline Hindlimb

Functional electrical stimulation (FES) has the capacity to regenerate motion for individuals with spinal cord injuries. However, it is not straightforward to determine the stimulation parameters to generate a coordinated movement. Musculoskeletal models can provide a noninvasive simulation environment to estimate muscle force and activation timing sequences for a variety of tasks. Therefore, the purpose of this study was to develop a musculoskeletal model of the feline hindlimb for simulations to determine stimulation parameters for intrafascicular multielectrode stimulation (a method of FES). Additionally, we aimed to explore the differences in modeling neuromuscular compartments compared with representing these muscles as a single line of action. When comparing the modeled neuromuscular compartments of biceps femoris, sartorius, and semimembranosus to representations of these muscles as a single line of action, we observed that modeling the neuromuscular compartments of these three muscles generated different force and moment generating capacities when compared with single muscle representations. Differences as large as 4 N m (∼400% in biceps femoris) were computed between the summed moments of the neuromuscular compartments and the single muscle representations. Therefore, modeling neuromuscular compartments may be necessary to represent physiologically reasonable force and moment generating capacities of the feline hindlimb.

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.

Hindlimb endpoint forces predict movement direction evoked by intraspinal microstimulation in cats

We measured the forces produced at the cat's hindpaw by microstimulation of the lumbar spinal cord and the movements resulting from those forces. We also measured the forces and movements produced by co- and sequential activation of two intraspinal sites. Isometric force responses were measured at nine limb configurations with the paw attached to a force transducer. The active forces elicited at different limb configurations were summarized as patterns representing the sagittal plane component of the forces produced at the paw throughout the workspace. The force patterns divided into the same distinct types found with the femur fixed. The responses during simultaneous activation of two spinal sites always resembled the response for activation of one of the two sites, i.e., winner-take-all, and we did not observe vectorial summation of the forces produced by activation of each site individually as reported in chronic spinal animals. The movements produced by activation of each of the sites were consistent with the force orientations, and different movements could be created by varying the sequence of activation of individual sites. Our results highlight the absence of a vectorial summation phenomenon during intraspinal microstimulation in decerebrate animals, and the preservation during movement of the orientation of isometric forces.

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.

Force Regulation of Ankle Extensor Muscle Activity in Freely Walking Cats

To gain insight into the relative importance of force feedback to ongoing ankle extensor activity during walking in the conscious cat, we isolated the medial gastrocnemius muscle (MG) by denervating the other ankle extensors and measured the magnitude of its activity at different muscle lengths, velocities, and forces accomplished by having the animals walk up and down a sloped pegway. Mathematical models of proprioceptor dynamics predicted afferent activity and revealed that the changes in muscle activity under our experimental conditions were strongly correlated with Ib activity and not consistently associated with changes in Ia or group II activity. This allowed us to determine the gains within the force feedback pathway using a simple model of the neuromuscular system and the measured relationship between MG activity and force. Loop gain increased with muscle length due to the intrinsic force–length property of muscle. The gain of the pathway that converts muscle force to motoneuron depolarization was independent of length. To better test for a causal relationship between modulation of force feedback and changes in muscle activity, a second set of experiments was performed in which the MG muscle was perturbed during ground contact of the hind foot by dropping or lifting the peg underfoot. Collectively, these investigations support a causal role for force feedback and indicate that about 30% of the total muscle activity is due to force feedback during level walking. Force feedback's role increases during upslope walking and decreases during downslope walking, providing a simple mechanism for compensating for changes in terrain.

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.

Reduction of neuromuscular redundancy for postural force generation using an intrinsic stability criterion

