Predicting Force Generation by Lamprey Muscle During Applied Sinusoidal Movement Using A Simple Dynamic Model

Abstract

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.

Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion

“…There remains a major gulf between our understanding of biomechanics (Alexander and Goldspink, 1977;Gray and Lissmann, 1964;Niebur and Erdos, 1991;Wu, 1971;Cheng et al, 1998;Hirose, 1993;Ijspeert, 2001) and molecular genetics (Bargmann, 1998;Francis et al, 2003) of undulatory movement. Studies of leech and lamprey (Friesen and Cang, 2001;Skinner and Mulloney, 1998;Lockery and Sejnowski, 1992;Marder and Calabrese, 1996;Williams, 1998;Cortez et al, 2004) have led to a systemlevel, mostly neural, understanding of such movement but have little connection to how such movement is specified by the genome. Molecular genetic studies have identified hundreds of genes involved in locomotory behavior in C. elegans and while functional connections among many of these genes have been elucidated, they have not yet ex-plained how the system works.…”

“…This model allows us to explain why some characteristics change or stay constant as a genetic perturbation is applied. In this respect, our model has a potential to provide richer information than standard, neural-level approaches in leech and lamprey (Friesen and Cang, 2001;Skinner and Mulloney, 1998;Lockery and Sejnowski, 1992;Marder and Calabrese, 1996;Williams, 1998).…”

IB2d: a Python and MATLAB implementation of the immersed boundary method

“…Once the membrane potential is found, it can be applied to the fiber model to activate pumping or initiate motion to which induces deformations of the structure to model desired biological or physical phenomena. Coupling the action potential to the generation of force can be done in many different ways for various applications, such as for cardiac contraction [50,19,20] or locomotion [51,52,10].…”

A Simple Integrated Mathematical Model of Neuromuscular Activation

“…• A model, proposed by Williams [6], of the calcium dynamics inside the muscle cell, • Hill-type model for the muscle contraction [7,8]. The coupling between the nerve impulse and the resulting calcium activity is made using a heuristic approach, following [3].…”

“…The result of the latter model is coupled with the following model of calcium dynamics inside the muscle cell and a Hill-type model for the muscle activity. The model was proposed by Williams [6] and used in a similar context to ours in [3]. It can be reduced to the following system of 3 ODEs after proper rescaling of the participating quantities (see [6], [3]).…”