Metastable oscillatory modes emerge from synchronization in the brain spacetime connectome

Capturing the emergent dynamical structure in biophysical neural models

Complex neural systems can display structured emergent dynamics. Capturing this structure remains a significant scientific challenge. Using information theory, we apply Dynamical Independence (DI) to uncover the emergent dynamical structure in a minimal 5-node biophysical neural model, shaped by the interplay of two key aspects of brain organisation: integration and segregation. In our study, functional integration within the biophysical neural model is modulated by a global coupling parameter, while functional segregation is influenced by adding dynamical noise, which counteracts global coupling. Leveraging transfer entropy, DI defines a dimensionally-reduced macroscopic variable (e.g., a coarse-graining) as emergent to the extent that it behaves as an independent dynamical process, distinct from the micro-level dynamics. Dynamical dependence (a departure from dynamical independence) is measured by minimising the transfer entropy from microlevel variables to macroscopic variables across spatial scales. Our results indicate that the degree of emergence of macroscopic variables is relatively minimised at balanced points of integration and segregation and maximised at the extremes. Additionally, our method identifies to which degree the macroscopic dynamics are localised across microlevel nodes, thereby elucidating the emergent dynamical structure through the relationship between microscopic and macroscopic processes. We find that deviation from a balanced point between integration and segregation results in a less localised, more distributed emergent dynamical structure as identified by DI. This finding suggests that a balance of functional integration and segregation is associated with lower levels of emergence (higher dynamical dependence), which may be crucial for sustaining coherent, localised emergent macroscopic dynamical structures. This work also provides a complete computational implementation for the identification of emergent neural dynamics that could be applied both in silico and in vivo.

Mapping Brain Lesions to Conduction Delays: The Next Step for Personalized Brain Models in Multiple Sclerosis

Multiple sclerosis (MS) is a clinically heterogeneous, multifactorial autoimmune disorder affecting the central nervous system. Structural damage to the myelin sheath, resulting in the consequent slowing of the conduction velocities, is a key pathophysiological mechanism. In fact, the conduction velocities are closely related to the degree of myelination, with thicker myelin sheaths associated to higher conduction velocities. However, how the intensity of the structural lesions of the myelin translates to slowing of nerve conduction delays is not known. In this work, we use large-scale brain models and Bayesian model inversion to estimate how myelin lesions translate to longer conduction delays across the damaged tracts. A cohort of 38 subjects (20 healthy and 18 with MS) underwent MEG recordings during an eyes-closed resting-state condition, along with MRI acquisitions and detailed white matter tractography analysis. We observed that MS patients consistently showed decreased power within the alpha frequency band (8-13 Hz) as compared to the healthy group. We also derived a lesion matrix indicating the percentage of lesions for each tract in every patient. Using large-scale brain modeling, the neural activity of each region was represented as a Stuart-Landau oscillator operating in a regime showing damped oscillations, and the regions were coupled according to subject-specific connectomes. We propose a linear formulation to the relationship between the conduction delays and the amount of structural damage in each white matter tract. Dependent upon the parameterγ $$ \upgamma $$ , this function translates lesions into edge-specific conduction delays (leading to shifts in the power spectra). Using deep neural density estimators, we found that the estimation ofγ $$ \upgamma $$ showed a strong correlation with the alpha peak in MEG recordings. The most probable inferredγ $$ \upgamma $$ for each subject is inversely proportional to the observed peaks, while power peaks themselves do not correlate with total lesion volume. Furthermore, the estimated parameters were predictive (cross-sectionally) of individual clinical disability. This study represents the initial exploration showcasing the location-specific impact of myelin lesions on conduction delays, thereby enhancing the customization of models for individuals with multiple sclerosis.

