Ising-like dynamics in large-scale functional brain networks

Resting state connectivity patterns with near-infrared spectroscopy data of the whole head

Resting state cerebral dynamics has been a useful approach to explore the brain's functional organization. In this study, we employed graph theory to deeply investigate resting state functional connectivity (rs-FC) as measured by near-infrared spectroscopy (NIRS). Our results suggest that network parameters are very similar across time and subjects. We also identified the most frequent connections between brain regions and the main hubs that participate in the spontaneous activity of brain hemodynamics. Similar to previous findings, we verified that symmetrically located brain areas are highly connected. Overall, our results introduce new insights in NIRS-based functional connectivity at rest.

From phenotype to genotype in complex brain networks

Generative models are a popular instrument for illuminating the relationships between the hidden variables driving the growth of a complex network and its final topological characteristics, a process known as the "genotype to phenotype problem". However, the definition of a complete methodology encompassing all stages of the analysis, and in particular the validation of the final model, is still an open problem. We here discuss a framework that allows to quantitatively optimise and validate each step of the model creation process. It is based on the execution of a classification task, and on estimating the additional precision provided by the modelled genotype. This encompasses the three main steps of the model creation, namely the selection of topological features, the optimisation of the parameters of the generative model, and the validation of the obtained results. We provide a minimum requirement for a generative model to be useful, prescribing the function mapping genotype to phenotype to be non-monotonic; and we further show how a previously published model does not fulfil such condition, casting doubts on its fitness for the study of neurological disorders. The generality of such framework guarantees its applicability beyond neuroscience, like the emergence of social or technological networks.

Ordering Dynamics in Neuron Activity Pattern Model: An Insight to Brain Functionality

We study the domain ordering kinetics in d = 2 ferromagnets which corresponds to populated neuron activities with both long-ranged interactions, V(r) ∼ r⁻ⁿ and short-ranged interactions. We present the results from comprehensive Monte Carlo (MC) simulations for the nonconserved Ising model with n ≥ 2, interaction range considering near and far neighbors. Our model results could represent the long-ranged neuron kinetics (n ≤ 4) in consistent with the same dynamical behaviour of short-ranged case (n ≥ 4) at far below and near criticality. We found that emergence of fast and slow kinetics of long and short ranged case could imitate the formation of connections among near and distant neurons. The calculated characteristic length scale in long-ranged interaction is found to be n independent (L(t) ∼ t^1/(n−2)), whereas short-ranged interaction follows L(t) ∼ t^1/2 law and approximately preserve universality in domain kinetics. Further, we did the comparative study of phase ordering near the critical temperature which follows different behaviours of domain ordering near and far critical temperature but follows universal scaling law.

Self-organized dynamical complexity in human wakefulness and sleep: different critical brain-activity feedback for conscious and unconscious states

Criticality reportedly describes brain dynamics. The main critical feature is the presence of scale-free neural avalanches, whose auto-organization is determined by a critical branching ratio of neural-excitation spreading. Other features, directly associated to second-order phase transitions, are: (i) scale-free-network topology of functional connectivity, stemming from suprathreshold pairwise correlations, superimposable, in waking brain activity, with that of ferromagnets at Curie temperature; (ii) temporal long-range memory associated to renewal intermittency driven by abrupt fluctuations in the order parameters, detectable in human brain via spatially distributed phase or amplitude changes in EEG activity. Herein we study intermittent events, extracted from 29 night EEG recordings, including presleep wakefulness and all phases of sleep, where different levels of mentation and consciousness are present. We show that while critical avalanching is unchanged, at least qualitatively, intermittency and functional connectivity, present during conscious phases (wakefulness and REM sleep), break down during both shallow and deep non-REM sleep. We provide a theory for fragmentation-induced intermittency breakdown and suggest that the main difference between conscious and unconscious states resides in the backwards causation, namely on the constraints that the emerging properties at large scale induce to the lower scales. In particular, while in conscious states this backwards causation induces a critical slowing down, preserving spatiotemporal correlations, in dreamless sleep we see a self-organized maintenance of moduli working in parallel. Critical avalanches are still present, and establish transient auto-organization, whose enhanced fluctuations are able to trigger sleep-protecting mechanisms that reinstate parallel activity. The plausible role of critical avalanches in dreamless sleep is to provide a rapid recovery of consciousness, if stimuli are highly arousing.

Lagged and instantaneous dynamical influences related to brain structural connectivity

Contemporary neuroimaging methods can shed light on the basis of human neural and cognitive specializations, with important implications for neuroscience and medicine. Indeed, different MRI acquisitions provide different brain networks at the macroscale; whilst diffusion-weighted MRI (dMRI) provides a structural connectivity (SC) coincident with the bundles of parallel fibers between brain areas, functional MRI (fMRI) accounts for the variations in the blood-oxygenation-level-dependent T2^* signal, providing functional connectivity (FC). Understanding the precise relation between FC and SC, that is, between brain dynamics and structure, is still a challenge for neuroscience. To investigate this problem, we acquired data at rest and built the corresponding SC (with matrix elements corresponding to the fiber number between brain areas) to be compared with FC connectivity matrices obtained by three different methods: directed dependencies by an exploratory version of structural equation modeling (eSEM), linear correlations (C) and partial correlations (PC). We also considered the possibility of using lagged correlations in time series; in particular, we compared a lagged version of eSEM and Granger causality (GC). Our results were two-fold: firstly, eSEM performance in correlating with SC was comparable to those obtained from C and PC, but eSEM (not C, nor PC) provides information about directionality of the functional interactions. Second, interactions on a time scale much smaller than the sampling time, captured by instantaneous connectivity methods, are much more related to SC than slow directed influences captured by the lagged analysis. Indeed the performance in correlating with SC was much worse for GC and for the lagged version of eSEM. We expect these results to supply further insights to the interplay between SC and functional patterns, an important issue in the study of brain physiology and function.

