The effect of muscle ultrastructure on the force, displacement and work capacity of skeletal muscle.

Skeletal muscle powers animal movement through interactions between the contractile proteins, actin and myosin. Structural variation contributes greatly to the variation in mechanical performance observed across muscles. In vertebrates, gross structural variation occurs in the form of changes in the muscle cross-sectional area : fibre length ratio. This results in a trade-off between force and displacement capacity, leaving work capacity unaltered. Consequently, the maximum work per unit volume-the work density-is considered constant. Invertebrate muscle also varies in muscle ultrastructure, i.e. actin and myosin filament lengths. Increasing actin and myosin filament lengths increases force capacity, but the effect on muscle fibre displacement, and thus work, capacity is unclear. We use a sliding-filament muscle model to predict the effect of actin and myosin filament lengths on these mechanical parameters for both idealized sarcomeres with fixed actin : myosin length ratios, and for real sarcomeres with known filament lengths. Increasing actin and myosin filament lengths increases stress without reducing strain capacity. A muscle with longer actin and myosin filaments can generate larger force over the same displacement and has a higher work density, so seemingly bypassing an established trade-off. However, real sarcomeres deviate from the idealized length ratio suggesting unidentified constraints or selective pressures.

How human runners regulate footsteps on uneven terrain.

Running stably on uneven natural terrain takes skillful control and was critical for human evolution. Even as runners circumnavigate hazardous obstacles such as steep drops, they must contend with uneven ground that is gentler but still destabilizing. We do not know how footsteps are guided based on the uneven topography of the ground and how those choices influence stability. Therefore, we studied human runners on trail-like undulating uneven terrain and measured their energetics, kinematics, ground forces, and stepping patterns. We find that runners do not selectively step on more level ground areas. Instead, the body's mechanical response, mediated by the control of leg compliance, helps maintain stability without requiring precise regulation of footsteps. Furthermore, their overall kinematics and energy consumption on uneven terrain showed little change from flat ground. These findings may explain how runners remain stable on natural terrain while devoting attention to tasks besides guiding footsteps.

Dynamics and stability of running on rough terrains.

Stability of running on rough terrain depends on the propagation of perturbations due to the ground. We consider stability within the sagittal plane and model the dynamics of running as a two-dimensional body with alternating aerial and stance phases. Stance is modelled as a passive, impulsive collision followed by an active, impulsive push-off that compensates for collisional losses. Such a runner has infinitely many strategies to maintain periodic gaits on flat ground. However, these strategies differ in how perturbations due to terrain unevenness are propagated. Instabilities manifest as tumbling (orientational instability) or failing to maintain a steady speed (translational instability). We find that open-loop strategies that avoid sensory feedback are sufficient to maintain stability on step-like terrains with piecewise flat surfaces that randomly vary in height. However, these open-loop runners lose orientational stability on rough terrains whose slope also varies randomly. The orientational instability is significantly mitigated by minimizing the tangential collision, which typically requires sensory information and anticipatory strategies such as leg retraction. By analysing the propagation of perturbations, we derive a single dimensionless parameter that governs stability. This parameter provides guidelines for the design and control of both biological and robotic runners.