A Conservative Numerical Framework for Modeling Nonlinear Ultrasound Propagation in Thermoviscous Tissue Phantom

Faculty of Marine Engineering, Chabahar Maritime University, Chabahar, Iran

*Corresponding Author: Mohammad Yaghoub Abdollahzadeh Jamalabadi, Faculty of Marine Engineering, Chabahar Maritime University, Chabahar, Iran, E-mails: [email protected]; [email protected]

Received Date: December 05, 2025

Published Date: December 31, 2025

Citation: Jamalabadi MYA. (2025). A Conservative Numerical Framework for Modeling Nonlinear Ultrasound Propagation in Thermoviscous Tissue Phantom. Mathews J Surg. 8(2):41.

Copyrights: Jamalabadi MYA. © (2025).

ABSTRACT

High-intensity focused ultrasound (HIFU) is increasingly used in surgical oncology, thermal ablation, lithotripsy, and other therapeutic procedures. Accurate prediction of ultrasound behavior within tissue is essential because nonlinear wave effects, shock formation, and tissue heating all depend on how pressure waves evolve as they travel through biological media. A new conservative hyperbolic formulation is introduced for modeling finite-amplitude acoustic wave propagation in homogeneous thermoviscous media. The proposed system, referred to as the Thermoviscous Acoustic System (TAS), is derived from the Navier-Stokes equations under small perturbation assumptions and cast into a first-order hyperbolic form. It captures nonlinear wave growth, high-order shock formation, and viscous/thermal absorption—all critical for predicting lesion size, peak pressures, and off-target heating. To make this practical for clinical or research settings, the method uses high-order WENO reconstructions, SSP-RK time integrators and GPU acceleration, achieving up to 300 GFLOPS in double precision.

Key results demonstrate: (1) strong agreement between NAS-WENO5 solutions and Westervelt FDTD solver for smooth waves, with superior shock-capturing capability at β = 100; (2) accurate reproduction of O'Neil's exact solution for focused beams in the linear regime; (3) successful capture of harmonic generation at the focal point with pressure amplitude amplification of approximately 10× and p₊/p₋ ratio of ~2, consistent with finite-amplitude propagation theory; (4) effective adaptive mesh refinement reducing computational cost while maintaining accuracy; and (5) validation of nonlinear waveform distortion and spectral evolution matching theoretical predictions from Westervelt and KZK equations.

Keywords: HIFU, Surgical Planning, Shock Waves, Thermal Ablation, Tissue Phantom.