Functional scale-free networks in the two-dimensional Abelian sandpile model

Recently, the similarity of the functional network of the brain and the Ising model was investigated by Chialvo [Nat. Phys. 6, 744 (2010)]. This similarity supports the idea that the brain is a self-organized critical system. In this study we derive a functional network of the two-dimensional Bak-Tang-Wiesenfeld sandpile model as a self-organized critical model, and compare its characteristics with those of the functional network of the brain, obtained from functional magnetic resonance imaging.

From Neural and Social Cooperation to the Global Emergence of Cognition

The recent article (Turalska et al., 2012) discusses the emergence of intelligence via criticality as a consequence of locality breakdown. Herein, we use criticality for the foundation of a novel generation of game theory making the local interaction between players yield long-range effects. We first establish that criticality is not confined to the Ising-like structure of the sociological model of (Turalska et al., 2012), called the decision making model (DMM), through the study of the emergence of altruism using the altruism-selfishness model (ASM). Both models generate criticality, one by imitation of opinion (DMM) and the other by imitation of behavior (ASM). The dynamics of a sociological network 𝒮 influences the behavioral network ℱ through two game theoretic paradigms: (i) the value of altruism; (ii) the benefit of rapid consensus. In (i), the network 𝒮 debates the moral issue of altruism by means of the DMM, while at the level ℱ the individuals operate according to the ASM. The individuals of the level 𝒮, through a weak influence on the individuals of the level ℱ, exert a societal control on ℱ, fitting the principle of complexity management and complexity matching. In (ii), the benefit to society is the rapid attainment of consensus in the 𝒮 level. The agents of the level ℱ operate according to the prisoner's dilemma prescription, with the defectors acting as DMM contrarians at the level 𝒮. The contrarians, acting as the inhibitory links of neural networks, exert on society the same beneficial effect of maintaining the criticality-induced resilience that they generate in neural networks. The conflict between personal and social benefit makes the networks evolve toward criticality. Finally, we show that the theory of this article is compatible with recent discoveries in the burgeoning field of social neuroscience.

A novel brain partition highlights the modular skeleton shared by structure and function

Elucidating the intricate relationship between brain structure and function, both in healthy and pathological conditions, is a key challenge for modern neuroscience. Recent progress in neuroimaging has helped advance our understanding of this important issue, with diffusion images providing information about structural connectivity (SC) and functional magnetic resonance imaging shedding light on resting state functional connectivity (rsFC). Here, we adopt a systems approach, relying on modular hierarchical clustering, to study together SC and rsFC datasets gathered independently from healthy human subjects. Our novel approach allows us to find a common skeleton shared by structure and function from which a new, optimal, brain partition can be extracted. We describe the emerging common structure-function modules (SFMs) in detail and compare them with commonly employed anatomical or functional parcellations. Our results underline the strong correspondence between brain structure and resting-state dynamics as well as the emerging coherent organization of the human brain.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Existence of anticorrelations for local field potentials recorded from mice reared in standard condition and environmental enrichment

In the present paper, we analyze local field potentials (LFPs) recorded from the secondary motor cortex (M2) and primary visual cortex (V1) of freely moving mice reared in environmental enrichment (EE) and standard condition (SC). We focus on the scaling properties of the signals by using an integrated approach combining three different techniques: the Higuchi method, detrended fluctuation analysis, and power spectrum. Each technique provides direct or indirect estimations of the Hurst exponent H and this prevents spurious identification of scaling properties in time-series analysis. It is well known that the power spectrum of an LFP signal scales as 1/f(β) with β>0. Our results indicate the existence of a particular power spectrum scaling law 1/f(β) with β<0 for low frequencies (f<4 Hz) for both SC and EE rearing conditions. This type of scaling behavior is associated to the presence of anticorrelation in the corresponding LFP signals. Moreover, since EE is an experimental protocol based on the enhancement of sensorimotor stimulation, we study the possible effects of EE on the scaling properties of secondary motor cortex (M2) and primary visual cortex (V1). Notably, the difference between Hurst's exponents in EE and SC for individual cortical regions (M2) and (V1) is not statistically significant. On the other hand, using the detrended cross-correlation coefficient, we find that EE significantly reduces the functional coupling between secondary motor cortex (M2) and visual cortex (V1).

Circuit to construct mapping: a mathematical tool for assisting the diagnosis and treatment in major depressive disorder

Major depressive disorder (MDD) is a serious condition with a lifetime prevalence exceeding 16% worldwide. MDD is a heterogeneous disorder that involves multiple behavioral symptoms on the one hand and multiple neuronal circuits on the other hand. In this review, we integrate the literature on cognitive and physiological biomarkers of MDD with the insights derived from mathematical models of brain networks, especially models that can be used for fMRI datasets. We refer to the recent NIH research domain criteria initiative, in which a concept of "constructs" as functional units of mental disorders is introduced. Constructs are biomarkers present at multiple levels of brain functioning - cognition, genetics, brain anatomy, and neurophysiology. In this review, we propose a new approach which we called circuit to construct mapping (CCM), which aims to characterize causal relations between the underlying network dynamics (as the cause) and the constructs referring to the clinical symptoms of MDD (as the effect). CCM involves extracting diagnostic categories from behavioral data, linking circuits that are causal to these categories with use of clinical neuroimaging data, and modeling the dynamics of the emerging circuits with attractor dynamics in order to provide new, neuroimaging-related biomarkers for MDD. The CCM approach optimizes the clinical diagnosis and patient stratification. It also addresses the recent demand for linking circuits to behavior, and provides a new insight into clinical treatment by investigating the dynamics of neuronal circuits underneath cognitive dimensions of MDD. CCM can serve as a new regime toward personalized medicine, assisting the diagnosis and treatment of MDD.

