Mechanisms underlying undulatory swimming: From neuromuscular activation to body-fluid interactions

Biological locomotion control systems provide an ideal research platform for the development of control theories for robotic locomotion. Two properties of significant practical value, adaptability and energy efficiency, are observed in biological systems. Systems-level modeling and analysis are needed to understand the control mechanisms of the neuronal circuits called the central pattern generator (CPC) that resides within the central nervous system (CNS). The dissertation studies the undulatory swimming of elongated invertebrate animal - leech, and addresses the question: how is a particular swimming gait chosen and realized by the CNS through muscle-body-fluid systems? The methods used in this study are to develop analytical models of neuromuscular dynamics and body-fluid interaction, and to predict the cascade of control signals from CNS to body-fluid interaction.;The leech body is modeled by a chain of rigid links and the fluid force is modeled by a static function of relative velocity and acceleration between body and fluid. The fluid model coefficients are determined from video-recorded kinematic motion data by minimizing the error in the simulated velocity of the center of gravity. To determine the fluid model coefficients, the body-fluid interaction dynamics are decouplcd into subsystems of body shape and inertial (translation and rotation) motion, which allows us to compute the inertial motion, muscle bending moment, and hydrodynamic force on the body from the measured body shape change. Muscle tension model is developed from available data obtained through "dual-sinusoid" experiments, where the muscle was activated periodically by MN activation in the presence of rhythmic strain to mimic the situation during swimming. Based on the tension model and predicted muscle bending moment (from body-fluid system), motoneuron (MN) activation impulse frequency and muscle tension are predicted. The propagation speeds are estimated for three waves: MN activation, muscle tension, and body curvature.;With these predictions of hydrodynamic force, MN activation impulse frequency, and muscle tension, together with video-recorded body curvature wave, we have revealed the CNS control mechanisms underlying leech undulatory swimming as follows. The leech swims forward by generating thrust via the normal fluid forces continuously along the body with increased magnitude towards the tail, where resistive forces dominate over the reactive forces. Drag, generated by tangential fluid forces, is nearly constant along the body. Energy for swimming is supplied primarily by the mid-body muscles, transmitted through the body in the form of elastic potential, and dissipated into the water near the tail. These different roles played by muscle resulted from speed difference between tension and body curvature waves. The body-fluid dynamics require a much faster tension wave along the body to generate the observed body curvature wave. On the other hand, the speed of neural activation wave along the body is, in general, different from that of the tension wave. The difference between the two speeds arises from the interference of muscle strain and the dynamics of tension development. The leech CPG receives fast tension waves as sensory feedback and generates slow activation waves. The wave speeds of the MN activation vMN, tension vT, and body curvature vB, are roughly related by vMN = vB = v T/2. The muscle activation by the CPG is strong in the mid-body and very weak at head and tail ends.;The control strategies of CNS thus revealed are tuned for achieving the observed sinusoid-like undulatory movements of the slender body. What remained to be answered is how the particular swimming gait (or body oscillation pattern) is determined. We found that leeches choose a gait minimizing the metabolic energy cost, which is characterized by the sum of the mechanical work output and heat liberation by muscles. Minimization of the energy loss to the fluid, without taking the heat liberation into account, could not explain the observed swimming gait. Overall, the leech CPG appears to provide an energy optimal control for undulatory swimming. Building on previous modeling efforts in our group, an integrated model of leech swim system is developed and validated by comparisons between simulations and experimental observations. The integrated model will be useful for further analysis of CPO control mechanisms. More generally, the framework for model-based analysis developed in this study will be effective for the study of undulatory swimming of other animals.