AI 中文总结
本文提出改进的角谱法（ASM），用于异质组织中超声非线性传播模拟，经颅超声与治疗超声场景，通过倾斜角校正、特殊离散化方案、源注入与边界处理优化，在精度相当的情况下较Fullwave 2显著降低内存与时间成本。
AI 中文摘要
本文开发了一种改进的角谱法（ASM），用于模拟三维非线性声波在异质组织中的传播，针对经颅超声和治疗超声场景。首先，对分步更新的线性算子和非线性算子均应用了一致的倾斜角校正：衰减与色散滤波器在完整的波数-频率网格上采用了逐模式的k/kz因子，使每个分量沿其真实路径长度dz/cos(θ)累积吸收和相位，而Burgers系数则按功率加权的平均声束倾斜角进行缩放。其次，采用带MUSCL重构和SSP-RK2时间积分的二阶Kurganov-Tadmor中心迎风格式对延迟时间Burgers更新进行离散化，并结合Strang分裂的衍射与衰减处理以及自适应CFL亚循环，无需有限差分时域（FDTD）方法因CFL耦合要求的时间细化即可解析充分发展的激波。第三，采用逐平面源注入方案，将深曲面碗状换能器分解为在正确传播深度注入的轴向切片，保留与孔径相关的激波形成距离。从颅骨CT数据导出的相位-振幅屏可模拟经颅像差和插入损耗，三种改进的吸收边界处理使边界反射降低了2.4倍。解析验证结果表明，该方法将障板活塞的远场图案复现至0.014的均方根误差，聚焦活塞的焦点压力预测误差在2.3%以内。在通过离体人颅骨的经颅基准测试中，ASM将焦点平面强度与Fullwave 2的匹配度达到1.1%的均方根误差，并预测得到5.4 dB的经颅骨插入损耗。对于半径R=80 mm、中心频率f0=1 MHz的碗状换能器，ASM将焦点深度与Fullwave 2的匹配度控制在2.3%以内，同时内存需求降低9倍，墙钟时间缩短2.9倍。
英文摘要
A modified angular spectrum method (ASM) is developed for three-dimensional nonlinear acoustic propagation through heterogeneous tissue, targeting transcranial and therapeutic ultrasound. First, a consistent obliquity correction is applied to both the linear and nonlinear operators of the split-step update. The attenuation and dispersion filter carries a per-mode k/kz factor on the full wavenumber-frequency grid, so each component accumulates absorption and phase over its true path length dz/cos(theta), while the Burgers coefficient is scaled by the power-weighted mean beam obliquity. Second, the retarded-time Burgers update is discretized with a second-order Kurganov-Tadmor central-upwind flux using MUSCL reconstruction and SSP-RK2 time integration, composed with diffraction and attenuation through Strang splitting with adaptive CFL sub-cycling, resolving fully developed shocks without the temporal refinement that the CFL coupling imposes on FDTD. Third, a plane-by-plane source-injection scheme decomposes deeply curved bowl transducers into axial slices injected at their correct propagation depths, preserving the aperture-dependent shock-formation distance. Phase-and-amplitude screens derived from skull CT data model transcranial aberration and insertion loss, and three enhanced absorbing-boundary treatments reduce boundary reflections by a factor of 2.4. Analytical validation reproduces the baffled-piston far-field pattern to 0.014 RMS and the focused-piston focal pressure to within 2.3 percent. In a transcranial benchmark through an ex vivo human skull, the ASM matches the Fullwave 2 focal-plane intensity to 1.1 percent RMS and predicts a 5.4 dB through-skull insertion loss. For a bowl transducer (R = 80 mm, f0 = 1 MHz), the ASM matches the Fullwave 2 focal depth to within 2.3 percent with 9x less memory and 2.9x less wall time.
