Distance Correlation-Based Brain Functional Connectivity Estimation and Non-Convex Multi-Task Learning for Developmental fMRI Studies

Abstract

Objective: Resting-state functional magnetic resonance imaging (rs-fMRI)-derived functional connectivity (FC) patterns have been extensively used to delineate global functional organization of the human brain in healthy development and neuropsychiatric disorders. In this paper, we investigate how FC in males and females differs in an age prediction framework.

Methods: We first estimate FC between regions-of-interest (ROIs) using distance correlation instead of Pearson's correlation. Distance correlation, as a multivariate statistical method, explores spatial relations of voxel-wise time courses within individual ROIs and measures both linear and nonlinear dependence, capturing more complex between-ROI interactions. Then, we propose a novel non-convex multi-task learning (NC-MTL) model to study age-related gender differences in FC, where age prediction for each gender group is viewed as one task, and a composite regularizer with a combination of the non-convex l_2,1-2 and l_1-2 terms is introduced for selecting both common and task-specific features.

Results and conclusion: We validate the effectiveness of our NC-MTL model with distance correlation-based FC derived from rs-fMRI for predicting ages of both genders. The experimental results on the Philadelphia Neurodevelopmental Cohort demonstrate that our NC-MTL model outperforms several other competing MTL models in age prediction. We also compare the age prediction performance of our NC-MTL model using FC estimated by Pearson's correlation and distance correlation, which shows that distance correlation-based FC is more discriminative for age prediction than Pearson's correlation-based FC.

Significance: This paper presents a novel framework for functional connectome developmental studies, characterizing developmental gender differences in FC patterns.

Fig. 1:

An illustration of the difference between dCor-based FC and pCor-based FC. At the top, each blue dot denotes an ROI; in the middle, each heatmap shows all voxel-wise time courses within the corresponding ROI; at the bottom, each line plot represents an ROI-wise time course calculated by averaging all voxel-wise time courses within the corresponding ROI.

Fig. 2:

An illustration of the proposed NC-MTL model in (8). The left-hand side shows the input datasets ${\left\{X_i,y_i\right\}}_{i=1}^M$, and the right-hand side shows the sparsity pattern of the learned weight matrix W.

Fig. 3:

Comparison of the rmse performance of all five MTL models, where box plots show the rmse results with the error bars representing the 25-th and 75-th percentiles, respectively, and the mean values are indicated by •.

Fig. 4:

(a) The ground-truth weight matrix $W\in {ℝ}^{100\times 10}$. (b)-(f) The average of the learned weight matrices over all runs of CV for each of the five MTL models (i.e., MTL_I, MTL_II, MTL_III, MTL_IV, NC-MTL), respectively.

Fig. 5:

Comparison of the rmse performance of all five MTL models with respect to different numbers of features, i.e., d = 500, 1000, 1500.

Fig. 6:

The Power atlas with an a priori assignment of ROIs to different functional modules. ROIs of the same color belong to the same module and ROIs’ colors indicate module memberships, where ROIs assigned to 10 key functional modules were visualized and the others (assigned to cerebellum and unsorted) not.

Fig. 7:

The average FC patterns estimated by dCor (upper triangle of a matrix heatmap) and pCor (lower triangle) across subjects for each gender group.

Fig. 8:

The prediction performance in terms of both corr and rmse for each gender group. Blue box plots exhibit corr results (the higher the better) for the left y-axis, and magenta box plots exhibit rmse results (the lower the better) for the right y-axis, where • and * indicate the corresponding mean values.

Fig. 9:

The two scatter plots illustrate the relationships between the predicted and observed ages of males and females, respectively, where the predicted ages were obtained by the proposed NC-MTL model. Each green dot represents one subject. Each red solid line represents the best-fit line of the green dots, and its 95% confidence interval is indicated by two dashed lines.

Fig. 10:

The corr results of both genders based on our NC-MTL model with different values of α and β.

Fig. 11:

The visualization of the 150 most discriminative age-related functional connections between and within the 10 functional modules for each gender group, i.e., (a)-(b) males and (c)-(d) females. The left are brain plots showing sagittal views of the functional graph in anatomical space, where node colors indicate module membership. The right are matrix plots showing the total numbers of within- and between-module connections.

Fig. 12:

The age prediction performance of the proposed NC-MTL model in terms of both corr and rmse for each gender group. Blue box plots exhibit corr results for the left y-axis, and magenta box plots exhibit rmse results for the right y-axis, where • and * indicate the corresponding mean values, the 1st, 2nd, 5th, and 6th box plots are for females, and the others are for males.