A mathematical model for the steady activation of a skeletal muscle

Gabriel, JeanPierre
Department of Mathematics, University of Fribourg, Switzerland

Studer, L. M.
Department of Computer Science and Economics, University of Applied Sciences, Sierre, Switzerland

Rüegg, Dieter
Department of Medicine, Division of Physiology, University of Fribourg, Switzerland

Schnetzer, M.A.
Department of Mathematics, University of Applied Sciences, Fribourg,Switzerland
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Published in:
 SIAM Journal on Applied Mathematics.  2008, vol. 68, no. 3, p. 869889
English
A skeletal muscle is composed of motor units, each consisting of a motoneuron and the muscle fibers it innervates. The input to the motor units is formed of electrical signals coming from higher motor centers and propagated to the motoneurons along a network of nerve fibers. Because of its complexity, this network still escapes actual direct observations. The present model describes the steady state activation of a muscle, i.e., of its motor units. It incorporates the network as an unknown quantity and, given the latter, predicts the inputforce relation (activation curve) of the muscle. Conversely, given a suitable activation curve, our model enables the recovery of the network. This step is performed by using experimental data about the activation curve, and the whole activation process of a muscle can then be theoretically investigated. In this way, this approach provides a link between the macroscopic (activation curve) and microscopic (network) levels. From a mathematical viewpoint, solving the preceding inverse problem is equivalent to solving an integral equation of a new type.

Faculty
 Faculté des sciences et de médecine

Department
 Département de Mathématiques, Département de Médecine

Language


Classification

Mathematics

License

License undefined

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Persistent URL

https://folia.unifr.ch/unifr/documents/300755
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