Design by stochastic simulations of the thermal ablation treatment of tumors with high intensity focused ultrasound

Abstract

High Intensity Focused Ultrasound (HIFU) is a noninvasive technique that can be applied for the thermal ablation of tumors with minimum side effects. Numerical simulations have been used for the selection of individualized thermal ablation treatments, but mathematical models depend on several parameters that are commonly known with large uncertainties. This computational work presents the design of the thermal ablation of tumors heated with HIFU by using the Markov Chain Monte Carlo method, implemented via the Metropolis-Hastings algorithm with sequential sampling of two blocks of parameters. Two-dimensional regions with tumors of different sizes were considered. The heating period and the position of the HIFU transducer were considered as the design variables, with priors modeled by uniform distributions. Other model parameters that appeared in the mathematical formulation were assumed Gaussian. The likelihood function, which represented the desired outcome of the thermal ablation treatment and its associated uncertainties, was modeled by a beta distribution for the probability of cell death due to heating. The obtained results revealed that the version of the Metropolis-Hastings algorithm used in this work could deal with uncertainties in the model parameters and allowed the robust design of the HIFU thermal ablation of the region of interest.