A comparison of voxel and surface based cortical thickness estimation methods
Research highlights
►We compare FreeSurfer with voxel based cortical thickness estimation methods. ►Choice of atlas makes a significant difference on regional statistics. ►FreeSurfer has lower variance on same day scans than voxel based methods. ►In cross-sectional comparison, voxel based methods compared well with FreeSurfer. ►In longitudinal comparison, FreeSurfer most clearly separates groups.
Introduction
The human cerebral cortex is a highly folded layer or ribbon of interconnected neurons, with an average thickness of around 2.5 mm — varying between 1 and 4.5 mm in different parts of the brain (Fischl and Dale, 2000, von Economo, 1929). There is a significant variability between individuals in disease and in health. The cortex plays a key role in most cognitive processes and demonstrates regional specification such that visual function, language, calculation, executive function and so on, have relatively localised cortical representation in different parts of the brain. The thickness of the cortex is of interest as it develops, follows the normal ageing process and changes under a wide variety of neurodegenerative diseases. Recently, imaging studies of cortical thickness have compared the group-wise differences between healthy control subjects and patients with conditions such as sporadic and familial Alzheimer's disease (AD) (Lerch et al., 2005, Gutierrez-Galve et al., 2009, Knight et al., 2009), fronto-temporal lobar degeneration (FTLD) (Du et al., 2007, Rohrer et al., 2009), posterior cortical atrophy (Lehmann et al., 2009), multiple sclerosis (Sailer et al., 2003), Huntington's disease (Rosas et al., 2008), and the changes that occur in healthy controls under normal ageing (Salat et al., 2004).
The methods for estimating cortical thickness from magnetic resonance (MR) images can be broadly categorised as surface based, or voxel based. Both of these methods require an initial segmentation to separate grey matter (GM), white matter (WM) and cerebrospinal fluid (CSF). In this paper the WM/GM boundary is referred to as the WM boundary, and the GM/CSF boundary as the pial boundary.
Surface based methods typically construct a triangulated mesh based on either the WM boundary (Dale et al., 1999, Fischl et al., 1999, Fischl and Dale, 2000, Shattuck and Leahy, 2002, Xu et al., 1999, Han et al., 2004), or the pial boundary (Davatzikos and Bryan, 1996), which is then deformed to find the opposing boundary. Alternatively, with WM and pial boundaries defined, both boundaries can be deformed simultaneously using either snake like deformable models (MacDonald et al., 2000, Kim et al., 2005) or level sets (Zheng et al., 1999), thereby utilising distance constraints to ensure a realistic coupling of the two surfaces. The use of explicit surface models enables sub-voxel accuracy (Fischl and Dale, 2000), high sensitivity (Lerch and Evans, 2005), and robustness to different field strengths, scanner upgrade and scanner manufacturer (Han et al., 2006). With the cortex closed at the brain stem, the resultant surface is topologically equivalent to a sphere. Surface based cortical thickness methods try to ensure correct topology of the surface after initial segmentation of the WM boundary (Shattuck and Leahy, 2001, Xu et al., 1999, Han et al., 2004), using smoothness and self intersection constraints (Dale et al., 1999, MacDonald et al., 2000), by correcting topological defects as they occur (Fischl et al., 2001, Segonne et al., 2005), or using a Laplacian function (Kim et al., 2005). Ensuring correct topology or surface regularity massively increases computational cost (Fischl et al., 2001, Han et al., 2004), may require a difficult balance of parameter weights (Kim et al., 2005, Scott et al., 2009), and reduces the model's ability to follow areas of high curvature such as extremely thin gyral stalks (Lohmann et al., 2003) or opposing sides of sulci with no clear CSF between, which can produce bias and error in thickness measurements (Scott et al., 2009).
In contrast, voxel based methods (Lohmann et al., 2003, Hutton et al., 2008, Acosta et al., 2009, Aganj et al., 2009, Das et al., 2009, Cardoso et al., 2011, Scott et al., 2009) work directly on the voxel grid and are computationally very efficient. However, they are considered to be less accurate due to the limited resolution of the voxel grid, less robust to noise and mis-segmentation and significantly affected by partial volume (PV) effects at the boundaries of convoluted structures such as deep sulci (Acosta et al., 2009). Methods include morphological (Lohmann et al., 2003), line integral (Aganj et al., 2009, Scott et al., 2009), Laplacian (Jones et al., 2000) and registration (Das et al., 2009) based approaches. Laplacian approaches (Hutton et al., 2008, Acosta et al., 2009, Cardoso et al., 2011), solve the Laplace equation (Jones et al., 2000) using boundary value relaxation (Press et al., 1991) or matrix methods (Haidar et al., 2005), calculate thickness by integrating the tangent to the Laplacian scalar field (Jones et al., 2000), summing the Euclidean distance from neighbouring voxels on the same streamline, or using a partial differential equation (Yezzi and Prince, 2003) with boundaries set to zero (Yezzi and Prince, 2003), half the mean voxel dimension (Diep et al., 2007) or using Lagrangian initialisation (Bourgeat et al., 2008, Acosta et al., 2009). In contrast, the registration based approach of Das et al. (2009) uses a greedy diffeomorphic registration algorithm to warp the WM segment to match the GM + WM segment. The thickness is then calculated as the distance that the WM/GM boundary moved during the registration. A potential advantage for voxel based methods may be in the fact that the runtimes can be significantly less than the surface based methods which may enable new application areas.
