High-resolution bone microstructure imaging based on ultrasonic frequency-domain full-waveform inversion
Yifang Li(李义方)1,2, Qinzhen Shi(石勤振)1, Ying Li(李颖)1, Xiaojun Song(宋小军)1, Chengcheng Liu(刘成成)3,†, Dean Ta(他得安)1,2,3,‡, and Weiqi Wang(王威琪)1
1 Department of Electronic Engineering, Fudan University, Shanghai, China; 2 Human Phenome Institute, Fudan University, Shanghai, China; 3 Academy for Engineering and Technology, Fudan University, Shanghai, China
Abstract The main challenge in bone ultrasound imaging is the large acoustic impedance contrast and sound velocity differences between the bone and surrounding soft tissue. It is difficult for conventional pulse-echo modalities to give accurate ultrasound images for irregular bone boundaries and microstructures using uniform sound velocity assumption rather than getting a prior knowledge of sound speed. To overcome these limitations, this paper proposed a frequency-domain full-waveform inversion (FDFWI) algorithm for bone quantitative imaging utilizing ultrasonic computed tomography (USCT). The forward model was calculated in the frequency domain by solving the full-wave equation. The inverse problem was solved iteratively from low to high discrete frequency components via minimizing a cost function between the modeled and measured data. A quasi-Newton method called the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm (L-BFGS) was utilized in the optimization process. Then, bone images were obtained based on the estimation of the velocity and density. The performance of the proposed method was verified by numerical examples, from tubular bone phantom to single distal fibula model, and finally with a distal tibia-fibula pair model. Compared with the high-resolution peripheral quantitative computed tomography (HR-pQCT), the proposed FDFWI can also clearly and accurately presented the wavelength scaled pores and trabeculae in bone images. The results proved that the FDFWI is capable of reconstructing high-resolution ultrasound bone images with sub-millimeter resolution. The parametric bone images may have the potential for the diagnosis of bone disease.
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11827808, 11874289, and 11804056), the National Science Fund for Distinguished Young Scholars of China (Grant No. 11525416), Shanghai Municipal Science and Technology Major Project, China (Grant No. 2017SHZDZX01), Shanghai Talent Development Fund (Grant No. 2018112), State Key Laboratory of ASIC and System Project (Grant No. 2018MS004), and China Postdoctoral Science Foundation (Grant No. 2019M661334).
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