The cost of being stable: Trade-offs between effort and stability across a landscape of redundant motor solutions

Current musculoskeletal modeling approaches cannot account for variability in muscle activation patterns seen across individuals, who may differ in motor experience, motor training, or neurological health. While musculoskeletal simulations typically select muscle activation patterns that minimize muscular effort, and generate unstable limb dynamics, a few studies have shown that maximum-effort solutions can improve limb stability. Although humans and animals likely adopt solutions between these two extremes, we lack principled methods to explore how effort and stability shape how muscle activation patterns differ across individuals. Here we characterized trade-offs between muscular effort and limb stability in selecting muscle activation patterns for an isometric force generation task in a musculoskeletal model of the cat hindlimb. We define effort as the sum of squared activation across all muscles, and limb stability by the maximum real part of the eigenvalues of the linearized musculoskeletal system dynamics, with more negative values being more stable. Surprisingly, stability increased rapidly with only small increases in effort from the minimum-effort solution, suggesting that very small amounts of muscle coactivation are beneficial for postural stability. Further, effort beyond 40% of the maximum possible effort did not confer further increases in stability. We also found multiple muscle activation patterns with equivalent effort and stability, which could underlie variability observed across individuals with similar motor ability. Trade-off between muscle effort and limb stability could underlie diversity in muscle activation patterns observed across individuals, disease, learning, and rehabilitation.Author summaryCurrent computational musculoskeletal models select muscle activation patterns that minimize the amount of muscle activity used to generate a movement, creating unstable limb dynamics. However, experimentally, muscle activation patterns with various level of co-activation are observed for performing the same task both within and across individuals that likely help to stabilize the limb. Here we show that a trade-off between muscular effort and limb stability across the wide range of possible muscle activation patterns for a motor task could explain the diversity of muscle activation patterns seen across individuals, disease, learning and rehabilitation. Increased muscle activity is necessary to stabilize the limb, but could also limit the ability to learn new muscle activation pattern, potentially providing a mechanism to explain individual-specific muscle coordination patterns in health and disease. Finally, we provide a straightforward method for improving the physiological relevance of muscle activation pattern and musculoskeletal stability in simulations.