Nonlinear acoustic waves coupled to diffusion equations modeling ultrasound heating

Abstract. Heating generated by high-intensity focused ultrasound (HIFU) waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this talk, we introduce models of nonlinear acoustic waves coupled to the heat equation, and an equation for the transport of drug delivery in human body. The well-posedness analysis of the coupled model for the Westervelt wave equation including non-local dumping term is briefly addressed. A semi-discrete numerical scheme fully based on $H^1$-conforming finite element spaces is presented. A priori error analysis is developed for the coupled semi-discrete system. The theoretically obtained optimal convergence rates in the energy norm are confirmed by the numerical experiments using different time approximations. Finally, simulations of the propagation of HIFU nonlinear acoustic waves in liver tissue are presented.