Directional constraint of endpoint force emerges from hindlimb anatomy

Abstract

SUMMARYPostural 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.

Stability Radius as a Method for Comparing the Dynamics of Neuromechanical Systems

“…This affects the ability to perform dynamic optimization of parameters that rely on completion of a movement [42]. In contrast, selection of muscle activation patterns that produce a system with stable eigenvalues generate simulations that are stable and can be run for much longer simulation times [43, 44]. Further, parameters selected based on stability criteria result in responses to perturbations that are more similar to experimentally-measured responses than those found using minimum muscle stress criteria alone [43].…”

“…In contrast, selection of muscle activation patterns that produce a system with stable eigenvalues generate simulations that are stable and can be run for much longer simulation times [43, 44]. Further, parameters selected based on stability criteria result in responses to perturbations that are more similar to experimentally-measured responses than those found using minimum muscle stress criteria alone [43]. Stability radius could be used as an additional optimization criterion to identify parameters that generate stable behaviors, which would improve both optimization speed, as well as identifying parameters that could generate more physiologically-realistic behaviors.…”

Body stability and muscle and motor cortex activity during walking with wide stance

“…We hypothesized that during wide-stance walking the cat's body stability would be higher than during walking with a selfselected (unconstrained) between-paw distance. We further hypothesized that muscles contributing to frontal-plane joint moments would show altered activity patterns during widestance walking.While the contribution of passive body mechanics to regulation of balance during standing and locomotion may be substantial (Bunderson et al 2010;Scrivens et al 2006;Ting et al 2009) 112: 504 -524, 2014. First published April 30, 2014 doi:10.1152/jn.00064.2014 0022 Musienko et al 2012;Stapley and Drew 2009;Zelenin et al 2010).…”

“…While the contribution of passive body mechanics to regulation of balance during standing and locomotion may be substantial (Bunderson et al 2010;Scrivens et al 2006;Ting et al 2009) 112: 504 -524, 2014. First published April 30, 2014 doi:10.1152/jn.00064.2014 0022 Musienko et al 2012;Stapley and Drew 2009;Zelenin et al 2010).…”

“…While the contribution of passive body mechanics to regulation of balance during standing and locomotion may be substantial (Bunderson et al 2010;Scrivens et al 2006;Ting et al 2009), active mechanisms of the spinal cord, brain stem, and motor cortex are critically important for maintaining stable posture and locomotion ; Honeycutt and Nichols 2010; Karayannidou et al 2009; Macpherson and Fung 1999;Musienko et al 2012;Stapley and Drew 2009;Zelenin et al 2010). In our previous studies we found that in standing quadruped animals, the rabbit and the cat, neurons from both fore-and hindlimb representations in the motor cortex modulate their activity in response to lateral tilts of the supporting surface (Beloozerova et al 2003b.…”