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 high-intensity focused ultrasound tumor ablation. Expanding compressible Navier-Stokes equations to second order demonstrates that a stationary cellular matrix suppresses acoustic streaming (${\mathbf{v}}_2=0$). This constraint forces the absorbed wave momentum flux to convert entirely into localized, time-averaged static pressure gradients ($\nabla ⟨p_2⟩={\mathbf{F}}_2$), bridging non-linear hydrodynamics with thermodynamic dissipation. Solving the non-diffusive Pennes bioheat equation under a $1.0\text{s}$ top-hat pulse reveals that a spherically focusing geometry ($\propto 1/r^2$) overrides exponential damping past a critical geometric threshold ($r_{\text{crit}}=2x_0$), preventing upstream skin overheating. We derive an optimization criterion where the absorption coefficient matches half the inverse target depth ($\alpha =1/2x_0$). Solving the non-isothermal Arrhenius integral yields a sharp lesion boundary radius at $r_b=0.75w_0$, where the volume average reaches $72.1^{\circ }\text{C}$ while the core peaks at $90.0^{\circ }\text{C}$. Post-pulse 2D free-space Green's function convolution confirms immediate monotonic thermal decay ($\partial \theta /\partial t^{\prime }<0$) outside this boundary. This closed-form framework provides explicit scaling laws for non-invasive wave-matter thermal confinement, bypassing computationally heavy numerical simulations.

arXiv commentsubmitted for publication, typos corrected, improvements made