Analysis of Shear Wave Propagation in Soft Biomaterials Using a Finite Element Model

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 using a finite element model. A finite element model was constructed based on the setup of our previous in vitro experiments on the elastography of gelatin. Briefly, a shear wave propagation was induced by a single indent with a frequency of 1 kHz. Following simulation, 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 investigated. Results have shown that finite element simulation agreed well with the previous in vitro experiments. The estimated stiffness increased by more than 10% as the depth increased from 1 mm to 7 mm. This increase was even larger for the material with a 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 after the distance of 4 mm. The feasibility of three algorithms, i.e., wavefront slope, cross-correlation algorithm, and finite differencing method (FDM), were investigated. The FDM proposed in this work can determine the shear wave speed based on local spatial and temporal data, while it demands high-frequency data. The understanding from this work may provide valuable information for optimizing the performance of elastography.