A Finite Element Model for Analyzing the Shear Wave Propagation in Soft Biomaterials

Abstract The elastography method has been widely used to estimate the stiffness of biomaterials based on the shear wave speed. The wave propagation excited by a single indent on the surface of the biomaterials is not always an ideal shear wave. The distance from the interested region to the indent, or different algorithms for elastography may affect the calculation of stiffness. This paper aims to analyze the shear wave propagation in soft biomaterials with a finite element model that was constructed based on the setup of our previous in-vitro experiments on gelatin. A shear wave propagation was induced by a single indent at 1kHz. The displacements along a path line, at three depths, were extracted for analyzing the shear wave propagation. The influence of the damping behavior and three different elastography algorithms were also investigated with our data. Results have shown that the finite element simulation agreed well with the previous in-vitro experiments. The stiffness increased by more than 10% as the depth increased from 1mm to 7mm, which is larger for materials with larger damping behavior (viscoelasticity). The precise estimation was related to the distance between the interested region and the indent for the material with a larger damping behavior. The feasibility of three algorithms: wavefront slope, cross-correlation algorithm, and finite differencing method (FDM), were investigated. The FDM can determine the shear wave speed based on local spatial and temporal data, while high-frequency data are required. This work provides valuable information for optimizing performance of elastography.