Optimal Trajectory Planning for Interstitial Hyperthermia Processes

This contribution deals with planning optimal trajectories for radiofrequency and microwave ablation in the course of interstitial hyperthermia. Rigorous mathematical modeling of these processes leads to systems of coupled partial differential equations with Dirichlet boundary control. To tackle the optimal trajectory planning problem by means of dynamic optimization, the Dirichlet boundary controls are approximated by suitable Neumann boundary controls. Consequently, the formal Lagrangian technique can be applied to derive the optimality conditions. A gradient algorithm in combination with state-of-the-art FEM software (FEM -finite element method) is used to numerically solve the problems straightforward.