Cortical thickness analysis examined through power analysis and a population simulation

We have previously developed a procedure for measuring the thickness of cerebral cortex over the whole brain using 3-D MRI data and a fully automated surface-extraction (ASP) algorithm. This paper examines the precision of this algorithm, its optimal performance parameters, and the sensitivity of the method to subtle, focal changes in cortical thickness.

The precision of cortical thickness measurements was studied using a simulated population study and single subject reproducibility metrics. Cortical thickness was shown to be a reliable method, reaching a sensitivity (probability of a true-positive) of 0.93. Six different cortical thickness metrics were compared. The simplest and most precise method measures the distance between corresponding vertices from the white matter to the gray matter surface. Given two groups of 25 subjects, a 0.6-mm (15%) change in thickness can be recovered after blurring with a 3-D Gaussian kernel (full-width half max = 30 mm). Smoothing across the 2-D surface manifold also improves precision; in this experiment, the optimal kernel size was 30 mm.

Introduction

The measurement of cortical thickness has long been of interest to the neurosciences, starting with the early reconstructions of Brodmann (1909) and von Economo and Koskinas (1925). Recent advances in image processing and image acquisition has allowed for the automatic extraction of cortical thickness from MRI (Fischl and Dale, 2000, MacDonald, 1997, 4 et al., 2000). This paper investigates and summarizes current methodology and evaluates the power and sensitivity of the different techniques.

The study of the morphometry of the cerebral cortex at the macroscopic level visible in current MRI provides the neurosciences with an opportunity to investigate both normal and abnormal change. Most such investigations use a combination of semiautomatic techniques, usually focusing on the manual delineation of structures of interest, followed by statistical comparisons of volumes (cf. Pruessner et al., 2001). This approach, while clearly quite capable of providing important information about the population under investigation, has several disadvantages. It is very labor intensive, it suffers from intra- and interrater reliability issues, and most importantly, it restricts the analysis to predetermined regions of interest.

Several fully automated approaches have also been developed; the most widely used of these is voxel-based morphometry (VBM) (Ashburner and Friston, 2000). At its most generic, VBM is the comparison of voxels in a series of linear models. Most methods (cf. Ashburner and Friston, 2000, Baron et al., 2001, Paus et al., 1999) employ a standard set of image processing steps involving linear registration, tissue classification, and creation of “voxel density” maps representing tissue concentration in a local neighborhood. The usual end result is an image that contains regions that have significantly increasing or decreasing signal that correlates with some independent neurobiological parameter. This latter parameter may be just a categorical difference between two groups, for example, separated by disease status or gender, or more generally, will be a continuous variable, such as age or behavioral performance, in which case a regression of image signal against that variable is plotted at each voxel (Paus et al., 1999, Wright et al., 1995).

Cortical thickness analysis is similar to VBM, albeit the analysis is performed at the nodes of a three-dimensional polygonal mesh rather than on a 3-D voxel grid, but it has the advantage of providing a direct quantitative index of cortical morphology. The metric captures the distance between the white matter surface and the gray CSF intersection according to some geometric definition; the output is a scalar value measured in millimeters. The regression slope at each vertex across the cortex in a statistical analysis is meaningful: not only can one determine that cortical thickness is significantly different between groups, but one can also measure that difference. This naturally leads to the ability to define clinical as well as statistical significance.

The use of cortical thickness analysis in MRI studies is relatively new, with only a small number of studies published on the methodology (Fischl and Dale, 2000, Jones et al., 2000, Kabani et al., 2001, MacDonald, 1997, 4 et al., 2000, Meyer et al., 1996, Miller et al., 2000, Tosun et al., 2001, Yezzi and Prince, 2003, Zeng et al., 1999) and even fewer on normal or abnormal populations (Fischl and Dale, 2000, 4 et al., 2000, Rosas et al., 2002). This is due to the difficult nature of extracting the inner and outer surfaces of the cerebral cortex at the limited resolution provided by today's MRI machines (usually 1 mm³), where the fine details of sulcal anatomy are often obscured by the partial volume effect. Moreover, manual delineation of cortical thickness is very difficult (whether from MRI or postmortem samples) due to the necessity of creating a correct cut or slice plane perpendicular to the surfaces.

Defining cortical thickness, even when models of the inner and outer surfaces are present, is not trivial. Cortical thickness is a distance metric but there are multiple ways of defining corresponding points on the two surfaces between which that distance is to be measured. Moreover, the distance need not be measured in a straight line but can be the result of a more complicated equation, such as fluid flow lines.

This paper examines the power of cortical thickness as an analysis tool; it compares the various definitions of cortical thickness proposed in the literature; the effect of different size blurring kernels; and analyzes the effect of correcting for multiple comparisons. These studies were performed using a simulated population study where the true difference between the two groups is artificially induced and therefore known. Furthermore, repeat scans of a single subject will be used to examine the variability inherent in the different cortical thickness metrics and make a first attempt at defining the power of the method.

Rather than addressing accuracy we focus on the question of precision. The distinction between the two is subtle but crucial:

Accuracy: The ability of a metric to capture the correct distance between the pial and white matter surfaces, as defined by anatomical criteria and validated through manual measurements or accurate MR simulations.

Precision: The ability of a metric to provide reproducible results from repeated estimations and thereby differentiate between two measures known to be different.

A metric can therefore be declared most accurate through the comparison of automated and manual measurements, or through directly simulating a cortical sheet with a known thickness and validating each metric against such a construct. Each of these methods has to overcome significant challenges. Manual measurements of cortical thickness are tremendously difficult to undertake, being highly dependent on a perfectly perpendicular cutting angle. Moreover, even using the exact same postmortem slice, individual raters can easily differ by over 0.5 mm at any one location due to the blurred cortical boundary at the white matter surface (von Economo and Koskinas, 1925). Furthermore, the traditional thickness measurements derived from postmortem slices are dependent on a straight-line measurement of cortical thickness, as these measurements are always carried out in two dimensions. Accurate validation of MR measurements of cortical thickness thus requires a three-dimensional reconstruction of high-resolution postmortem data. The alternative of validation through construction of a cortical sheet with known thickness is very attractive but difficult to use in comparing thickness metrics. The reason is that the construction of such a cortex would be dependent on a preexisting definition of cortical thickness and would therefore be biased towards that metric from the beginning. Furthermore, accurately simulating MRI from polygonal models of the cortex has to first address the issue of correctly incorporating partial volume into the tissue model. We plan to address the question of accuracy both through the use of a simulator as well as high-resolution postmortem reconstructions; that, however, is the subject of future work. This paper examines the precision of cortical thickness analysis through the use of repeated acquisitions of the same subject as well as a population simulation.