Anguilliform body dynamics: modelling the interaction between muscle activation and body curvature

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Abstract
A simple two-dimensional rod and pivot model is proposed for the mechanical structure of the lamprey, each pivot being controlled by a muscle segment attached via perpendicular extensions to the two rods. The elastic and viscous properties of the body tissues (including muscle) are described as linear functions of the relative displacement and angular velocity of the rods at each pivot. The contractile properties of the muscle are introduced as time-dependent forcing torques at the pivots, which are generated by a travelling wave of activation. The angles between the rods at each pivot are used as adapted coordinates, and the equations of motion are linearized by assuming low curvature dynamics, corresponding to slow swimming speeds. Investigation of these equations with varying viscous and elastic parameters leads to a reconstruction of a lamprey viewed in motion on a smooth flat surface out of water. The most striking feature is of an apparently standing wave motion, which is indeed observed in the real animal but which on careful examination in the model corresponds to a travelling wave of varying amplitude.