Deep Geometric Learning With Monotonicity Constraints for Alzheimer’s Disease Progression

초록

Alzheimer’s disease (AD) is a devastating neurodegenerative condition that precedes progressive and irreversible dementia; thus predicting its progression over time is vital for clinical diagnosis and treatment. For this numerous studies have implemented structural magnetic resonance imaging (MRI) to model AD progression focusing on three integral aspects: 1) temporal variability; 2) incomplete observations; and 3) temporal geometric characteristics. However many pioneer deep learning-based approaches addressing data variability and sparsity have yet to consider inherent geometrical properties sufficiently. These properties are integral to modeling as they correlate with brain region size thickness volume and shape in AD progression. The ordinary differential equation-based geometric modeling method (ODE-RGRU) has recently emerged as a promising strategy for modeling time-series data by intertwining a recurrent neural network (RNN) and an ODE in Riemannian space. Despite its achievements ODE-RGRU encounters limitations when extrapolating positive definite symmetric matrices from incomplete samples leading to feature reverse occurrences that are particularly problematic especially within the clinical facet. Therefore this study proposes a novel geometric learning approach that models longitudinal MRI biomarkers and cognitive scores by combining three modules: topological space shift ODE-RGRU and trajectory estimation. We have also developed a training algorithm that integrates the manifold mapping with monotonicity constraints to reflect measurement transition irreversibility. We verify our proposed method’s efficacy by predicting clinical labels and cognitive scores over time in regular and irregular settings. Furthermore we thoroughly analyze our proposed framework through an ablation study. IEEE

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