Identification of viable regions in "in vitro" spheroidal tumors: a mathematical investigation

A computer simulation of simultaneous heat and oxygen transport during heterogeneous three dimensional tumor hyperthermia

Hyperthermia is a developing modelity for the treatment of cancer. This therapy is occasionally used by itself, however, usually it is used as an adjuvate with chemo or radiation therapy. The mechanism for this treatment is based on the fact that cancer cells are heated preferentially by heat application due to lower vascularity in the tumor tissue as compared with the surrounding normal tissue and that, when used with radiation therapy or chemo therapy, higher oxygen partial pressure in the tumor results in increased tumor cell damage. Appropriate mathematical models and their real time prediction of oxygen and temperature profiles could be very helpful in achieving optimal results via hyperthermia and to avoid possible danger which might occur during the treatment. Because of the complexity and the heterogeneous nature of physiological system, it is necessary to include heterogeneous properties in the mathematical models for them to be useful for biomedical calculations. Of course, it is much more difficult to solve mathematically the heterogeneous system than the homogeneous one. In this paper, the importance of the implementation of heterogeneities in the heat and mass transport for biological system mathematical modelling is discussed. Results of a three dimensional computer simulation of mass and heat transfer in tumor tissue with different capillary geometries during hyperthermia are demonstrated. The method used for the computer simulation is a deterministic/probabilistic technique, Williford-Bruley calculational strategy.