Elasticity–density and viscoelasticity–density rel

Authors: Simon Bernard Joannes Schneider Peter Varga Pascal Laugier Kay Raum Quentin Grimal

Publish Date: 2015/06/13

Volume: 15, Issue: 1, Pages: 97-109

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Abstract

Cortical bone tissue is an anisotropic material characterized by typically five independent elastic coefficients for transverse isotropy governing shear and longitudinal deformations in the different anatomical directions It is well established that the Young’s modulus in the direction of the bone axis of long bones has a strong relationship with mass density It is not clear however whether relationships of similar strength exist for the other elastic coefficients for they have seldom been investigated and the results available in the literature are contradictory The objectives of the present work were to document the anisotropic elastic properties of cortical bone at the tibia middiaphysis and to elucidate their relationships with mass density Resonant ultrasound spectroscopy RUS was used to measure the transverse isotropic stiffness tensor of 55 specimens from 19 donors Except for Poisson’s ratios and the nondiagonal stiffness coefficient strong linear correlations between the different elastic coefficients 07 r2 099 and between these coefficients and density 079 r2 089 were found Comparison with previously published data from femur specimens suggested that the strong correlations evidenced in this study may not only be valid for the midtibia RUS also measures the viscous part of the stiffness tensor An anisotropy ratio close to two was found for damping coefficients Damping increased as the mass density decreased The data suggest that a relatively accurate estimation of all the midtibia elastic coefficients can be derived from mass density This is of particular interest 1 to design organscale bone models in which elastic coefficients are mapped according to Hounsfield values from computed tomography scans as a surrogate for mass density and 2 to model ultrasound propagation at the midtibia which is an important site for the in vivo assessment of bone status with axial transmission techniquesThis work has been conducted within the European Associated Laboratory ‘Ultrasound Based Assessment of Bone’ ULAB a cooperation of centers in Paris France and Kiel and Berlin Germany funded by CNRS France This work was funded by the Agence Nationale pour la Recherche under a Grant No ANR13BS09000601 the ElsbethBonhoff foundation project sharp 36 ‘Verbesserung der Abschätzung der Knochenbruchfestigkeit am proximalen Femur durch multitimodale Bestimmung von festigkeitsrelevanten Knochenmaterialeigenschaften’ and was supported by the Deutsche Forschungsgemeinschaft SPP 1420 grant Ra1380/73 Ra1380/91 JS is grateful for the support from the BSRT We acknowledge Robert Wendlandt from UKSH Lübeck for the collection of the samples

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