Quantification of tissue stiffness with magnetic resonance elastography and finite difference time domain (FDTD) simulation-based spatiotemporal neural network

Abstract

Quantification of tissue stiffness with magnetic resonance elastography (MRE) is an inverse problem that is sensitive to noise. Conventional methods for the purpose include direct inversion (DI) and local frequency estimation (LFE). In this study, we propose to train a spatiotemporal neural network using MRE data simulated by the Finite Difference Time Domain method (FDTDNet), and to use the trained network to estimate tissue stiffness from MRE data. The proposed method showed significantly better robustness to noise than DI or LFE. For simulated data with signal-to-noise ratio (SNR) of 15 dB, tissue stiffness by FDTDNet had mean absolute error of 0.41 kPa or 7 %, 77.8 % and 84.4 % lower than those by DI and LFE respectively (P < 0.0001). For a homogeneous phantom with driver power decreasing from 30 % to 5 %, FDTDNet, DI and LFE provided stiffness estimates with deviation of 6.9 % (0.21 kPa), 9.2 % (0.28 kPa) and 45.8 % (1.20 kPa) of the respective stiffness level at driver power of 30 %. Detectability of small inclusions in estimated stiffness maps is also critical. For simulated data with inclusions of radius of 0.31 cm, FDTDNet achieved contrast-to-noise ratio (CNR) of 4.20, 6900 % and 347 % higher than DI and LFE respectively (P < 0.0001), and structural similarity index (SSIM) of 0.61, 27 % and 177 % higher than DI and LFE respectively (P < 0.0001). For phantom with inclusion of radius 0.39 cm, CNR of FDTDNet was 2.98, 90 % and 80 % higher than DI and LFE respectively (P < 0.0001) and SSIM was 0.80, 89 % and 28 % higher than DI and LFE respectively (P < 0.0001). We also demonstrated the feasibility of FDTDNet in MRE data acquired from calf muscles of human subjects. In conclusion, by using a spatiotemporal neural network trained with simulated data, FDTDNet estimated tissue stiffness from MRE with superior noise robustness and detectability of focal inclusions, therefore showed potential in precisely quantifying MRE of human subjects.