In this article, we describe a detailed method for automatically generating tetrahedral meshes from 3D images having multiple region labels. An adaptively sized tetrahedral mesh modeling approach is described that is capable of producing meshes conforming precisely to the voxelized regions in the image. Efficient tetrahedral mesh improvement is then performed minimizing an energy function containing three terms: a smoothing term to remove the voxelization, a fidelity term to maintain continuity with the image data, and a novel elasticity term to prevent the tetrahedra from becoming flattened or inverted as the mesh deforms while allowing the voxelization to be removed entirely. The meshing algorithm is applied to structural MR image data that has been automatically segmented into 56 neuroanatomical sub-divisions as well as on two other examples. The resulting tetrahedral representation has several desirable properties such as tetrahedra with dihedral angles away from 0 and 180 degrees, smoothness, and a high resolution. Tetrahedral modeling via the approach described here has applications in modeling brain structure in normal as well as diseased brain in human and non-human data and facilitates examination of 3D object deformations resulting from neurological illness (e.g. Alzheimer's disease), development, and/or aging. © 2010 Elsevier Inc. All rights reserved. Approaches to the geometric modeling of neuroimaging data have existed for a number of years and have been aggregated into a commonly used framework for assessing, representing, and displaying the results from structural and functional magnetic resonance (MR) investigations (Joshi et al., 1997; Miller et al., 2009; Thompson et al., 2009 ). These methods seek to, at once, model the 2D embedded surfaces of the brain, measure the inherent geometric properties of those surface manifolds, and to use collections of 2D surfaces to measure sub-elements of brain thickness and volume that lie between them. Yet, such surface meshes alone do not typically capture the 3D nature of the cerebrum, its defined sub-divisions, and embedded subelements, i.e. closed surface meshes work well for modeling 2D edges and boundaries of an object but they do not account for the space inside of the surface. What is needed are efficient methods for generating space filling meshes that not only represent the surface of the object of interest but fill that object with a connected lattice that facilitates more comprehensive registration and resulting statistical analysis of brain structural change. In this paper, a robust model is described for the generation of 3D tetrahedral meshes applied to MR brain data. Such finite element modeling approaches provide a useful extension for surface-based modeling and give rise to many applications in the study of 3D brain architecture. In what follows, the use of surface mesh modeling in the neuroimaging literature is discussed, the use of finite element modeling approaches is examined, a detailed method for generating tetrahedral meshes is introduced, mesh generation on MRI data from several human subjects and on animal data is illustrated, and several other applications where tetrahedral meshes are advantageous are described. The paper concludes with summary of this approach and a brief description of future work in the application of tetrahedral meshes for neuroscience imaging data.
Lederman et al. REF employed a grid-based approach to generate initial tetrahedral mesh, and then performed mesh improvement on related material interfaces.
The generation of tetrahedral mesh models for neuroanatomical MRI
NeuroImage
NeuroImage
Computer Science Medicine