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Dynamic elastography with finite element-based inversion Honarvar, Mohammad


Tissue stiffness is often correlated to its pathological state and can be used as a basis for initial recognition of many tissue abnormalities. The term elastography refers to the class of medical imaging techniques that non-invasively measure the viscoelastic properties of soft tissue. Elastography involves deforming the tissue using an exciter, measuring the deformations using an imaging technique such as ultrasound (US) or magnetic resonance imaging (MRI), and then calculating the tissue elasticity distribution by solving an inverse problem. The focus of this thesis is on the inverse problem. Specifically, this thesis studies the inverse problem of elastography using direct finite element methods under the condition of applying continuous harmonic excitation to measure the absolute value of the elasticity. First, the “mixed-FEM” inversion technique that solves for both the shear modulus and the pressure is considered. Different regularization techniques are investigated for this method. New sparsity and strain-based regularization techniques, which improve the accuracy, robustness to noise, and speed of the reconstruction, are developed. A comparison of the iterative and direct FEM techniques is performed using simulations. The results show the superiority of the direct method over the iterative method. In order to reduce the number of unknowns, the pressure parameters are removed using the curl operator in a new curl-based direct FEM technique (c-FEM). In this technique, unlike in all previous curl-based methods, the local homogeneity assumption is not used. One of the main observations of this thesis is the importance of the deleterious effect of the tissue homogeneity assumption on the reconstruction results for regions with large variations in the elasticity of the region. A new simplified direct FEM technique without the homogeneity assumption (shear-FEM) is also developed for cases where only partial displacement data is available, such as in US elastography. It is shown that using multi-frequency excitations in both c-FEM and shear-FEM techniques is beneficial by providing multiple measurements of the shear waves and reducing the problem of low-amplitude nodes. To conclude the thesis, the methods developed in this thesis, plus two other established reconstruction algorithms, are compared using simulations, phantoms, ex-vivo and in-vivo data.

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