Thus far, surface based methods have been more widely used than voxel based methods. This may be partly due to long running software efforts, producing accessible software packages such as BrainSuite1 (Shattuck and Leahy, 2001, Shattuck and Leahy, 2002), BrainVISA2 (Mangin et al., 1995) and FreeSurfer3 (Dale et al., 1999, Fischl et al., 1999, Fischl and Dale, 2000). Of these, FreeSurfer is the most widely used (Nakamura et al., 2010), and the FreeSurfer wiki lists many references on both the methodology and clinical studies.
Recently there has been significant interest in the development of voxel based methods (Hutton et al., 2008, Scott et al., 2009, Acosta et al., 2009, Aganj et al., 2009, Cardoso et al., 2011, Das et al., 2009). In addition, voxel based methods have featured in a comparison with voxel based morphometry (Hutton et al., 2009), been used to correlate changes of cortical thickness with diffusion measures using sparse canonical correlation analysis (Avants et al., 2010) and used in clinical studies (Querbes et al., 2009). However, evaluation of these approaches has been limited by a lack of studies comparing voxel based and surface based methods. This paper aims to provide such a comparison, comparing the freely available surface based FreeSurfer (version 4.5.0) method with our implementations of two voxel based methods. We call these voxel-based methods a Laplacian based method and a Registration based method, and describe both of these below. We chose FreeSurfer as it is the most widely used of the surface based methods (Nakamura et al., 2010). Of the voxel based methods, we chose a Laplacian method similar to Acosta et al. (2009) as many of the references above are Laplacian based, and a registration method similar to Das et al. (2009) as there is current interest in diffeomorphic registration algorithms, many of which could be applied to this application. The methods are compared in terms of reproducibility, disease differentiation and the ability to detect changes of cortical thickness in longitudinal imaging studies.
Section snippets
The FreeSurfer method
The FreeSurfer cortical thickness pipeline has been described and validated in previous publications (Dale et al., 1999, Fischl et al., 1999, Fischl and Dale, 2000, Han et al., 2006). Briefly, processing involves intensity normalisation, registration to Talairach space, skull stripping, segmentation of white matter, tesselation of the WM boundary, smoothing of the tesselated surface and automatic topology correction. The tesselated surface is used as the starting point for a deformable surface
Experiments
Our four experiments were chosen to help inform the reader in a manner that was most relevant to the existing literature, and to clinical research studies. Cortical thickness studies may use different atlases to provide regional based statistics. The first experiment tests the hypothesis that there is no difference in regional statistics when using different atlases. In the absence of a gold-standard, the second experiment assesses the reproducibility of each method. The third and fourth
Discussion
In this paper we have compared the surface based cortical thickness method FreeSurfer with two voxel based methods. This is a challenging task as the methodologies are significantly different, and we must err on the side of caution in the interpretation of the results. Furthermore, to add to the challenge, it is difficult to obtain a gold standard. Previous authors have used simulated MRI phantoms (Lee et al., 2006) at one time point, or simulations of atrophy (Camara et al., 2008, Lerch and
Conclusions
This paper is the first to compare voxel and surface based cortical thickness estimation methods. The choice of atlas produces a significant effect on regional based statistics, suggesting that the comparison of cortical thickness results across different papers, where the authors have used different atlases should proceed with caution. FreeSurfer produced more reproducible results on same day scans than both the Laplacian and Registration methods in all but one cortical regions, with the
Acknowledgments
This work was undertaken at UCL/UCLH who received a proportion of funding from the Department of Health's NIHR Biomedical Research Centres funding scheme. The Dementia Research Centre is an Alzheimer's Research Trust Co-ordinating centre and has also received equipment funded by the Alzheimer's Research Trust. MC and KL were supported by TSB grant M1638A. MC was additionally funded by CBRC grant 168. NCF was funded by the MRC (UK).
References (69)
- et al.
Automated voxel-based 3D cortical thickness measurement in a combined Lagrangian–Eulerian PDE approach using partial volume maps
Med. Image Anal.
(2009) - et al.
Lagrangian frame diffeomorphic image registration: morphometric comparison of human and chimpanzee cortex
Med. Image Anal.
(2006) - et al.
Dementia induces correlated reductions in white matter integrity and cortical thickness: a multivariate neuroimaging study with sparse canonical correlation analysis
NeuroImage
(2010) - et al.
Automatic calculation of hippocampal atrophy rates using a hippocampal template and the boundary shift integral
Neurobiol. Aging
(2007) - et al.
Increased hippocampal atrophy rates in AD over 6 months using serial MR imaging
Neurobiol. Aging
(2008) - et al.
Accuracy assessment of global and local atrophy measurement techniques with realistic simulated longitudinal Alzheimer's disease images
NeuroImage
(2008) - et al.
The Alzheimer's Disease Neuroimaging Initiative, 2011. LoAd: a locally adaptive cortical segmentation algorithm
NeuroImage
(2011) - et al.
Cortical surface-based analysis I. Segmentation and surface reconstruction
NeuroImage
(1999) - et al.
Registration based cortical thickness measurement
NeuroImage
(2009) - et al.
Cortical surface-based analysis II. Inflation, flattening and a surface-based coordinate system
NeuroImage
(1999)