16: Topological functional analysis of longitudinal brain MRI data

Thomas M. Menino Convention & Exhibition Center 

Neurodegenerative diseases such as Alzheimer’s disease progress gradually, with structural brain changes accumulating over years. Standard longitudinal imaging analyses based on voxelwise comparisons or region-level summaries are often fail to capture how structural patterns evolve across spatial scales. In this work, we study whether Alzheimer’s brain dynamics can be identified through longitudinal topological summaries of brain structure. Using longitudinal structural MRI from the Alzheimer’s Disease Neuroimaging Initiative (ADNI), we extract persistent homology features from preprocessed brain volumes and represent them as betti curves across filtration thresholds. Treating betti curves as functional data, we align trajectories across visits using the square-root velocity function framework to reduce phase variability and then apply longitudinal functional principal component analysis to separate subject-specific baseline patterns from patterns of change over time. The analysis reveals stable topological signatures across visits and systematic time-varying components that capture longitudinal brain dynamics, reflect disease progression, and enable score-based sex comparisons.

Longitudinal functional data analysis

Functional principal component analysis

Persistent homology

Betti curves

Square-root velocity function 

Section on Statistics in Imaging