Abstract-Two major factors preventing the routine clinical use of finite element analysis for image registration are (1) the substantial labor required to construct a finite element model for an individual patient's anatomy and (2) the difficulty of determining an appropriate set of finite element boundary conditions. This work addresses these issues by presenting algorithms that automatically generate a high quality hexahedral finite element mesh and automatically calculate boundary conditions for an imaged patient. Medial shape models called m-reps are used to facilitate these tasks and reduce the effort required to apply finite element analysis to image registration. Encouraging results are presented for the registration of CT image pairs which exhibit deformation caused by pressure from an endorectal imaging probe and deformation due to swelling.
Abstract. Models that predict the soft tissue deformation caused by needle insertion could improve the accuracy of procedures such as brachytherapy and needle biopsy. Prior work on needle insertion modeling has focused on static deformation; the experiments presented here show that dynamic effects such as relaxation are important. An experimental setup is described for recording and measuring the deformation that occurs with needle insertion into a soft tissue phantom. Analysis of the collected data demonstrates the time-and velocity-dependent nature of the deformation. Deformation during insertion is shown to be well represented using a velocity-dependent force function with a linear elastic finite element model. The model's accuracy is limited to the period during needle motion, indicating that a viscoelastic tissue model may be required to capture tissue relaxation after the needle stops.
We present a finite-element solution method that is well suited for interactive simulations of cutting meshes in the regime of linear elastic models. Our approach features fast updates to the solution of the stiffness system of equations to account for real-time changes in mesh connectivity and boundary conditions. Updates are accomplished by augmenting the stiffness matrix to keep it consistent with changes to the underlying model, without refactoring the matrix at each step of cutting. The initial stiffness matrix and its Cholesky factors are used to implicitly form and solve a Schur complement system using an iterative solver. As changes accumulate over many simulation timesteps, the augmented solution method slows down due to the size of the augmented matrix. However, by periodically refactoring the stiffness matrix in a concurrent background process, fresh Cholesky factors that incorporate recent model changes can replace the initial factors. This controls the size of the augmented matrices and provides a way to maintain a fast solution rate as the number of changes to a model grows. We exploit sparsity in the stiffness matrix, the right-hand-side vectors and the solution vectors to compute the solutions fast, and show that the time complexity of the update steps is bounded linearly by the size of the Cholesky factor of the initial matrix. Our complexity analysis and experimental results demonstrate that this approach scales well with problem size. Results for cutting and deformation of 3D linear elastic models are reported for meshes representing the brain, eye, and model problems with element counts up to 167,000; these show the potential of this method for real-time interactivity. An application to limbal incisions for surgical correction of astigmatism, for which linear elastic models and small deformations are sufficient, is included.
Abstract. The finite element method (FEM) is well suited for use in the non-rigid registration of magnetic resonance spectroscopy images (MRSI) with intraoperative ultrasound images of the prostate because FEM provides a principled method for modeling the physical deformation caused when the MRSI intra-rectal imaging probe compresses the prostate. However, FEM requires significant labor and computational time to construct a finite element model and solve the resulting large system of equations. In particular, any finite element based registration method must address the questions of how to generate a mesh from an image and how to solve the system of finite element equations efficiently. This paper focuses on how m-rep image segmentations can be used to generate high quality multi-scale hexahedral meshes for use with FEM. Results from the application of this method to the registration of CT images of a prostate phantom with implanted brachytherapy seeds are presented.
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