Joint Analysis of Cortical Area and Thickness as a Replacement for the Analysis of the Volume of the Cerebral Cortex

Abstract

Cortical surface area is an increasingly used brain morphology metric that is ontogenetically and phylogenetically distinct from cortical thickness and offers a separate index of neurodevelopment and disease. However, the various existing methods for assessment of cortical surface area from magnetic resonance images have never been systematically compared. We show that the surface area method implemented in FreeSurfer corresponds closely to the exact, but computationally more demanding, mass-conservative (pycnophylactic) method, provided that images are smoothed. Thus, the data produced by this method can be interpreted as estimates of cortical surface area, as opposed to areal expansion. In addition, focusing on the joint analysis of thickness and area, we compare an improved, analytic method for measuring cortical volume to a permutation-based nonparametric combination (NPC) method. We use the methods to analyze area, thickness and volume in young adults born preterm with very low birth weight, and show that NPC analysis is a more sensitive option for studying joint effects on area and thickness, giving equal weight to variation in both of these 2 morphological features.

Keywords: cortical gray matter volume; cortical surface area; cortical thickness; nonparametric combination.

Figure 1.

A diagram in 2 dimensions of the problem of measuring cortical volume. (a) If volume is computed using multiplication of thickness by area, considerable amount of tissue is left unmeasured in the gyri, or measured repeatedly in sulci. The problem is minimized, but not solved, with the use of the mid-surface. (b) Instead, vertex coordinates can be used to compute analytically the volume of tissue between matching faces of white and pial surfaces, leaving no tissue under- or over-represented.

Figure 2.

(a) In the surface representation, the cortex is limited internally by the white and externally by the pial surface. (b) and (c) These 2 surfaces have matching vertices that can be used to delineate an oblique truncated triangular pyramid. (d) The 6 vertices of this pyramid can be used to define 3 tetrahedra, the volumes of which can be computed analytically.

Figure 3.

Pairwise average differences (in mm²) and correlations between the 4 interpolation methods, using the IC7 as target, with or without smoothing with a Gaussian kernel of FWHM = 10 mm, projected to the average white surface. Although the 4 methods differ, with some leading to substantial, undesirable losses and gains in surface area, and the introduction of noise manifested by lower correlations, the average variation was zero for nearest neighbor, redistributive and pycnophylactic. The retessellation method led to substantial losses of area that could not be recovered or compensated by blurring. Although this method showed excellent correlation with pycnophylactic, quantitative results after interpolation are biased downwards. For the medial views, for the right hemisphere, for IC3 and IC5, and for projections to the pial and inflated surfaces, consult the Supplementary Material.

Figure 4.

Average difference (in mm³) between the 2 methods of assessing volume and their correlation (across subjects), using the highest resolution (IC7) as the interpolation target, projected to the average inflated surface. As predicated from Figure 1, differences are larger in the crowns of gyri and in the depths of sulci, with gains/losses in volume in these locations following opposite patterns. Although the correlations tend to be generally high, and increase with smoothing, they are lower in regions of higher interindividual morphological variability, such as at the anterior end of the cuneus, and in the insular cortex. For IC3 and IC5, and for projections to the white and pial surfaces, consult the Supplementary Material.

Figure 5.

Separate (light blue background) and joint (green) analysis of cortical area and thickness, as well as volume (red), using the IC7 resolution and smoothing with FWHM = 30 mm. Analysis of area indicates no increases in the VLBW group anywhere in the cortex (A), and reductions in, among other regions, the subgenual region of the cingulate cortex (B). Analysis of thickness indicates that VLBW subjects have thicker cortex in the medial orbitofrontal cortex (C) and in the right medial occipital cortex, as well as diffuse bilateral thinning in parietal and middle temporal regions (D). Analysis of volume alone broadly mimics analysis of area, with no evidence of increased volume in VLBW subjects (E), although in some maps there seems to be a partial superimposition of the effects seen separately for area and thickness, with signs of bilaterally decreased volume throughout the parietal lobe (F) but, contrary to the analysis of area, no signs of reduction in the subgenual cortex (G). Jointly analyzing area and thickness gives equal weight to both measurements, and allows directional effects to be inferred. Contrary to the case for volume, it is possible to know that there is an increase in the amount of cortical tissue in VLBW subjects in the medial orbitofrontal cortex (H) when compared with controls, and a bilateral decrease throughout most of the parietal cortex, stronger in the middle temporal and fusiform gyri, in both hemispheres (I). Moreover, the joint analysis allows search for effects that can negate each other, such as in this case weaker effects in the parietal region (J), that partially overlap in space with those shown in (I). Finally, strong effects in the middle orbitofrontal, which were missed with a simple volume analysis (G), become clearly visible (K).