Elsevier

Journal of Biomechanics

Volume 46, Issue 7, 26 April 2013, Pages 1363-1368
Journal of Biomechanics

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

https://doi.org/10.1016/j.jbiomech.2013.01.020Get rights and content

Abstract

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.

Introduction

Musculoskeletal redundancy (Bernstein, 1967) in biomechanical models is often addressed through optimizations that identify a unique muscle activation pattern among many possible. One popular criterion is minimizing muscle stress (Crowninshield and Brand, 1981) which has been widely applied to predict muscle coordination in simulations (Anderson and Pandy, 2001, Thelen et al., 2003, Erdemir et al., 2007). However, measured muscle activity often varies significantly from these predictions (Buchanan and Shreeve, 1996, Herzog and Leonard, 1991, Thelen and Anderson, 2006, van der Krogt et al., 2012). We currently lack methods for analyzing high-dimensional musculoskeletal models that would allow us to quantify the degree to which muscle activity may feasibly vary for a given motor task.

The first step to understand the variability in muscle activity with respect to musculoskeletal redundancy is to identify absolute biomechanical constraints on muscle activity for a given task. In contrast to optimization, this approach seeks to find the full range of possible solution sets available to the nervous system (Kutch and Valero-Cuevas, 2011). In particular, identifying the explicit bounds on muscle activation can reveal whether predicted or measured muscle activity is due to biomechanical requirements necessary to perform the task, or because of allowable variability in how the task can be achieved. Identifying feasible bounds of muscle activity can also describe the degree to which muscle activity may deviate from optimal solutions.

This study was motivated by experimentally-observed inter- and intra-subject variability during reactive balance control (Horak and Nashner, 1986, Torres-Oviedo et al., 2006, Torres-Oviedo and Ting, 2007). For example in cats, when producing an extensor force vector (Fig. 1A, FEXT), knee extensor vastus medialis (VM) was recruited consistently across animals, but hip and knee flexor medial sartorius (SARTm) was recruited at different levels across animals (Fig. 1B, FEXT). Conversely, when producing a flexor force vector (Fig. 1A, FFLEX), VM recruitment varied across animals but SARTm was recruited consistently in all animals (Fig. 1B, FFLEX).

Here, we identified feasible ranges of muscle activation during static force production in a detailed model of the cat hindlimb (Fig. 1C; Burkholder and Nichols, 2004, McKay and Ting, 2008). We identified the upper and lower bounds on muscle activity in each of 31 muscles during endpoint force production in different directions and magnitudes. Muscles with non-zero lower bounds were classified as “necessary”, whereas muscles with zero lower bounds were classified as “optional”. Muscles were further classified to have “sub-maximal upper bound” or “maximal upper bound”. To examine the degree to which feasible muscle activation patterns could deviate from an optimal solution, we compared these bounds to muscle activation patterns predicted by minimizing muscle stress (Crowninshield and Brand, 1981), or scaling the pattern required for maximum force generation (Valero-Cuevas, 2000).

Section snippets

Musculoskeletal model

The static three-dimensional musculoskeletal model of the cat hindlimb (Burkholder and Nichols, 2004) included seven rotational degrees of freedom (Fig. 1C). 31 muscles (Table 1) produced net joint torque τ (7×1), and a resulting endpoint wrench (force and moment vector) FEnd (6×1) at the metatarsophalangeal (MTP) joint. The MTP was connected to the ground via a gimbal joint (Fig. 1C), representing the experimental condition of a freely standing cat where the foot never lost contact or

Bounds on muscle activation during endpoint force production

The feasible range of muscle activity for each muscle changed non-uniformly as force magnitude α increased from zero to maximal in a given target endpoint force direction (e.g. Fig. 2B, shaded region). This range was defined by the difference between the lower bound (Fig. 2B, bottom trace) and upper bound (Fig. 2B, top trace) at a given α. In each animal, similar patterns of the feasible range of muscle activity was identified across muscles and force directions. Therefore, two force directions

Discussion

Here, we identified the feasible ranges of individual muscle activation during endpoint force generation as a way of understanding the degree to which biomechanical redundancy allows for variability in muscle activation patterns. Feasible ranges of muscle activation were relatively unconstrained across force magnitudes in a cat hindlimb model (7 non-orthogonal DoFs, 31 muscles). Although we identified muscles that became biomechanically “necessary” at higher levels of force (e.g. nonzero lower

Conflict of interest statement

The authors declare that they have no conflicts of interest.

Acknowledgments

Funding for this study was provided by NIH Grant No. HD46922. The NIH had no role in the design, performance, or interpretation of the study.

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