Spin-glass model predicts metastable brain states that diminish in anesthesia

Patterns of resting state connectivity change dynamically and may represent modes of cognitive information processing. The diversity of connectivity patterns (global brain states) reflects the information capacity of the brain and determines the state of consciousness. In this work, computer simulation was used to explore the repertoire of global brain states as a function of cortical activation level. We implemented a modified spin glass model to describe UP/DOWN state transitions of neuronal populations at a mesoscopic scale based on resting state BOLD fMRI data. Resting state fMRI was recorded in 20 participants and mapped to 10,000 cortical regions (sites) defined on a group-aligned cortical surface map. Each site represented the population activity of a ~20 mm(2) area of the cortex. Cross-correlation matrices of the mapped BOLD time courses of the set of sites were calculated and averaged across subjects. In the model, each cortical site was allowed to interact with the 16 other sites that had the highest pair-wise correlation values. All sites stochastically transitioned between UP and DOWN states under the net influence of their 16 pairs. The probability of local state transitions was controlled by a single parameter T corresponding to the level of global cortical activation. To estimate the number of distinct global states, first we ran 10,000 simulations at T = 0. Simulations were started from random configurations that converged to one of several distinct patterns. Using hierarchical clustering, at 99% similarity, close to 300 distinct states were found. At intermediate T, metastable state configurations were formed suggesting critical behavior with a sharp increase in the number of metastable states at an optimal T. Both reduced activation (anesthesia, sleep) and increased activation (hyper-activation) moved the system away from equilibrium, presumably incompatible with conscious mentation. During equilibrium, the diversity of large-scale brain states was maximum, compatible with maximum information capacity-a presumed condition of consciousness.

A mathematics for medicine: The Network Effect

The theory of medicine and its complement systems biology are intended to explain the workings of the large number of mutually interdependent complex physiologic networks in the human body and to apply that understanding to maintaining the functions for which nature designed them. Therefore, when what had originally been made as a simplifying assumption or a working hypothesis becomes foundational to understanding the operation of physiologic networks it is in the best interests of science to replace or at least update that assumption. The replacement process requires, among other things, an evaluation of how the new hypothesis affects modern day understanding of medical science. This paper identifies linear dynamics and Normal statistics as being such arcane assumptions and explores some implications of their retirement. Specifically we explore replacing Normal with fractal statistics and examine how the latter are related to non-linear dynamics and chaos theory. The observed ubiquity of inverse power laws in physiology entails the need for a new calculus, one that describes the dynamics of fractional phenomena and captures the fractal properties of the statistics of physiological time series. We identify these properties as a necessary consequence of the complexity resulting from the network dynamics and refer to them collectively as The Network Effect.

Functional brain networks: great expectations, hard times and the big leap forward

Many physical and biological systems can be studied using complex network theory, a new statistical physics understanding of graph theory. The recent application of complex network theory to the study of functional brain networks has generated great enthusiasm as it allows addressing hitherto non-standard issues in the field, such as efficiency of brain functioning or vulnerability to damage. However, in spite of its high degree of generality, the theory was originally designed to describe systems profoundly different from the brain. We discuss some important caveats in the wholesale application of existing tools and concepts to a field they were not originally designed to describe. At the same time, we argue that complex network theory has not yet been taken full advantage of, as many of its important aspects are yet to make their appearance in the neuroscience literature. Finally, we propose that, rather than simply borrowing from an existing theory, functional neural networks can inspire a fundamental reformulation of complex network theory, to account for its exquisitely complex functioning mode.

Highlighting the structure-function relationship of the brain with the Ising model and graph theory

With the advent of neuroimaging techniques, it becomes feasible to explore the structure-function relationships in the brain. When the brain is not involved in any cognitive task or stimulated by any external output, it preserves important activities which follow well-defined spatial distribution patterns. Understanding the self-organization of the brain from its anatomical structure, it has been recently suggested to model the observed functional pattern from the structure of white matter fiber bundles. Different models which study synchronization (e.g., the Kuramoto model) or global dynamics (e.g., the Ising model) have shown success in capturing fundamental properties of the brain. In particular, these models can explain the competition between modularity and specialization and the need for integration in the brain. Graphing the functional and structural brain organization supports the model and can also highlight the strategy used to process and organize large amount of information traveling between the different modules. How the flow of information can be prevented or partially destroyed in pathological states, like in severe brain injured patients with disorders of consciousness or by pharmacological induction like in anaesthesia, will also help us to better understand how global or integrated behavior can emerge from local and modular interactions.

Marginally subcritical dynamics explain enhanced stimulus discriminability under attention

Recent experimental and theoretical work has established the hypothesis that cortical neurons operate close to a critical state which describes a phase transition from chaotic to ordered dynamics. Critical dynamics are suggested to optimize several aspects of neuronal information processing. However, although critical dynamics have been demonstrated in recordings of spontaneously active cortical neurons, little is known about how these dynamics are affected by task-dependent changes in neuronal activity when the cortex is engaged in stimulus processing. Here we explore this question in the context of cortical information processing modulated by selective visual attention. In particular, we focus on recent findings that local field potentials (LFPs) in macaque area V4 demonstrate an increase in γ-band synchrony and a simultaneous enhancement of object representation with attention. We reproduce these results using a model of integrate-and-fire neurons where attention increases synchrony by enhancing the efficacy of recurrent interactions. In the phase space spanned by excitatory and inhibitory coupling strengths, we identify critical points and regions of enhanced discriminability. Furthermore, we quantify encoding capacity using information entropy. We find a rapid enhancement of stimulus discriminability with the emergence of synchrony in the network. Strikingly, only a narrow region in the phase space, at the transition from subcritical to supercritical dynamics, supports the experimentally observed discriminability increase. At the supercritical border of this transition region, information entropy decreases drastically as synchrony sets in. At the subcritical border, entropy is maximized under the assumption of a coarse observation scale. Our results suggest that cortical networks operate at such near-critical states, allowing minimal attentional modulations of network excitability to substantially augment stimulus representation in the LFPs.

