A Stochastic Model for Wound Healing |
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Authors: | Thomas Callaghan Evgeniy Khain Leonard M Sander Robert M Ziff |
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Institution: | (1) School of Mathematics, Georgia Institute of Technology, Georgia, USA;(2) Michigan Center for Theoretical Physics, Michigan, USA;(3) Department of Physics, University of Michigan, Michigan, USA;(4) Department of Chemical Engineering, University of Michigan, Michigan, USA |
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Abstract: | 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 ≈ 1. 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. |
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Keywords: | front propagation wound healing stochastic modeling Fisher-Kolmogorov equation |
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