Causal interactions between amplitude correlation and phase coupling in cortical networks

Phase coherence and amplitude correlations across brain regions are two main mechanisms of connectivity that govern brain dynamics at multiple scales. However, despite the increasing evidence that associates these mechanisms with brain functions and cognitive processes, the relationship between these different coupling modes is not well understood. Here, we study the causal relation between both types of functional coupling across multiple cortical areas. While most of the studies adopt a definition based on pairs of electrodes or regions of interest, we here employ a multichannel approach that provides us with a time-resolved definition of phase and amplitude coupling parameters. Using data recorded with a multichannel µECoG array from the ferret brain, we found that the transmission of information between both modes can be unidirectional or bidirectional, depending on the frequency band of the underlying signal. These results were reproduced in magnetoencephalography (MEG) data recorded during resting from the human brain. We show that this transmission of information occurs in a model of coupled oscillators and may represent a generic feature of a dynamical system. Together, our findings open the possibility of a general mechanism that may govern multi-scale interactions in brain dynamics.

Collective decision making by embodied neural agents

Collective decision making using simple social interactions has been studied in many types of multiagent systems, including robot swarms and human social networks. However, existing multiagent studies have rarely modeled the neural dynamics that underlie sensorimotor coordination in embodied biological agents. In this study, we investigated collective decisions that resulted from sensorimotor coordination among agents with simple neural dynamics. We equipped our agents with a model of minimal neural dynamics based on the coordination dynamics framework, and embedded them in an environment with a stimulus gradient. In our single-agent setup, the decision between two stimulus sources depends solely on the coordination of the agent's neural dynamics with its environment. In our multiagent setup, that same decision also depends on the sensorimotor coordination between agents, via their simple social interactions. Our results show that the success of collective decisions depended on a balance of intra-agent, interagent, and agent-environment coupling, and we use these results to identify the influences of environmental factors on decision difficulty. More generally, our results illustrate how collective behaviors can be analyzed in terms of the neural dynamics of the participating agents. This can contribute to ongoing developments in neuro-AI and self-organized multiagent systems.

Functional connectotomy of a whole-brain model reveals tumor-induced alterations to neuronal dynamics in glioma patients

Brain tumors can induce pathological changes in neuronal dynamics that are reflected in functional connectivity measures. Here, we use a whole-brain modeling approach to investigate pathological alterations to neuronal activity in glioma patients. By fitting a Hopf whole-brain model to empirical functional connectivity, we investigate glioma-induced changes in optimal model parameters. We observe considerable differences in neuronal dynamics between glioma patients and healthy controls, both on an individual and population-based level. In particular, model parameter estimation suggests that local tumor pathology causes changes in brain dynamics by increasing the influence of interregional interactions on global neuronal activity. Our approach demonstrates that whole-brain models provide valuable insights for understanding glioma-associated alterations in functional connectivity.

Where are higher-order cognitive functions? The paradox of non-locality in awake cognitive mapping using a complex dynamic system framework

This study addresses the challenge in identifying and preserving higher-order cognitive functions within a complex dynamic systems framework during neurosurgery. Traditionally, neurosurgical practice has prioritized avoiding language and motor deficits, while higher-order functions-such as social cognition and executive processes-remain underexplored. These functions arise from dynamic large-scale networks operating in an optimal balance between synchronization and metastability rather than from isolated and localized cortical regions. This complexity highlights a paradox of non-locality in awake cognitive mapping: no single area "contains" a function, but certain "critical points" can transiently disrupt network dynamics when stimulated intraoperatively. Direct electrical stimulation provides unique real-time insights by inducing brief dyssynchronizations that elicit observable behavioral changes, allowing neurosurgeons and neuropsychologists to pinpoint crucial cortical and subcortical "connectome-stop points" and minimize damage. Preserving deep white-matter tracts is essential, given their limited neuroplasticity and the profound, often irreversible impact of tract lesions on cognition. To address these challenges, we propose a three-step awake cognitive mapping approach: (1) localizing critical points of networks via DES-driven behavioral impairment, (2) constant monitoring of multiple cognitive domains as tumor resection progresses, and (3) halting resection at connectome-stop points to prevent irreversible deficits. An illustrative case involving a right parietal glioma demonstrates how this methodology integrates computational neuroscience, network theory, and clinical practice to achieve optimal functional preservation and maintain the patient's quality of life.

