The Elasticity Coefficients Measurement of Human Dentin Based on RUS

Abstract

This paper proposed to take advantages of resonant ultrasound spectroscopy (RUS) to measure the mechanical properties of human dentin specimen. The resonant spectroscopy of the dentin specimen was obtained between the frequency bands 155 and 575 kHz, and resonant frequencies were extracted by linear predictive filter and then by Levenberg-Marquardt method. By inverse problem approach, 13 experimental resonant frequencies progressively matched to the first 30 orders of theoretical resonant frequencies calculated by Lagrangian variational method. The full second-order elastic tensor of dentin specimen was adjusted. The whole set of human dentin engineering moduli, including Young's moduli (E11 = 22.641 GPa, E33 = 13.637 GPa), shear moduli (G12 = 10.608 GPa, G23 = 7.742 Gpa), and Poisson's ratios (ν12 = 0.067, ν31 = 0.378), were finally calculated. This study demonstrates that RUS can be successfully adapted to measure the mechanical properties of low quality factor biomaterials.

Elastic properties measurement of human enamel based on resonant ultrasound spectroscopy

“…Comparing the resonance ultrasound spectra of the enamel specimens from this study (Fig. 4) with the resonance ultrasound spectra recorded for a dentin specimen in a previous study [(Fan et al, 2017), Fig. 2], the resonant peaks of enamel were found to be sharper and the overlaps between the peaks were found to be smaller, reflecting a higher Q value of enamel compared to dentin.…”

“…Compared to the stiffness constants of dentin similarly calculated by the RUS method (Kinney et al, 2003(Kinney et al, , 2004Fan et al, 2017), the stiffness constants of enamel were higher, which might be attributed to the higher mineralization of enamel and a denser and less porous material structure of enamel material. This result was consistent with previous researches (Ye et al, 1994;Stanford et al, 1958).…”

“…The limitations of the measurement techniques have led to large differences in the measurement results. As one of the most accurate methods to measure the stiffness of high Q solid materials (Bernard et al, 2013(Bernard et al, , 2014(Bernard et al, , 2015Migliori and Maynard, 2005;Migliori and Sarrao, 1997;Migliori et al, 1993;Kinney et al, 2003Kinney et al, , 2004Fan et al, 2017) for small-sized specimens, RUS was applied to measure the stiffness of six small-sized human enamel specimens in this study, which is believed to be the first study to investigate the anisotropic elastic properties of enamel using this method.…”

“…We will not detail here the entire procedure implemented to retrieve the stiffness constants from RUS measurements. It has been described extensively in reports to which the reader may refer (Bernard et al, 2013(Bernard et al, , 2014(Bernard et al, , 2015Migliori and Maynard, 2005;Migliori and Sarrao, 1997;Migliori et al, 1993;Fan et al, 2017). For the sake of clarity, however, we briefly describe hereinafter the main steps.…”

“…Kinney et al measured the elastic properties of human dentin in both the dry and humid states using RUS (Kinney et al, 2003(Kinney et al, , 2004. Fan et al used RUS combined with an improved resonant frequency extraction method to estimate the full stiffness constants, as well as engineering elastic moduli, including Young's moduli, shear moduli, and Poisson's ratios, of human dentin specimens (Fan et al, 2017).…”