Mesh deformation-based multi-tissue mesh generation for brain images

Multi-tissue meshing is necessary for the realistic building of a biomechanical model of the brain, which has been widely used in brain surgery simulation, brain shift, and non-rigid registration. A two step multi-tissue mesher is developed. First, a coarse multi-tissue mesh is generated by redistributing labels of a body-centered cubic (BCC) mesh. Second, all the surfaces of the submeshes are deformed to their corresponding tissue boundaries. To deform the mesh, two strategies are developed. One is based on a point-based registration (PBR) and the other is based on a robust point matching (RPM). The PBR method explicitly calculates the correspondence, which takes both smoothing and quality into account, then resolves the displacement vector by minimizing an energy function. Unlike PBR method, RPM does not require the correspondence between the source points and the target points to be known in advance. To simultaneously resolve the displacement vector and the correspondence, the Expectation and Maximization optimization is employed to alternately estimate the correspondence and the displacement vector. To effectively cope with outliers, least trimmed square, a robust regression technique, is employed to correct the regression bias induced by outliers. Both methods are effective in deforming the multi-tissue mesh. However, the PBR method favors quality and smoothing, and the RPM method favors fidelity. The resulting mesh is characterized by its flexible control of four mesh properties: (1) tissue-dependent resolution, (2) fidelity to tissue boundaries, (3) smoothness of mesh surfaces, and (4) element quality. Each mesh property can be controlled on a tissue level. Our experiments conducted on synthetic data, clinic MRI, visible human data, and brain atlas effectively demonstrate these features of this multi-tissue mesher.