Multiscale optimization of the probe placement for radiofrequency ablation

Rationale and Objectives. We present a model for the optimal placement of mono- and bipolar probes in radiofrequency (RF) ablation. The model is based on a system of partial differential equations that describe the electric potential of the probe and the steady state of the induced heat distribution. Materials and Methods. To optimize the probe placement we minimize a temperature-based objective function under the constraining system of partial differential equations. Further, the extension of the resulting optimality system for the use of multiple coupled RF probes is discussed. We choose a multiscale gradient descent approach to solve the optimality system. Results. This article describes the discretization and implementation of the approach with finite elements on three-dimensional hexahedral grids. Conclusion. Applications of the optimization to artificial test scenarios as well as a comparison to a real RF ablation show the usefulness of the approach.