Postural control requires the coordination of multiple muscles to achieve both endpoint force production and postural stability. Multiple muscle activation patterns can produce the required force for standing, but the mechanical stability associated with any given pattern may vary, and has implications for the degree of delayed neural feedback necessary for postural stability. We hypothesized that muscular redundancy is reduced when muscle activation patterns are chosen with respect to intrinsic musculoskeletal stability as well as endpoint force production. We used a three-dimensional musculoskeletal model of the cat hindlimb with 31 muscles to determine the possible contributions of intrinsic muscle properties to limb stability during isometric force generation. Using dynamic stability analysis we demonstrate that within the large set of activation patterns that satisfy the force requirement for posture, only a reduced subset produce a mechanically stable limb configuration. Greater stability in the frontal-plane suggests that neural control mechanisms are more highly active for sagittal-plane and for ankle joint control. Even when the limb was unstable, the time-constants of instability were sufficiently great to allow long-latency neural feedback mechanisms to intervene, which may be preferential for movements requiring maneuverability versus stability. Local joint stiffness of muscles was determined by the stabilizing or destabilizing effects of moment-arm versus joint angle relationships. By preferentially activating muscles with high local stiffness, muscle activation patterns with feedforward stabilizing properties could be selected. Such a strategy may increase intrinsic postural stability without co-contraction, and may be useful criteria in the force-sharing problem.

Movement-related receptive fields of spinal motoneurones with active dendrites

The primary control of spinal motoneurone excitability is mediated by descending monoaminergic systems, which have diffuse effects on multiple motor pools. Much of the sensory input evoked by movement is also distributed broadly to multiple joints. The muscle spindle Ia afferent system, however, is sharply focused, with Ia excitation restricted to close synergists and Ia reciprocal inhibition only shared between antagonists acting at a single joint. We studied the interaction of neuromodulatory and sensory inputs in determining the movement-related receptive field (MRRF) of motoneurones during passive joint movements of the cat hindlimb. In a decerebrate preparation with tonic monoaminergic input to the cord, the MRRFs tended to be focused for the ankle and knee extensor motor pools studied. Ankle rotation produced larger synaptic currents in ankle extensors than knee or hip rotations and knee rotation dominated input to the knee extensors. The persistent inward current (PIC) in motoneurone dendrites, which is facilitated by monoaminergic input, amplified the MRRF about 2-fold, consistent with its effects on other inputs. Acute spinal transaction markedly broadened MRRFs, with hip rotation generating large currents in both ankle and knee extensors. Spinalization also eliminated amplification of MRRFs, as expected from elimination of descending monoaminergic input. Ia reciprocal inhibition is very effective in suppressing dendritic PICs and thus provides a local and specific PIC control system to oppose the diffuse PIC facilitation from descending monoaminergic systems. The focused MRRF seen in the intact cord state would allow reciprocal inhibition to fulfil this role without undue interference from multijoint input from other afferent systems.

A three-dimensional model of the rat hindlimb: musculoskeletal geometry and muscle moment arms

As a first step towards developing a dynamic model of the rat hindlimb, we measured muscle attachment and joint center coordinates relative to bony landmarks using stereophotogrammetry. Using these measurements, we analyzed muscle moment arms as functions of joint angle for most hindlimb muscles, and tested the hypothesis that postural change alone is sufficient to alter the function of selected muscles of the leg. We described muscle attachment sites as second-order curves. The length of the fit parabola and residual errors in the orthogonal directions give an estimate of muscle attachment sizes, which are consistent with observations made during dissection. We modeled each joint as a moving point dependent on joint angle; relative endpoint errors less than 7% indicate this method as accurate. Most muscles have moment arms with a large range across the physiological domain of joint angles, but their moment arms peak and vary little within the locomotion domain. The small variation in moment arms during locomotion potentially simplifies the neural control requirements during this phase. The moment arms of a number of muscles cross zero as angle varies within the quadrupedal locomotion domain, indicating they are intrinsically stabilizing. However, in the bipedal locomotion domain, the moment arms of these muscles do not cross zero and thus are no longer intrinsically stabilizing. We found that muscle function is largely determined by the change in moment arm with joint angle, particularly the transition from quadrupedal to bipedal posture, which may alter an intrinsically stabilizing arrangement or change the control burden.

