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Diffusion regulated growth characteristics of a spherical prevascular carcinoma. (English) Zbl 0712.92010
Summary: Recently a mathematical model of the prevascular phases of tumor growth by diffusion has been investigated by the authors [Math. Comput. Modelling 13, No.5, 23-38 (1990; Zbl 0706.92010)]. In this paper we examine in detail the results and implications of that mathematical model, particularly in the light of recent experimental work carried out on multicellular spheroids. The overall growth characteristics are determined in the present model by four parameters: Q, $$\gamma$$, b, and $$\delta$$, which depend on information about inhibitor production rates, oxygen consumption rates, volume loss and cell proliferation rates, and measures of the degree of non-uniformity of the various diffusion processes that take place.
The integro-differential growth equation is solved for the outer spheroid radius $$R_ 0(t)$$ and three related inner radii subject to the solution of the governing time-independent diffusion equations (under conditions of diffusive equilibrium) and the appropriate boundary conditions. Hopefully, future experimental work will enable reasonable bounds to be placed on parameter values referred to in this model: meanwhile, specific experimentally-provided initial data can be used to predict subsequent growth characteristics of in vitro multicellular spheroids. This will be one objective of future studies.

##### MSC:
 92C50 Medical applications (general) 65L99 Numerical methods for ordinary differential equations 65R20 Numerical methods for integral equations
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