Multi-objective optimization and stochastic analysis in focused ultrasonic therapy simulation

We present new results in stochastic multi-objective optimization applied to focused ultrasonic therapy planning. This type of non-invasive therapy uses focused ultrasound for the destruction of tumor cells and magnetic resonance tomography for identification of tumor volume and healthy organs. During the therapy planning the treatment parameters, such as frequency and intensity of ultrasound, are adjusted to achieve maximal tumor destruction and minimal influence to the healthy organs. For this purpose multi-objective optimization is used. RBF metamodeling is employed for continuous representation of discretely sampled results of numerical simulation and for evaluation of inherent uncertainties. We apply two algorithms for multi-objective optimization capable of non-convex Pareto front detection in the considered problem. Cross-validation procedure and sensitivity analysis are used for estimation of uncertainties. A realistic application case demonstrates the efficienc y of the approach.