A Mathematical Model for the Steady Activation of a Skeletal Muscle

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 complexit...

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Bibliographic Details
Published in:SIAM journal on applied mathematics 2008-01, Vol.68 (3), p.869-889
Main Authors: Gabriel, J.-P, Studer, L. M., Rüegg, D. G., Schnetzer, M.-A.
Format: Article
Language:English
Subjects:
Applied mathematics
Continuous functions
Differential equations
Electric current
Force
Frequency modulation
Integral equations
Inverse problems
Mathematical functions
Mathematical models
Mathematical theorems
Muscles
Musculoskeletal system
Perceptron convergence procedure
Physiology
Random variables
Skeletal muscle
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Summary: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.
ISSN:0036-1399
1095-712X
DOI:10.1137/05064271X