Data-driven decomposition and staging of flortaucipir uptake in Alzheimer's disease.

INTRODUCTION: Previous approaches pursuing in vivo staging of tau pathology in Alzheimer's disease (AD) have typically relied on neuropathologically defined criteria. In using predefined systems, these studies may miss spatial deposition patterns which are informative of disease progression. METHODS: We selected discovery (n = 418) and replication (n = 132) cohorts with flortaucipir imaging. Non-negative matrix factorization (NMF) was applied to learn tau covariance patterns and develop a tau staging system. Flortaucipir components were also validated by comparison with amyloid burden, gray matter loss, and the expression of AD-related genes. RESULTS: We found eight flortaucipir covariance patterns which were reproducible and overlapped with relevant gene expression maps. Tau stages were associated with AD severity as indexed by dementia status and neuropsychological performance. Comparisons of flortaucipir uptake with amyloid and atrophy also supported our model of tau progression. DISCUSSION: Data-driven decomposition of flortaucipir uptake provides a novel framework for tau staging which complements existing systems. HIGHLIGHTS: NMF reveals patterns of tau deposition in AD. Data-driven staging of flortaucipir tracks AD severity. Learned flortaucipir patterns overlap with AD-related gene expression.

Patterns of Glucose Metabolism in [ 18 F]FDG PET Indicate Regional Variability and Neurodegeneration in the Progression of Alzheimer's Dementia.

In disorders of cognitive impairment, such as Alzheimer's disease, neurodegeneration is the final common pathway of disease progression. Modulating, reversing, or preventing disease progression is a clinical imperative most likely to succeed following accurate and explanatory understanding of neurodegeneration, requiring enhanced consistency with quantitative measurements and expanded interpretability of complex data. The on-going study of neurodegeneration has robustly demonstrated the advantages of accumulating large amounts of clinical data that include neuroimaging, motiving multi-center studies such as the Alzheimer's Disease Neuroimaging Initiative (ADNI). Demonstrative advantages also arise from highly multivariate analysis methods, and this work reports advances provided by non-negative matrix factorization (NMF). NMF revealed patterns of covariance for glucose metabolism, estimated by positron emission tomography of [ 18 F]fluorodeoxyglucose, in 243 healthy normal participants of ADNI. Patterns for glucose metabolism provided cross-sectional inferences for 860 total participants of ADNI with and without cerebral amyloidosis and clinical dementia ratings (CDR) ranging 0-3. Patterns for glucose metabolism were distinct in number and topography from patterns identified in previous studies of structural MRI. They were also distinct from well-establish topographies of resting-state neuronal networks mapped by functional magnetic resonance imaging. Patterns for glucose metabolism identified significant topographical landmarks relating age, sex, APOE ε4 alleles, amyloidosis, CDR, and neurodegeneration. Patterns involving insular and orbitofrontal cortices, as well as midline regions of frontal and parietal lobes demonstrated the greatest neurodegeneration with progressive Alzheimer's dementia. A single pattern for the lateral parietal and posterior superior temporal cortices demonstrated preserved glucose metabolism for all diagnostic groups, including Alzheimer's dementia. Patterns correlated significantly with topical terms from the Neurosynth platform, thereby providing semantic representations for patterns such as attention, memory, language, fear/reward, movement and motor planning. In summary, NMF is a data-driven, principled, supervised statistical learning method that provides interpretable patterns of neurodegeneration. These patterns can help inform the understanding and treatment of Alzheimer's disease. Highlights: ▪ Data-driven non-negative matrix factorization (NMF) identified 24 canonical patterns of spatial covariance of cerebral glucose metabolism. The training data comprised healthy older participants (CDR = 0 without amyloidosis) cross-sectionally drawn from ADNI. ▪ In healthy participants, mean SUVRs for specific patterns in precuneus, lateral parietal cortex, and subcortical areas including superficial white matter and striatum, demonstrated increasing glucose metabolism with advancing age. ▪ In asymptomatic participants with amyloidosis , glucose metabolism increased compared to those who were asymptomatic without amyloid , particularly in medial prefrontal cortex, frontoparietal cortex, occipital white, and posterior cerebellar regions. ▪ In symptomatic participants with amyloidosis , insular cortex, medial frontal cortex, and prefrontal cortex demonstrated the most severe losses of glucose metabolism with increasing CDR. Lateral parietal and posterior superior temporal cortices retained glucose metabolism even for CDR > 0.5. ▪ NMF models of glucose metabolism are consistent with models arising from principal components, or eigenbrains, while adding additional regional interpretability. ▪ NMF patterns correlated with regions catalogued in Neurosynth. Following corrections for spatial autocorrelations, NMF patterns revealed meta-analytic identifications of patterns with Neurosynth topics of fear/reward, attention, memory, language, and movement with motor planning. Patterns varied with degrees of cognitive impairment.

Scalable Orthonormal Projective NMF via Diversified Stochastic Optimization.

The increasing availability of large-scale neuroimaging initiatives opens exciting opportunities for discovery science of human brain structure and function. Data-driven techniques, such as Orthonormal Projective Non-negative Matrix Factorization (opNMF), are well positioned to explore multivariate relationships in big data towards uncovering brain organization. opNMF enjoys advantageous interpretability and reproducibility compared to commonly used matrix factorization methods like Principal Component Analysis (PCA) and Independent Component Analysis (ICA), which led to its wide adoption in clinical computational neuroscience. However, applying opNMF in large-scale cohort studies is hindered by its limited scalability caused by its accompanying computational complexity. In this work, we address the computational challenges of opNMF using a stochastic optimization approach that learns over mini-batches of the data. Additionally, we diversify the stochastic batches via repulsive point processes, which reduce redundancy in the mini-batches and in turn lead to lower variance in the updates. We validated our framework on gray matter tissue density maps estimated from 1000 subjects part of the Open Access Series of Imaging (OASIS) dataset. We demonstrated that operations over mini-batches of data yield significant reduction in computational cost. Importantly, we showed that our novel optimization does not compromise the accuracy or interpretability of factors when compared to standard opNMF. The proposed model enables new investigations of brain structure using big neuroimaging data that could improve our understanding of brain structure in health and disease.

Scalable NMF via linearly optimized data compression.

Orthonormal projective non-negative matrix factorization (opNMF) has been widely used in neuroimaging and clinical neuroscience applications to derive representations of the brain in health and disease. The non-negativity and orthonormality constraints of opNMF result in intuitive and well-localized factors. However, the advantages of opNMF come at a steep computational cost that prohibits its use in large-scale data. In this work, we propose novel and scalable optimization schemes for orthonormal projective non-negative matrix factorization that enable the use of the method in large-scale neuroimaging settings. We replace the high-dimensional data matrix with its corresponding singular value decomposition (SVD) and QR decompositions and combine the decompositions with opNMF multiplicative update algorithm. Empirical validation of the proposed methods demonstrated significant speed-up in computation time while keeping memory consumption low without compromising the accuracy of the solution.