Unraveling Alzheimer's Disease: Investigating Dynamic Functional Connectivity in the Default Mode Network through DCC-GARCH Modeling

Abstract

Alzheimer's disease (AD) has a prolonged latent phase. Sensitive biomarkers of amyloid beta ( $A\beta$ ), in the absence of clinical symptoms, offer opportunities for early detection and identification of patients at risk. Current $A\beta$ biomarkers, such as CSF and PET biomarkers, are effective but face practical limitations due to high cost and limited availability. Recent blood plasma biomarkers, though accessible, still incur high costs and lack physiological significance in the Alzheimer's process. This study explores the potential of brain functional connectivity (FC) alterations associated with AD pathology as a non-invasive avenue for $A\beta$ detection. While current stationary FC measurements lack sensitivity at the single-subject level, our investigation focuses on dynamic FC using resting-state functional MRI (rs-fMRI) and introduces the Generalized Auto-Regressive Conditional Heteroscedastic Dynamic Conditional Correlation (DCC-GARCH) model. Our findings demonstrate the superior sensitivity of DCC-GARCH to CSF $A\beta$ status, and offer key insights into dynamic functional connectivity analysis in AD.

Keywords: Alzheimer’s Disease; Amyloid Beta Biomarker; Default Mode Network; Dynamic Brain Functional Connectivity; Resting-state fMRI.

Figure 1:

Flow chart of the analysis procedure.

Figure 2:

Illustration of the simulated dynamic profile of correlations with respect to different $\alpha$ and $\beta$ values. We simulate three sets of time series observations for a 3-node network based on DCC-GARCH model. Each set has different parameter values for $(\alpha ,\beta )$. The left side plots show the simulated signals from three nodes, and the right side plots show the dynamic profile of the corresponding pairwise correlations.

Figure 3:

The dynamic correlation profile obtained via the sliding window approach, using the raw data and the whitened data, for an example subject. We visualize the correlation profile of four chosen brain node pairs. Correlations are computed using the rectangular window function at window length = 50s, 100s, 200s, 400s. The dashed lines represent the standard static correlation coefficient for each node pair, computed using data from the full time course.

Figure 4:

The dynamic correlation profile of three example subjects, using the whitened data, based on the sliding window approaches (top three rows) and the DCC-GARCH approach (last row). The sliding window approach applies the rectangular window function at window length = 50s, 100s, 200s. We visualize the correlation profile of four chosen brain node pairs. The dashed lines represent the standard static correlation coefficient for each node pair, computed using data from the full time course.

Figure 5:

(a) Boxplots of estimated DCC-GARCH $\alpha$ and $\beta$ parameters calculated using the proposed method for all subjects. Each dot represents the parameter estimate for a single subject. Subjects were divided into two groups based on their CSF $A\beta$ profile: 1) AD patients (CSF $A\beta 42/A\beta 40<0.11$), and 2) control (CSF $A\beta 42/A\beta 40\ge 0.11$). p-values of two-sample t-test for group differences in parameter estimates are reported. (b) Boxplots of average stationary functional connectivity in DMN, calculated using dual-regression ICA analysis.

Figure 6:

ROC curves and AUC for identifying AD patients based on estimated DCC-GARCH parameters. The ‘DCC $\alpha$ only’ and ‘DCC $\beta$ only’ curves are based on thresholding the estimated $\alpha$ or $\beta$ values separately, the ‘DCC Combined’ ROC curve is yielded from using $\alpha$ and $\beta$ values via the SVM approach. The ‘Dual-Regression Analysis’ ROC curve is based on average DMN strength computed from dual-regression ICA analysis.