Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity

Abstract

An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart–Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.

On the edge of criticality: strength-dependent perturbation unveils delicate balance between fluctuation and oscillation in brain dynamics

“…Where η i ( t ) is an additive Gaussian noise with standard deviation ν and G is a factor that scales the coupling strength equally for all the nodes. This whole-brain model has been shown to reproduce essential features of brain dynamics observed in different neuroimaging recordings ( 16, 37 ) in the subcritical regime (i.e., a <0) and no shearing effect (β=0).…”

“…More generally, the Hopf whole-brain model integrates anatomical connections (32)(33)(34) with local dynamics to explain and fit the emergence of global dynamics in empirical data (16,(35)(36)(37)(38) (Figure 1D).…”

“…The Hopf whole-brain model can fit the complex spatiotemporal brain dynamics in terms of both functional connectivity and turbulence ( Figure 1C ). More generally, the Hopf whole-brain model integrates anatomical connections (Hagmann et al, 2007, 2010; Johansen-Berg & Rushworth, 2009) with local dynamics to explain and fit the emergence of global dynamics in empirical data (Deco, Cabral, et al, 2017; Deco, Kringelbach, et al, 2017; Freyer et al, 2012; Ipiña et al, 2020; Piccinini et al, 2021) ( Figure 1D ). For decades, brain signals have been recorded with a plethora of different techniques showing them to be combinations of at least three different regimes: noise, fluctuating, and oscillatory.…”

“…On the one hand, amplitude turbulence that takes place in a system of oscillators has been studied exclusively in the supercritical regime of the Stuart-Landau coupled oscillators ( 43, 58 ). On the other, during the last years, a set of papers have demonstrated that the Hopf whole-brain model fit the neuroimaging brain data when used the subcritical regime on the edge of the bifurcation ( 16, 19, 37 ). In particular, Deco and Kringelbach have demonstrated that this model in the subcritical regime is good at fitting the empirical level of turbulence and the functional connectivity at the same time ( 10 ).…”

“…The level of metastability measure was implemented in previous research to characterize the dynamics of the fluctuations in brain activity in different brain states Jobst et al, 2017;Piccinini et al, 2021). Briefly, the metastability denotes the variability of the global synchronization as measured by the Kuramoto order parameter (gKoP), gR(t),:…”