Exploring the high-dimensional structure of muscle redundancy via subject-specific and generic musculoskeletal models

Abstract

Subject-specific and generic musculoskeletal models are the computational instantiation of hypotheses, and stochastic techniques help explore their validity. We present two such examples to explore the hypothesis of muscle redundancy. The first addresses the effect of anatomical variability on static force capabilities for three individual cat hindlimbs, each with seven kinematic degrees of freedom (DoFs) and 31 muscles. We present novel methods to characterize the structure of the 31-dimensional set of feasible muscle activations for static force production in every 3-D direction. We find that task requirements strongly define the set of feasible muscle activations and limb forces, with few differences comparing individual vs. species-average results. Moreover, muscle activity is not smoothly distributed across 3-D directions. The second example explores parameter uncertainty during a flying disc throwing motion, by using a generic human arm with five DoFs and 17 muscles to predict muscle fiber velocities. We show that the measured joint kinematics fully constrain the eccentric and concentric fiber velocities of all muscles via their moment arms. Thus muscle activation for limb movements is likely not redundant: there is little, if any, latitude in synchronizing alpha-gamma motoneuron excitation-inhibition for muscles to adhere to the time-critical fiber velocities dictated by joint kinematics. Importantly, several muscles inevitably exhibit fiber velocities higher than thought tenable, even for conservative throwing speeds. These techniques and results, respectively, enable and compel us to continue to revise the classical notion of muscle redundancy for increasingly more realistic models and tasks.

Similar movements are associated with drastically different muscle contraction velocities

“…This work justifies and enables future research directions by combining the Sherringtonian perspective with experimental (An et al, 1983) and analytical (Valero-Cuevas et al, 2015; Valero-Cuevas, 2015) demonstrations of the over-determined nature of muscle contraction velocities. This neo-Sherringtonian perspective towards kinematic redundancy has profound implications to the learning, execution, and rehabilitation of natural movements.…”

“…12, a given limb movement fully determines the time history of muscle lengths and velocities and, therefore, the muscle proprioceptive signals that affect stretch reflexes. Thus, any muscle that fails to appropriately lengthen (either by failure to modulate or silence the stretch reflex, or by inappropriate activation) will disrupt the movement trajectory in some way (Sherrington, 1913; Loeb, 1984; Prochazka et al, 1985; Valero-Cuevas, 2015; Valero-Cuevas et al, 2015). Some muscles undergoing concentric contractions could, in principle, go slack so long as other muscles contribute to drive the limb (Valero-Cuevas et al, 2015).…”

“…Failure to modulate or silence the stretch reflex will prevent the desired joint rotations—and thus disrupt the movement trajectory unless other joint rotations compensate the disruption. Thus, different muscle eccentric contraction velocities (i.e., movement trajectories) will require distinct reflex modulation strategies; and faster muscle velocities will require appropriately faster and more time-critical reflex modulation strategies (Valero-Cuevas, 2015; Valero-Cuevas et al, 2015; Duchateau and Enoka, 2016). The different concentric contraction velocities may also require distinct and time-sensitive strategies to ensure that muscles do not go slack and cease to produce force, and to ensure that the work loops of all muscles contribute appropriately to accomplish the task well (Tobalske et al, 2003).…”

“…But why is it that practice or mimicry alone do not suffice to accomplish a professional level of accuracy and repeatability? In recent work, we re-emphasized that the neural control of limb movements is in fact over-determined, where the rotations of a few joints determine length changes in many muscles (Valero-Cuevas, 2015; Valero-Cuevas et al, 2015). While some muscles that are shortening during the movement can, of course, become lax, those that are lengthening must all do so by a prescribed amount.…”

Feasible muscle activation ranges based on inverse dynamics analyses of human walking

“…Based on torque-producing properties of muscles (moment arms, force-length and -velocity relationships) and joint torque requirements across the entire gait cycle, we identified feasible muscle activation ranges that define the upper and lower bounds on muscle activation levels (Sohn et al, 2013; Valero-Cuevas et al, 2015) from which a particular solution may be selected for a task. The largely unconstrained feasible muscle activation ranges reflect a large degree of musculoskeletal redundancy in human walking, allowing a wide range of deviations from optimal muscle activation patterns in the activation of any individual muscle while satisfying joint torque requirements.…”