Information transfer and criticality in the Ising model on the human connectome

We implement the Ising model on a structural connectivity matrix describing the brain at two different resolutions. Tuning the model temperature to its critical value, i.e. at the susceptibility peak, we find a maximal amount of total information transfer between the spin variables. At this point the amount of information that can be redistributed by some nodes reaches a limit and the net dynamics exhibits signature of the law of diminishing marginal returns, a fundamental principle connected to saturated levels of production. Our results extend the recent analysis of dynamical oscillators models on the connectome structure, taking into account lagged and directional influences, focusing only on the nodes that are more prone to became bottlenecks of information. The ratio between the outgoing and the incoming information at each node is related to the the sum of the weights to that node and to the average time between consecutive time flips of spins. The results for the connectome of 66 nodes and for that of 998 nodes are similar, thus suggesting that these properties are scale-independent. Finally, we also find that the brain dynamics at criticality is organized maximally to a rich-club w.r.t. the network of information flows.

Reviewing the ketamine model for schizophrenia

The observation that antagonists of the N-methyl-D-aspartate receptor (NMDAR), such as phencyclidine (PCP) and ketamine, transiently induce symptoms of acute schizophrenia had led to a paradigm shift from dopaminergic to glutamatergic dysfunction in pharmacological models of schizophrenia. The glutamate hypothesis can explain negative and cognitive symptoms of schizophrenia better than the dopamine hypothesis, and has the potential to explain dopamine dysfunction itself. The pharmacological and psychomimetic effects of ketamine, which is safer for human subjects than phencyclidine, are herein reviewed. Ketamine binds to a variety of receptors, but principally acts at the NMDAR, and convergent genetic and molecular evidence point to NMDAR hypofunction in schizophrenia. Furthermore, NMDAR hypofunction can explain connectional and oscillatory abnormalities in schizophrenia in terms of both weakened excitation of inhibitory γ-aminobutyric acidergic (GABAergic) interneurons that synchronize cortical networks and disinhibition of principal cells. Individuals with prenatal NMDAR aberrations might experience the onset of schizophrenia towards the completion of synaptic pruning in adolescence, when network connectivity drops below a critical value. We conclude that ketamine challenge is useful for studying the positive, negative, and cognitive symptoms, dopaminergic and GABAergic dysfunction, age of onset, functional dysconnectivity, and abnormal cortical oscillations observed in acute schizophrenia.

Biological motion coding in the brain: analysis of visually driven EEG functional networks

Herein, we address the time evolution of brain functional networks computed from electroencephalographic activity driven by visual stimuli. We describe how these functional network signatures change in fast scale when confronted with point-light display stimuli depicting biological motion (BM) as opposed to scrambled motion (SM). Whereas global network measures (average path length, average clustering coefficient, and average betweenness) computed as a function of time did not discriminate between BM and SM, local node properties did. Comparing the network local measures of the BM condition with those of the SM condition, we found higher degree and betweenness values in the left frontal (F7) electrode, as well as a higher clustering coefficient in the right occipital (O2) electrode, for the SM condition. Conversely, for the BM condition, we found higher degree values in central parietal (Pz) electrode and a higher clustering coefficient in the left parietal (P3) electrode. These results are discussed in the context of the brain networks involved in encoding BM versus SM.

Fading signatures of critical brain dynamics during sustained wakefulness in humans

Sleep encompasses approximately a third of our lifetime, yet its purpose and biological function are not well understood. Without sleep optimal brain functioning such as responsiveness to stimuli, information processing, or learning may be impaired. Such observations suggest that sleep plays a crucial role in organizing or reorganizing neuronal networks of the brain toward states where information processing is optimized. Increasing evidence suggests that cortical neuronal networks operate near a critical state characterized by balanced activity patterns, which supports optimal information processing. However, it remains unknown whether critical dynamics is affected in the course of wake and sleep, which would also impact information processing. Here, we show that signatures of criticality are progressively disturbed during wake and restored by sleep. We demonstrate that the precise power-laws governing the cascading activity of neuronal avalanches and the distribution of phase-lock intervals in human electroencephalographic recordings are increasingly disarranged during sustained wakefulness. These changes are accompanied by a decrease in variability of synchronization. Interpreted in the context of a critical branching process, these seemingly different findings indicate a decline of balanced activity and progressive distance from criticality toward states characterized by an imbalance toward excitation where larger events prevail dynamics. Conversely, sleep restores the critical state resulting in recovered power-law characteristics in activity and variability of synchronization. These findings support the intriguing hypothesis that sleep may be important to reorganize cortical network dynamics to a critical state thereby assuring optimal computational capabilities for the following time awake.

The diminishing role of hubs in dynamical processes on complex networks

It is notoriously difficult to predict the behaviour of a complex self-organizing system, where the interactions among dynamical units form a heterogeneous topology. Even if the dynamics of each microscopic unit is known, a real understanding of their contributions to the macroscopic system behaviour is still lacking. Here, we develop information-theoretical methods to distinguish the contribution of each individual unit to the collective out-of-equilibrium dynamics. We show that for a system of units connected by a network of interaction potentials with an arbitrary degree distribution, highly connected units have less impact on the system dynamics when compared with intermediately connected units. In an equilibrium setting, the hubs are often found to dictate the long-term behaviour. However, we find both analytically and experimentally that the instantaneous states of these units have a short-lasting effect on the state trajectory of the entire system. We present qualitative evidence of this phenomenon from empirical findings about a social network of product recommendations, a protein–protein interaction network and a neural network, suggesting that it might indeed be a widespread property in nature.

