Automated 3-D extraction and evaluation of the inner and outer cortical surfaces using a Laplacian map and partial volume effect classification
Introduction
Accurate reconstruction of cerebral cortical surfaces from magnetic resonance images (MRI) is an important issue in quantitative brain analysis, visualization, cortical mapping, and multimodal registration. In particular, accurate reconstruction of the inner- and outer-surfaces of the cortex is essential to obtain reliable measurements of cortical thickness. Most MR images however, suffer from partial volume effects (PVE) due to the limited resolution of MRI scanners which can cause voxels on the boundary between tissues to be blurred, making accurate surface determination difficult. This problem is most pronounced in tightly folded sulci, where cerebrospinal fluid (CSF) is often hardly detected due to the fact that opposing sulcal banks can be closer than the MRI resolution, thus exhibiting a fused appearance. As a result, the boundary surface between gray matter (GM) and CSF, referred to hereafter as the pial surface, might not be correctly localized, and hence any derived morphometric information such as cortical thickness may be inaccurate. The worst case partial volume effect is having no CSF within identified sulci, and thus, no apparent sulci. Fig. 1 shows a surface deformed to fit the pial surface and gray-white boundary, hereafter referred to as the white matter (WM) surface. The WM surface contains well formed sulci, but the pial surface does not due to the fact that partial volume effects are resulting in little CSF being identified in buried sulci. This observation motivated the original ASP authors to use information about the relative position of the WM surface in order to improve the pial surface extraction.
A number of methods currently exist for identifying the cortical surface. They can be classified into bottom-up approaches using edge detection and top-down approaches using model based deformation. One of the most common bottom-up approaches is the “Marching Cubes” algorithm which is of restricted utility for cortical surface extraction, since noise and the complex cortical folds make it difficult to obtain a smooth topologically correct surface reconstruction (Lorensen and Cline, 1987). Although there have been approaches to fix the topology of marching cubes surfaces (Han et al., 2002, Shattuck and Leahy, 2001), it is difficult to define the correct outer-cortical boundary because of tightly opposed sulcal banks.
In recent years, several excellent methods using a top-down approach or mixed approach with bottom-up methods have been developed for automatically extracting the cortical surface. Dale et al. introduced an automatic approach that is implemented in the freely-available FreeSurfer program (Dale et al., 1999, Fischl et al., 1999). This program initially finds the WM surface, and then fits smooth WM and pial surfaces using deformable models involving spring, curvature, and intensity-based terms. The authors developed morphological operations to improve the topology of a binary WM volume and then expanded a deformable surface toward the outer GM boundary. This approach was a significant advance, but the algorithm lacked a method for preventing self-intersecting topologies. To preserve topology, MacDonald et al. developed a cortical surface extraction procedure known as Anatomic Segmentation using Proximity (ASP) (MacDonald, 1998, MacDonald et al., 2000). This method is an improved version of Multiple Surface Deformation (MSD) for simultaneous deformation of multiple curves and surfaces to an MRI, with inter-surface constraints and self-intersection avoidance (MacDonald et al., 1994). ASP uses a topology-preserving deformation model with proximities, and automatically identifies the WM and pial surfaces of the cerebral cortex in a robust way with respect to partial volume effects by means of forcing the cortical thickness to lie within a defined anatomically-plausible range of values. Since the ASP algorithm deforms from a spherical polygonal model with proximities, it preserves the topology of a spherical sheet which, once deformed, serves as a model of the cortical sheet. But since this approach imposes a thickness constraint in order to insure topological correctness, it introduces a bias in the true calculation of cortical thickness in populations which may have much thicker or much thinner cortices than the constraints in the algorithm currently allow, such as children or specific diseased populations. Moreover, since the ASP method does not account for the poor differentiation between the putamen and the insula in the discretely classified image it uses as input, thickness values in the insular cortex are very inaccurate. Han et al. also introduced a topology preserving geometric deformable model (Han et al., 2001a, Han et al., 2001b), which reconstructs the pial surface by correcting the topology of a GM segmentation. This method estimates the position of sulci by assuming that they are equidistant, on either side, to the WM surface. While this approach was successful at preventing self-intersection, creating the representative topology based on the WM surface misplaces asymmetrically folded sulci. Kriegeskorte and Goebel developed a method which detects and removes topological errors as part of tissue classification (Kriegeskorte and Goebel, 2001). Their method uses a self-touching sensitive region growing process prioritized by distance-to-surface voxels considered for inclusion, and topologically corrects reconstructions of a cortical sheet. The use of region growing methods for detecting edges is an efficient and fast approach to surface extraction, however, the topology correction does not perfectly reconstruct the pial surface in the buried sulci where the intensity level in regions which contain CSF are very similar to that for GM due to partial volume effects.
