AI 中文总结
该研究推导了简化粘弹性FDTD格式，用于高效建模软组织中超声驱动剪切波传播，经多类验证其精度高、成本低，可适配异质性组织并与声学模拟器集成。
AI 中文摘要
软组织中超声驱动的剪切波传播是剪切波弹性成像（SWE）和新兴的超声神经调节弹性力学假说的基础，两者都需要对辐射力诱导的组织运动进行准确、高效的建模。通用有限元弹性动力学求解器对于以剪切运动为主的应用而言，通常计算成本高昂且功能过于宽泛。我们通过对完整纳维方程应用近不可压缩性、小应变线性化、亥姆霍兹分解和无散体力投影，推导出一种简化粘弹性格式，得到仅保留与辐射力诱导运动相关的横向动力学的开尔文-沃伊特（Kelvin-Voigt）剪切波方程。采用二阶空间和时间精度的显式时域有限差分（FDTD）实现，通过无矩阵共轭梯度泊松求解器强制执行无散体力约束。对于可分离的辐射力源，预计算的投影将该成本降低1至2个数量级。在均匀介质中，求解器恢复的理论剪切波速误差小于0.1%，表现出明显的二阶网格收敛性（迹-L2自收敛，p≳2），在16点粘度扫描（η∈[0,1.5] Pa·s）范围内，与解析开尔文-沃伊特衰减和相速度的匹配度分别约为3%和小于1%。端到端的RSNA QIBA体模基准在十倍剪切模量范围（G=1–10 kPa）内，恢复的剪切波速误差约为1%。该框架可适应剪切模量、密度和粘度的空间异质性，并可与声学模拟器集成。通过显微CT颅骨几何结构的经颅演示，产生的剪切位移为1.7–5 μm，与临床ARFI结果一致。
英文摘要
Ultrasound-driven shear wave propagation in soft tissue underlies shear wave elastography (SWE) and emerging elastomechanical hypotheses of ultrasonic neuromodulation, both of which require accurate, efficient modeling of radiation-force--induced tissue motion. General-purpose finite-element elastodynamic solvers are often computationally expensive and unnecessarily broad for shear-dominant applications. We derive a reduced viscoelastic formulation by applying near-incompressibility, small-strain linearization, Helmholtz decomposition, and solenoidal force projection to the full Navier equations, yielding a Kelvin--Voigt shear wave equation that retains only the transverse dynamics relevant to radiation-force--induced motion. An explicit finite-difference time-domain (FDTD) implementation with second-order spatial and temporal accuracy enforces the solenoidal body-force constraint via a matrix-free conjugate-gradient Poisson solve. For separable radiation-force sources, a pre-computed projection reduces this cost by one to two orders of magnitude. In homogeneous media the solver recovers the theoretical shear wavespeed to within $<$0.1\%, exhibits clear second-order grid convergence (trace-$L_2$ self-convergence, $p\gtrsim2$), and matches analytical Kelvin--Voigt attenuation and phase speed to within ${\sim}3\%$ and $<$1\% over a 16-point viscosity sweep ($η\in[0,1.5]$~Pa$\cdot$s). An end-to-end RSNA QIBA phantom benchmark recovers shear wave speeds to within ${\sim}1\%$ across a tenfold shear-modulus range ($G=1$--$10$~kPa). The framework accommodates spatial heterogeneity in shear modulus, density, and viscosity, and integrates with acoustic simulators. Transcranial demonstrations through micro-CT skull geometries produce shear displacements of 1.7--5~$μ$m consistent with clinical ARFI.
