3D Maps of Brain Atrophy (based on the method of averaging individual differences). The top rows of panel a and b show the level of atrophy in 40 AD patients and 40 MCI subjects as a percentage reduction in volume relative to controls, respectively. The bottom rows show the significance of these reductions, revealing highly significant atrophy in AD but a more anatomically restricted pattern of atrophy in MCI. The high Jacobian values immediately adjacent to the ventricle result from the limited spatial resolution of the deformation fields, which are computed via a Fourier transform on a 32³ grid. The ventricles expand presumably due to cell or myelin loss in broad areas overlying the ventricular surface; not in the narrow band of tissue immediately adjacent to the ventricular surface, in which voxels are partial volumed with voxels where expansion is detected. This is also the case with PET and fMRI imaging, where imaging signals ‘bleed’ into the CSF space where the signal differs (and typically there is no CSF signal). As with those modalities, sharp boundaries are not found in group averaged deformation maps, so the image resolution should be interpreted with this in mind. Higher resolution morphometry is possible in longitudinal studies, where it is feasible (and makes sense) to perform image registration at a finer spatial scale.

Mean Jacobian of Normal, MCI and AD in each lobar ROI (N=40 for each group, 9P linear registration). This plot shows TBM-based volume estimates (relative to the normal subjects) for each tissue type in each lobe. To ease comparison of volumes across lobes, values are expressed as a proportion of the control average volume. The * indicates that there is significant atrophy relative to normal subjects.

3D maps of brain atrophy (based on aligning group averages). These maps show the level of volumetric atrophy in AD and MCI relative to controls. In the top left panel, AD patients show prominent atrophy of up to 30% regionally in the temporal lobes, widespread reductions in the white matter, and notable expansion of the interhemispheric fissure (coded in red colors). MCI subjects show atrophy in the same regions but to a lesser degree. These maps are computed after spatial normalization of all brains to the same global scale, so regions with apparent excess tissue indicate regions with either absolute volumetric gains, or relatively greater tissue in proportion to overall brain scale. The bottom row shows the significance of these changes, computed using the variance of the individual deformation mappings, and color-coded according to the scale at the bottom.

Single-subject analysis. Here regional brain volumes in a single subject with AD are locally 20–30% lower than the control group average (top panel, blue colors) and 20–30% larger in some of the CSF spaces (red colors). Using the variance in the control group to assess the percentile, for regional volumes, at which this subject would fall relative to normal controls, most regions are well outside the confidence limits for normal volumes (lower panel, red colors). For caveats regarding the significance and interpretation of single-subject TBM maps, see the main text.

Two Alternative TBM Designs. Inter-group differences in brain structure may be assessed with TBM, using two alternative designs, which differ in terms of which images are registered to each other. The first approach, termed “Averaging Individual Differences”, (a), a mean template is created for the control subjects. Then, every image in the study is nonlinearly aligned to the control average template and the set of individual differences between each subject and the template is analyzed statistically. In panel a, the mean template was built from controls only; arguably, it could instead be re-built each time based on all subjects relevant to a specific hypothesis (e.g., Controls and MCI only, for an MCI-control comparison), but this would mean that the results of different contrasts would not be spatially registered with each other. The second approach, termed “Aligning Group Averages”, reflects a relatively new concept in TBM design (Rohlfing et al., 2005; Aljabar et al., 2006, 2008), (b), and creates minimal deformation targets (MDTs) for each diagnostic group separately using nonlinear registrations of subjects within the group (A1, A2, …; N1, N2, …; etc.) to create a template reflecting the group's mean geometry. Systematic anatomical differences between groups may then be assessed using direct alignment of these group-specific templates. In panel b, J_AD and J_MCI denote the Jacobians of these mappings, which contain information on the level of atrophy in the MCI and AD groups versus controls. We compare these two methods at the end of the Results section; for all statistical tests, the standard method of “averaging individual differences” is used.

Comparing Effect Sizes with CDF Plots: Influences of Sample Size and Registration Model (9 vs. 12 parameter linear registration) on the Statistical Effect size in Discriminating MCI and AD from Normal Subjects, using the TBM design of averaging individual differences. With some caveats (see Discussion), higher CDF curves denote greater effect sizes, i.e., a large number of significant voxels detected within the temporal lobes. Three aspects are notable: (1) Atrophy is detected with a greater effect size in the AD group compared to the MCI group, regardless of the method; (2) in AD, effect sizes are greater when larger samples are used (e.g., 40 per group versus 30, 20 or 10); (3) Using 9-parameter versus 12-parameter initial registration may provide slight gains in power, but these are no greater than the improvements gained by adding 10 subjects to the sample. The omnibus (corrected) significance for each experiment is the q-value obtained from the positive FDR method. 40 subjects per group are needed to detect atrophy significantly in AD and at trend level in MCI, using the entire temporal lobe as an ROI. Atrophy is detected in MCI with 40 subjects per group, but only in the left temporal lobe. Perhaps surprisingly, the jump in effect size as one goes from a sample size of 30 to 40 is much greater for normal vs AD than normal vs MCI. This may be because the true effect size in AD is greater, but it may also be because CDFs rely on thresholdings of the statistical maps, leading to many voxels reaching significance within a small range of sample sizes.

Mean Jacobian Values within the Hippocampus, for Normal, MCI and AD Groups, using a Manually-Defined Traces of the Hippocampal Formation Delineated on the Control Average Template (N=40 for each group, 9P linear registration). This plot shows TBM-based volume estimates (relative to the normal subjects) for each tissue type in ROIs of the left and right hippocampi. The * indicates that there is significant atrophy relative to normal subjects.

CDF Plots of Group Differences based on Aligning Group Average Images (N=40; 9P linear registration). Voxel-wise two-sample t tests were conducted using the Jacobians derived from direct alignment of group average templates and the variance term obtained from the method of averaging individual differences. The green curve (MCI vs. Normal) overlaps with the black curve which represents the empirically confirmed null distribution of statistics (registering one normal group template to the other). These lines are far from diagonal, and the method of aligning group averages, when used with a variance term from individual registrations, does not control false positives properly (FDR q-value for controls: 0.0001).