Patient-Specific Planning for Radio-Frequency Ablation of Tumors in the Presence of Uncertainty
Abstract The radio frequency (RF) ablation is a promising minimally invasive form of treatment for hepatic metastases and primary tumors. Thereby a needle like applicator, which is interstitially placed into the lesion, induces an electric current that causes heating and consequent destruction of the tissue due to its Ohmic resistance. In order to be a true alternative to the standard surgical resection, RF ablation must lead to a result similar to R0 resections. Here, patient specific mathematical modeling and numerical simulation of the bio-physical processes lead to a valuable support of the therapy planning, because they allow for an a priori estimation of the success as well as an optimization of the therapy parameters. In this article we discuss a mathematical model of partial differential equations (PDEs) for the patient specific numerical simulation of RF ablation. A particular focus lies on the consideration of uncertainties in the material properties, the underlying image data as well as the computational results. We discuss a stochastic PDE model, which allows for a sensitivity analysis of the computational results with respect to perturbations in the material properties. Furthermore a method for the fast estimation of the thermal necrosis is shown, which bases on the separation of non patient specific pre-calculations and patient specific computations, leading to an interactive real-time simulation tool.
Read more