A method for inferring regional origins of neurodegeneration

Abstract

Alzheimer's disease, the most common form of dementia, is characterized by the emergence and spread of senile plaques and neurofibrillary tangles, causing widespread neurodegeneration. Though the progression of Alzheimer's disease is considered to be stereotyped, the significant variability within clinical populations obscures this interpretation on the individual level. Of particular clinical importance is understanding where exactly pathology, e.g. tau, emerges in each patient and how the incipient atrophy pattern relates to future spread of disease. Here we demonstrate a newly developed graph theoretical method of inferring prior disease states in patients with Alzheimer's disease and mild cognitive impairment using an established network diffusion model and an L1-penalized optimization algorithm. Although the 'seeds' of origin using our inference method successfully reproduce known trends in Alzheimer's disease staging on a population level, we observed that the high degree of heterogeneity between patients at baseline is also reflected in their seeds. Additionally, the individualized seeds are significantly more predictive of future atrophy than a single seed placed at the hippocampus. Our findings illustrate that understanding where disease originates in individuals is critical to determining how it progresses and that our method allows us to infer early stages of disease from atrophy patterns observed at diagnosis.

Figure 1

Average global atrophy patterns. The size of the spheres corresponds to the magnitude of atrophy (Z-scores with respect to controls), and the colour of each node indicates whether there is hypotrophy (blue) or hypertrophy (red). The node size scale is linear. The shading as represented by the colour bars corresponds to the coefficient of variation, with lighter shades indicating a higher degree of variation. The scale of the spheres in the early MCI glass brains is two times larger than the reference for easier visualization. AD = Alzheimer’s disease; EMCI = early MCI; LMCI = late MCI.

Figure 2

Seed parameterization and distribution. (A) L-curves for each weighting parameter plotted over a range of penalty parameters for the Alzheimer’s disease cohort, with the best combination (λ = 0.06, w = 0.17) circled in red. See Supplementary Fig. 1 for the late MCI and early MCI L-curves. (B) Glass brain representations of the average seed atrophy patterns for each pair of parameters. The range closely corresponds to the elbows of the L-curves for each cohort. As either λ or w is increased, the sparsity of the average seed also increases until no regions show significant atrophy. The glass brains outlined in red reflect the parameter choices used for further analysis. (C) Distribution of seeds. We quantified the frequency with which patients in each cohort showed nonzero atrophy on a node-by-node basis. The results are visualized as a bar graph, where regions were binned based on gross anatomical location. Seeds are particularly enriched in the temporal lobe compared with the other regions of the brain for all three groups (P < 0.001). AD = Alzheimer’s disease; EMCI = early MCI; LMCI = late MCI.

Figure 3

Individual seed investigation. (A) Baseline and seed atrophy patterns for two pairs of patients, one exhibiting high correlation (left) and the other high anticorrelation (right). (B) Histograms of the pairwise correlations between patients within the Alzheimer’s disease, late MCI, and early MCI cohorts, respectively. We calculated the correlations between baseline atrophy patterns and seed atrophy patterns for all pairs of patients. (C) The same data as in B represented as scatterplots, with each patient pair represented by a single point. There is a strong correlation between pairwise baseline comparisons and pairwise seed comparisons for all three cohorts, as shown by the best-fit lines and mean R-values between both sets of correlations. AD = Alzheimer’s disease; EMCI = early MCI; LMCI = late MCI.

Figure 4

Forward predictions of baseline atrophy patterns with the inferred and hippocampal seeds. We initialize the forward NDM with either the inferred seed or a static seed located at the hippocampus and compare these predictions with baseline. The forward prediction using the inferred seeds performs well, while the hippocampal seed largely fails at reproducing each patient’s baseline. Note that the choice of parameters differs here from previous figures; see Supplementary Fig. 3.

Figure 5

PCA inferred seeds on Alzheimer’s disease, early MCI, and late MCI groups. The top row shows only Alzheimer’s disease and early MCI and bottom row shows all three groups. Principal Component Analysis (PCA) for inferred seeds showed no distinct clusters within the Alzheimer’s disease, early MCI, and late MCI cohort. Seed values were calculated using optimal L-curve parameters for the each cohort as described earlier. Alzheimer’s disease patients are shown in magenta and early MCI patients in blue. While there were significant differences in the atrophy pattern (consistent with Noh et al., 2014; Dong et al., 2017; Park et al., 2017), PCA did not reveal distinct/separate clusters for the seed patterns. However, we recapitulate significant separation between patients with Alzheimer’s disease (in magenta) versus patients with early MCI (in blue) regarding atrophy scores. AD = Alzheimer’s disease; EMCI = early MCI; LMCI = late MCI.

Figure 6

Seed investigation for amyloid-β and PCA inferred seeds on distinct amyloid-β subgroups. (A) Seed investigation for amyloid-β. Comparison between amyloid-β-negative (red) and amyloid-β-positive (blue) early MCI cohorts. Ctx-lh-entorhinal region was identified with higher seeds for amyloid-β-positive versuss ctx-lh-temporal pole region was identified with higher seeds for amyloid-β-negative subgroups in early MCI subjects. Atrophy patterns on top depict (scaled) nodes with average Z-scores above 0.05 and seed patterns on bottom show (scaled) nodes with average seed values above 0.15. Seed values were calculated using optimal L-curve parameters for the early MCI cohort (λ = 0.02, w = 0.33). (B) Seed investigation for amyloid-β. Histograms (normalized probability) for different R_max values for amyloid-β-negative (red) and amyloid-β-positive (blue) in early MCI cohorts. The positive distribution favors higher R_max values and is significantly more left-skewed than the negative distribution. (C) PCA inferred seeds on distinct amyloid-β subgroups. PCA for inferred seeds showed no distinct clusters for different amyloid-β subgroups within the early MCI cohort. Seed values were calculated using optimal L-curve parameters for the early MCI cohort (λ = 0.02, w = 0.33). Ctx = cortex; lh = left hemisphere.