Cortical thickness and central surface estimation

Abstract

Several properties of the human brain cortex, e.g., cortical thickness and gyrification, have been found to correlate with the progress of neuropsychiatric disorders. The relationship between brain structure and function harbors a broad range of potential uses, particularly in clinical contexts, provided that robust methods for the extraction of suitable representations of the brain cortex from neuroimaging data are available. One such representation is the computationally defined central surface (CS) of the brain cortex. Previous approaches to semi-automated reconstruction of this surface relied on image segmentation procedures that required manual interaction, thereby rendering them error-prone and complicating the analysis of brains that were not from healthy human adults. Validation of these approaches and thickness measures is often done only for simple artificial phantoms that cover just a few standard cases. Here, we present a new fully automated method that allows for measurement of cortical thickness and reconstructions of the CS in one step. It uses a tissue segmentation to estimate the WM distance, then projects the local maxima (which is equal to the cortical thickness) to other GM voxels by using a neighbor relationship described by the WM distance. This projection-based thickness (PBT) allows the handling of partial volume information, sulcal blurring, and sulcal asymmetries without explicit sulcus reconstruction via skeleton or thinning methods. Furthermore, we introduce a validation framework using spherical and brain phantoms that confirms accurate CS construction and cortical thickness measurement under a wide set of parameters for several thickness levels. The results indicate that both the quality and computational cost of our method are comparable, and may be superior in certain respects, to existing approaches.

Introduction

The cerebral cortex is a highly folded sheet of gray matter (GM) that lies inside the cerebrospinal fluid (CSF) and surrounds a core of white matter (WM). Besides the separation into two hemispheres, the cortex is macroscopically structured into outwardly folded gyri and inwardly folded sulci (Fig. 1). The cortex can be described by the outer surface (or boundary) between GM and CSF, the inner surface (or boundary) between GM and WM, and the central surface (CS) (Fig. 1). Cortical structure and thickness were found to be an important biomarker for normal development and aging (Fjell et al., 2006, Sowell et al., 2004, Sowell et al., 2007) and pathological changes (Kuperberg et al., 2003, Rosas et al., 2008, Sailer et al., 2003, Thompson et al., 2004) in not only humans, but also other mammals (Hofman, 1989, Zhang and Sejnowski, 2000).

Although MR images allow in vivo measurements of the human brain, data is often limited by its sampling resolution that is usually around 1 mm³. At this resolution, the CSF is often hard to detect in sulcal areas due to the partial volume effect (PVE). The PVE comes into effect for voxels that contain more than one tissue type and have an intensity gradient that lies somewhere between that of the pure tissue classes. Normally, the PVE describes the boundary with a sub-voxel accuracy, but within a sulcus the CSF volume is small and affected by noise, rendering it difficult to describe the outer boundary in this region (blurred sulcus, Fig. 2). Thus, to obtain an accurate thickness measurement, an explicit reconstruction of the outer boundary based on the inner boundary is necessary. This can be done by skeleton (or thinning) methods or alternatively by model-based deformation of the inner surface. Skeleton-based reconstruction of the outer boundary is used by CLASP (Kim et al., 2005, Lee et al., 2006a, Lee et al., 2006b, Lerch and Evans, 2005), CRUISE (Han et al., 2004, Tosun et al., 2004, Xu et al., 1999), Caret (Van Essen et al., 2001), the Laplacian approach (Acosta et al., 2009, Haidar and Soul, 2006, Hutton et al., 2008, Jones et al., 2000, Rocha et al., 2007, Yezzi and Prince, 2003), and other volumetric methods (Eskildsen and Ostergaard, 2006, Eskildsen and Ostergaard, 2007, Hutton et al., 2008, Lohmann et al., 2003). Methods without sulcal modeling will tend to overestimate thickness in blurred regions (Jones et al., 2000, Lohmann et al., 2003) or must concentrate exclusively on non-blurred gyral regions (Sowell et al., 2004). Alternatively, cortical thickness may be estimated via deformation of the inner surface (FreeSurfer (Dale et al., 1999, Fischl and Dale, 2000), DiReCT (Das et al., 2009), Brainvoyager (Kriegeskorte and Goebel, 2001), Brainsuite (Shattuck and Leahy, 2001, Zeng et al., 1999) or coupled surfaces (ASP (Kabani et al., 2001, MacDonald et al., 2000). Considering that the accuracy of the measurement depends strongly upon the precision of cortical surface reconstruction at the inner and outer boundaries, and that the computation time is often related to the anatomical accuracy of the reconstruction, such measurements may require intensive computational resources in order to achieve the final measurement.

Here, we present a new volume-based algorithm, PBT (Projection Based Thickness), that uses a projection scheme which considers blurred sulci to create a correct cortical thickness map. For validation, we compare PBT to the volumetric Laplacian approach and the surface-based approach included in the FreeSurfer (v 4.5) software package. If the results from PBT are approximately the same as that achieved by FreeSurfer and a significant improvement over the Laplacian approach, it may be concluded that PBT is a highly accurate volume-based method for measuring cortical thickness. For situations in which extensive surface analysis is not required, PBT would allow the exclusion of cortical surface reconstruction steps with no loss of accuracy for cortical thickness measurements.

We also propose a suite of test cases using a variety of phantoms with different parameters as a suggestion for how a cortical thickness measurement approach could be rigorously tested for validity and stability. Previously published validation approaches that used a spherical phantom (Acosta et al., 2009, Das et al., 2009) often addressed only one thickness and curvature (radii) of the inner and outer boundary. The problem is that the measure may work well for this special combination of parameters, but performance can change for different radii. Another limitation is that this phantom describes only areas where the CSF intensity is high enough, but most sulcal areas (that comprise over half of the human cortex) are blurred. Our test suite directly addresses these concerns.

The cortical thickness map may also be subsequently used to generate a reconstruction of the CS. Compared to the inner or outer surface, the CS allows a better representation of the cortical sheet (Van Essen et al., 2001), since neither sulcal or gyral regions are over- or underestimated (Scott and Thacker, 2005). As the average of two boundaries, it is less error-prone to noise and it allows a better mapping of volumetric data (Liu et al., 2008, Van Essen et al., 2001). Generally, a surface reconstruction allows surface-based analysis that is not restricted to the grid and allows metrics, such as the gyrification index (Schaer et al., 2008) or other convolution measurements (Luders et al., 2006, Mietchen and Gaser, 2009, Rodriguez-Carranza et al., 2008, Toro et al., 2008), that can only be measured using surface meshes (Dale et al., 1999). It provides surface-based smoothing that gives results superior to that obtained from volumetric smoothing (Lerch and Evans, 2005). Furthermore, surface meshes allow a better visualization of structural and functional data, especially when they are inflated (Fischl et al., 1999) or flattened (Van Essen and Drury, 1997). Due to these considerations, we have explored the quality of the cortical surface reconstructions.