Multi-layer velocity model based synthetic aperture ultrasound imaging of cortical bone

Abstract

With the advantages of non-ionizing and low cost, ultrasound imaging has been widely used in clinical diagnosis and treatment. However, due to the significant velocity changes between cortical bone and soft-tissue, the traditional ultrasound beamforming method under the assumption of constant velocity fails to reconstruct the cortical bone image. The velocity model based beamforming has been used in geophysics and non-destructive testing as an effective way to solve the challenges resulting from the velocity changes in multi-layer structure. Since the cortical bone can be modeled as a three-layer structure consisting of soft tissue, cortical bone and marrow, a multi-layer velocity model based synthetic aperture ultrasound method is introduced for cortical bone imaging. In this study, we first utilize synthetic transmit aperture ultrasound to obtain the full-matrix dataset to increase the signal-to-noise ratio. Second, a three-layer cortical bone velocity model is built with the compressed sensing estimated arriving time delay. The bases of compressed sensing consist of a series of excitation pulses with different delays. The received signals are regarded as a composition of the bases with different weights, thus can be projected into the bases by using compressed sensing. The time-delay of each received element is estimated by compressed sensing. According to the time-delay, the full-matrix dataset is reformed into a zero-offset format. By extracting the bases corresponded with the interface reflected signals, the time-delay between and the thickness values of the interfaces can be estimated. The velocity model can thus be built with the estimated cortical bone thickness. Based on the velocity model and zero-offset data, the phase shift migration method is used to reconstruct the cortical bone image. The finite-difference time-domain (FDTD) method is used to simulate the wave propagation in a 3.4-mm-thick cortical bone. The transmitting pulse is a Gaussian-function enveloped tone-burst signal with 6.25 MHz center frequency and 250 MHz iteration rate. The reconstructed image of simulation shows a clear top interface and bottom interface of cortical bone with correct thickness. Further FDTD simulations are carried out on a 3-mm-to-5-mm-thick cortical bone, and the average relative error of estimated thickness is 4.9% with a 13.5% variance. <i>In vitro</i> experiment is performed on a 3.4-mm-thick bovine bone plate to test the feasibility of the proposed method by using Verasonics platform (128-element linear array). The transmitting pulse is a Gaussian-function enveloped tone-burst signal with 6.25 MHz center frequency and 25 MHz sampling rate. The reconstructed image in experiment reveals a clear top interface and bottom interface of cortical bone with correct thickness. The experiment is repeated several times and the average relative error of estimated thickness is 3.6% with a 5.4% variance. The results of simulation and experiment both indicate that compressed sensing is effective in estimating the delay parameters of the velocity model. Finally, we evaluate the capability of compressed sensing in time-delay estimation, and the result shows that compressed sensing is more accurate than Hilbert transform even in a 20 dB-noise condition. In conclusion, the proposed method can be useful in the thickness estimation and the ultrasound imaging of cortical bone. <i>In vivo</i> experiment and clinical application should be further investigated.