Deformable Multi-Modality Image Registration Based on Finite Element Modeling and Moving Least Squares

Abstract

<p>During the past two decades, there has been an increasing demand for medical image registration. Deformable image registration has a great importance, because the majority of the registration applications deal with the conditions in which the rigid assumption would not create accurate results. Soft tissue organs (e.g. liver, kidney, and prostate) can change in shape during an intervention. Therefore, a sophisticated registration essentially needs to take into account the geometrical deformations.</p> <p>In this thesis, we study the problem of deformable liver image registration between Magnetic Resonance (MR) and Ultrasound (US) images of the liver. In our approach, a tracking system is proposed to acquire and rigidly register a 2D US image <em>(I_us)</em> with the previously taken MR volume. According to the information obtained from the tracking system, a 2D MR image (<em>I_MR</em>) is reconstructed as the match of Ius. Mutual information is chosen as the similarity measure between the two modalities in our rigid registration problem. A search optimization problem on the registration parameters is then performed, to provide us with a fine tuned reconstructed <em>I_MR</em>.</p> <p>Our proposed strategy begins with visually identifying corresponding anatomical landmarks on <em>I_us</em>and <em>I_MR</em>. These landmarks are the inputs of the two proposed methods of deformation in this thesis. The first method, Finite Element Modeling (FEM) approach, produces the deformed images based on the linear elasticity and the static analysis assumptions. This method uses the positions of landmarks to solve a linear system of equations, in order to generate the final deformations of the MR images. The second method of deformation is the Moving Least Squares (MLS). To the best of our knowledge, MLS has never been used in medical image registration. This technique analytically solves a number of least squares problems to find the local rigid transformations. Applying these local rigid transformations on the MR volume creates the deformations throughout the MR images.</p> <p>In our experiments, Root Mean Square Target Registration Error (RMS TRE) is used as the quantitative measure for the evaluation of performance. FEM-based method produces the best result with an RMS TRE of 7.2mm, while MLS-based method creates an RMS TRE of 8.9mm. According to the literature, an accuracy of 7.2mm is acceptable for most intra-operative abdominal procedures, particularly those involving the liver. The drawback of FEM-based method is its higher computational complexity. Our implementation of the MLS-based method could be executed at least 20 times faster than that of the FEM-based method. Therefore, in applications, where the accuracy is critical, FEM-based method should be used. The MLS-based method is more suitable of the applications demanding higher speed or a parallel implementation of the FEM-based method can solve the computation speed problem.</p>