A 2D Hydrothermodynamic Analytical Model for Rapid Tumor Ablation using High-Intensity Focused Ultrasound

Abstract

We establish a self-consistent 2D hydrothermodynamic analytical model for the localized thermal ablation of dense human tumors using high-intensity focused ultrasound. By expanding compressible Navier-Stokes equations up to second order, we demonstrate that within a structurally stationary cellular tumor matrix, acoustic streaming (acoustic wind) velocity is suppressed. This constraint forces the absorbed wave momentum flux to transfer entirely into localized, time-averaged, static, second order, pressure gradients, converting the bulk acoustic energy directly into localized heat. Using a short, 1 s, duration, high-amplitude top-hat pulse, we solve the simplified Pennes bioheat transfer equation within non-diffusive timescales. Adapting the hydrodynamic optimization framework established by Tsiklauri~(2026), we derive a natural physical criterion where the acoustic absorption coefficient matches half the inverse target depth, $\alpha =1/(2x_0)$, proving that the optimal operational frequency scales inversely with transmission distance. We show that while incident plane waves overheat upstream tissues due to exponential decay, a spherically focusing wave geometry effectively bypasses healthy tissue boundaries via geometric convergence ($\propto 1/r^2$). Analytically solving the non-isothermal Arrhenius injury integral yields a sharp lesion boundary radius at $r_b=0.75w_0$. Volumetric averaging bounded strictly within this necrosis perimeter demonstrates that the average tumor temperature reaches $72.1^{\circ }\text{C}$ while central point values peak at $90^{\circ }\mathrm{C}$. Finally, convolving the post-pulse thermal profile with a 2D free-space Green's function verifies immediate, monotonic temperature decay below $60^{\circ }\mathrm{C}$ at the boundary, demonstrating complete structural containment and explaining the $>90\%$ localization rates observed in clinical applications.

submitted for publication