Abstract
Functional connectivity analyses are typically based on matrices containing bivariate measures of covariability, such as correlations. Although this has been a fruitful approach, it may not be the optimal strategy to fully explore the complex associations underlying brain activity. Here, we propose extending connectivity to multivariate functions relating to the temporal dynamics of a region with the rest of the brain. The main technical challenges of such an approach are multidimensionality and its associated risk of overfitting or even the non-uniqueness of model solutions. To minimize these risks, and as an alternative to the more common dimensionality reduction methods, we propose using two regularized multivariate connectivity models. On the one hand, simple linear functions of all brain nodes were fitted with ridge regression. On the other hand, a more flexible approach to avoid linearity and additivity assumptions was implemented through random forest regression. Similarities and differences between both methods and with simple averages of bivariate correlations (i.e., weighted global brain connectivity) were evaluated on a resting state sample of N = 173 healthy subjects. Results revealed distinct connectivity patterns from the two proposed methods, which were especially relevant in the age-related analyses where both ridge and random forest regressions showed significant patterns of age-related disconnection, almost completely absent from the much less sensitive global brain connectivity maps. On the other hand, the greater flexibility provided by the random forest algorithm allowed detecting sex-specific differences. The generic framework of multivariate connectivity implemented here may be easily extended to other types of regularized models.
Highlights
MATERIALS AND METHODSMatrices based on correlations or similar bivariate measures have frequently been the starting point of many functional connectivity analyses (Raichle, 2011; Bassett and Bullmore, 2017)
As it can be appreciated from the figure, there are clear commonalities among the three maps, including the low connectivity levels in ventral and subcortical structures and the high connectivity values in posterior cingulate and medial frontal structures. As it can be appreciated from the scatterplots in this figure, there is a clear linear relation between RIDGEC and global brain connectivity (GBC) and between random forest connectivity (RANFORC) and GBC, both regularized maps contain differential connectivity patterns not provided by the averages of bivariate correlations
Values from ridge regression coefficients and variable importances are compared with bivariate correlations in models fit for an regions of interest (ROIs) in the right dorsolateral prefrontal cortex (Figure 3) and an ROI in the left posterior cingulate (Figure 4)
Summary
Matrices based on correlations or similar bivariate measures have frequently been the starting point of many functional connectivity analyses (Raichle, 2011; Bassett and Bullmore, 2017). We propose extending functional connectivity analyses by fitting multivariate functions that relate the temporal dynamics of a region with the rest of the brain This is carried out by means of two different regularization methods. Fitting Eq 3 to fMRI data using standard methods (i.e., ordinary least squares) will, if even possible, lead to unreliable estimates, as N (the number of regions) will be similar or even larger than the number of available time points (p), causing either overfitting or leading to the non-uniqueness of solutions Such limitations, can be overcome by setting a restriction on the parameter estimates (i.e., regularizing). In all analyses a False Discovery Rate (FDR) correction was applied to account for multiple comparisons
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