Sensitivity and robustness aspects in focused ultrasonic therapy simulation

Focused ultrasound in combination with magnetic resonance tomography is a well established method for non-invasive tumor therapy. The image data serve for specification of tumor volume and healthy organs. Then the energy is selectively injected into the tissue via acoustic waves leading to the destruction of tumor cells. For successful therapy planning numerical simulation is used based on experimentally validated physical models describing non-linear wave propagation, absorption in soft tissue, heat transfer, and a hierarchical structure of the biological materials involved. The major purpose of therapy planning is to adjust treatment parameters, such as position of focal point and intensity of ultrasound, to achieve simultaneously a maximal level of tumor destruction and a minimal influence to the healthy organs. For this purpose multi-objective optimization is used combined with metamodeling of numerical simulation results. Inherent uncertainties of the numerical model are taken into account such as variation of biomechanical properties of the tissues, positioning of the patient, displacement and deformation of organs due to the breathing process. A realistic application case is used to demonstrate efficiency of the approach. 208 MRT images are used to compute motion vector fields characterizing the breathing process. These fields together with given uncertainties for 28 material parameters have been used in sensitivity analysis. The analysis has been applied to the results of focused ultrasonic simulation with 10 seconds of exposure time. 68%-confidence intervals for the resulting thermal doses inside and outside the therapy region have been determined enabling robust multi-objective optimization in therapy planning.