Functional Connectivity’s Degenerate View of Brain Computation

Brain computation relies on effective interactions between ensembles of neurons. In neuroimaging, measures of functional connectivity (FC) aim at statistically quantifying such interactions, often to study normal or pathological cognition. Their capacity to reflect a meaningful variety of patterns as expected from neural computation in relation to cognitive processes remains debated. The relative weights of time-varying local neurophysiological dynamics versus static structural connectivity (SC) in the generation of FC as measured remains unsettled. Empirical evidence features mixed results: from little to significant FC variability and correlation with cognitive functions, within and between participants. We used a unified approach combining multivariate analysis, bootstrap and computational modeling to characterize the potential variety of patterns of FC and SC both qualitatively and quantitatively. Empirical data and simulations from generative models with different dynamical behaviors demonstrated, largely irrespective of FC metrics, that a linear subspace with dimension one or two could explain much of the variability across patterns of FC. On the contrary, the variability across BOLD time-courses could not be reduced to such a small subspace. FC appeared to strongly reflect SC and to be partly governed by a Gaussian process. The main differences between simulated and empirical data related to limitations of DWI-based SC estimation (and SC itself could then be estimated from FC). Above and beyond the limited dynamical range of the BOLD signal itself, measures of FC may offer a degenerate representation of brain interactions, with limited access to the underlying complexity. They feature an invariant common core, reflecting the channel capacity of the network as conditioned by SC, with a limited, though perhaps meaningful residual variability.Author Summary: The human brain is characterized by both the way its neurons are connected (the anatomy) and the way they emit signals to interact (the dynamics). At the typical scale of measurements, by analogy with the road network, anatomy (the ‘roads’) is expected to remain relatively stable over time and reproducible from person to person, while neuronal dynamics propagating in the network (the ‘traffic’) can be expected to vary widely, both over time and between people. But, paradoxically, patterns of functional connectivity (FC), a convenient proxy to quantify interactions between pairs of brain regions in magnetic resonance imaging (MRI), have been found to be reproducible both within and between subjects across several studies, while other studies, on the contrary, have featured variable FC patterns, often in relation to cognitive processes. We investigate this unsettled issue quantitatively using multivariate statistics and generative models of brain activity. We show, across a range of estimators, that FC offers a degenerate representation of brain interactions and strongly depends on anatomy.