Influence of porosity and direction of measurement on ultrasound velocities in a homogeneous material with aligned pores measured via bidirectional axial transmission

Cortical bone porosity is associated with fracture risk of long bones and leads to an increase in anisotropy. Simulation studies showed that the porosity associated decrease of the ultrasound velocity in a homogenous material with cylindrical, aligned pores depends on the measurement direction. Therefore, velocity measurements in different directions might enable an estimation of the porosity. Following this finding we developed a probe which is capable of measuring ultrasound velocities in three different directions (0° and ±37.5°) without repositioning. The feasibility of this approach and the operating mode of the probe were tested on porosity phantoms by measuring in two positions: with the 0° direction of the probe parallel and perpendicular to the pore direction. For the first position an estimated anisotropy index (eAI) was calculated using all velocities measured without repositioning. An additional through transmission measurement using an insertion method was used to verify the velocity values obtained by the probe parallel and perpendicular to the pores. Velocities in all measured directions decreased with increasing porosity and increasing angle relative to the pore direction: the slopes were -6.3 m/s, -10.1 m/s and -13.1 m/s resp. for 0°, 37.5° and 90° angle. The velocity values measured by the probe and the insertion method were in good agreement (RMSE 5.5 m/s). eAI ranged from 1.00 to 1.09 and correlated with the porosity, which could be estimated from eAI with an RMSE of 0.013 (95% confidence interval 0.011-0.016).