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 (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">11</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">22.64</mml:mn><mml:mn fontstyle="italic">1</mml:mn></mml:math> GPa, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">33</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">13.637</mml:mn></mml:math> GPa), shear moduli (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">12</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">10.608</mml:mn></mml:math> GPa, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M4"><mml:msub><mml:mrow><mml:mi>G</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">23</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">7.742</mml:mn></mml:math> Gpa), and Poisson’s ratios (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M5"><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">12</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">0.067</mml:mn></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M6"><mml:msub><mml:mrow><mml:mi>ν</mml:mi></mml:mrow><mml:mrow><mml:mn fontstyle="italic">31</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mn fontstyle="italic">0</mml:mn><mml:mo>.</mml:mo><mml:mn fontstyle="italic">378</mml:mn></mml:math>), were finally calculated. This study demonstrates that RUS can be successfully adapted to measure the mechanical properties of low quality factor biomaterials.