A Bayesian Framework for Quantifying Association Between Functional and Structural Data in Neuroimaging

Abstract

Structural and functional neuroimaging modalities provide complementary windows into brain organization: structural imaging characterizes neural tissue anatomy and microstructure, while functional imaging captures dynamic patterns of neural activity and connectivity. Together, they offer a more complete picture than either alone. Recent multimodal neuroimaging work has focused on joint modeling of structural and functional data, often assuming a strong association between them to improve prediction and interpretability. However, relatively little attention has been given to developing statistically principled frameworks for formally testing hypotheses about these associations. Existing approaches typically rely on simple correlation-based measures or heuristic integration strategies, which may fail to capture the complex dependencies inherent in neuroimaging data, particularly when functional data are represented as brain networks and structural data as region-specific anatomical measures. We address this gap by developing an explicit Bayesian hypothesis testing framework for quantifying associations between structural and functional neuroimaging data. Our approach constructs functional brain networks from fMRI data, then integrates them with structural measurements through a hierarchical Bayesian model. The Bayesian formulation naturally accommodates two types of datasets with different structures, incorporates prior knowledge, and yields full posterior uncertainty quantification. Through extensive empirical studies, we demonstrate that the proposed method achieves excellent performance in detecting associations under a wide range of settings, including varying signal-to-noise ratios, different numbers of brain regions, and diverse sets of structural imaging measures.

Figures (8)

• Figure 1: Overview of the proposed Bayesian framework. Functional MRI time series are summarized as functional connectivity networks with edges $a_{i,v,v'}$ (connecting ROIs $\mathcal{R}_v$ and $\mathcal{R}_{v'}$), and structural MRI data provide ROI-wise structural measures $y_{i,v,k}$ at ROI $\mathcal{R}_v$. Both modalities are linked through shared latent factors $\eta_{i,v}$. A Gibbs sampler is used to obtain the joint posterior over all parameters, from which we derive a global association measure $A_G$ (overall coupling across modalities) and local association measures $A_{L,k}$ (modality-specific structure--function coupling).
• Figure 2: Dotplots present the posterior distributions of $A_G$ across the twelve simulation scenarios under high SNR conditions. On the y-axis, the red point indicates the true value of $A_G$. The layout assigns the first column to scenarios 1–3, the second to 4–6, the third to 7–9, and the fourth to 10–12. Across all scenarios, the posterior probability that $A_G$ matches its true value is close to 1, underscoring the robust accuracy of the proposed method.
• Figure 3: Dotplots present the posterior distributions of $A_G$ across the twelve simulation scenarios under moderate SNR conditions. On the y-axis, the red point indicates the true value of $A_G$. The layout assigns the first column to scenarios 1–3, the second to 4–6, the third to 7–9, and the fourth to 10–12. Across all scenarios, the posterior probability that $A_G$ matches its true value is close to 1, underscoring the robust accuracy of the proposed method.
• Figure 4: Dotplots display the posterior distributions of $A_G$ for each of the twelve simulation scenarios under very low SNR conditions. The red point on the y-axis marks the true value of $A_G$. The arrangement places scenarios 1–3 in the first column, 4–6 in the second, 7–9 in the third, and 10–12 in the fourth. In these low-signal settings, the method has difficulty assigning the highest posterior probability to the true value of $A_G$ when $A_G^*$ is nonzero, that is, as the true strength of association increases, the model’s recovery performance diminishes.
• Figure 5: Structural node-holdout imputation: (a) MSPE, (b) 95% PI Coverage, and (c) 95% PI Length for Joint and Separate models across associated scenarios ($A_G^* > 0$), evaluated under high (blue), moderate (green), and low (orange) SNR levels. Results are averaged over 20 replications.

Theorems & Definitions (2)

• Proposition 1: Invariance of $A_G$ and $A_{L,k}$
• proof