Olsen, L. and Maini, P. K. and Sherratt, J. A. (1998) Spatially varying equilibria of mechanical models: Application to dermal wound contraction. Mathematical Biosciences, 147 (1). pp. 113-129.
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.
|Subjects:||A - C > Biology and other natural sciences|
|Research Groups:||Centre for Mathematical Biology|
|Deposited By:||Philip Maini|
|Deposited On:||27 Nov 2006|
|Last Modified:||29 May 2015 18:22|
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