Impact of nonlinear heat transfer on temperature control in regional hyperthermia

We describe an optimization process specially designed for regional hyperthermia of deep-seated tumors in order to achieve desired steady-state temperature distributions. A nonlinear three-dimensional heat transfer model based on temperature-dependent blood perfusion is applied to predict the temperature. Using linearly implicit methods in time and adaptive multilevel finite elements in space, we are able to integrate efficiently the instationary nonlinear heat equation with high accuracy. Optimal heating is obtained by minimizing an integral objective function which measures the distance between desired and model predicted temperatures. A sequence of minima is calculated from successively improved constant-rate perfusion models employing a damped Newton method in an inner iteration. We compare temperature distributions for two individual patients calculated on coarse and fine spatial grids and present numerical results of optimizations for a Sigma 60 Applicator of the BSD 2000 Hyperthermia System.