Cerebral energy metabolism and the brain's functional network architecture: an integrative review

Recent functional magnetic resonance imaging (fMRI) studies have emphasized the contributions of synchronized activity in distributed brain networks to cognitive processes in both health and disease. The brain's 'functional connectivity' is typically estimated from correlations in the activity time series of anatomically remote areas, and postulated to reflect information flow between neuronal populations. Although the topological properties of functional brain networks have been studied extensively, considerably less is known regarding the neurophysiological and biochemical factors underlying the temporal coordination of large neuronal ensembles. In this review, we highlight the critical contributions of high-frequency electrical oscillations in the γ-band (30 to 100 Hz) to the emergence of functional brain networks. After describing the neurobiological substrates of γ-band dynamics, we specifically discuss the elevated energy requirements of high-frequency neural oscillations, which represent a mechanistic link between the functional connectivity of brain regions and their respective metabolic demands. Experimental evidence is presented for the high oxygen and glucose consumption, and strong mitochondrial performance required to support rhythmic cortical activity in the γ-band. Finally, the implications of mitochondrial impairments and deficits in glucose metabolism for cognition and behavior are discussed in the context of neuropsychiatric and neurodegenerative syndromes characterized by large-scale changes in the organization of functional brain networks.

Nanopsychiatry--the potential role of nanotechnologies in the future of psychiatry: a systematic review

Nanomedicine is defined as the area using nanotechnology's concepts for the benefit of human beings' health and well being. In this article, we aimed to provide an overview of areas where nanotechnology is applied and how they could be extended to care for psychiatric illnesses. The main applications of nanotechnology in psychiatry are (i) pharmacology. There are two main difficulties in neuropharmacology: drugs have to pass the blood-brain barrier and then to be internalized by targeted cells. Nanoparticles could increase drugs bioavailability and pharmacokinetics, especially improving safety and efficacy of psychotropic drugs. Liposomes, nanosomes, nanoparticle polymers, nanobubbles are some examples of this targeted drug delivery. Nanotechnologies could also add new pharmacological properties, like nanoshells and dendrimers (ii) living analysis. Nanotechnology provides technical assistance to in vivo imaging or metabolome analysis (iii) central nervous system modeling. Research teams have succeeded to modelize inorganic synapses and mimick synaptic behavior, a step essential for further creation of artificial neural systems. Some nanoparticle assemblies present the same small worlds and free-scale networks architecture as cortical neural networks. Nanotechnologies and quantum physics could be used to create models of artificial intelligence and mental illnesses. We are not about to see a concrete application of nanomedicine in daily psychiatric practice. Even if nanotechnologies are promising, their safety is still inconsistent and this must be kept in mind. However, it seems essential that psychiatrists do not forsake this area of research the perspectives of which could be decisive in the field of mental illness.

Critical avalanches and subsampling in map-based neural networks coupled with noisy synapses

Many different kinds of noise are experimentally observed in the brain. Among them, we study a model of noisy chemical synapse and obtain critical avalanches for the spatiotemporal activity of the neural network. Neurons and synapses are modeled by dynamical maps. We discuss the relevant neuronal and synaptic properties to achieve the critical state. We verify that networks of functionally excitable neurons with fast synapses present power-law avalanches, due to rebound spiking dynamics. We also discuss the measuring of neuronal avalanches by subsampling our data, shedding light on the experimental search for self-organized criticality in neural networks.

Brain organization into resting state networks emerges at criticality on a model of the human connectome

The relation between large-scale brain structure and function is an outstanding open problem in neuroscience. We approach this problem by studying the dynamical regime under which realistic spatiotemporal patterns of brain activity emerge from the empirically derived network of human brain neuroanatomical connections. The results show that critical dynamics unfolding on the structural connectivity of the human brain allow the recovery of many key experimental findings obtained from functional magnetic resonance imaging, such as divergence of the correlation length, the anomalous scaling of correlation fluctuations, and the emergence of large-scale resting state networks.

[Nanopsychiatry. The potential role of nanotechnologies in the future of psychiatry. A systematic review]

INTRODUCTION

Nanomedicine is defined as the area using nanotechnology's concepts for the benefit of human beings, their health and well being. The field of nanotechnology opened new unsuspected fields of research a few years ago.

AIM OF THE STUDY

To provide an overview of nanotechnology application areas that could affect care for psychiatric illnesses.

METHODS

We conducted a systematic review using the PRISMA criteria (preferred reporting items for systematic reviews and meta-analysis). Inclusion criteria were specified in advance: all studies describing the development of nanotechnology in psychiatry. The research paradigm was: "(nanotechnology OR nanoparticles OR nanomedicine) AND (central nervous system)" Articles were identified in three research bases, Medline (1966-present), Web of Science (1975-present) and Cochrane (all articles). The last search was carried out on April 2, 2012. Seventy-six items were included in this qualitative review.

RESULTS

The main applications of nanotechnology in psychiatry are (i) pharmacology. There are two main difficulties in neuropharmacology. Drugs have to pass the blood brain barrier and then to be internalized by targeted cells. Nanoparticles could increase drugs' bioavailability and pharmacokinetics, especially improving safety and efficacy of psychotropic drugs. Liposomes, nanosomes, nanoparticle polymers, nanobubbles are some examples of this targeted drug delivery. Nanotechnologies could also add new pharmacological properties, like nanohells and dendrimers; (ii) living analysis. Nanotechnology provides technical assistance to in vivo imaging or metabolome analysis; (iii) central nervous system modeling. Research teams have modelized inorganic synapses and mimicked synaptic behavior, essential for further creation of artificial neural systems. Some nanoparticle assemblies present the same small world and free-scale network architecture as cortical neural networks. Nanotechnologies and quantum physics could be used to create models of artificial intelligence and mental illnesses.

DISCUSSION

Even if nanotechnologies are promising, their safety is still tricky and this must be kept in mind.

CONCLUSION

We are not about to see a concrete application of nanomedicine in daily psychiatric practice. However, it seems essential that psychiatrists do not forsake this area of research the perspectives of which could be decisive in the field of mental illness.