Functional muscle synergies constrain force production during postural tasks

We recently demonstrated that a set of five functional muscle synergies were sufficient to characterize both hindlimb muscle activity and active forces during automatic postural responses in cats standing at multiple postural configurations. This characterization depended critically upon the assumption that the endpoint force vector (synergy force vector) produced by the activation of each muscle synergy rotated with the limb axis as the hindlimb posture varied in the sagittal plane. Here, we used a detailed, 3D static model of the hindlimb to confirm that this assumption is biomechanically plausible: as we varied the model posture, simulated synergy force vectors rotated monotonically with the limb axis in the parasagittal plane (r2=0.94+/-0.08). We then tested whether a neural strategy of using these five functional muscle synergies provides the same force-generating capability as controlling each of the 31 muscles individually. We compared feasible force sets (FFSs) from the model with and without a muscle synergy organization. FFS volumes were significantly reduced with the muscle synergy organization (F=1556.01, p<<0.01), and as posture varied, the synergy-limited FFSs changed in shape, consistent with changes in experimentally measured active forces. In contrast, nominal FFS shapes were invariant with posture, reinforcing prior findings that postural forces cannot be predicted by hindlimb biomechanics alone. We propose that an internal model for postural force generation may coordinate functional muscle synergies that are invariant in intrinsic limb coordinates, and this reduced-dimension control scheme reduces the set of forces available for postural control.

Role of biomechanics and muscle activation strategy in the production of endpoint force patterns in the cat hindlimb

We used a musculoskeletal model of the cat hindlimb to compare the patterns of endpoint forces generated by all possible combination of 12 hindlimb muscles under three different muscle activation rules: homogeneous activation of muscles based on uniform activation levels, homogeneous activation of muscles based on uniform (normalized) force production, and activation based on the topography of spinal motoneuron pools. Force patterns were compared with the patterns obtained experimentally by microstimulation of the lumbar spinal cord in spinal intact cats. Magnitude and orientation of the force patterns were compared, as well as the proportion of the types found, and the proportions of patterns exhibiting points of zero force (equilibrium points). The force patterns obtained with the homogenous activation and motoneuron topography models were quite similar to those measured experimentally, with the differences being larger for the patterns from the normalized endpoint forces model. Differences in the proportions of types of force patterns between the three models and the experimental results were significant for each model. Both homogeneous activation and normalized endpoint force models produced similar proportions of equilibrium points as found experimentally. The results suggest that muscle biomechanics play an important role in limiting the number of endpoint force pattern types, and that muscle combinations activated at similar levels reproduced best the experimental results obtained with intraspinal microstimulation.

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90 degrees in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.

Biarticular hip extensor and knee flexor muscle moment arms of the feline hindlimb

Moment arms are important for understanding muscular behavior and for calculating internal muscle forces in musculoskeletal simulations. Biarticular muscles cross two joints and have moment arms that depend on the angle of both joints the muscles cross. The tendon excursion method was used to measure the joint angle-dependence of hamstring (biceps femoris, semimembranosus and semitendinosus) moment arm magnitudes of the feline hindlimb at the knee and hip joints. Knee angle influenced hamstring moment arm magnitudes at the hip joint; compared to a flexed knee joint, the moment arm for semimembranosus posterior at the hip was at most 7.4 mm (25%) larger when the knee was extended. On average, hamstring moment arms at the hip increased by 4.9 mm when the knee was more extended. In contrast, moment arm magnitudes at the knee varied by less than 2.8 mm (mean=1.6 mm) for all hamstring muscles at the two hip joint angles tested. Thus, hamstring moment arms at the hip were dependent on knee position, while hamstring moment arms at the knee were not as strongly associated with relative hip position. Additionally, the feline hamstring muscle group had a larger mechanical advantage at the hip than at the knee joint.

The effects of self-reinnervation of cat medial and lateral gastrocnemius muscles on hindlimb kinematics in slope walking