In this paper, we introduce a fully automatic method to reconstruct the pial surface, called CLASP, which stands for Constrained Laplacian-based ASP, a modification of the original ASP algorithm (MacDonald et al., 2000). This method uses a more complex classification method with a statistical probabilistic anatomical map (SPAM) to estimate the boundary of the insula. Moreover, CLASP makes use of a novel geometric deformable surface model which estimates the pial surface through the use of partial volume effect information. We specifically focus on improving the accuracy of reconstructing the pial interface, as this surface presents the most serious morphological challenges to the conventional ASP method. To remove the necessity of a cortical thickness constraint, we incorporated a classification method for detecting the partial volume fraction of CSF in deep sulci. The pial interface is created by expanding from the WM surface, while the WM surface is extracted by the same technique used in the original ASP procedure. The expansion path for creating the pial surface is defined as a Laplacian map between the WM surface and a skeletonized CSF map. The Laplacian approach is similar to a method presented by Jones (Jones et al., 2000) to estimate cortical thickness, but differs in that it is performed in voxel space and is used for surface expansion. This algorithm solves Laplace's equation with the cortical volume as the domain for solution of the differential equation, as well as separate boundary conditions at the gray-white junction and the gray-CSF junction. Distinct from other methods, we use measured CSF from partial volume classification to preserve the morphology of the boundary between GM and CSF, particularly in buried sulci, while the outer bound of the GM surface expansion is defined by the GM/CSF interface from a discrete classification. This framework ensures that the method will yield surfaces that are topologically equivalent to a sphere and that do not self-intersect, completely removing any requirement of prior information about a range of allowable thickness values as a constraint. Moreover, we use the Laplacian term so as to locally vary the expansion force of the pial surface by predicted cortical thickness at each vertex.
In order to compare the results, we made use of three evaluation procedures. These included a volume-based evaluation which compared GM voxels identified by discrete tissue classification with a GM voxel map created by each of ASP and CLASP. This voxel map is essentially cortex voxels bounded by the WM and pial surfaces. Secondly, a surface-based evaluation was used which compared a pial surface extracted by ASP or CLASP with a simulated, “ground truth” template surface. Lastly, we analyzed the consistency of the CLASP procedure using surfaces extracted from 16 scans of the same individual.
Section snippets
Method
The CLASP algorithm consists of several stages as follows: (1) acquired T1 MR images are preprocessed by intensity inhomogeneity correction and spatial normalization to stereotaxic space. (2) Preprocessed images are classified into GM, WM, and CSF tissues. (3) Processed volumes are divided into left and right hemispheres for reconstructing two hemispheric cortical surfaces. (4) The WM surface is reconstructed by deforming a spherical polygon model to the white matter boundary. (5) A Laplacian
Evaluation
To evaluate the CLASP algorithm, we used T1-weighted images of 70 pediatric brains with tightly folded gyri, possessing an age range of 16 ± 2.8, each of 1.0 mm × 1.0 mm × 1.0 mm resolution and 181 × 217 × 181 voxel dimension. In each brain, the pial surface was extracted by both the CLASP and the ASP methods. The accuracy of each method was evaluated by both volume- and surface-based comparisons as detailed below. In addition, a repeatability test was performed with 16 MRI scans of the same
Discussion and summary
We have described a novel Laplacian-based modification of the ASP surface extraction algorithm, which we have shown to be more accurate at finding the boundaries of the cerebral cortex compared with the original ASP method. The main difference is that the algorithm makes use of a partial volume classification to insure topology preservation. Another difference is that it classifies subcortical structures with SPAMs to reconstruct the insular region properly. The accurate estimation of the outer
Acknowledgments
This work was supported by the Post-doctoral Fellowship Program of Korea Science and Engineering Foundation (KOSEF).
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