Estimation of thickness and speed of sound in cortical bone using multi-focus pulse-echo ultrasound.

Most bone loss during the development of osteoporosis occurs in cortical bone at the peripheral skeleton. Decreased cortical thickness ( Ct.Th ) and the prevalence of large pores at the tibia are associated with reduced bone strength at the hip. Ct.Th and cortical sound velocity, i.e., a surrogate marker for changes of cortical porosity ( Ct.Po ), are key biomarkers for the identification of patients at high fracture risk. In this study, we have developed a method using a conventional ultrasound array transducer to determine thickness ( Ct.Th ) and the compressional sound velocity propagating in the radial bone direction ( Ct. $\nu _{11}$ ) using a refraction-corrected multifocus imaging approach. The method was validated in-silico on porous bone plate models using a 2-D finite-difference time-domain method and ex vivo on plate-shaped plastic reference materials and on plate-shaped cortical bovine tibia samples. Plane-wave pulse-echo measurements provided reference values to assess precision and accuracy of our method. In-silico results revealed the necessity to account for inclination-dependent transmission losses at the bone surface. Moreover, the dependence of Ct. $\nu _{11}$ on both porosity and pore density was observed. Ct.Th and Ct. $\nu _{11}$ obtained ex vivo showed a high correlation $(R 2>0.99$ ) with reference values. The ex-vivo accuracy and precision for Ct. $\nu _{11}$ were 29.9 m/s and 0.94%, respectively, and those for Ct.Th were 0.04 mm and 1.09%, respectively. In conclusion, this numerical and experimental study demonstrates an accurate and precise estimation of Ct.Th and Ct. $\nu _{11}$ . The developed multifocus technique may have high clinical potential to improve fracture risk prediction using noninvasive and nonionizing conventional ultrasound technology with image guidance.