IDENTIFICATION OF BONE MICROSTRUCTURE FROM EFFECTIVE COMPLEX MODULUS

Abstract

This work deals with the problem of reconstruction of bone structure from measurements of its effective mechanical properties. We propose a novel method of calculation of bone porosity from measured effective complex modulus. Bone is modelled as a medium with a microstructure composed of trabecular bone (elastic component) and bone marrow (viscoelastic component). We model bone as a cylinder subjected to torsion and assume that the effective complex modulus can be measured as a result of experiment. The analytical representation of the effective complex modulus of the two-component composite material is exploited to recover information about porosity of the bone. The microstructural information is contained in the spectral measure in the Stieltjes representation of the effective complex modulus and can be recovered from the measurements over a range of frequencies. The problem of reconstruction of the spectral measure is very ill-posed and requires regularization. To verify the approach we apply it to analytically and numerically simulated response of a cylinder subjected to torsion assuming that it is filled with a composite material with known (laminated) microstructure. The values of porosity calculated from the effective shear modulus are in good agreement with the model values.