A mathematical analysis of physiological and morphological aspects of wound closure

Fundamentals of Advanced Materials, Delft University of Technology, Delft, The Netherlands.
Journal of Mathematical Biology (Impact Factor: 1.85). 11/2009; 59(5):605-30. DOI: 10.1007/s00285-008-0242-7
Source: PubMed


A computational algorithm to study the evolution of complex wound morphologies is developed based on a model of wound closure by cell mitosis and migration due to Adam [Math Comput Model 30(5-6):23-32, 1999]. A detailed analysis of the model provides estimated values for the incubation and healing times. Furthermore, a set of inequalities are defined which demarcate conditions of complete, partial and non-healing. Numerical results show a significant delay in the healing progress whenever diffusion of the epidermic growth factor responsible for cell mitosis is slower than cell migration. Results for general wound morphologies show that healing is always initiated at regions with high curvatures and that the evolution of the wound is very sensitive to physiological parameters.

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Available from: E. Javierre
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    • "Because wound healing involves so many biological processes, there have been many different types of modeling technique used. Some research is concerned with the geometry of the wound and focused on the formation of the skin matrix (Almeida et al. 2011; Javierre et al. 2009). These models do not implement the effect of inflammation, an important stage of wound healing, particularly for wounds that fail to heal. "
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    • "Note that Eq. (1) is of Fisher– Kolmogorov type, which in the absence of passive convection admits solutions with a traveling wave structure. The mechanism of fibroblast differentiation to myofibroblasts has not yet been taken into account as was done in Olsen et al. (1995) and Javierre et al. (2009a). Biologically, one could interpret our simplified approach as assuming that c f ib models the density of both fibroblasts and myofibroblasts. "
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    Full-text · Article · Nov 2011 · Journal of Mathematical Biology
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    • "The first model describes a traveling wave analysis, whereas the second paper assesses fundamental mathematical questions on existence, uniqueness of solutions, and the mathematical nature of the moving boundary separating the wound from the undamaged tissue. Javierre et al. (2009) presents a numerical solution method for the moving boundary problem. an upward traction force on the substrate. "
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