Robust Reconstruction of Elasticity Using Ultrasound Imaging and Multi-Frequency Excitations

Biomedical parameters of tissue can be important indicators for clinical diagnosis. One such parameter that reflects tissue stiffness is elasticity, the imaging of which is called elastography. In this paper, we use displacements from harmonic excitations to solve the inverse problem of elasticity based on a finite-element method (FEM) formulation. This leads to iterative solution of nonlinear and nonconvex problems. In this paper, we show the importance and selection of viable initializations in numerical simulation studies and propose techniques for the fusion of multiple initializations for ideal reconstructions of unknown tissue as well as combining information from excitations at multiple frequencies. Results show that our method leads up to 76% decrease in root-mean-squared error (RMSE) and 9.9 dB increase in contrast-to-noise ratio (CNR) in simulations with noise, when compared to conventional iterative FEM without multiple initializations and frequencies. As the wave patterns in individually selected frequencies may introduce artifacts, a joint inverse-problem solution of multi-frequency excitations is introduced as a robust solution, where CNR improvements of up to 11.9 dB are observed. We also present the methods on a tissue-mimicking gelatin phantom study using mechanical excitation and ultrafast plane-wave ultrasound imaging, where the RMSE was improved by up to 51%. An experiment of ablation via heating an ex-vivo bovine liver shows that reconstruction artifacts are reduced with our proposed method.