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Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective

Saurabh Sihag, Gonzalo Mateos, Alejandro Ribeiro

Abstract

Neurodegeneration, characterized by the progressive loss of neuronal structure or function, is commonly assessed in clinical practice through reductions in cortical thickness or brain volume, as visualized by structural MRI. While informative, these conventional approaches lack the statistical sophistication required to fully capture the spatially correlated and heterogeneous nature of neurodegeneration, which manifests both in healthy aging and in neurological disorders. To address these limitations, brain age gap has emerged as a promising data-driven biomarker of brain health. The brain age gap prediction (BAGP) models estimate the difference between a person's predicted brain age from neuroimaging data and their chronological age. The resulting brain age gap serves as a compact biomarker of brain health, with recent studies demonstrating its predictive utility for disease progression and severity. However, practical adoption of BAGP models is hindered by their methodological obscurities and limited generalizability across diverse clinical populations. This tutorial article provides an overview of BAGP and introduces a principled framework for this application based on recent advancements in graph signal processing (GSP). In particular, we focus on graph neural networks (GNNs) and introduce the coVariance neural network (VNN), which leverages the anatomical covariance matrices derived from structural MRI. VNNs offer strong theoretical grounding and operational interpretability, enabling robust estimation of brain age gap predictions. By integrating perspectives from GSP, machine learning, and network neuroscience, this work clarifies the path forward for reliable and interpretable BAGP models and outlines future research directions in personalized medicine.

Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective

Abstract

Neurodegeneration, characterized by the progressive loss of neuronal structure or function, is commonly assessed in clinical practice through reductions in cortical thickness or brain volume, as visualized by structural MRI. While informative, these conventional approaches lack the statistical sophistication required to fully capture the spatially correlated and heterogeneous nature of neurodegeneration, which manifests both in healthy aging and in neurological disorders. To address these limitations, brain age gap has emerged as a promising data-driven biomarker of brain health. The brain age gap prediction (BAGP) models estimate the difference between a person's predicted brain age from neuroimaging data and their chronological age. The resulting brain age gap serves as a compact biomarker of brain health, with recent studies demonstrating its predictive utility for disease progression and severity. However, practical adoption of BAGP models is hindered by their methodological obscurities and limited generalizability across diverse clinical populations. This tutorial article provides an overview of BAGP and introduces a principled framework for this application based on recent advancements in graph signal processing (GSP). In particular, we focus on graph neural networks (GNNs) and introduce the coVariance neural network (VNN), which leverages the anatomical covariance matrices derived from structural MRI. VNNs offer strong theoretical grounding and operational interpretability, enabling robust estimation of brain age gap predictions. By integrating perspectives from GSP, machine learning, and network neuroscience, this work clarifies the path forward for reliable and interpretable BAGP models and outlines future research directions in personalized medicine.
Paper Structure (10 sections, 2 theorems, 15 equations, 3 figures, 2 tables)

This paper contains 10 sections, 2 theorems, 15 equations, 3 figures, 2 tables.

Table of Contents

  1. Brain Age Gap Prediction Models
  2. GSP Foundations for Neuroimaging Data Analysis
  3. Towards Explainable Brain Age Gap Prediction from Structural MRI
  4. Conclusions and Future Outlook
  5. Acknowledgement
  6. Biographies

Key Result

Theorem 1

Consider a random vector ${\mathbf{x}} \in {\mathbb{R}}^{M}$, such that, $\|{\mathbf{x}}\|\leq 1$, and its corresponding ensemble covariance matrix ${\mathbf{C}} = \mathbb{E}[({\mathbf{x}} - {\mathbb{E}}[{\mathbf{x}}])({\mathbf{x}} - {\mathbb{E}}[{\mathbf{x}}])^{\top}]$. For a sample covariance matr where $\alpha_n$ scales as ${\cal O}(1/n^{1/2-\varepsilon})$ for some $\varepsilon \in(0,1/2)$. Fur

Figures (3)

  • Figure 1: Schematic of brain age gap prediction using ML. (A) Neuroimaging data, formed by T1-weighted structural MRI scans, from a set of healthy individuals are labelled with their respective chronological age. Pre-processing pipelines using standard tools, such as Freesurfer, may be applied to extract relevant features from the MRI scan. A regression model is trained using the extracted features or the raw MRI scans, as preferred. The outputs of the ML model are then corrected for any age biases using an appropriate statistical correction procedure. Note that the age-bias correction is applied after training the regression model. The age-bias corrected outputs form the estimate of the brain age. (B) The trained ML model and its associated age-bias correction module can then be deployed to predict brain age using neuroimaging data pre-processed from a new dataset. The brain age gap is obtained as the difference between the predicted brain age and the chronological age.
  • Figure 2: Performance-driven approaches to $\Delta$-Age prediction prioritize a near-perfect fit on the chronological age of the HC, yet they lack the conceptual or statistical justifications to ensure the relevance of inferred $\Delta$-Age as a biomarker for neurodegeneration.
  • Figure 3: Extracting graph signals and a data-driven graph from structural MRI. Pre-processing of structural MRI yields anatomical features across the brain cortex. These anatomical features have a vector representation ${{\mathbf{x}}}$ of length $M$, each element of which corresponds to a distinct brain region. From a dataset of anatomical features from $n$ individuals, we can estimate the anatomical covariance matrix $\hat{{\mathbf{C}}}_n \in \mathbb{R}^{M\times M}$. Here, the shorthand notation $\bar{{\mathbf{x}}}_i$ stands for $({\mathbf{x}}_i - \bar{{\mathbf{x}}})$ in \ref{['sample_cov']}. The anatomical covariance matrix comprises the graph representation of brain anatomy, with its off-diagonal elements characterizing the correlation between anatomical features associated with different brain regions.

Theorems & Definitions (3)

  • Theorem 1: Stability of coVariance Filters and VNNs (Informal) sihag2022covariance
  • Remark 1: Sparsifying the anatomical covariance matrix in VNNs
  • Theorem 2: Transference of VNNs (Informal) sihagJSTSP