Influence of porosity, pore size, and cortical thickness on the propagation of ultrasonic waves guided through the femoral neck cortex: a simulation study

The femoral neck is a common fracture site in elderly people. The cortical shell is thought to be the major contributor to the mechanical competence of the femoral neck, but its microstructural parameters are not sufficiently accessible under in vivo conditions with current X-ray-based methods. To systematically investigate the influences of pore size, porosity, and thickness of the femoral neck cortex on the propagation of ultrasound, we developed 96 different bone models (combining 6 different pore sizes with 4 different porosities and 4 different thicknesses) and simulated the ultrasound propagation using a finite-difference time-domain algorithm. The simulated singleelement emitter and receiver array consisting of 16 elements (8 inferior and 8 superior) were placed at anterior and posterior sides of the bone, respectively (transverse transmission). From each simulation, we analyzed the waveform collected by each of the inferior receiver elements for the one with the shortest time of flight. The first arriving signal of this waveform, which is associated with the wave traveling through the cortical shell, was then evaluated for its three different waveform characteristics (TOF: time point of the first point of inflection of the received signal, Δt: difference between the time point at which the signal first crosses the zero baseline and TOF, and A: amplitude of the first extreme of the first arriving signal). From the analyses of these waveform characteristics, we were able to develop multivariate models to predict pore size, porosity, and cortical thickness, corresponding to the 96 different bone models, with remaining errors in the range of 50 μm for pore size, 1.5% for porosity, and 0.17 mm for cortical thickness.