**Design of the HIFU thermal ablation treatment of cancer
with stochastic simulations**

Rodrigo Silva^{2}, Mohsen
Alaeian^{2}, Helcio
Orlande^{1, ⋆}

^{⋆} : helcio@mecanica.coppe.ufrj.br

^{1} Federal University
of Rio de Janeiro, Mechanical Engineering Program and Oncobiology
Program

^{2} Federal University
of Rio de Janeiro, Mechanical Engineering Program

**Mots clés :** Design under uncertainties, Markov Chain
Monte Carlo, Metropolis-Hastings algorithm, bioheat transfer

**Résumé :**

High intensity focused ultrasound (HIFU) is a non-invasive technique that can be used for the thermal ablation of tumors with minimum side effects. During the heating procedure, the concentration of energy may not be properly performed, since the increase of temperature depends on different tissue parameters that are not previously known. Therefore, it can be difficult to obtain the desired results without having any prior information regarding these parameters. In order to deal with the uncertainties associated to the physical model, this work presents the design under uncertainties of the thermal ablation of tumors heated by HIFU. Two-dimensional regions with tumors of different sizes were considered here. The acoustic problem was simulated with the numerical solution of the mass and momentum conservation equations, in order to evaluate the heat generation rate provided by the ultrasound after reaching the steady state condition. The heat transfer problem involving biological tissues was then solved with the explicit finite differences method, where the effects of blood perfusion and metabolism were neglected. An Arrhenius’ model was adopted to compute the thermal effects provided to the tissues, so it was possible to calculate the probability of having thermally damaged cells after the heating procedure. The heating protocol was then optimally designed under uncertainties in the model parameters by using the Markov Chain Monte Carlo method, implemented via the Metropolis-Hastings algorithm with sampling by block of parameters. The heating period and the position of the ultrasound transducer were considered as design variables, with prior information modeled by uniform distributions. Physical properties that appear in the mathematical formulation assumed prior information modeled by normal distributions, so that all the uncertainties related to the group of parameters that does not include the design variables were formally taken in account. The likelihood was modeled as a beta distribution for the probability of cell death due to the heating. The obtained results revealed that the presente approach could deal with all associated uncertainties and provided a robust design for the problem under analysis.

Work In Progress