Derivation of elastic stiffness from site-matched mineral density and acoustic impedance maps

Abstract

200 MHz acoustic impedance maps and site-matched synchrotron radiation micro computed tomography (SR-μCT) maps of tissue degree of mineralization of bone (DMB) were used to derive the elastic coefficient c33 in cross sections of human cortical bone. To accomplish this goal, a model was developed to relate the DMB accessible with SR-μCT to mass density. The formulation incorporates the volume fractions and densities of the major bone tissue components (collagen, mineral and water), and accounts for tissue porosity. We found that the mass density can be well modelled by a second-order polynomial fit to DMB (R2 = 0.999) and appears to be consistent with measurements of many different types of mineralized tissues. The derived elastic coefficient c33 correlated more strongly with the acoustic impedance (R2 = 0.996) than with mass density (R2 = 0.310). This finding suggests that estimates of c33 made from measurements of the acoustic impedance are more reliable than those made from density measurements. Mass density and elastic coefficient were in the range between 1.66 and 2.00 g cm−3 and 14.8 and 75.4 GPa, respectively. Although SAM inspection is limited to the evaluation of carefully prepared sample surfaces, it provides a two-dimensional quantitative estimate of elastic tissue properties at the tissue level.