A fractal approach to dynamic inference and distribution analysis

Event-distributions inform scientists about the variability and dispersion of repeated measurements. This dispersion can be understood from a complex systems perspective, and quantified in terms of fractal geometry. The key premise is that a distribution's shape reveals information about the governing dynamics of the system that gave rise to the distribution. Two categories of characteristic dynamics are distinguished: additive systems governed by component-dominant dynamics and multiplicative or interdependent systems governed by interaction-dominant dynamics. A logic by which systems governed by interaction-dominant dynamics are expected to yield mixtures of lognormal and inverse power-law samples is discussed. These mixtures are described by a so-called cocktail model of response times derived from human cognitive performances. The overarching goals of this article are twofold: First, to offer readers an introduction to this theoretical perspective and second, to offer an overview of the related statistical methods.

Robust short-term memory without synaptic learning

Short-term memory in the brain cannot in general be explained the way long-term memory can – as a gradual modification of synaptic weights – since it takes place too quickly. Theories based on some form of cellular bistability, however, do not seem able to account for the fact that noisy neurons can collectively store information in a robust manner. We show how a sufficiently clustered network of simple model neurons can be instantly induced into metastable states capable of retaining information for a short time (a few seconds). The mechanism is robust to different network topologies and kinds of neural model. This could constitute a viable means available to the brain for sensory and/or short-term memory with no need of synaptic learning. Relevant phenomena described by neurobiology and psychology, such as local synchronization of synaptic inputs and power-law statistics of forgetting avalanches, emerge naturally from this mechanism, and we suggest possible experiments to test its viability in more biological settings.

Linear response at criticality

We study a set of cooperatively interacting units at criticality, and we prove with analytical and numerical arguments that they generate the same renewal non-Poisson intermittency as that produced by blinking quantum dots, thereby giving a stronger support to the results of earlier investigation. By analyzing how this out-of-equilibrium system responds to harmonic perturbations, we find that the response can be described only using a new form of linear response theory that accounts for aging and the nonergodic behavior of the underlying process. We connect the undamped response of the system at criticality to the decaying response predicted by the recently established nonergodic fluctuation-dissipation theorem for dichotomous processes using information about the second moment of the fluctuations. We demonstrate that over a wide range of perturbation frequencies the response of the cooperative system is greatest when at criticality.

Intracellular calcium signals display an avalanche-like behavior over multiple lengthscales

Many natural phenomena display “self-organized criticality” (SOC), (Bak et al., 1987). This refers to spatially extended systems for which patterns of activity characterized by different lengthscales can occur with a probability density that follows a power law with pattern size. Differently from power laws at phase transitions, systems displaying SOC do not need the tuning of an external parameter. Here we analyze intracellular calcium (Ca²⁺) signals, a key component of the signaling toolkit of almost any cell type. Ca²⁺ signals can either be spatially restricted (local) or propagate throughout the cell (global). Different models have suggested that the transition from local to global signals is similar to that of directed percolation. Directed percolation has been associated, in turn, to the appearance of SOC. In this paper we discuss these issues within the framework of simple models of Ca²⁺ signal propagation. We also analyze the size distribution of local signals (“puffs”) observed in immature Xenopus Laevis oocytes. The puff amplitude distribution obtained from observed local signals is not Gaussian with a noticeable fraction of large size events. The experimental distribution of puff areas in the spatio-temporal record of the image has a long tail that is approximately log-normal. The distribution can also be fitted with a power law relationship albeit with a smaller goodness of fit. The power law behavior is encountered within a simple model that includes some coupling among individual signals for a wide range of parameter values. An analysis of the model shows that a global elevation of the Ca²⁺ concentration plays a major role in determining whether the puff size distribution is long-tailed or not. This suggests that Ca²⁺-clearing from the cytosol is key to determine whether IP₃-mediated Ca²⁺ signals can display a SOC-like behavior or not.

What kind of noise is brain noise: anomalous scaling behavior of the resting brain activity fluctuations

The study of spontaneous fluctuations of brain activity, often referred as brain noise, is getting increasing attention in functional magnetic resonance imaging (fMRI) studies. Despite important efforts, much of the statistical properties of such fluctuations remain largely unknown. This work scrutinizes these fluctuations looking at specific statistical properties which are relevant to clarify its dynamical origins. Here, three statistical features which clearly differentiate brain data from naive expectations for random processes are uncovered: First, the variance of the fMRI mean signal as a function of the number of averaged voxels remains constant across a wide range of observed clusters sizes. Second, the anomalous behavior of the variance is originated by bursts of synchronized activity across regions, regardless of their widely different sizes. Finally, the correlation length (i.e., the length at which the correlation strength between two regions vanishes) as well as mutual information diverges with the cluster's size considered, such that arbitrarily large clusters exhibit the same collective dynamics than smaller ones. These three properties are known to be exclusive of complex systems exhibiting critical dynamics, where the spatio-temporal dynamics show these peculiar type of fluctuations. Thus, these findings are fully consistent with previous reports of brain critical dynamics, and are relevant for the interpretation of the role of fluctuations and variability in brain function in health and disease.

Input-dependent wave attenuation in a critically-balanced model of cortex

A number of studies have suggested that many properties of brain activity can be understood in terms of critical systems. However it is still not known how the long-range susceptibilities characteristic of criticality arise in the living brain from its local connectivity structures. Here we prove that a dynamically critically-poised model of cortex acquires an infinitely-long ranged susceptibility in the absence of input. When an input is presented, the susceptibility attenuates exponentially as a function of distance, with an increasing spatial attenuation constant (i.e., decreasing range) the larger the input. This is in direct agreement with recent results that show that waves of local field potential activity evoked by single spikes in primary visual cortex of cat and macaque attenuate with a characteristic length that also increases with decreasing contrast of the visual stimulus. A susceptibility that changes spatial range with input strength can be thought to implement an input-dependent spatial integration: when the input is large, no additional evidence is needed in addition to the local input; when the input is weak, evidence needs to be integrated over a larger spatial domain to achieve a decision. Such input-strength-dependent strategies have been demonstrated in visual processing. Our results suggest that input-strength dependent spatial integration may be a natural feature of a critically-balanced cortical network.

