Revisiting Nonlinear Functional Brain Co-activations: Directed, Dynamic, and Delayed

Abstract

The center stage of neuro-imaging is currently occupied by studies of functional correlations between brain regions. These correlations define the brain functional networks, which are the most frequently used framework to represent and interpret a variety of experimental findings. In the previous study, we first demonstrated that the relatively stronger blood oxygenated level dependent (BOLD) activations contain most of the information relevant to understand functional connectivity, and subsequent work confirmed that a large compression of the original signals can be obtained without significant loss of information. In this study, we revisit the correlation properties of these epochs to define a measure of nonlinear dynamic directed functional connectivity (nldFC) across regions of interest. We show that the proposed metric provides at once, without extensive numerical complications, directed information of the functional correlations, as well as a measure of temporal lags across regions, overall offering a different and complementary perspective in the analysis of brain co-activation patterns. In this study, we provide further details for the computations of these measures and for a proof of concept based on replicating existing results from an Autistic Syndrome database, and discuss the main features and advantages of the proposed strategy for the study of brain functional correlations.

Non-linear Functional Brain Co-activations in Short-Term Memory Distortion Tasks

“…The precise interpretation of an ROI’s role following such statements as “ higher correlation with an ROI predicts fewer correct responses” is thus contingent on that delay. Incorporating delays into the non-linear correlation analysis is actually possible, as shown in Cifre et al (2021) . In this study, we provide only a proof of concept of that additional feature, a topic that deserves further investigation.…”

“…In the classical approach (dynamic functional connectivity), one estimates the resting state correlation by calculating some kind of sliding-window linear Pearson correlation between pairs of BOLD time series. In contrast, the method introduced by Tagliazucchi et al (2011 , 2012) and subsequent authors ( Liu and Duyn, 2013 ; Petridou et al, 2013 ; Allan et al, 2015 ; Karahanoğlu and Van De Ville, 2015 ; Cifre et al, 2020 , 2021 ) relies on detecting for a given source BOLD time series the relatively high amplitude activity (“events”) and correlating only these epochs with the other target time series, see Figure 1 . The amplitude threshold, or Heaviside step function, is in fact a very simple non-linear filter (akin to the sigmoid functions used, e.g., as a non-linear activation in artificial neural networks) used for signal denoising.…”

“…The approach is naturally connected to the hemodynamic response function (HRF; Wu et al, 2013 ) and has allowed to demonstrate the correspondence between rest and task BOLD activations ( Petridou et al, 2013 ). Additionally, such a procedure provides the correlations with a straightforward directionality and time-stamps ( Cifre et al, 2021 ). Thanks to these features, we were able to apply the method to the task setting with the series of task stimuli serving as a synthetic source time series, as described below.…”

“…For a finer resolution, a parabolic interpolation of the extremum can be used ( Mitra et al, 2014 ). In the approach by Cifre et al (2021) , which we used, the delay is defined as the time between the peak of each individual BOLD-triggered event (substituted in the task paradigm by the synthetic stimulus HRF convolutions) and the closest BOLD peak irrespective of its size. Given the objective of the present study, we looked for the peaks in the range [0, 9] TRs (viz.…”

“…Following that work, the present correlation approach focuses on the analysis of the brief instances of large-amplitude signals (so-called events); such amplitude thresholding acts as a simple non-linear filter (similarly, to e.g., the effect of using sigmoid activation functions in artificial neural networks), a feature that by design increases the signal-to-noise ratio significantly. This method and its related implementations mentioned above, has been proven effective in analyzing the brain functional connectivity in restingstate conditions (Tagliazucchi et al, 2011(Tagliazucchi et al, , 2012Cifre et al, 2021), where it is essential to identify the most significant events from the spontaneously fluctuating signals. The present study is the first to implement a similar approach to characterize the responses evoked by a task.…”