Dwelling Quietly in the Rich Club: Brain Network Determinants of Slow Cortical Fluctuations

For more than a century, cerebral cartography has been driven by investigations of structural and morphological properties of the brain across spatial scales and the temporal/functional phenomena that emerge from these underlying features. The next era of brain mapping will be driven by studies that consider both of these components of brain organization simultaneously -- elucidating their interactions and dependencies. Using this guiding principle, we explored the origin of slowly fluctuating patterns of synchronization within the topological core of brain regions known as the rich club, implicated in the regulation of mood and introspection. We find that a constellation of densely interconnected regions that constitute the rich club (including the anterior insula, amygdala, and precuneus) play a central role in promoting a stable, dynamical core of spontaneous activity in the primate cortex. The slow time scales are well matched to the regulation of internal visceral states, corresponding to the somatic correlates of mood and anxiety. In contrast, the topology of the surrounding "feeder" cortical regions show unstable, rapidly fluctuating dynamics likely crucial for fast perceptual processes. We discuss these findings in relation to psychiatric disorders and the future of connectomics.Comment: 35 pages, 6 figure

Fractals in the Nervous System: conceptual Implications for Theoretical Neuroscience

This essay is presented with two principal objectives in mind: first, to document the prevalence of fractals at all levels of the nervous system, giving credence to the notion of their functional relevance; and second, to draw attention to the as yet still unresolved issues of the detailed relationships among power law scaling, self-similarity, and self-organized criticality. As regards criticality, I will document that it has become a pivotal reference point in Neurodynamics. Furthermore, I will emphasize the not yet fully appreciated significance of allometric control processes. For dynamic fractals, I will assemble reasons for attributing to them the capacity to adapt task execution to contextual changes across a range of scales. The final Section consists of general reflections on the implications of the reviewed data, and identifies what appear to be issues of fundamental importance for future research in the rapidly evolving topic of this review

The connected brain: Causality, models and intrinsic dynamics

Recently, there have been several concerted international efforts - the BRAIN initiative, European Human Brain Project and the Human Connectome Project, to name a few - that hope to revolutionize our understanding of the connected brain. Over the past two decades, functional neuroimaging has emerged as the predominant technique in systems neuroscience. This is foreshadowed by an ever increasing number of publications on functional connectivity, causal modeling, connectomics, and multivariate analyses of distributed patterns of brain responses. In this article, we summarize pedagogically the (deep) history of brain mapping. We will highlight the theoretical advances made in the (dynamic) causal modelling of brain function - that may have escaped the wider audience of this article - and provide a brief overview of recent developments and interesting clinical applications. We hope that this article will engage the signal processing community by showcasing the inherently multidisciplinary nature of this important topic and the intriguing questions that are being addressed

Markov Blankets in the Brain

Recent characterisations of self-organising systems depend upon the presence of a Markov blanket: a statistical boundary that mediates the interactions between what is inside of and outside of a system. We leverage this idea to provide an analysis of partitions in neuronal systems. This is applicable to brain architectures at multiple scales, enabling partitions into single neurons, brain regions, and brain-wide networks. This treatment is based upon the canonical micro-circuitry used in empirical studies of effective connectivity, so as to speak directly to practical applications. This depends upon the dynamic coupling between functional units, whose form recapitulates that of a Markov blanket at each level. The nuance afforded by partitioning neural systems in this way highlights certain limitations of modular perspectives of brain function that only consider a single level of description.Comment: 25 pages, 5 figures, 1 table, Glossar

Adiabatic dynamic causal modelling

This technical note introduces adiabatic dynamic causal modelling, a method for inferring slow changes in biophysical parameters that control fluctuations of fast neuronal states. The application domain we have in mind is inferring slow changes in variables (e.g., extracellular ion concentrations or synaptic efficacy) that underlie phase transitions in brain activity (e.g., paroxysmal seizure activity). The scheme is efficient and yet retains a biophysical interpretation, in virtue of being based on established neural mass models that are equipped with a slow dynamic on the parameters (such as synaptic rate constants or effective connectivity). In brief, we use an adiabatic approximation to summarise fast fluctuations in hidden neuronal states (and their expression in sensors) in terms of their second order statistics; namely, their complex cross spectra. This allows one to specify and compare models of slowly changing parameters (using Bayesian model reduction) that generate a sequence of empirical cross spectra of electrophysiological recordings. Crucially, we use the slow fluctuations in the spectral power of neuronal activity as empirical priors on changes in synaptic parameters. This introduces a circular causality, in which synaptic parameters underwrite fast neuronal activity that, in turn, induces activity-dependent plasticity in synaptic parameters. In this foundational paper, we describe the underlying model, establish its face validity using simulations and provide an illustrative application to a chemoconvulsant animal model of seizure activity

Structure-function relation in a stochastic whole-brain model at criticality

Understanding the relation between brain architecture and function is one of the central issues in neuroscience nowadays. In the last few years, important efforts have been devoted to map the large-scale structure of the human cortex, the so-called "connectome". An example is the neuroanatomical connectivity matrix of the entire human brain obtained through MR diffusion tractography. Recent studies proposed a stochastic model built on top of this connectivity matrix that displays a phase-transition and is able to reproduce several aspects of brain functioning when tuned to its critical point. This master thesis is aimed to review recent results on this subject and to get a deeper insight into the model by studying the distribution of the avalanches, the dynamical range and to investigate how the use of simulated connectivity matrices affects the dynamics. Furthermore, a theoretical description of the dynamics is proposed by introducing a master equation in order to understand the nature of the phase transition and the role of stochasticity.ope

Dynamical systems applied to consciousness and brain rhythms in a neural network

This thesis applies the great advances of modern dynamical systems theory (DST) to consciousness. Consciousness, or subjective experience, is faced here in two different ways: from the global dynamics of the human brain and from the integrated information theory (IIT), one of the currently most prestigious theories on consciousness. Before that, a study of a numerical simulation of a network of individual neurons justifies the use of the Lotka-Volterra model for neurons assemblies in both applications. All these proposals are developed following this scheme: • First, summarizing the structure, methods and goal of the thesis. • Second, introducing a general background in neuroscience and the global dynamics of the human brain to better understand those applications. • Third, conducting a study of a numerically simulated network of neurons. This network, which displays brain rhythms, can be employed, among other objectives, to justify the use of the Lotka-Volterra model for applications. • Fourth, summarizing concepts from the mathematical DST such as the global attractor and its informational structure, in addition to its particularization to a Lotka-Volterra system. • Fifth, introducing the new mathematical concepts of model transform and instantaneous parameters that allow the application of simple mathematical models such as Lotka-Volterra to complex empirical systems as the human brain. • Sixth, using the model transform, and specifically the Lotka-Volterra transform, to calculate global attractors and informational structures in global dynamics of the human brain. • Seventh, knowing the probably most prestigious theory on consciousness, the IIT developed by G. Tononi. • Eighth, using informational structures to develop a continuous version of IIT. And ninth, establishing some final conclusions and commenting on new open questions from this work. These nine points of this scheme correspond to the nine chapters of this thesis