Finite-Difference Time-Domain Simulations of Ultrasound Backscattered Waves in Cancellous Bone

Abstract

In this study, using an elastic finite-difference time-domain (FDTD) method with numerical cancellous bone models reconstructed from microcomputed tomographic (μCT) images of bovine bone, numerical simulations of the backscattered waves in cancellous bone was performed for clarifying the backscatter characteristics. In the simulation model, an ultrasound pulse wave was transmitted toward the front surface of cancellous bone from a circular concave transmitter/receiver in water. Then, two cancellous bone models with different thicknesses, in which an artificial absorbing boundary was set at the back surface opposite to the ultrasound transmission. By calculating the difference between the simulated results of the received signals in the cases of these cancellous bone models, the reflected wave from the front surface could be canceled, and only the backscattered waves inside the bone could be extracted. Using the cancellous bone models with porosities between 0.53 and 0.86 (53% and 86%), which had main trabecular orientation parallel to the thickness direction (or the transmitted ultrasound direction), the peak-to-peak amplitude of the backscattered waves were derived as a function of the porosity. The determination coefficient between the backscattered wave amplitude and the porosity was R² = 0.49 (P < 0.001). The correlation was moderate, which was considered to be because the backscattered waves could be affected by not only the porosity but also the trabecular microstructure.