P5A-5 Dependence of Both Slow and Fast Wave Mode Properties on Bone Volume Fraction and Structural Anisotropy in Human Trabecular Bone: A 3D Simulation Study

Quantitative ultrasonic techniques are clinically used to estimate bone mechanical properties. Two longitudinal wave modes may be observed in vitro in trabecular bone, but the observation of the two waves depends on bone volume fraction (BV/TV), structural anisotropy and on the direction of propagation relatively to the direction of main trabecular alignment (MTA). Both wave modes are predicted by the Biot's theory. In some circumstances, the overlapping of both waves in the time domain is such that only a single pulse seems to be transmitted. Analytical predictions have been unable so far to establish reliable relationships between structural anisotropy, BV/TV and the behavior of both wave modes. The aim of this work was to investigate the conditions on BV/TV and structural anisotropy under which the fast and slow waves may be observed. Our approach uses 3D finite-difference time-domain simulations coupled with 34 real human femoral trabecular microstructures measured using synchrotron radiation micro computed tomography. The structural anisotropy (MTA, degree of anisotropy (DA)) of each sample was determined using a 3D image processing method. Our hypothesis was that the time separability of both waves results from a combination of appropriate values of BV/TV and structural anisotropy for the 3 perpendicular directions of propagation. The influence of BV/TV on both waves was studied using an image processing algorithm modifying all initial 3D microstructures. A heuristic signal processing method was developed aiming at determining when both wave modes overlap in time and when they can be distinguished. Both wave modes generally overlap in time when the MTA is perpendicular to the direction of propagation. When MTA is parallel to the direction of propagation, both separated wave modes can be observed for samples with high values of DA and BV/TV. Our results show that simultaneous conditions on structural anisotropy and BV/TV have to be fulfilled to be able to separate both wave modes.