Beyond Pairwise: Examining Higher-Order Interactions (HOI) to Decode Brain Dynamics and Function

Traditional models of brain activity typically represent interactions between regions as pairwise connections, which limits the understanding of more complex interactions involving multiple regions simultaneously. To address this limitation, we introduce a novel topologically grounded framework that reconstructs the temporal evolution of higher-order interactions (HOIs) from fMRI data, capturing dependencies among three or more regions. By analysing fMRI data from the 100 unrelated subjects Human Connectome Project, we show that higher-order models, unlike traditional pairwise approaches, significantly enhance task decoding, improve the individual identification of unimodal and transmodal functional subsystems, and strengthen the associations between brain activity and behavior. Overall, our approach sheds new light on the higher-order organization of fMRI time series, improving the characterization of dynamic group dependencies in rest and tasks, and revealing a vast space of unexplored structures within human functional brain data, which may remain hidden when using traditional pairwise approaches.  

The functional connectivity network, constructed from pairwise dependencies between brain regions, is a well-established tool for studying the brain. While powerful, functional connectivity is limited by its inability to capture interactions between more than two brain regions (higher-order interactions). In this talk, I will explore how multivariate information theory reveals higher-order dependencies in the human brain and allows us to identify two types of types of interactions: redundant and synergistic. I will present results from applying the O-information [1] to resting state fMRI data, showing that both functional connectivity and canonical functional systems capture primarily redundant interactions. However, subsystems dominated by synergistic interactions are widespread in the cortex. In contrast to redundant subsystems, highly synergistic subsystems are typically composed of brain regions from multiple functional systems. Like functional connectivity, redundant and synergistic interactions are time-varying. I will show results indicating that the same set of brain regions can become redundant and synergistic throughout the length of a scan, and that the location of the most strongly redundant and most strongly synergistic interaction changes in time but exhibits notable recurrence. As a whole, my talk will argue that higher-order interactions in the brain are an under-explored space that, made accessible with the tools of multivariate information theory, may offer novel insights. 

Edge time series are increasingly used in brain imaging to study the node functional connectivity (nFC) dynamics at the finest temporal resolution while avoiding sliding windows. Here, we lay the mathematical foundations for the edge-centric analysis of neuroimaging time series, explaining why a few high-amplitude cofluctuations drive the nFC across datasets. Our exposition also constitutes a critique of the existing edge-centric studies, showing that their main findings can be derived from the nFC under a static null hypothesis that disregards temporal correlations. Testing the analytic predictions on functional MRI data from the Human Connectome Project confirms that the nFC can explain most variation in the edge FC matrix, the edge communities, the large cofluctuations, and the corresponding spatial patterns. We encourage the use of dynamic measures in future research, which exploit the temporal structure of the edge time series and cannot be replicated by static null models. 

In order to better understand the dynamic interactions between brain structures that underlie our thoughts, the tools and data we use must reflect the complexity of this system. We have developed a computationally tractable model, Timecorr, to estimate higher-order correlations that combines a technique to calculate dynamic correlations with dimensionality reduction. We have applied this model to explore dynamic higher-order correlations in brain data collected using a naturalistic paradigm at varying levels of engagement. In an fMRI dataset collected by Simony et al. (2016), participants listened to a story presented in three conditions: intact, paragraph-scrambled, and word-scrambled. We used a subset of the data to train across-participant classifiers to decode listening times, and we trained the classifiers using iteratively increasing orders of dynamic correlation which we inferred using our method. By training decoding models on different types of neural features, we can better understand which specific aspects of the neural activity patterns are informative, and important for higher order cognition.
We found that classifiers trained to decode from high-order dynamic correlations yield the best performance on data collected as participants listened to the (unscrambled) story. In contrast, classifiers trained to decode data from scrambled versions of the story yielded the best performance when they were trained using first-order dynamic correlations or non-correlational activity patterns. Our results suggest that as our thoughts become more complex, they are reflected in higher-order patterns of dynamic network interactions throughout the brain. We have enhanced and expanded on this work, using other fMRI datasets from the ‘Narratives’ collection Nastase et al. (2020), and diving deeper into the choices of dimensionality reduction and hyperparameters across these datasets. By exploring these parameters across these datasets, we can evaluate the similarities in task-evoked brain responses and explore the level of interactions that support complex thought.