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Mathematical model of prevascular growth of a spherical carcinoma. (English) Zbl 0706.92010
Summary: A mathematical model of prevascular tumor growth by diffusion, which is an extension of previous models, has been constructed. The effects of nonuniform nutrient consumption and nonuniform inhibitor production on the growth rate of a spherically symmetric carcinoma are examined in this model, and the complete growth history of the tissue is followed analytically. A four-layer structure in the dormant steady state is predicted, and the evolution of a multicellular spheroid from an initial form is determined by an integro-differential (growth) equation. A parameter is used to measure the degree of nonuniformity of the inhibitor production rate, and growth patterns are presented for several values of this parameter. As this nonuniformity parameter is varied from zero to unity, there is a considerable relative increase in the asymptotic steady-state outer tumor radius, and also in the corresponding inner necrotic core size. A detailed understanding of the mathematical model presented here can form the basis for a further level of description in deterministic models of tumor growth.

92C50 Medical applications (general)
Full Text: DOI
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