Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks

TL;DR

This work addresses the need for interpretable brain age gap biomarkers in neurodegenerative conditions by deploying coVariance Neural Networks (VNNs) that operate on the anatomical covariance matrix. A two-layer VNN is pre-trained on healthy controls to learn representations tied to healthy aging, enabling $\,Delta$-Age predictions that are anatomically interpretable through regional residuals and their relationship to the covariance eigenvectors. Applied to cortical thickness data from AD, FTD, APD, and PD cohorts, the approach reveals disease-specific anatomic patterns and demonstrates explainability via differential eigenvector engagement, linking distinct aging signatures to underlying pathology. The study advances beyond black-box brain-age models by providing intrinsic explainability grounded in covariance structure, with potential for clinical validation and longitudinal monitoring of brain health.

Abstract

Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing \textit{brain age gap} characterized by an elevated brain age relative to the chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. Hence, brain age gap is a promising biomarker for monitoring brain health. However, black-box machine learning approaches to brain age gap prediction have limited practical utility. Recent studies on coVariance neural networks (VNN) have proposed a relatively transparent deep learning pipeline for neuroimaging data analyses, which possesses two key features: (i) inherent \textit{anatomically interpretablity} of derived biomarkers; and (ii) a methodologically interpretable perspective based on \textit{linkage with eigenvectors of anatomic covariance matrix}. In this paper, we apply the VNN-based approach to study brain age gap using cortical thickness features for various prevalent neurodegenerative conditions. Our results reveal distinct anatomic patterns for brain age gap in Alzheimer's disease, frontotemporal dementia, and atypical Parkinsonian disorders. Furthermore, we demonstrate that the distinct anatomic patterns of brain age gap are linked with the differences in how VNN leverages the eigenspectrum of the anatomic covariance matrix, thus lending explainability to the reported results.

Figures (5)

• Figure 1: One layer of a VNN model. The covariance filter implicitly manipulates input data according to the eigenvectors of the covariance matrix ${\mathbf{C}}$, thus tying the output ${\bf y}$ to specific eigenvectors of ${\mathbf{C}}$.
• Figure 2: A VNN-based pipeline for $\Delta$-Age prediction.
• Figure 3: Brain age estimates and associated anatomic characterizations for ( a) AD, ( b) APD, and ( c) FTD.
• Figure 4: $\Delta$-Age for PD and respective HC group.
• Figure 5: Explaining $\Delta$-Age in disease groups (( a) AD and ( b) FTD) in terms of the group differences between inner products of VNN representations and eigenvectors of anatomical covariance matrices. ($^{\ast\ast\ast\ast}:$$p$-value $\leq 1\exp-4$)

Theorems & Definitions (2)

• Remark 1: Multi-layer VNN
• Remark 2: Statistical inference using VNNs