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

Supplementary Material

Winkler AM, Greve DN, Bjuland KJ, Nichols TE, Sabuncu MR, Håberg AK, Skranes J, Rimol LM


Section S1: Overview

The figure below shows an overview of the steps for the analysis of surface area and the relationship between different methods. The magnetic resonance images (MRI) for each subject are used to reconstruct a pair of surfaces (pial and white) representing the cortex, which initially are in the native space of each subject, using an individual geometry. From this pair of surfaces, cortical thickness, area and volume can be measured. Finally, the coordinates of the vertices can be stored for subsequent use. The subject native surfaces are homeomorphically transformed to a sphere, registered to a spherical atlas, and used for the interpolation (resampling), which for thickness can be either nearest neighbour or barycentric, for area can be nearest neighbour, redistributive or pycnophylactic, and for the vertex coordinates can be barycentric. In the latter, the interpolation of coordinates allows the construction of a new retessellated surface in subject space, from which area can alternatively be measured. The interpolated quantities are then ready to undergo statistical analyses. See references in the main text.

The dashed arrows (in red) indicate separate, mutually exclusive branches; the continuous arrows (in black) apply to all cases, including all within the larger gray boxes.


Section S2: Interpolation methods

A detailed comparison of the four interpolation methods, assessed via correlation (scatter) plots, Bland–Altman plots, spatial maps for group differences, group correlations, averages, and standard deviations both at the group level (considering all subjects) and at the subject level for 12 subjects selected by chance. The comparisons use three different resolutions for the target for the interpolation (ic3, ic5 and ic7) and two registration methods (FS: FreeSurfer method; SD: Spherical Demons). See the main text for references.

a) Group level

ic3 ic5 ic7
Scatter plots FS SD FS SD FS SD
White surface maps FS SD FS SD FS SD
Pial surface maps FS SD FS SD FS SD
Inflated surface maps FS SD FS SD FS SD
Global area FS

b) Subject level

FWHM = 0 FWHM = 10
ic3 ic5 ic7 ic3 ic5 ic7
Bland–Altman plots FS SD FS SD FS SD FS SD FS SD FS SD
Correlation plots FS SD FS SD FS SD FS SD FS SD FS SD
White surface maps FS SD FS SD FS SD FS SD FS SD FS SD
Pial surface maps FS SD FS SD FS SD FS SD FS SD FS SD
Inflated surface maps FS SD FS SD FS SD FS SD FS SD FS SD
Total area tables FS SD FS SD FS SD
Spatial correlation tables FS SD FS SD FS SD FS SD FS SD FS SD

Section S3: Volume measurements

A similar comparison for two volume measurements: "volume" is the conventional volume, produced through the multiplication of thickness by area; "newvol" is the proposed analytical cortical volume. For these analyses, nearest neighbour interpolation was used, with the FreeSurfer registration.

a) Group level

ic3 ic5 ic7
Scatter plots FS FS FS
White surface maps FS FS FS
Pial surface maps FS FS FS
Inflated surface maps FS FS FS

b) Subject level

FWHM = 0 FWHM = 10
ic3 ic5 ic7 ic3 ic5 ic7
Bland–Altman plots FS FS FS FS FS FS
Correlation plots FS FS FS FS FS FS
White surface maps FS FS FS FS FS FS
Pial surface maps FS FS FS FS FS FS
Inflated surface maps FS FS FS FS FS FS
Total area tables FS FS FS
Spatial correlation tables FS FS FS FS FS FS

Section S4: Global measurements and variability

a) Relationship between global measurements

Scatter plots showing the relationship between cortical thickness, area, and volume, as well as Bland–Altman plots comparing the two methods to assess volume, are available here.

b) Variability

For the analysis of variability of the cortical indices, nearest neighbour interpolation was used, with FS registration and the ic7 resolution.

white pial inflated

Section S5: Statistical analysis

a) Overview

For the statistical analysis, nearest neighbour interpolation was used, with FS registration and the ic7 resolution. Thickness, area and volume (both methods, i.e., multiplicative and analytic) can be analysed separately via permutation tests, or NPC can be used to jointly investigate changes in thickness and area, replacing what otherwise would be the role of volume; the latter is influenced mostly by area only, with a poor association with cortical thickness.

b) Results

The results are for two contrasts of parameter estimates:

For each case, two models were run: (i) either without any global variable as nuisance and (ii) with global cortical thickness and global surface area; the latter are indicated in the tables under the caption "nuis". The NPC results are either using concordant signs, or with the thickness with the signs reversed (indicated by the word "opposite"). Results for a conjunction (IUT) are also shown.

In the table, "fwep" indicates that the p-values have been corrected for familywise error rate across vertices (both hemispheres); "cfwep" indicates that these p-values have been further corrected across both contrasts (positive and negative, i.e., C1 and C2).

White Pial Inflated
FWHM =
10 mm
cfwep open open open
fwep open open open
FWHM =
30 mm
cfwep open open open
fwep open open open