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Cognitive activity requires the collective behavior of cortical, thalamic and spinal neurons across large-scale systems of the CNS. This paper provides an illustrated introduction to dynamic models of large-scale brain activity, from the tenets of the underlying theory to challenges, controversies and recent breakthroughs. Movement, cognition and perception arise from the collective activity of neurons within cortical circuits and across large-scale systems of the brain. While the causes of single neuron spikes have been understood for decades, the processes that support collective neural behavior in large-scale cortical systems are less clear and have been at times the subject of contention. Modeling large-scale brain activity with nonlinear dynamical systems theory allows the integration of experimental data from multiple modalities into a common framework that facilitates prediction, testing and possible refutation. This work reviews the core assumptions that underlie this computational approach, the methodological framework that fosters the translation of theory into the laboratory, and the emerging body of supporting evidence. While substantial challenges remain, evidence supports the view that collective, nonlinear dynamics are central to adaptive cortical activity. Likewise, aberrant dynamic processes appear to underlie a number of brain disorders.

Sliding-window correlation is an emerging method for mapping time-resolved, resting-state functional connectivity. To avoid mapping spurious connectivity fluctuations (false positives), Leonardi and Van De Ville recently recommended choosing a window length exceeding the longest wavelength composing the BOLD signal, usually assumed to be ~100s. Here, we provide further statistical support for this rule of thumb. However, we demonstrate that non-stationary fluctuations in functional connectivity can in theory be detected with much shorter window lengths (e.g. 40s), while maintaining nominal control of false positives. We find that statistical power is near-maximal for window lengths chosen according to Leonardi and Van De Ville's rule of thumb. Furthermore, we lay some foundations for a parametric test to identify non-stationary fluctuations in functional connectivity, also noting limitations of the sinusoidal model upon which our work, and the work of Leonardi and Van De Ville, is based. Most notably, our analytical results pertain to covariances, as does our statistical test, whereas functional connectivity is more commonly measured using correlations. •We consider window length choice when computing dynamic functional connectivity.•We provide statistical support for Leonardi and Van De Ville's 1/f rule of thumb.•We discuss limitations of Leonardi and Van De Ville's sinusoidal model.•We develop a test to identify non-stationary connectivity fluctuations.

The human brain is a complex, interconnected network par excellence. Accurate and informative mapping of this human connectome has become a central goal of neuroscience. At the heart of this endeavor is the notion that brain connectivity can be abstracted to a graph of nodes, representing neural elements (e.g., neurons, brain regions), linked by edges, representing some measure of structural, functional or causal interaction between nodes. Such a representation brings connectomic data into the realm of graph theory, affording a rich repertoire of mathematical tools and concepts that can be used to characterize diverse anatomical and dynamical properties of brain networks. Although this approach has tremendous potential — and has seen rapid uptake in the neuroimaging community — it also has a number of pitfalls and unresolved challenges which can, if not approached with due caution, undermine the explanatory potential of the endeavor. We review these pitfalls, the prevailing solutions to overcome them, and the challenges at the forefront of the field. •Reviews progress and pitfalls associated with graph analysis of connectomic data•Focuses on issues associated with building an analyzing such graphs•Discusses characteristics of ideal connectomic map•Considers issues associated with accurate node and edge definition•Discusses key issues associated with analyzing and interpreting graph models

Neuronal dynamics display a complex spatiotemporal structure involving the precise, context-dependent coordination of activation patterns across a large number of spatially distributed regions. Functional magnetic resonance imaging (fMRI) has played a central role in demonstrating the nontrivial spatial and topological structure of these interactions, but thus far has been limited in its capacity to study their temporal evolution. Here, using high-resolution resting-state fMRI data obtained from the Human Connectome Project, we mapped time-resolved functional connectivity across the entire brain at a subsecond resolution with the aim of understanding how nonstationary fluctuations in pairwise interactions between regions relate to large-scale topological properties of the human brain. We report evidence for a consistent set of functional connections that show pronounced fluctuations in their strength over time. The most dynamic connections are intermodular, linking elements from topologically separable subsystems, and localize to known hubs of default mode and fronto-parietal systems. We found that spatially distributed regions spontaneously increased, for brief intervals, the efficiency with which they can transfer information, producing temporary, globally efficient network states. Our findings suggest that brain dynamics give rise to variations in complex network properties over time, possibly achieving a balance between efficient information-processing and metabolic expenditure.

The anatomy of the brain necessarily constrains its function, but precisely how remains unclear. The classical and dominant paradigm in neuroscience is that neuronal dynamics are driven by interactions between discrete, functionally specialized cell populations connected by a complex array of axonal fibres 1 – 3 . However, predictions from neural field theory, an established mathematical framework for modelling large-scale brain activity 4 – 6 , suggest that the geometry of the brain may represent a more fundamental constraint on dynamics than complex interregional connectivity 7 , 8 . Here, we confirm these theoretical predictions by analysing human magnetic resonance imaging data acquired under spontaneous and diverse task-evoked conditions. Specifically, we show that cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain’s geometry (that is, its shape) rather than from modes of complex interregional connectivity, as classically assumed. We then use these geometric modes to show that task-evoked activations across over 10,000 brain maps are not confined to focal areas, as widely believed, but instead excite brain-wide modes with wavelengths spanning over 60 mm. Finally, we confirm predictions that the close link between geometry and function is explained by a dominant role for wave-like activity, showing that wave dynamics can reproduce numerous canonical spatiotemporal properties of spontaneous and evoked recordings. Our findings challenge prevailing views and identify a previously underappreciated role of geometry in shaping function, as predicted by a unifying and physically principled model of brain-wide dynamics. Cortical and subcortical activity can be parsimoniously understood as resulting from excitations of fundamental, resonant modes of the brain’s geometry rather than from modes of complex interregional connectivity.

