Brain Effective Connectome based on fMRI and DTI Data: Bayesian Causal Learning and Assessment

TL;DR

The paper tackles accurate and reliable brain effective connectome (EC) discovery under limited fMRI temporal resolution and high dimensionality by introducing Bayesian causal frameworks, BGOLEM and BFGES, that leverage DTI-derived priors. It defines the Pseudo False Discovery Rate (PFDR) as a practical accuracy metric and demonstrates that both Bayesian methods achieve higher PFDR and greater test–retest reliability (via Rogers-Tanimoto index) than traditional GOLEM/FGES on synthetic, hybrid, and HCP data. The methods integrate prior structure through $P(G)$, with BGOLEM modifying the sparsity penalty and BFGES altering the decomposable score to favor graphs consistent with structural connectivity. Empirically, ECs learned with these Bayesian priors show improved accuracy and reproducibility, highlighting the value of multimodal priors for advancing our understanding of brain organization and function.

Abstract

Neuroscientific studies aim to find an accurate and reliable brain Effective Connectome (EC). Although current EC discovery methods have contributed to our understanding of brain organization, their performances are severely constrained by the short sample size and poor temporal resolution of fMRI data, and high dimensionality of the brain connectome. By leveraging the DTI data as prior knowledge, we introduce two Bayesian causal discovery frameworks -- the Bayesian GOLEM (BGOLEM) and Bayesian FGES (BFGES) methods -- that offer significantly more accurate and reliable ECs and address the shortcomings of the existing causal discovery methods in discovering ECs based on only fMRI data. Through a series of simulation studies on synthetic and hybrid (DTI of the Human Connectome Project (HCP) subjects and synthetic fMRI) data, we demonstrate the effectiveness of the proposed methods in discovering EC. To numerically assess the improvement in the accuracy of ECs with our method on empirical data, we first introduce the Pseudo False Discovery Rate (PFDR) as a new computational accuracy metric for causal discovery in the brain. We show that our Bayesian methods achieve higher accuracy than traditional methods on HCP data. Additionally, we measure the reliability of discovered ECs using the Rogers-Tanimoto index for test-retest data and show that our Bayesian methods provide significantly more reproducible ECs than traditional methods. Overall, our study's numerical and graphical results highlight the potential for these frameworks to advance our understanding of brain function and organization significantly.

Figures (8)

• Figure 1: Steps in Bayesian causal learning and Assessment of effective connectomes. Deriving effective connectomes for both hybrid and empirical data with introduced Bayesian causal frameworks, computing the PFDR value and performing reliability tests.
• Figure 2: The mean FDR and the mean Percent of Total Errors for graphs with different number edges. (a): The mean FDR for the FGES and BFGES methods (b): The mean Percent of Total Errors for the FGES and BFGES methods
• Figure 3: The mean FDR and the mean Percent of Total Errors for graphs with different number edges. (a): The mean FDR for the GOLEM and BGOLEM methods (b): The mean Percent of Total Errors for the GOLEM and BGOLEM methods
• Figure 4: Dependency of the PFDR and FDR metrics for ECs derived with Bayesian and Non-Bayesian methods on hybrid data with 164 nodes. (a): The correlation coefficients ($R$) of PFDR and FDR values for the ECs of the GOLEM and BGOLEM are $98.9\%$ and $99.9\%$, respectively (b): The correlation coefficients of PFDR and FDR values for FGES and BFGES are $80.9\%$ and $97.7\%$, respectively.
• Figure 5: Comparison of Structural connectome, functional connectome and ECs discovered with the FGES, BFGES, GOLEM and BGOLEM methods. The first row compares the symmetry of structural connectomes, correlation-based, and ECs and edges between two hemispheres of each connectome. The second row, compares the results of ECs discovered with $\textrm{SC}_\textrm{P}$, functional connectome, and ECs of non-Bayesian methods.