Thermal modeling in cylindrical coordinates using effective conductivity.

Predictive thermometry, utilizing minimally invasive sampling techniques, is an essential ingredient in the development of hyperthermia treatment planning capabilities. The authors demonstrate a powerful, but simple approach toward predicting temperature distributions in tissues, based on analytic solution, using in cylindrical symmetry, of the heat diffusion equation. Conduction and localized perfusion effects are combined as an effective conductivity term, readily measurable, and parametrized in a general exponential form. The proposed approach allows a first-order approximation to modeling three typical situations: hypoxic or necrotic tumor core with homogeneously perfused periphery; highly perfused periphery (in rapidly growing tumors); or perfused central cover with a less well-supplied periphery (such as for some invasive tumors). The utility and strength of this approach is that it provides a rapid, accurate model of directly observing the technical quality to be expected for different heating methods, making it possible to optimally configure source distributions in a treatment planning setting.