Estimation of Trabecular Thickness Using Ultrasonic Backcatter

We present a method to estimate trabecular thickness (Tb.Th) in trabecular bones from ultrasound backscatter measurements. The estimation scheme is based on a nonlinear adjustment of predictions from a model to experimental data. The model assumes weak scattering from bone, where scattering is assumed to arise from the elastic solid trabeculae. The fluctuations of acoustical properties between bone tissue and the saturating fluid are assumed to be random and are described by the 3-D spatial autocorrelation function of the medium. In this paper, a Gaussian autocorrelation function is used. The inversion procedure is applied to a set of data measured on 33 femoral bone specimens. Results show that the model can predict both the magnitude and the frequency-dependence of the backscatter coefficient (root mean square error RMSE = 1 dB). The estimated trabecular thickness values are compared to the true trabecular thickness measured on high resolution microcomputed tomography 3-D reconstruction of bones microarchitecture. A close agreement is obtained on average over the group of specimens between predictions and the reference values: true Tb.Th is 132 ± 12 μm and estimated Tb.Th is 134 ± 15 μm. However, a moderate correlation between actual and estimated Tb.Th values is found (R2 = 0.44, p<10−4, RMSE = 8.7 μm) suggesting a modest predictability at the individual level. Sources for the variability of the estimator are studied. Using synthetic rf signals, we demonstrate that the fundamental limitation of the estimator due to speckle noise is approximately 5 μm. Taking into account the measurement errors, the total uncertainty on Tb.Th estimates is of the order of 7 μm. The influence of the attenuation compensation function used to derive the backscatter coefficient is studied. In particular, we demonstrate the necessity of compensating for the effect of the gating time window. The results are discussed with respect to their meaningful clinical value. The requirements to be fulfilled by the performance of the technique change with regard to the question being posed. Two different strategies are examined: 1. characterize trabecular thickness without consideration of bone quantity (or bone mineral density) and 2. estimate trabecular thickness after adjustment for BMD. Considering the first strategy, a comparison between the precision of our estimator and the biological variability leads us to the conclusion that our estimator should only permit to distinguish between micro-architectures characterized by extreme values of trabecular thickness (i.e., very thin or very thick trabecular thickness). In this respect, it would be interesting to test whether the estimator is able to discriminate between rod-like (thin) and plate-like (thick) structures that are known to influence differently bone strength. The second strategy is more demanding in terms of technique performance and our estimator is not able yet to catch small differences in Tb.Th values expected after adjustment to bone density. Progress in the field will require a significant reduction in speckle noise and measurement errors and/or the development of other and more efficient microstructural estimators.