Westervelt-based modeling of ultrasound-enhanced drug delivery

TL;DR

This paper develops and analyzes a comprehensive nonlinear multiphysics model for ultrasound-enhanced drug delivery, incorporating acoustic wave propagation, tissue heating, and drug transport, supported by theoretical analysis and numerical simulations.

Contribution

It introduces a coupled Westervelt-based wave model with fractional damping and temperature dependence, providing a rigorous mathematical framework for ultrasound drug delivery modeling.

Findings

Nonlinear effects are significant in ultrasound-targeted drug delivery.

The model's well-posedness depends on initial data smoothness and smallness conditions.

Numerical results highlight the importance of nonlinear modeling in realistic scenarios.

Abstract

We investigate a nonlinear multiphysics model motivated by ultrasound-enhanced drug delivery. The acoustic pressure field is modeled by Westervelt's quasilinear wave equation to adequately capture the nonlinear effects in ultrasound propagation. The nonlocal attenuation characteristic for soft biological media is modeled by acoustic damping of the time-fractional type. Additionally, acoustic medium parameters are allowed to depend on the temperature of the medium. The wave equation is coupled to the nonlinear Pennes heat equation with a pressure-dependent source to account for ultrasound waves heating up the tissue. Finally, the drug concentration is obtained as the solution to an advection-diffusion equation with a pressure-dependent velocity. Toward gaining a rigorous understanding of this system, we set up a fixed-point argument in the analysis combined with devising energy estimates that can accommodate the time-fractional damping. The energy arguments are, in part, carried out by employing time-weighted test functions to reduce the regularity assumptions on the initial temperature. The analysis reveals that different smoothness of the initial pressure, temperature, and concentration fields is needed as well as smallness of the pressure-temperature data in order to ensure non-degeneracy of the system and establish well-posedness. Our theoretical considerations are complemented by a numerical investigation of the system under more realistic boundary conditions. The numerical experiments, performed in different computational scenarios, underline the importance of considering nonlinear effects when modeling ultrasound-targeted drug delivery.