Self-Regulated Dynamical Criticality in Human ECoG

Mounting experimental and theoretical results indicate that neural systems are poised near a critical state. In human subjects, however, most evidence comes from functional MRI studies, an indirect measurement of neuronal activity with poor temporal resolution. Electrocorticography (ECoG) provides a unique window into human brain activity: each electrode records, with high temporal resolution, the activity resulting from the sum of the local field potentials of ∼10⁵ neurons. We show that the human brain ECoG recordings display features of self-regulated dynamical criticality: dynamical modes of activation drift around the critical stability threshold, moving in and out of the unstable region and equilibrating the global dynamical state at a very fast time scale. Moreover, the analysis also reveals differences between the resting state and a motor task, associated with increased stability of a fraction of the dynamical modes.

The Functional Benefits of Criticality in the Cortex

Rapidly growing empirical evidence supports the hypothesis that the cortex operates near criticality. Although the confirmation of this hypothesis would mark a significant advance in fundamental understanding of cortical physiology, a natural question arises: What functional benefits are endowed to cortical circuits that operate at criticality? In this review, we first describe an introductory-level thought experiment to provide the reader with an intuitive understanding of criticality. Second, we discuss some practical approaches for investigating criticality. Finally, we review quantitative evidence that three functional properties of the cortex are optimized at criticality: 1) dynamic range, 2) information transmission, and 3) information capacity. We focus on recently reported experimental evidence and briefly discuss the theory and history of these ideas.

Signal integration enhances the dynamic range in neuronal systems

The dynamic range measures the capacity of a system to discriminate the intensity of an external stimulus. Such an ability is fundamental for living beings to survive: to leverage resources and to avoid danger. Consequently, the larger is the dynamic range, the greater is the probability of survival. We investigate how the integration of different input signals affects the dynamic range, and in general the collective behavior of a network of excitable units. By means of numerical simulations and a mean-field approach, we explore the nonequilibrium phase transition in the presence of integration. We show that the firing rate in random and scale-free networks undergoes a discontinuous phase transition depending on both the integration time and the density of integrator units. Moreover, in the presence of external stimuli, we find that a system of excitable integrator units operating in a bistable regime largely enhances its dynamic range.

Cooperation-induced topological complexity: a promising road to fault tolerance and hebbian learning

According to an increasing number of researchers intelligence emerges from criticality as a consequence of locality breakdown and long-range correlation, well known properties of phase transition processes. We study a model of interacting units, as an idealization of real cooperative systems such as the brain or a flock of birds, for the purpose of discussing the emergence of long-range correlation from the coupling of any unit with its nearest neighbors. We focus on the critical condition that has been recently shown to maximize information transport and we study the topological structure of the network of dynamically linked nodes. Although the topology of this network depends on the arbitrary choice of correlation threshold, namely the correlation intensity selected to establish a link between two nodes; the numerical calculations of this paper afford some important indications on the dynamically induced topology. The first important property is the emergence of a perception length as large as the flock size, thanks to some nodes with a large number of links, thus playing the leadership role. All the units are equivalent and leadership moves in time from one to another set of nodes, thereby insuring fault tolerance. Then we focus on the correlation threshold generating a scale-free topology with power index ν ≈ 1 and we find that if this topological structure is selected to establish consensus through the linked nodes, the control parameter necessary to generate criticality is close to the critical value corresponding to the all-to-all coupling condition. We find that criticality in this case generates also a third state, corresponding to a total lack of consensus. However, we make a numerical analysis of the dynamically induced network, and we find that it consists of two almost independent structures, each of which is equivalent to a network in the all-to-all coupling condition. This observation confirms that cooperation makes the system evolve toward favoring consensus topological structures. We argue that these results are compatible with both Hebbian learning and fault tolerance.

Letting the brain speak for itself

Metaphors of Computation and Information tended to detract attention from the intrinsic modes of neural system functions, uncontaminated by the observer's role in collection, and interpretation of experimental data. Recognizing the self-referential mode of function, and the propensity for self-organization to critical states requires a fundamentally new orientation, based on Complex System Dynamics as non-ergodic, non-stationary processes with inverse-power-law statistical distributions. Accordingly, local cooperative processes, intrinsic to neural structures, and of fractal nature, call for applying Fractional Calculus and models of Random Walks with long-term memory in Theoretical Neuroscience studies.

Temporal complexity of the order parameter at the phase transition

We study a decision making model in a condition where it is equivalent to the two-dimensional Ising model, and we show that at the onset of phase transition it generates temporal complexity, namely, nonstationary and nonergodic fluctuations. We argue that this is a general property of criticality, thereby opening the door to the application of the recently discovered phenomenon of complexity matching: For an efficient transfer of information to occur, a perturbing complex network must share the same temporal complexity as the perturbed complex network.

Kernel canonical-correlation Granger causality for multiple time series

Canonical-correlation analysis as a multivariate statistical technique has been applied to multivariate Granger causality analysis to infer information flow in complex systems. It shows unique appeal and great superiority over the traditional vector autoregressive method, due to the simplified procedure that detects causal interaction between multiple time series, and the avoidance of potential model estimation problems. However, it is limited to the linear case. Here, we extend the framework of canonical correlation to include the estimation of multivariate nonlinear Granger causality for drawing inference about directed interaction. Its feasibility and effectiveness are verified on simulated data.

Biological physics in México: Review and new challenges

Biological and physical sciences possess a long-standing tradition of cooperativity as separate but related subfields of science. For some time, this cooperativity has been limited by their obvious differences in methods and views. Biological physics has recently experienced a kind of revival (or better a rebirth) due to the growth of molecular research on animate matter. New avenues for research have been opened for both theoretical and experimental physicists. Nevertheless, in order to better travel for such paths, the contemporary biological physicist should be armed with a set of specialized tools and methods but also with a new attitude toward multidisciplinarity. In this review article, we intend to somehow summarize what has been done in the past (in particular, as an example we will take a closer look at the Mexican case), to show some examples of fruitful investigations in the biological physics area and also to set a proposal of new curricula for physics students and professionals interested in applying their science to get a better understanding of the physical basis of biological function.

