Effect of porosity, tissue density, and mechanical properties on radial sound speed in human cortical bone

Purpose: The purpose of this study was to investigate the effect of simultaneous changes in cortical porosity, tissue mineral density, and elastic properties on radial speed of sound (SOS) in cortical bone. The authors applied quantitative pulse-echo (PE) ultrasound techniques that hold much potential especially for screening of osteoporosis at primary healthcare facilities. Currently, most PE measurements of cortical thickness, a well-known indicator of fracture risk, use a predefined estimate for SOS in bone to calculate thickness. Due to variation of cortical bone porosity, the use of a constant SOS value propagates to an unknown error in cortical thickness assessment by PE ultrasound. Methods: The authors conducted 2.25 and 5.00 MHz focused PE ultrasound time of flight measurements on femoral diaphyses of 18 cadavers in vitro. Cortical porosities of the samples were determined using microcomputed tomography and related to SOS in the samples. Additionally, the effect of cortical bone porosity and mechanical properties of the calcified matrix on SOS was investigated using numerical finite difference time domain simulations. Results: Both experimental measurements and simulations demonstrated significant negative correlation between radial SOS and cortical porosity (R2 ≥ 0.493, p < 0.01 and R2 ≥ 0.989, p < 0.01, respectively). When a constant SOS was assumed for cortical bone, the error due to variation of cortical bone porosity (4.9%–16.4%) was about 6% in the cortical thickness assessment in vitro. Conclusions: Use of a predefined, constant value for radial SOS in cortical bone, i.e., neglecting the effect of measured variation in cortical porosity, propagated to an error of 6% in cortical thickness. This error can be critical as characteristic cortical thinning of 1.10% ± 1.06% per yr decreases bending strength of the distal radius and results in increased fragility in postmenopausal women. Provided that the cortical porosity can be estimated in vivo, the relationship between radial SOS and cortical porosity can be utilized and a porosity based radial SOS estimate could be implemented to determine cortical thickness. This would constitute a step toward individualized quantitative ultrasound diagnostics of osteoporosis.