Elastic constants identification of irregular hard biological tissue materials using FEM-based resonant ultrasound spectroscopy

This paper aims to apply the resonant ultrasound spectroscopy technique (RUS) combined with micro computed tomography (μ-CT) and finite element method (FEM) to quantify the elastic constants of the irregular hard biological tissue material such as enamel. In this method, the resonant frequencies of an irregular shaped sample tested under stress-free boundary conditions are measured first. Then, micro-computed tomography (μ-CT) is used to acquire three-dimensional (3-D) geometry information of the sample, and the resonant frequencies are calculated with FEM. Thereby, an optimization procedure using the Levenberg-Marquardt algorithm updates the elastic constants in the FEM model until the output natural frequencies from the model fit the results from the RUS experiments. The proposed method has been tested first on a calibration material. To this purpose, titanium has been selected. The elastic constants of a rectangular parallelepiped shaped titanium sample obtained by the conventional RUS method and those of five irregular samples obtained by FEM-based RUS were in good agreement, displaying differences less than 2%. Once the method has been validated on titanium, it was applied to an enamel sample. The results show that the FEM-based RUS method can effectively identify the elastic constants of irregular titanium and enamel samples. This study expands the application range of RUS technology and provides a new method for the measurement of elastic properties of irregular hard biological tissue materials.