Defining feasible bounds on muscle activation in a redundant biomechanical task: practical implications of redundancy
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 (7×1), and a resulting endpoint wrench (force and moment vector) (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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2015, Journal of BiomechanicsCitation Excerpt :Similarly, Martelli et al. showed wide possible variations in a model of human walking (10 DoFs, 82 muscles), however the Markov Chain Monte Carlo methods they used cannot find explicit limits of activation (Martelli et al., 2015, 2013). Here, our goal was to identify the feasible muscle activation ranges during a full gait cycle of human walking by extending the methods of Sohn et al. (2013) to a dynamic task. We identified feasible muscle activation ranges during human walking using experimental data (John et al., 2013) and a detailed musculoskeletal model of the human lower extremity with 23 DoF and 92 muscles (Delp et al., 2007; Delp et al., 1990).
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2015, Journal of BiomechanicsCitation Excerpt :Still, for most tasks in healthy individuals, some redundancy is bound to remain; regions of feasible activation solutions that are not a single point will consist of a neighborhood or subspace that naturally contains an infinite number of solutions (i.e., points). The nervous system is still confronted with the need to choose a specific solution to implement at any point in time; however, that collection of feasible solutions remains highly structured due to both the mechanics of the limb and the constraints of the task (Bizzi and Cheung, 2013; Kutch and Valero-Cuevas, 2011, 2012; Sohn et al., 2013; Tresch and Jarc, 2009; Valero-Cuevas et al., 1998). The purpose of this work, therefore, is to begin to address the need posed by us (Kutch and Valero-Cuevas, 2011, 2012; Valero-Cuevas et al., 1998), and others (Loeb, 2000; Sohn et al., 2013; Tresch and Jarc, 2009), to improve computational methods for understanding and visualizing the dimensionality and structure of feasible solutions sets for limbs with large numbers of muscles performing tasks with realistic constraints.