AN ANALYSIS OF SYSTEMIC TUMOR OXYGENATION USING MULTI-REGION MODELS

Temperature rise in tumor tissue during high-dose-rate photoradiation

The bioheat transfer equation and optical diffusion theory are used to develop a mathematical model for describing the thermal field in a spherical tumor and its surrounding normal tissue resulting from photoradiation. Analytical solutions to the model equations are presented for determining both the steady-state and transient temperature profiles. The effect of the optical and thermal properties of the surrounding normal tissue on the thermal field generated within the tumor is explored.

Diffusion regulated growth characteristics of a spherical prevascular carcinoma

Recently a mathematical model of the prevascular phases of tumor growth by diffusion has been investigated (S.A. Maggelakis and J.A. Adam, Math. Comput. Modeling, in press). 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 R0(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.