Anguilliform swimming has been investigated by using a computational model combining the dynamics of both the creature's movement and the two-dimensional fluid flow of the surrounding water. The model creature is self-propelled; it follows a path determined by the forces acting upon it,as generated by its prescribed changing shape. The numerical solution has been obtained by applying coordinate transformations and then using finite difference methods. Results are presented showing the flow around the creature as it accelerates from rest in an enclosed tank. The kinematics and dynamics associated with the creature's centre of mass are also shown. For a particular set of body shape parameters, the final mean swimming speed is found to be 0.77 times the speed of the backward-travelling wave. The corresponding movement amplitude envelope is shown. The magnitude of oscillation in the net forward force has been shown to be approximately twice that in the lateral force. The importance of allowing for acceleration and deceleration of the creature's body (rather than imposing a constant swimming speed) has been demonstrated. The calculations of rotational movement of the body and the associated moment of forces about the centre of mass have also been included in the model. The important role of viscous forces along and around the creature's body and in the growth and dissolution of the vortex structures has been illustrated.
Experiments were performed on single-myotome preparations of lamprey muscle, to discover whether force developed by intermittent tetanic stimulation during imposed sinusoidal movement could be predicted by data collected from isometric and constant-velocity experiments. We developed a simple dynamic model consisting of a set of simultaneous ordinary differential equations with unknown parameters. Appropriate values of the parameters were found by fitting numerical solutions of the differential equations to data from the isometric and constant-velocity experiments. Predictions were made of the time course of force developed during imposed sinusoidal movement in which the phase between muscle shortening and tetanic stimulation was varied to cover the whole phase spectrum. The match between the predicted and recorded time courses was very good for all phases, and particularly for those phases that are seen during swimming in the intact animal.
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.
A two dimensional continuum model for the body mechanics of the lamprey is derived from a simple discrete rod and pivot structure. Each element in the discrete structure consists of two smoothly jointed light rods with perpendicular extensions at each of the midpoints between which is fixed a quasi muscle segment. The muscle segment is attributed with the viscous and elastic properties of all the animal tissue plus the ability to produce force. The travelling wave of muscle activation in the real animal is modelled by a corresponding time dependent forcing term at each segment. A linearisation of the ensuing continuum model, corresponding to low curvature dynamics, is investigated. The profiles obtained compare favourably with those of a lamprey moving out of water on a smooth surface. In addition the phase difference at each point on the body between the wave of muscle activation and the mechanical wave observed on the body indicates that the mechanical wave progresses slower than, but at the same frequency as, the wave of activation; this is a property that is also observed in the freely swimming lamprey.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.