Modelling low-dimensional interacting brain networks reveals organising principle in human cognition

Abstract

The discovery of resting-state networks shifted the focus from the role of local regions in cognitive tasks to the ongoing spontaneous dynamics in global networks. Recently, efforts have been invested to reduce the complexity of brain activity recordings through the application of nonlinear dimensionality reduction algorithms. Here, we investigate how the interaction between these networks emerges as an organising principle in human cognition. We combine deep variational autoencoders with computational modelling to construct a dynamical model of brain networks fitted to the whole-brain dynamics measured with functional magnetic resonance imaging (fMRI). Crucially, this allows us to infer the interaction between these networks in resting state and seven different cognitive tasks by determining the effective functional connectivity between networks. We found a high flexible reconfiguration of task-driven network interaction patterns and we demonstrate that this reconfiguration can be used to classify different cognitive tasks. Importantly, compared with using all the nodes in a parcellation, we obtain better results by modelling the dynamics of interacting networks in both model and classification performance. These findings show the key causal role of manifolds as a fundamental organising principle of brain function, providing evidence that interacting networks are the computational engines' brain during cognitive tasks.

Keywords: Human cognition; Low-dimensional manifold; Nonequilibrium dynamics; Whole-brain modelling.

Figure 1.

Overview of the pipeline. (A) We trained a variational autoencoder (VAE) using the parcellation with N = 62 brain regions, which consists of the same three structures—encoder, latent space, and decoder—including a regularization loss function that gives VAEs generative properties. To model the dynamics of each network in the latent space, we utilized a nonlinear Stuart-Landau oscillator near the bifurcation point, that is, near the critical regime. In order to determine the connections between the latent variables, we employed the GCAT framework developed by Kringelbach and colleagues. We explored the performance of that models at different numbers of latent dimensions from 5 to 12. The result of this procedure is an optimised effective connectivity between the latent variables, Latent Generative Effective Connectivity (LGEC), which captures the departure from detailed balance and generates the nonequilibrium dynamics observed in brain signals. We also created whole-brain models in the source space to fit the same empirical data by repeating the same optimisation procedure for the latent space mode, that is, the inference of the GEC by implementing the GCAT framework. We compared the performance of both models, and we found that models in the latent space more faithfully reproduce the empirical data quantified by the similarity between the empirical and modelled functional connectivity (FC). (B) We trained the VAE with nine dimensions in the latent space using the spatial patterns over time obtained from the combined fMRI data from seven cognitive tasks from the HCP dataset. We investigated which brain regions contributed to each of the nine latent modes previously found in terms of brain functional networks. To do so, we created a set of surrogate signals in the latent space by introducing standard Gaussian noise into one latent dimension while keeping the other eight dimensions devoid of any signal. We repeated by changing the noise signal for each of the nine modes. We then decoded the surrogate latent signals in each case, obtaining the spatial pattern for each mode in the source space. We then associate these patterns with the activation or deactivation of the seven resting-state networks (RSNs) from Yeo. Finally, we assessed whether the interaction of these networks is driven by task activity by building computational models, obtaining a network interaction matrix for each task. We found that these interactions are flexible, showing high variability across tasks, allowing us to train a high-performance classifier based on that information, surpassing the classification capability of models trained in the source space.

Figure 2.

Modelling the low-dimensional brain manifold reconstructs empirical data, outperforming models in the original state space. (A) We generated with a VAE a low-dimensional manifold representation of fMRI data from resting-state healthy participants in the Human Connectome Project (HCP) using a coarse-grained parcellation scheme consisting of 62 regions. To model the dynamics of each latent dimension within the manifold, we employed nonlinear Stuart-Landau oscillators. These oscillators exhibit dynamic characteristics that are governed by a Hopf bifurcation. We constructed a manifold mode model that accurately fit the $F{C}_L^{Emp}$ and $FC{f}_L^{Emp}$, which represent the pairwise Pearson’s correlation between the signals in the latent space and the same signals with the corresponding shifted forward in time, respectively. The results of the performance of the complete framework in terms of reconstruction of ${FC}_S^{Emp}$ and ${FCf}_S^{Emp}$ are quantified as the correlation between these matrices and the ones obtained through decoding the manifold models for each dimension. The maximum correlations are reaching for Latent Dimension 9 and decreasing for both low and high dimension. Importantly, we demonstrated that these models overcome the performance of a model developed in the high-dimensional source space (blue boxplot), not only for the optimal dimensions but also for all latent dimension explored. (B) The hybrid matrices display in the upper diagonal triangle—the ${FC}_S^{Emp}$—and in the lower diagonal triangle—the ${FC}_{LS}^{\mathit{mod}}$—to observe the similarity between both matrices when exploring different latent dimensions ranging from 5 to 12.

Figure 3.

RSNs are formed from the latent networks revealed by VAE. (A) We determined the brain regions associated with each mode. We show as an example the brain renders corresponding to the spatial pattern of the Mode 3 divided in Mode 3 positive and Mode 3 negative, standing for brain regions that present high correlation and anticorrelation to the DMN and Vis network, respectively. (B) We identified each latent mode with a pattern in the source space of 62 brain regions. We associated each spatial patterns with the Yeo7 RSNs by computing the correlation of each pattern with the percentage of belonging of each region to each RSN (* indicates the correlation that are significant after false discovery rate correction). The reference functional brain networks estimated by Yeo and colleagues are named as follows: Visual (VIS), Somatomotor (SM), Dorsal Attention (DA), Ventral Attention (VA), Limbic (Lim), Frontoparietal (FP), and Default Mode (DMN).

Figure 4.

Modelling the low-dimensional manifold network shows a flexible reconfiguration of network interaction during cognitive tasks. (A) We constructed models for each task and evaluated the performance of each model by quantifying the correlation between the ${FC}_S^{Emp}$ and ${FC}_{LS}^{\mathit{mod}}$ in each case. (B) The output of each model was the inferred connectivity between the latent variables, called the LGEC, for each task. We show the average LGEC across 100 models for each case. (C) We computed the total level of connectivity (TC) of each network as the sum of all outcome and income interactions. We found significant differences (Wilcoxon rank-sum test, false discovery rate corrected) in the level of TC for almost all networks (except for N7) in the comparison between resting state and social task. (*** means p < 0.001;* means 0.01 < p < 0.05). (D) The highest interactions between networks (above 0.1) represented as a graph. In the left column is the outcome’s connections, representing how each network drives the others, and in the right column is the income’s connections standing for the impact that the rest of the networks have on each network.

Figure 5.

Interaction between low-dimensional manifold networks that better distinguishes between cognitive tasks. (A) We trained a support vector machine (SVM) using the 100 LGEC generated by modelling the manifold in each task to evaluate whether the information condensed in each matrix is a fingerprint for each task. We also trained the same SVM classifier by using as an input the elements of the ${FC}_S^{Emp}$, elements of the ${FC}_S^{Mod}$, and also the LGEC with scrambled labels. (B) We found that the best classification is reached using the LGEC (0.89 ± 0.01) compared with the ${FC}_S^{Emp}$ (0.76 ± 0.02), the ${FC}_S^{Mod}$ (0.78 ± 0.01), and the scrambled LGEC (0.13 ± 0.03). (C) The confusion matrix obtained for the SVM classifier in the task that distinguishes between eight classes (resting and the seven cognitive states).