Coupled Cross-sectional and Longitudinal NMF for Modeling Brain Aging Heterogeneity

Poster No:

1159 

Submission Type:

Late-Breaking Abstract Submission 

Authors:

Ioanna Skampardoni1, Guray Erus1, Christos Davatzikos1

Institutions:

1AI2D Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania, Philadelphia, PA

First Author:

Ioanna Skampardoni  
AI2D Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania
Philadelphia, PA

Co-Author(s):

Guray Erus  
AI2D Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania
Philadelphia, PA
Christos Davatzikos  
AI2D Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania
Philadelphia, PA

Late Breaking Reviewer(s):

Sylvain Baillet  
Montreal Neurological Institute
Montreal, Quebec
Michael Breakspear, PhD  
The University of Newcastle
New Lambton Heights, NSW
Sofie Valk  
Max Planck Institute for Human Cognitive and Brain Sciences
Leipzig, Saxony

Introduction:

Understanding the heterogeneity of brain aging is crucial for the early detection of neurodegenerative diseases and optimizing participant selection in clinical trials. Existing machine learning (ML) methods for identifying heterogeneity rely exclusively on cross-sectional data, overlooking valuable longitudinal information that captures individual trajectories of pathological changes (Yang et al. 2024; Young et al. 2018; Zhang et al. 2016). This study presents Coupled Cross-sectional and Longitudinal Nonnegative Matrix Factorization (CCL-NMF), a method that jointly analyzes cross-sectional and longitudinal neuroimaging data to identify heterogeneous brain aging patterns.

Methods:

Cross-sectional data capture cumulative brain changes over time but lack individual trajectories, while longitudinal data track within-subject progression but typically suffer from small sample sizes. CCL-NMF addresses these limitations by performing a joint factorization of the two complementary data types: (1) C-map, which quantifies cross-sectional deviations of an aging population from a reference middle-aged healthy cohort, and (2) L-map, which estimates individualized brain change rates from longitudinal data. A mutually constrained NMF formulation extracts brain aging components (dictionary) shared across both maps and computes individual-specific coefficients (loadings) in both data types. Unlike rigid subtype classification approaches, CCL-NMF allows for continuous loadings, enabling the modeling of simultaneous occurrences of multiple patterns within individuals.
The proposed CCL-NMF formulation is generic and is applicable to identify heterogeneity in any disease characterized by monotonic brain alterations - changes that progress in a single direction over time, such as neurodegeneration-driven atrophy and pathological protein accumulation. This results in single-signed maps, ensuring consistency with NMF constraints. Here, it was validated on a semi-synthetic dataset generated by simulating controlled atrophy patterns in a cognitively normal UK Biobank (Alfaro-Almagro et al. 2018) cohort (N=4,517). A reference group (20%) remained unchanged, while 80% underwent simulated atrophy following five predefined patterns (frontal, occipital, parietal, subcortical, temporal), applied progressively over 40 synthetic years. Atrophy onset ages followed a normal distribution (μ=7, σ=3), with affected regions shrinking by 1% annually and non-affected regions undergoing 0.1% background shrinkage.
CCL-NMF input data comprised a C-map (cross-sectional deviations) and an L-map (longitudinal change rates). Since longitudinal data availability is typically limited, the L-map was generated using a subset of participants with multiple timepoints, reflecting real-world data constraints. Three models were compared: C-NMF (C-map only), L-NMF (L-map only), and CCL-NMF (joint factorization). Performance was assessed based on the accuracy of the atrophy patterns recovery/reconstruction, measured by the alignment between extracted components and groundtruth patterns.

Results:

CCL-NMF demonstrated the most accurate recovery of simulated atrophy patterns, achieving the lowest divergence between extracted components and the groundtruth. Divergence was defined as the norm of the difference between the identity matrix and the inner product matrix of the groundtruth atrophy patterns and the NMF-derived dictionary. Divergence values were 1.67 (C-NMF), 1.46 (L-NMF), and 1.39 (CCL-NMF), confirming that integrating cross-sectional and longitudinal information improves accuracy.

Conclusions:

CCL-NMF provides a novel framework for integrating cross-sectional and longitudinal neuroimaging data to identify a unified set of brain aging patterns that capture the complex interplay between static and dynamic aspects of brain alterations. Individual loadings of identified brain aging patterns allow us to quantify co-expression of heterogeneous brain changes, capturing overlapping pathologies.

Disorders of the Nervous System:

Neurodegenerative/ Late Life (eg. Parkinson’s, Alzheimer’s)

Lifespan Development:

Aging 2

Modeling and Analysis Methods:

Classification and Predictive Modeling 1
Methods Development

Keywords:

Aging
Other - Nonnegative Matrix Factorization, Heterogeneity, Neurodegeneration

1|2Indicates the priority used for review

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Provide references using APA citation style.

Alfaro-Almagro, F., et al. (2018). Image processing and quality control for the first 10,000 brain imaging datasets from UK Biobank. NeuroImage, 166, 400–424.
Yang, Z., et al. (2024). Brain aging patterns in a large and diverse cohort of 49,482 individuals. Nature Medicine, 30(10), 3015–3026.
Young, A. L., et al. (2018). Uncovering the heterogeneity and temporal complexity of neurodegenerative diseases with subtype and stage inference. Nature Communications, 9(1), 1–16.
Zhang, X., et al. (2016). Bayesian model reveals latent atrophy factors with dissociable cognitive trajectories in Alzheimer’s disease. Proceedings of the National Academy of Sciences, 113(42).

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