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A stochastic model for wound healing. (English) Zbl 1095.92050

Summary: We present a discrete stochastic model which represents many of the salient features of the biological process of wound healing. The model describes fronts of cells invading a wound. We have numerical results in one and two dimensions. In one dimension we can give analytic results for the front speed as a power series expansion in a parameter, \(p\), that gives the relative size of proliferation and diffusion processes for the invading cells. In two dimensions the model becomes the Eden model for \(p \approx 1\) [M. Eden, A two-dimensional growth process. Proc. 4th Berkeley Symp. Math. Stat. Probab. 4, 223–239 (1961; Zbl 0104.13801)]. In both one and two dimensions for small \(p\), front propagation for this model should approach that of the Fisher-Kolmogorov equation. However, as in other cases, this discrete model approaches Fisher-Kolmogorov behavior slowly.

MSC:

92C50 Medical applications (general)
92C17 Cell movement (chemotaxis, etc.)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
82D99 Applications of statistical mechanics to specific types of physical systems

Citations:

Zbl 0104.13801
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References:

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