The dependence of ultrasonic backscatter on trabecular thickness in human calcaneus: theoretical and experimental results

Trabecular thickness within cancellous bone is an important determinant of osteoporotic fracture risk. Noninvasive assessment of trabecular thickness potentially could yield useful diagnostic information. Faran's theory of elastic scattering from a cylindrical object immersed in a fluid has been used to predict the dependence of ultrasonic backscatter on trabecular thickness. The theory predicts that, in the range of morphological and material properties expected for trabecular bone, the backscatter coefficient at 500 kHz should be approximately proportional to trabecular thickness to the power of 2.9. Experimental measurements of backscatter coefficient were performed on 43 human calcaneus samples in vitro. Mean trabecular thicknesses on the 43 samples were assessed using micro computed tomography (CT). A power law fit to the data showed that the backscatter coefficient empirically varied as trabecular thickness to the 2.8 power. The 95% confidence interval for this exponent was 1.7 to 3.9. The square of the correlation coefficient for the linear regression to the log transformed data was 0.40. This suggests that 40% of variations in backscatter may be attributed to variations in trabecular thickness. These results reinforce previous studies that offered validation for the Faran cylinder model for prediction of scattering properties of cancellous bone, and provide added evidence for the potential diagnostic utility of the backscatter measurement.