Spatially Adaptive Varying Correlation Analysis for Multimodal Neuroimaging Data

Cortical hypometabolism reflects local atrophy and tau pathology in symptomatic Alzheimer's disease

Posterior cortical hypometabolism measured with [18F]-Fluorodeoxyglucose (FDG)-PET is a well-known marker of Alzheimer's disease-related neurodegeneration, but its associations with underlying neuropathological processes are unclear. We assessed cross-sectionally the relative contributions of three potential mechanisms causing hypometabolism in the retrosplenial and inferior parietal cortices: local molecular (amyloid and tau) pathology and atrophy, distant factors including contributions from the degenerating medial temporal lobe or molecular pathology in functionally connected regions, and the presence of the apolipoprotein E (APOE) ε4 allele. Two hundred and thirty-two amyloid-positive cognitively impaired patients from two cohorts (University of California, San Francisco, UCSF, and Alzheimer's Disease Neuroimaging Initiative, ADNI) underwent MRI and PET with FDG, amyloid-PET using [11C]-Pittsburgh Compound B, [18F]-Florbetapir, or [18F]-Florbetaben, and [18F]-Flortaucipir tau-PET within one year. Standard uptake value ratios (SUVR) were calculated using tracer-specific reference regions. Regression analyses were run within cohorts to identify variables associated with retrosplenial or inferior parietal FDG SUVR. On average, ADNI patients were older and were less impaired than UCSF patients. Regional patterns of hypometabolism were similar between cohorts, though there were cohort differences in regional gray matter atrophy. Local cortical thickness and tau-PET (but not amyloid-PET) were independently associated with both retrosplenial and inferior parietal FDG SUVR (ΔR2 = .09 to .21) across cohorts in models that also included age and disease severity (local model). Including medial temporal lobe volume improved the retrosplenial FDG model in ADNI (ΔR2 = .04, p = .008) but not UCSF (ΔR2 < .01, p = .52), and did not improve the inferior parietal models (ΔR2s < .01, ps > .37). Interaction analyses revealed that medial temporal volume was more strongly associated with retrosplenial FDG SUVR at earlier disease stages (p = .06 in UCSF, p = .046 in ADNI). Exploratory analyses across the cortex confirmed overall associations between hypometabolism and local tau pathology and thickness and revealed associations between medial temporal degeneration and hypometabolism in retrosplenial, orbitofrontal, and anterior cingulate cortices. Finally, our data did not support hypotheses of a detrimental effect of pathology in connected regions or of an effect of the APOE ε4 allele in impaired participants. Overall, in two independent groups of patients at symptomatic stages of Alzheimer's disease, cortical hypometabolism mainly reflected structural neurodegeneration and tau, but not amyloid, pathology.

Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction

In the form of multidimensional arrays, tensor data have become increasingly prevalent in modern scientific studies and biomedical applications such as computational biology, brain imaging analysis, and process monitoring system. These data are intrinsically heterogeneous with complex dependencies and structure. Therefore, ad-hoc dimension reduction methods on tensor data may lack statistical efficiency and can obscure essential findings. Model-based clustering is a cornerstone of multivariate statistics and unsupervised learning; however, existing methods and algorithms are not designed for tensor-variate samples. In this article, we propose a tensor envelope mixture model (TEMM) for simultaneous clustering and multiway dimension reduction of tensor data. TEMM incorporates tensor-structure-preserving dimension reduction into mixture modeling and drastically reduces the number of free parameters and estimative variability. An expectation-maximization-type algorithm is developed to obtain likelihood-based estimators of the cluster means and covariances, which are jointly parameterized and constrained onto a series of lower dimensional subspaces known as the tensor envelopes. We demonstrate the encouraging empirical performance of the proposed method in extensive simulation studies and a real data application in comparison with existing vector and tensor clustering methods.