Analysis of regional cerebral blood flow data to discriminate among Alzheimer's disease, frontotemporal dementia, and elderly controls: a multi-block barycentric discriminant analysis (MUBADA) methodology

Abstract

We present a generalization of mean-centered partial least squares correlation called multiblock barycentric discriminant analysis (MUBADA) that integrates multiple regions of interest (ROIs) to analyze functional brain images of cerebral blood flow or metabolism obtained with SPECT or PET. To illustrate MUBADA we analyzed data from 104 participants comprising Alzheimer's disease (AD) patients, frontotemporal dementia (FTD) patients, and elderly normal controls. Brain images were analyzed via 28 ROIs (59,845 voxels) selected for clinical relevance. This is a discriminant analysis (DA) question with several blocks (one per ROI) and with more variables than observations, a configuration that precludes using DA. MUBADA revealed two factors explaining 74% and 26% of the total variance: Factor 1 isolated FTD, and Factor 2 isolated AD. A random effects model correctly classified 64% (chance = 33%) of "new" participants (p < 0.0001). MUBADA identified ROIs that best discriminated groups: ROIs separating FTD were bilateral inferior, middle frontal, left inferior, and middle temporal gyri, while ROIs separating AD were bilateral thalamus, inferior parietal gyrus, inferior temporal gyrus, left precuneus, middle frontal, and middle temporal gyri. MUBADA classified participants at levels comparable to standard methods (i.e., SVM, PCA-LDA, and PLS-DA) but provided information (e.g., discriminative ROIs and voxels) not easily accessible to these methods.

Figure 1

Schematic organization of MUBADA.

Figure 2

(a) Projection of the barycenters on the GPCA space; (b) Projection of the observations as supplementary elements. EN = Elderly Normal, AD = Alzheimer's Disease, FTD = Fronto-Temporal Dementia.

Figure 3

(a) Tolerance intervals, (b) Prediction intervals, and (c) Confidence intervals.

Figure 4

ROI contribution to group discrimination: (a) right hemisphere and (b) left hemisphere partial contributions of the ROIs to the discriminant factors. Axes represent increasing factor weight. Circle diameters are proportional to the ROI's contribution to the total variance.

Figure 5. The X matrix with participants nested in clinical groups and voxels nested in ROIs

Figure 6

Computing the R matrix of the group barycenters (i.e., means) of the groups of participants.

Figure 7

Computing the PCA (i.e., singular value decomposition) of R provides factors scores for participants (and loadings for the voxels).

Figure 8. The projections of a participant (as a supplementary element) in the group factor score space provides a factor scores for this participant

Figure 9

Drawing ellipsoid that comprises 95% of the participants' factor scores provides tolerance ellipsoids.

Figure 10

Fitting ellipsoids that comprises 95% of the bootstrapped means provides confidence ellipsoids.

Figure 11

Projecting an ROI onto the groups factor space provides a partial factor score for this ROIs (note the mean of the ROIs' partial scores is equal to the group factor scores).

Figure 12

Summing all the contribution of the voxels of a given ROI provides the inertia (i.e., variance) explained by this ROI. The inertia explained by all the ROIs can be plotted as 2D maps.