用于高强度聚焦超声快速肿瘤消融的二维热流体动力学分析模型
A 2D Hydrothermodynamic Analytical Model for Rapid Tumor Ablation using High-Intensity Focused Ultrasound
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中文总结 AI 辅助
该研究建立用于高强度聚焦超声快速肿瘤消融的二维热流体动力学分析模型，推导最优频率准则，验证球面聚焦波可避开健康组织，实现>90%的热定位率。
中文摘要 AI 辅助
我们建立了一种自洽的二维热流体动力学分析模型，用于利用高强度聚焦超声对致密人肿瘤进行局部热消融。通过将可压缩纳维-斯托克斯方程展开至二阶，我们证明在结构静止的细胞肿瘤基质内，声流（acoustic wind）速度会受到抑制。这一约束使得吸收的波动动量通量完全转移为局部的、时间平均的、静态的二阶压力梯度，将体声波能量直接转化为局部热量。采用持续时间仅1秒的短时长高振幅平顶脉冲，我们在非扩散时间尺度内求解简化的Pennes生物热传递方程。适配Tsiklauri（2026）提出的流体动力学优化框架，我们推导得到一个自然物理准则：声吸收系数等于目标深度倒数的一半，即α = 1/(2x₀)，证明最优工作频率与传输距离成反比。我们表明，入射平面波会因指数衰减导致上游组织过热，而球面聚焦波几何结构则通过几何收敛（∝1/r²）有效避开健康组织边界。通过解析求解非等温Arrhenius损伤积分，得到清晰的损伤边界半径r_b = 0.75w₀。在该坏死周长内进行体积平均后，肿瘤平均温度达到72.1℃，中心点峰值温度为90℃。最后，将脉冲后的热分布与二维自由空间格林函数进行卷积，验证边界处温度立即单调衰减至60℃以下，证明热场被完全限制，解释了临床应用中观察到的>90%的定位率。
英文摘要
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 ($\nabla \langle p_2 \rangle = \mathbf{F}_2$), 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 ($α= 1/2x_0$). Solving the non-isothermal Arrhenius integral yields a sharp lesion boundary radius at $r_b = 0.75\,w_0$, 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 ($\partial θ/\partial t' < 0$) outside this boundary. This closed-form framework provides explicit scaling laws for non-invasive wave-matter thermal confinement, bypassing computationally heavy numerical simulations.
