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.