Adaptive mesh refinement for elastic modulus reconstruction in elastography

Abstract

Meshes play a crucial role in determining the accuracy of the elastic modulus reconstruction in the elastography when the finite element method is employed. In this article, we propose an adaptive mesh refinement strategy which can ensure the coincidence of the meshes with the shape of the inclusions in the observed tissue. This strategy is based on the intensity distribution of the strain image where the variance of the strain distribution in each element of the meshes is used to measure the homogeneity of the element, that is, the larger the strain variance is the more inhomogeneous the element will be and hence more detailed information will be included in this element. For more accurate reconstruction of such detailed information, mesh refinement procedure is implemented in such elements. Besides, two refinement steps are employed for the reconstruction to improve the fitness of the reconstructed image and the observed tissue. Simulation results show that the two-stage adaptive mesh refinement algorithm performs well without needing any prior information about the internal geometric shape in tissue. Not only Young's moduli of models but also shapes of the inclusions can be reconstructed perfectly and quickly with our proposed method.

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