A mathematical model for the steady activation of a skeletal muscle
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Gabriel, Jean-Pierre
Department of Mathematics, University of Fribourg, Switzerland
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Studer, L. M.
Department of Computer Science and Economics, University of Applied Sciences, Sierre, Switzerland
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Rüegg, Dieter
Department of Medicine, Division of Physiology, University of Fribourg, Switzerland
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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. 869-889
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 input-force 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.
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Faculty
- Faculté des sciences et de médecine
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Department
- Département de Mathématiques, Département de Médecine
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Language
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Classification
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Mathematics
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License
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License undefined
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Identifiers
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Persistent URL
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https://folia.unifr.ch/unifr/documents/300755
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