Causal Brain Connectivity: Integrating Granger Directed Graphs in fMRI Analysis Público

Abstract

Functional Magnetic Resonance Imaging (fMRI) has significantly advanced our understanding of human brains by capturing dynamic neural activities, providing basis for causal analysis between brain regions. However, conventional correlationbased analyses often fail to account for the directionality and complexity of neural interactions. We propose an approach that integrates Granger causality with graphbased deep learning to better capture effective connectivity between brain regions. Specifically, we compare three methods: MLP-based approaches on flattened time series, Graph Convolutional Networks (GCNs) using undirected connectivity, and a GCN framework incorporating directed Granger-causal influences into brain graph construction. Through the optimization of Granger parameters such as the lag order via Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), we investigate the impact of different graph construction methods on connectomebased outcome prediction. The directed graph framework demonstrates robustness to hyperparameter variations, while also providing biologically plausible insights into brain functionalities that complement undirected correlation-based graphs. Evaluations on classification and regression tasks using large-scale fMRI datasets reveal that directionality preserves predictive performance while offering additional understanding of information flow within brain networks. These findings emphasize the potential of Granger-causality-informed graphs for robust, nuanced, and causality-aware fMRI analyses.

Table of Contents

Contents 1 Introduction 1 2 Related Works 3 2.1 Graph Neural Networks for Brain Connectome Analysis . . . . . . . . 3 2.2 Functional and Effective Connectivity . . . . . . . . . . . . . . . . . . 4 2.3 Causality and Directionality in Brain Networks . . . . . . . . . . . . 5 3 Problem Formulation 7 4 Method 10 4.1 MLP-Based Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Graph-Based Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2.1 Undirected Graphs: Functional Connectivity. . . . . . . . . . . 11 4.2.2 Directed Graphs: Effective Connectivity. . . . . . . . . . . . . 12 4.3 Rationale for Selecting Granger Causality . . . . . . . . . . . . . . . 14 4.3.1 Overview of Connectivity Inference Methods . . . . . . . . . . 15 5 Experiments 16 5.1 Experimental Settings . . . . . . . . . . . . . . . . . . . . . . . . . . 17 5.2 Model Performance (RQ1) . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2.1 Graph-Based Models Outperform MLP. . . . . . . . . . . . . . 19 5.2.2 Compatibility of Directed and Undirected Graphs. . . . . . . . 19 i 5.3 Hyperparameter Study for Directed Graphs (RQ2) . . . . . . . . . . 20 5.3.1 Effects of Window Size, Step, and Lag on Directed Connectivity Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 5.4 Neurological Insights (RQ3) . . . . . . . . . . . . . . . . . . . . . . . 27 5.4.1 Comparison of Undirected and Directed Connectivity Matrices 27 5.4.2 Consistent Directed Connectivity Patterns in the ABCD Cohort 32 6 Analysis 34 7 Conclusion 37 A Granger Causality Algorithms 39 A.1 Data Partitioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 A.2 VAR Modeling and Hypothesis Testing . . . . . . . . . . . . . . . . . 40 A.3 Aggregation of Test Results . . . . . . . . . . . . . . . . . . . . . . . 41 A.4 Granger Causality Graph Construction . . . . . . . . . . . . . . . . . 42 B Model Description 44 B.1 Multilayer Perceptron (MLP) . . . . . . . . . . . . . . . . . . . . . . 44 B.2 Graph Convolutional Network (GCN) . . . . . . . . . . . . . . . . . . 44 Bibliography 46

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School	Emory College
Department	Quantitative Science
Degree	B.S.
Submission	Honors Thesis
Language	English
Research Field	Computer Science
Palabra Clave	Brain Network GNN NeuroAI Causal Inference Machine Learning fMRI
Committee Chair / Thesis Advisor	DR. CARL YANG, Emory University
Committee Members	DR. WEI JIN, Emory University DR. JINHO CHOI, Emory University

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