Measuring and comparing brain cortical surface area and other areal quantities
Highlights
► Introduces the concept of facewise analysis. ► Emphasizes the difference between point and area measurements in the cerebral cortex. ► Presents a method for analysis of cortical surface area and other areal quantities. ► Demonstrates that the local surface area is log-normally distributed. ► Discusses interpretation and potential applications.
Introduction
The surface area of the cerebral cortex greatly differs across species, whereas the cortical thickness has remained relatively constant during evolution (Fish et al., 2008, Mountcastle, 1998). At a microanatomic scale, regional morphology is closely related to functional specialization (Roland and Zilles, 1998, Zilles and Amunts, 2010), contrasting with the columnar organization of the cortex, in which cells from different layers respond to the same stimulus (Buxhoeveden and Casanova, 2002, Jones, 2000). In addition, Rakic (1988) proposed an ontogenetic model that explains the processes that lead to cortical arealization and differentiation of cortical layers according to related, yet independent mechanisms. Supporting evidence for this model has been found in studies with both rodent and primates, including humans (Chenn and Walsh, 2002, Rakic et al., 2009), as well as in pathological states (Bilgüvar et al., 2010, Rimol et al., 2010).
At least some of the variability of the distinct genetic and developmental processes that seem to determine regional cortical area and thickness can be captured using polygon mesh (surface-based) representations of the cortex derived from T1-weighted magnetic resonance imaging (MRI) (Panizzon et al., 2009, Sanabria-Diaz et al., 2010, Winkler et al., 2010). In contrast, volumetric (voxel-based) representations, also derived from MRI, were shown to be unable to readily disentangle these processes (Winkler et al., 2010).
Mesh representations of the brain allow measurements of the cortical thickness at every point in the cortex, as well as estimation of the average thickness for pre-specified regions. However, to date, analyses of cortical surface area have been generally limited to two types of studies: (1) vertexwise comparisons with a standard brain, using some kind of expansion or contraction measurement, either of the surface itself (Hill et al., 2010, Joyner et al., 2009, Lyttelton et al., 2009, Palaniyappan et al., 2011, Rimol et al., 2010), of linear distances between points in the brain (Sun et al., 2009a, Sun et al., 2009b), or of geometric distortion (Wisco et al., 2007), or (2) analyses of the area of regions of interest (ROI) defined from postulated hypotheses or from macroscopic morphological landmarks (Dickerson et al., 2009, Durazzo et al., 2011, Eyler et al., 2011, Kähler et al., 2011, Nopoulos et al., 2010, Schwarzkopf et al., 2011, Chen et al., 2011). Analyses of expansion, however, do not deal with area directly, depending instead on non-linear functions associated with the warp to match the standard brain, such as the Jacobian of the transformation. Moreover, by not quantifying the amount of area, these analyses are only interpretable with respect to the brain used for the comparisons. ROI-based analyses, on the other hand, entail the assumption that each region is homogeneous with regard to the feature under study, and have maximum sensitivity only when the effect of interest is present throughout the ROI.
These difficulties can be obviated by analyzing each point on the cortical surface of the mesh representation, a method already well established for cortical thickness (Fischl and Dale, 2000). Pointwise measurements, such as thickness, are generally taken at and assigned to each vertex of the mesh representation of the cortex. This kind of measurement can be transferred to a common grid and subjected to statistical analysis. Standard interpolation techniques, such as nearest neighbor, barycentric (Yiu, 2000), spline-based (De Boor, 1962) or distance-weighted (Shepard, 1968) can be used for this purpose. The resampled data can be further spatially smoothed to alleviate residual interpolation errors. However, this approach is not suitable for areal measurements, since area is not inherently a point feature. To illustrate this aspect, an example is given in Fig. 1. Methods that can be used for interpolation of point features do not necessarily compensate for inclusion or removal of datapoints,1 unduly increasing or reducing the global or regional sum of the quantities under study, precluding them for use with measurements that are, by nature, areal. The main contribution of this article is to address the technical difficulties in analyzing the local brain surface area, as well as any other cortical quantity that is areal by nature. We propose a framework to analyze areal quantities and argue that a mass preserving interpolation method is a necessary step. We also study different processing strategies and characterize the distribution of facewise cortical surface area.
Section snippets
Method
An overview of the method is presented in Fig. 2. Comparisons of cortical area between subjects require a surface model for the cortex to be constructed. A number of approaches are available (Dale et al., 1999, Kim et al., 2005, Mangin et al., 1995, van Essen et al., 2001) and, in principle, any could be used. Here we adopt the method of Dale et al. (1999) and Fischl et al. (1999a), as implemented in the FreeSurfer software package (FS).2 In this
Evaluation
We illustrate the method using data from the Genetics of Brain Structure and Function Study, GOBS, a collaborative effort involving the Texas Biomedical Institute, the University of Texas Health Science Center at San Antonio (UTHSCSA) and the Yale University School of Medicine. The participants are members of 42 families, and total sample size, at the time of the selection for this study, is 868 subjects. We randomly chose 84 subjects (9.2%), with the sparseness of the selection minimizing the
Registration
To be valid, facewise analyses rely on the assumption that microscopic structures can be localized using as reference the features that are identifiable with MRI and which drive the registration. Features with such localizing power are important because they help to ensure good overlap of homologous areas between subjects. Despite an implicit assumption already present in most imaging studies, only recently it has been demonstrated valid for some cytoarchitetonic areas when the references are
Conclusion
We presented an interpolation method for between-subject analyses of cortical surface area. The method is also suitable for other quantities that are areal by nature and which require mass conservation (pycnophylactic property) during interpolation and analysis. We demonstrated that, when the quantity under study is surface area itself, the distribution of the data does not follow a normal distribution, being instead better characterized as lognormal, and proposed a framework for statistical
Acknowledgments
We thank the anonymous reviewers for their helpful remarks. M. R. Sabuncu received support from a KL2 Medical Research Investigator Training grant awarded via Harvard Catalyst (NIH grant 1 KL2 RR025757-01 and financial contributions from Harvard University and its aliations). P. Kochunov received support from the NIBIB grant EB006395. This study was supported by NIMH grants MH0708143 (PI: D. C. Glahn), MH078111 (PI: J. Blangero) and MH083824 (PI: D. C. Glahn). Support for FreeSurfer was
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