Granular resistive force theory explains the neuromechanical phase lag during sand-swimming

Undulatory locomotion is a common gait used by a diversity of animals in a range of environments. This mode of locomotion is characterized by the propagation of a traveling wave of body bending, which propels the animal in the opposite direction of the wave. Previous studies of undulatory locomotion in fluids, on land, and even within sand revealed that the wave of muscle activation progresses faster than the traveling wave of curvature. This leads to an increasing phase lag between activation and curvature at more posterior segments, known as the neuromechanical phase lag. In this study, we compare biological measurements of phase lag during the sand-swimming of the sandfish lizard to predictions of a simple model of undulatory swimming that consists of prescribed kinematics and granular resistive forces. The neuromechanical phase lag measured using electromyography (EMG) quantitatively matches the predicted phase lag between the local body curvature and torque exerted by granular resistive forces. Two effects are responsible for the phase lag in this system: the yaw motion of the body and different integration length over a traveling force pattern for different positions along the body.