Decades of neurobiological research have disclosed the diverse manners in which the response properties of neurons are dynamically modulated to support adaptive cognitive functions. This neuromodulation is achieved through alterations in the biophysical properties of the neuron. However, changes in cognitive function do not arise directly from the modulation of individual neurons, but are mediated by population dynamics in mesoscopic neural ensembles. Understanding this multiscale mapping is an important but nontrivial issue. Here, we bridge these different levels of description by showing how computational models parametrically map classic neuromodulatory processes onto systems-level models of neural activity. The ensuing critical balance of systems-level activity supports perception and action, although our knowledge of this mapping remains incomplete. In this way, quantitative models that link microscale neuronal neuromodulation to systems-level brain function highlight gaps in knowledge and suggest new directions for integrating theoretical and experimental work. Drawing from advances in mathematics and related fields, we show that biophysical models of large-scale neural dynamics can help to bridge the gap between neuromodulation at the cellular scale and mesoscale systems dynamics at the whole-brain level.

Adaptive brain function requires that sensory impressions of the social and natural milieu are dynamically incorporated into intrinsic brain activity. While dynamic switches between brain states have been well characterised in resting state acquisitions, the remodelling of these state transitions by engagement in naturalistic stimuli remains poorly understood. Here, we show that the temporal dynamics of brain states, as measured in fMRI, are reshaped from predominantly bistable transitions between two relatively indistinct states at rest, toward a sequence of well-defined functional states during movie viewing whose transitions are temporally aligned to specific features of the movie. The expression of these brain states covaries with different physiological states and reflects subjectively rated engagement in the movie. In sum, a data-driven decoding of brain states reveals the distinct reshaping of functional network expression and reliable state transitions that accompany the switch from resting state to perceptual immersion in an ecologically valid sensory experience. The transition from resting to perceiving one’s milieu requires a fundamental reorganization of brain activity. Here, the authors show how a fundamental reshaping of brain state dynamics supports perceptual engagement in naturalistic stimuli.

Traveling patterns of neuronal activity—brain waves—have been observed across a breadth of neuronal recordings, states of awareness, and species, but their emergence in the human brain lacks a firm understanding. Here we analyze the complex nonlinear dynamics that emerge from modeling large-scale spontaneous neural activity on a whole-brain network derived from human tractography. We find a rich array of three-dimensional wave patterns, including traveling waves, spiral waves, sources, and sinks. These patterns are metastable, such that multiple spatiotemporal wave patterns are visited in sequence. Transitions between states correspond to reconfigurations of underlying phase flows, characterized by nonlinear instabilities. These metastable dynamics accord with empirical data from multiple imaging modalities, including electrical waves in cortical tissue, sequential spatiotemporal patterns in resting-state MEG data, and large-scale waves in human electrocorticography. By moving the study of functional networks from a spatially static to an inherently dynamic (wave-like) frame, our work unifies apparently diverse phenomena across functional neuroimaging modalities and makes specific predictions for further experimentation. Large-scale brain activity arises from inter-areal interactions determined by the underlying connectivity. Here, the authors develop a whole-brain model based on connectivity data that captures activity patterns such as cortical waves and metastability, relating these to underlying brain anatomy.

Understanding the fundamental mechanisms governing fluctuating oscillations in large-scale cortical circuits is a crucial prelude to a proper knowledge of their role in both adaptive and pathological cortical processes. Neuroscience research in this area has much to gain from understanding the Kuramoto model, a mathematical model that speaks to the very nature of coupled oscillating processes, and which has elucidated the core mechanisms of a range of biological and physical phenomena. In this paper, we provide a brief introduction to the Kuramoto model in its original, rather abstract, form and then focus on modifications that increase its neurobiological plausibility by incorporating topological properties of local cortical connectivity. The extended model elicits elaborate spatial patterns of synchronous oscillations that exhibit persistent dynamical instabilities reminiscent of cortical activity. We review how the Kuramoto model may be recast from an ordinary differential equation to a population level description using the nonlinear Fokker-Planck equation. We argue that such formulations are able to provide a mechanistic and unifying explanation of oscillatory phenomena in the human cortex, such as fluctuating beta oscillations, and their relationship to basic computational processes including multistability, criticality, and information capacity.

Lesions of anatomical brain networks result in functional disturbances of brain systems and behavior which depend sensitively, often unpredictably, on the lesion site. The availability of whole-brain maps of structural connections within the human cerebrum and our increased understanding of the physiology and large-scale dynamics of cortical networks allow us to investigate the functional consequences of focal brain lesions in a computational model. We simulate the dynamic effects of lesions placed in different regions of the cerebral cortex by recording changes in the pattern of endogenous (\"resting-state\") neural activity. We find that lesions produce specific patterns of altered functional connectivity among distant regions of cortex, often affecting both cortical hemispheres. The magnitude of these dynamic effects depends on the lesion location and is partly predicted by structural network properties of the lesion site. In the model, lesions along the cortical midline and in the vicinity of the temporo-parietal junction result in large and widely distributed changes in functional connectivity, while lesions of primary sensory or motor regions remain more localized. The model suggests that dynamic lesion effects can be predicted on the basis of specific network measures of structural brain networks and that these effects may be related to known behavioral and cognitive consequences of brain lesions.