The aim of this study was to investigate the effects of self-reinnervation of the medial (MG) and lateral gastrocnemius (LG) muscles on joint kinematics of the whole hindlimb during overground walking on surfaces of varying slope in the cat. Hindlimb kinematics were assessed (1) with little or no activity in MG and LG (short-term effects of self-reinnervation), and (2) after motor function of these muscles was presumably recovered but their proprioceptive feedback permanently disrupted (long-term effects of self-reinnervation). The stance phase was examined in three walking conditions: downslope (-50%, i.e. -26.6 degrees ), level (0%) and upslope (+50%, +26.6 degrees ). Measurements were performed prior to and at consecutive time points (between 1 and 57 weeks) after transecting and immediately suturing MG and LG nerves. It was found that MG-LG self-reinnervation did not significantly change hip height and hindlimb orientation in any of the three walking conditions. Substantial short-term effects were observed in the ankle joint (e.g., increased flexion in early stance) as well as in metatarsophalangeal and knee joints, leading to altered interjoint coordination. Hindlimb kinematics in level and upslope walking progressed back towards baseline within 14-19 weeks. Thus in these two conditions the cats were walking without any detectable kinematic deficits, despite the absence of length feedback from two major ankle extensors. This was verified in a decerebrate preparation for four of the five cats. In contrast, ankle joint kinematics as well as interjoint coordination in downslope walking gradually progressed towards, but never reached their baseline patterns. The short-term effects can be explained by both mechanical and neural factors that are affected by the functional elimination of MG and LG. Permanent changes in kinematics during downslope walking indicate the importance of proprioceptive feedback from the MG and LG muscles in regulating locomotor activity of ankle extensors. Full recovery of hindlimb kinematics during level and upslope walking suggests that the proprioceptive loss is compensated by other sensory sources (e.g. cutaneous receptors) or altered central drive.

Biomechanical capabilities influence postural control strategies in the cat hindlimb

During postural responses to perturbations, horizontal plane forces generated by the cat hindlimb are stereotypically directed either towards or away from the animal's center of mass, independent of perturbation direction. We used a static, three-dimensional musculoskeletal model of the hindlimb to investigate possible biomechanical determinants of this "force constraint strategy." We hypothesized that directions in which the hindlimb can produce large forces are preferentially used in postural control. We computed feasible force sets (FFSs) based on hindlimb configurations of three cats during postural equilibrium tasks and compared them to horizontal plane postural force directions. The grand mean FFS was bimodal, with maxima near the posterior-anterior axis (-86+/-8 degrees and 71+/-4 degrees ), and minima near the medial-lateral axis (177+/-8 degrees and 8+/-8 degrees ). Experimental postural force directions clustered near both maxima; there were no medial postural forces near the absolute minimum. However, the medians of the anterior and posterior postural force direction histograms in the right hindlimb were rotated counter-clockwise from the FFS maxima (p<0.05; Wilcoxon signed-rank test). Because the posterior-anterior alignment of the FFS is consistent with a hindlimb structure optimized for locomotion, we conclude that the biomechanical capabilities of the hindlimb strongly influence, but do not uniquely determine the force directions observed in the force constraint strategy. Forces used in postural control may reflect a balance between a neural preference for using forces in the directions of large feasible forces and other criteria, such as the stabilization of the center of mass, and muscular coordination strategies.

Control of ground reaction forces by hindlimb muscles during cat locomotion

It has been proposed that biarticular muscles are primarily responsible for the control of the direction of external forces, as their activation is closely related and highly sensitive to the direction of external forces. This functional role for biarticular muscles has been supported qualitatively by experimental evidence, but has never been tested quantitatively for lack of a mathematical/mechanical formulation of this theory and the difficulty of measuring individual muscle forces during voluntary movements. The purposes of this study were: (1) to define rules for muscular coordination based on the control of external forces; (2) to develop a model of the cat hindlimb that allows for the calculation of the magnitude and direction of the ground reaction forces (GRFs) produced by individual hindlimb muscles; and (3) to test if the coordination of mono- and biarticular cat hindlimb muscles is related to the control of the resultant GRF. We measured the GRF, hindlimb kinematics, selected muscle forces and activations during cat locomotion. Then, the measured muscle forces were used as input to the hindlimb model to compute the muscle-induced GRF. We assume that if activation (and possibly force) increased as the muscle-induced component of GRF approximated the resultant GRF, then that muscle was used by the central nervous system (CNS) to help control the direction of the external GRF. During cat walking, medial gastrocnemius (MG) and plantaris (PL) forces increased with increasing proximity to the GRF, while soleus (SOL) forces and vastus lateralis (VL) activations did not. SOL and VL activation were most strongly related to the vertical and parallel (braking/accelerating) component of the GRF, respectively. We concluded from these results that MG and PL are primarily responsible for the control of the direction of the GRF, while SOL primarily functions as an anti-gravity muscle, and VL as an acceleration/deceleration muscle.