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Interpretable Spatio-Temporal Embedding for Brain Structural-Effective Network with Ordinary Differential Equation

Haoteng Tang, Guodong Liu, Siyuan Dai, Kai Ye, Kun Zhao, Wenlu Wang, Carl Yang, Lifang He, Alex Leow, Paul Thompson, Heng Huang, Liang Zhan

TL;DR

This work addresses the limitation of synchronous, undirected brain-connectivity analyses by modeling time-varying, directional influences between brain regions. It introduces STE-ODE, a framework that combines a directed graph embedding layer constrained by structural connectivity with an Ordinary Differential Equation (ODE) to capture spatial-temporal brain dynamics, enabling predictions of clinical phenotypes and interpretable identification of important connectomes. Evaluations on the HCP and OASIS datasets demonstrate superior predictive performance over static and dynamic baselines and reveal neurobiologically meaningful connectomes linked to Alzheimer's disease and depression. The approach integrates Dynamic Causal Modeling, interpretable edge-weighting, and ODE-based dynamics to advance brain network modeling and potential biomarker discovery.

Abstract

The MRI-derived brain network serves as a pivotal instrument in elucidating both the structural and functional aspects of the brain, encompassing the ramifications of diseases and developmental processes. However, prevailing methodologies, often focusing on synchronous BOLD signals from functional MRI (fMRI), may not capture directional influences among brain regions and rarely tackle temporal functional dynamics. In this study, we first construct the brain-effective network via the dynamic causal model. Subsequently, we introduce an interpretable graph learning framework termed Spatio-Temporal Embedding ODE (STE-ODE). This framework incorporates specifically designed directed node embedding layers, aiming at capturing the dynamic interplay between structural and effective networks via an ordinary differential equation (ODE) model, which characterizes spatial-temporal brain dynamics. Our framework is validated on several clinical phenotype prediction tasks using two independent publicly available datasets (HCP and OASIS). The experimental results clearly demonstrate the advantages of our model compared to several state-of-the-art methods.

Interpretable Spatio-Temporal Embedding for Brain Structural-Effective Network with Ordinary Differential Equation

TL;DR

This work addresses the limitation of synchronous, undirected brain-connectivity analyses by modeling time-varying, directional influences between brain regions. It introduces STE-ODE, a framework that combines a directed graph embedding layer constrained by structural connectivity with an Ordinary Differential Equation (ODE) to capture spatial-temporal brain dynamics, enabling predictions of clinical phenotypes and interpretable identification of important connectomes. Evaluations on the HCP and OASIS datasets demonstrate superior predictive performance over static and dynamic baselines and reveal neurobiologically meaningful connectomes linked to Alzheimer's disease and depression. The approach integrates Dynamic Causal Modeling, interpretable edge-weighting, and ODE-based dynamics to advance brain network modeling and potential biomarker discovery.

Abstract

The MRI-derived brain network serves as a pivotal instrument in elucidating both the structural and functional aspects of the brain, encompassing the ramifications of diseases and developmental processes. However, prevailing methodologies, often focusing on synchronous BOLD signals from functional MRI (fMRI), may not capture directional influences among brain regions and rarely tackle temporal functional dynamics. In this study, we first construct the brain-effective network via the dynamic causal model. Subsequently, we introduce an interpretable graph learning framework termed Spatio-Temporal Embedding ODE (STE-ODE). This framework incorporates specifically designed directed node embedding layers, aiming at capturing the dynamic interplay between structural and effective networks via an ordinary differential equation (ODE) model, which characterizes spatial-temporal brain dynamics. Our framework is validated on several clinical phenotype prediction tasks using two independent publicly available datasets (HCP and OASIS). The experimental results clearly demonstrate the advantages of our model compared to several state-of-the-art methods.
Paper Structure (13 sections, 8 equations, 3 figures, 2 tables)

This paper contains 13 sections, 8 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Preliminaries
  4. Construction of Brain Effective Network
  5. Interpretable Structural-Effective Network Embedding
  6. Spatio-Temporal Embedding with ODE
  7. STE-ODE Framework for Brain Network Predictions
  8. Experiments
  9. Dataset Description and Preprocessing
  10. Implementation Details and Experimental Setup
  11. Brain Network Predictions
  12. Biological Insights and Model Interpretability
  13. Conclusion

Figures (3)

  • Figure 1: (a) describes the construction of brain effective networks from the BOLD signals. (b) is the directed graph embedding layer for structural and effective networks. (c) presents the STE-ODE framework for different clinical prediction tasks.
  • Figure 2: $\lambda$ parameter analysis. The optimal points are encompassed by black boxes.
  • Figure 3: (a) illustrates the importance of various effective connectomes (i.e., $|\gamma|$) for disease classification and DSM-Depr regression, with the most crucial connectomes highlighted in bold red. (b) visualizes the brain dynamics of the identified effective connectomes during an fMRI scan period, where colors tending towards red indicate large values. (c) quantifies the change in the average strength of identified connectomes during an fMRI scan period.