2026/07/30 by Gianmarco Pinton
Physics and Astronomy · #physics.med-ph
arxiv created 2026/07/30 · arxiv updated 2026/07/31
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-L2 self-convergence, p\gtrsim2), and matches analytical Kelvin--Voigt attenuation and phase speed to within ∼3% and <1% over a 16-point viscosity sweep (η∈[0,1.5]~Pa⋅s). An end-to-end RSNA QIBA phantom benchmark recovers shear wave speeds to within ∼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~μm consistent with clinical ARFI.