Non-parametric model selection for subject-specific topological organization of resting-state functional connectivity

In recent years, graph theory has been successfully applied to study functional and anatomical connectivity networks in the human brain. Most of these networks have shown small-world topological characteristics: high efficiency in long distance communication between nodes, combined with highly interconnected local clusters of nodes. Moreover, functional studies performed at high resolutions have presented convincing evidence that resting-state functional connectivity networks exhibits (exponentially truncated) scale-free behavior. Such evidence, however, was mostly presented qualitatively, in terms of linear regressions of the degree distributions on log-log plots. Even when quantitative measures were given, these were usually limited to the r(2) correlation coefficient. However, the r(2) statistic is not an optimal estimator of explained variance, when dealing with (truncated) power-law models. Recent developments in statistics have introduced new non-parametric approaches, based on the Kolmogorov-Smirnov test, for the problem of model selection. In this work, we have built on this idea to statistically tackle the issue of model selection for the degree distribution of functional connectivity at rest. The analysis, performed at voxel level and in a subject-specific fashion, confirmed the superiority of a truncated power-law model, showing high consistency across subjects. Moreover, the most highly connected voxels were found to be consistently part of the default mode network. Our results provide statistically sound support to the evidence previously presented in literature for a truncated power-law model of resting-state functional connectivity.

Theoretical model for mesoscopic-level scale-free self-organization of functional brain networks

In this paper, we provide theoretical and numerical analysis of a geometric activity flow network model which is aimed at explaining mathematically the scale-free functional graph self-organization phenomena emerging in complex nervous systems at a mesoscale level. In our model, each unit corresponds to a large number of neurons and may be roughly seen as abstracting the functional behavior exhibited by a single voxel under functional magnetic resonance imaging (fMRI). In the course of the dynamics, the units exchange portions of formal charge, which correspond to waves of activity in the underlying microscale neuronal circuit. The geometric model abstracts away the neuronal complexity and is mathematically tractable, which allows us to establish explicit results on its ground states and the resulting charge transfer graph modeling functional graph of the network. We show that, for a wide choice of parameters and geometrical setups, our model yields a scale-free functional connectivity with the exponent approaching 2, which is in agreement with previous empirical studies based on fMRI. The level of universality of the presented theory allows us to claim that the model does shed light on mesoscale functional self-organization phenomena of the nervous system, even without resorting to closer details of brain connectivity geometry which often remain unknown. The material presented here significantly extends our previous work where a simplified mean-field model in a similar spirit was constructed, ignoring the underlying network geometry.

Self-similar correlation function in brain resting-state functional magnetic resonance imaging

Adaptive behaviour, cognition and emotion are the result of a bewildering variety of brain spatio-temporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons and 100 trillion synapses manage to produce this large repertoire of cortical configurations in a flexible manner. In addition, it is recognized that temporal correlations across such configurations cannot be arbitrary, but they need to meet two conflicting demands: while diverse cortical areas should remain functionally segregated from each other, they must still perform as a collective, i.e. they are functionally integrated. Here, we investigate these large-scale dynamical properties by inspecting the character of the spatio-temporal correlations of brain resting-state activity. In physical systems, these correlations in space and time are captured by measuring the correlation coefficient between a signal recorded at two different points in space at two different times. We show that this two-point correlation function extracted from resting-state functional magnetic resonance imaging data exhibits self-similarity in space and time. In space, self-similarity is revealed by considering three successive spatial coarse-graining steps while in time it is revealed by the 1/f frequency behaviour of the power spectrum. The uncovered dynamical self-similarity implies that the brain is spontaneously at a continuously changing (in space and time) intermediate state between two extremes, one of excessive cortical integration and the other of complete segregation. This dynamical property may be seen as an important marker of brain well-being in both health and disease.

Fractal complexity in spontaneous EEG metastable-state transitions: new vistas on integrated neural dynamics

Resting-state EEG signals undergo rapid transition processes (RTPs) that glue otherwise stationary epochs. We study the fractal properties of RTPs in space and time, supporting the hypothesis that the brain works at a critical state. We discuss how the global intermittent dynamics of collective excitations is linked to mentation, namely non-constrained non-task-oriented mental activity.

Exploring the brain network: a review on resting-state fMRI functional connectivity

Our brain is a network. It consists of spatially distributed, but functionally linked regions that continuously share information with each other. Interestingly, recent advances in the acquisition and analysis of functional neuroimaging data have catalyzed the exploration of functional connectivity in the human brain. Functional connectivity is defined as the temporal dependency of neuronal activation patterns of anatomically separated brain regions and in the past years an increasing body of neuroimaging studies has started to explore functional connectivity by measuring the level of co-activation of resting-state fMRI time-series between brain regions. These studies have revealed interesting new findings about the functional connections of specific brain regions and local networks, as well as important new insights in the overall organization of functional communication in the brain network. Here we present an overview of these new methods and discuss how they have led to new insights in core aspects of the human brain, providing an overview of these novel imaging techniques and their implication to neuroscience. We discuss the use of spontaneous resting-state fMRI in determining functional connectivity, discuss suggested origins of these signals, how functional connections tend to be related to structural connections in the brain network and how functional brain communication may form a key role in cognitive performance. Furthermore, we will discuss the upcoming field of examining functional connectivity patterns using graph theory, focusing on the overall organization of the functional brain network. Specifically, we will discuss the value of these new functional connectivity tools in examining believed connectivity diseases, like Alzheimer's disease, dementia, schizophrenia and multiple sclerosis.

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.