An important field in RF ablation planning is the investigation of the inverse problem of finding an optimal placement for the RF probe such that a given tumor lesion is completely destroyed. Thereto, we minimize a temperature-based objective function measuring the quality of an RF ablation for a given temperature distribution under the constraining system of partial differential equations (PDE) modeling the electric potential and heat distribution in the tissue. To accelerate the solution process, we take a multi-scale approach into account. Thereby, optimal probe locations for coarse resolutions are computed and taken as initial guess for fine resolution optimizations. Besides the optimization of only one single probe (used only for very small tumors), we also consider the optimization of several probes arranged in a fixed parallel cluster. In this case, the rotation of the probe cluster becomes an additional optimization parameter.
In the figure on the right, the computed optimal probe placement for a cluster of three parallel probes is shown together with the segmented tumor (dark gray) and vascular system (red). In addition, the 60 degree iso-surface of the temperature is depicted in a transparent yellow color.