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Spatially varying equilibria of mechanical models: Application to dermal wound contraction

By L. Olsen, P. K. Maini and J. A. Sherratt

Abstract

Mechanochemical models based on the Oster-Murray continuum framework have been applied to a variety of biological settings to obtain an understanding of the morphogenesis of living tissues. Wound-healing in mammalian skin is an important example, because a complex sequence of biochemical and biomechanical responses are orchestrated to close a wound by a combination of new tissue formation and wound contraction. Mechanical interactions between dermal fibroblastic cells and the collagen-rich extracellular matrix are crucial in the development of a contracted wound state. We and others have previously proposed mechanochemical models for wound repair to gain a greater understanding of both normal and abnormal healing. In the present work, the existence of spatially varying equilibria of these models is investigated by using a small-stain approximation and phase-plane techniques, with numerical simulations to confirm the analytical predictions. These results are sources of novel insight into the roles of key biological parameters in determining the mechanical properties of a contracted wound. These methods may also be relevant to other morphogenetic scenarios for which similar mechanochemical models have been proposed

Topics: Biology and other natural sciences
Year: 1998
DOI identifier: 10.1016/S0025-5564(97)00075-8
OAI identifier: oai:generic.eprints.org:440/core69

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