Longitudinal Principal Manifold Estimation

TL;DR

This paper introduces a longitudinal principal manifold estimation method that smooths shape trajectories over time in neuroimaging data, improving the analysis of brain atrophy in neurodegenerative diseases.

Contribution

It proposes a novel smoothing spline-based approach for longitudinal manifold estimation, including a data augmentation technique for self-intersecting manifolds, enhancing shape analysis over time.

Findings

Improved surface estimation of hippocampus and thalamus.

Enhanced segmentation accuracy using longitudinal trends.

Demonstrated advantages on Alzheimer's neuroimaging data.

Abstract

Longitudinal magnetic resonance imaging data is used to model trajectories of change in brain regions of interest to identify areas susceptible to atrophy in those with neurodegenerative conditions like Alzheimer's disease. Most methods for extracting brain regions are applied to scans from study participants independently, resulting in wide variability in shape and volume estimates of these regions over time in longitudinal studies. To address this problem, we propose a longitudinal principal manifold estimation method, which seeks to recover smooth, longitudinally meaningful manifold estimates of shapes over time. The proposed approach uses a smoothing spline to smooth over the coefficients of principal manifold embedding functions estimated at each time point. This mitigates the effects of random disturbances to the manifold between time points. Additionally, we propose a novel data augmentation approach to enable principal manifold estimation on self-intersecting manifolds. Simulation studies demonstrate performance improvements over naive applications of principal manifold estimation and principal curve/surface methods. The proposed method improves the estimation of surfaces of hippocampuses and thalamuses using data from participants of the Alzheimer's Disease Neuroimaging Initiative. An analysis of magnetic resonance imaging data from 236 individuals shows the advantages of our proposed methods that leverage regional longitudinal trends for segmentation.