Naturally, the simulation of RF ablation depends on the material properties of the tissue as e.g. its electrical and thermal conductivity. These tissue parameters vary inter-individually (i.e. from patient to patien) and even from day to day depending on the patients physical constitution. Hence, a relevant field of our ongoing research is the implementation of a sensitivity analysis of the optimal probe placement with respect to material parameter uncertainty. Substituting the probabilistically distributed conductivity values into the PDE-model for the simulation of RF ablation yields a system of stochastich partial differential equations (SPDE) which we analyze by employing a stochastic collocation approach.
The figures display the segmented tumor and vessel system together with the sensitivity of the probe's position (left) and orientation (right) with respect to variations in the thermal and electrical conductivity, respectively. The sensitivity of the probe's position is visualized through an ellipsoidal representation of the covariance matrix (scaled by a factor of 10), and the sensitivity of the probe's orientation is represented by a color coding of the sphere (green: unlikely orientations, red: likely orientations), where the size of the sphere is arbitrary. In all figures the RF probe is drawn at the mean of the placement's distribution.
Sensitivity of the probe's position and orientation with respect to variations in the thermal conductivity.
Sensitivity of the probe's position and orientation with respect to variations in the electrical conductivity.