A new constraint-based formulation for hydrodynamically resolved computational neuromechanics of swimming animals

Undulatory motion in aquatic animals is attained through waves of muscle contraction. Coordinated muscle contraction is produced by the orchestration of contralaterally anti-phased, caudally propagating waves of neural activity that deliver stimuli to skeletal muscles. This physical deformation generates muscle bending moments along the length of the body. These resultant moments in combination with hydrodynamic, inertial, and the body's constitutive forces (e.g., elasticity) determine the deformation kinematics for swimming. Hydrodyamically resolved simulations of neurally controlled locomotion can facilitate experimental neurobiologists in identifying and decoding activation patterns associated with distinct motor behaviors in swimming animals. When neurally activated, muscle stiffness and consequently the effective body stiffness dynamically increases. Computationally resolving large deformations for an effectively stiff, viscoelastic body immersed in fluid is expensive. For methods that explicitly couple the fluid–body interactions, the body's large elastic modulus imposes severe limitations on the time step size required to ensure numerical stability. Fully implicit methods are generally no more computationally efficient. When the effective body stiffness is sufficiently large, the realized deformation kinematics closely follow the time-varying preferred (or reference) configuration which is implied by the muscle dynamics. Rather than resolving the numerically stiff, elastic equations for the body, a fast and efficient, constraint-based self-propulsion formulation is employed to directly impose the preferred swimming kinematics. With this approach, the exploration of neuromechanical model for propulsion using fully resolved computational fluid dynamics becomes more tractable. The presented method is robust and may be employed to investigate the neuromechanics of motor control and locomotion. Two and three dimensional simulations (2D and 3D) demonstrating the neural activation patterns' effect on maneuverability, speed, and feedback driven obstacle navigation are presented. The phase lag between curvature and moment waves, a manifestation of neurally controlled propulsion, is reproduced, further signifying the robustness of the presented method.