The relevant boundary conditions are now
In the first equation, substituting for N0 = i/(1 + i), multiplying through by the integrating factor (1 + 1/i)2 and integrating gives
Using L'Hopital's rule again, as above, shows that the boundary conditions are satisfied. Then (9.29) gives C1, and again using L'Hopital's rule confirms that the boundary conditions are satisfied. By repeating this process we can derive (albeit with a lot of messy algebra) all the terms in the expansion, showing in particular that X, Dc and a occur in each term of the series (9.28), and so in the solution as a whole, only within the groupings q± and X/«J 1 + 4Xk.
It is encouraging that such a relatively simple model for epidermal wound healing in which the parameter values are based as far as possible on experimental fact give such good comparison with either chemical activation or inhibition of mitosis with experimental data on the normal healing of circular wounds. These results tend to support the view that biochemical regulation of mitosis is fundamental to the process of epidermal migration in wound healing. The analytical investigation of the solutions was possible because these numerical solutions approximate travelling waves during most of the healing process. Analysis of the two biologically relevant approximations gives information about the accuracy of these approximations and, usefully, the roles of the various model parameters in the speed of healing of the wound.
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