Architectural gear ratio depends on actuator spacing in a physical model of pennate muscle

Pennate muscles are defined by the architectural arrangement of their muscle fibers, which run at an angle to the primary axis of muscle shortening. Pennation angles can vary dynamically over the course of individual contractions, influencing the speed and distance of muscle shortening. Despite their relevance to muscle performance, the physical mechanisms that drive dynamic changes in pennation angle remain poorly understood. Muscle fibers bulge radially as they shorten, a consequence of maintaining a constant internal fluid volume, and we hypothesized that radial interactions between tightly packed muscle fibers are essential to dynamic pennation angle changes. To explore this, we built physical models of pennate muscles in which the radial distance between fiber-like actuators could be experimentally altered. Models were built from pennate arrays of McKibben actuators, a type of pneumatic actuator that forcefully shortens and bulges radially when inflated with compressed air. Consistent with past studies of biological muscle and engineered pennate actuators, we found that the magnitude of pennation angle change during contraction varied with load. Importantly, however, we found that pennation angle changes were also strongly influenced by the radial distance between neighboring McKibben actuators. Increasing the radial distance between neighboring actuators reduced pennation angle change during contraction and effectively eliminated variable responses to load. Radial interactions between muscle fibers are rarely considered in theoretical and experimental analyses of pennate muscle; however, these findings suggest that radial interactions between fibers drive pennation angle changes and influence pennate muscle performance. Our results provide insight into the fundamental mechanism underlying dynamic pennation angle changes in biological muscle and highlight design considerations that can inform the development of engineered pennate arrays.