Understanding Altered Dynamics in Cocaine Use Disorder Through State Transitions Mediated by Artificial Perturbations

Background/Objectives: Cocaine use disorder (CUD) poses a worldwide health challenge, with severe consequences for brain function. However, the phase dynamics underlying CUD and the transitions between CUD and health remain poorly understood. Methods: Here, we used resting-state functional magnetic resonance imaging (fMRI) data from 43 CUD patients and 45 healthy controls (HCT). We performed empirical analysis to identify phase-coherence states and compared their probabilities of occurrence between conditions. To further explore the underlying mechanism, we employed computational modeling to replicate the observed state probabilities for each condition. These generated whole-brain models enabled us to simulate external perturbations and identify optimal brain regions mediating transitions between HCT and CUD. Results: We found that CUD was associated with a reduced occurrence probability of the state dominated by the default mode network (DMN). Perturbing the nucleus accumbens, thalamus, and specific regions within the default mode, limbic and frontoparietal networks drives transitions from HCT to CUD, while perturbing the hippocampus and specific regions within the visual, dorsal attention, and DMN facilitates a return from CUD to HCT. Conclusions: This study revealed altered DMN-related dynamics in CUD from the phase perspective and provides potential regions critical for state transitions. The results contribute to understanding the pathogenesis of CUD and the development of therapeutic stimulation strategies.

Contributions of short- and long-range white matter tracts in dynamic compensation with aging

Optimal brain function is shaped by a combination of global information integration, facilitated by long-range connections, and local processing, which relies on short-range connections and underlying biological factors. With aging, anatomical connectivity undergoes significant deterioration, which affects the brain's overall function. Despite the structural loss, previous research has shown that normative patterns of functions remain intact across the lifespan, defined as the compensatory mechanism of the aging brain. However, the crucial components in guiding the compensatory preservation of the dynamical complexity and the underlying mechanisms remain uncovered. Moreover, it remains largely unknown how the brain readjusts its biological parameters to maintain optimal brain dynamics with age; in this work, we provide a parsimonious mechanism using a whole-brain generative model to uncover the role of sub-communities comprised of short-range and long-range connectivity in driving the dynamic compensation process in the aging brain. We utilize two neuroimaging datasets to demonstrate how short- and long-range white matter tracts affect compensatory mechanisms. We unveil their modulation of intrinsic global scaling parameters, such as global coupling strength and conduction delay, via a personalized large-scale brain model. Our key finding suggests that short-range tracts predominantly amplify global coupling strength with age, potentially representing an epiphenomenon of the compensatory mechanism. This mechanistically explains the significance of short-range connections in compensating for the major loss of long-range connections during aging. This insight could help identify alternative avenues to address aging-related diseases where long-range connections are significantly deteriorated.

Excitatory-inhibitory homeostasis and bifurcation control in the Wilson-Cowan model of cortical dynamics

Although the primary function of excitatory-inhibitory (E-I) homeostasis is the maintenance of mean firing rates, the conjugation of multiple homeostatic mechanisms is thought to be pivotal to ensuring edge-of-bifurcation dynamics in cortical circuits. However, computational studies on E-I homeostasis have focused solely on the plasticity of inhibition, neglecting the impact of different modes of E-I homeostasis on cortical dynamics. Therefore, we investigate how the diverse mechanisms of E-I homeostasis employed by cortical networks shape oscillations and edge-of-bifurcation dynamics. Using the Wilson-Cowan model, we explore how distinct modes of E-I homeostasis maintain stable firing rates in models with varying levels of input and how it affects circuit dynamics. Our results confirm that E-I homeostasis can be leveraged to control edge-of-bifurcation dynamics and that some modes of homeostasis maintain mean firing rates under higher levels of input by modulating the distance to the bifurcation. Additionally, relying on multiple modes of homeostasis ensures stable activity while keeping oscillation frequencies within a physiological range. Our findings tie relevant features of cortical networks, such as E-I balance, the generation of gamma oscillations, and edge-of-bifurcation dynamics, under the framework of firing-rate homeostasis, providing a mechanistic explanation for the heterogeneity in the distance to the bifurcation found across cortical areas. In addition, we reveal the functional benefits of relying upon different homeostatic mechanisms, providing a robust method to regulate network dynamics with minimal perturbation to the generation of gamma rhythms and explaining the correlation between inhibition and gamma frequencies found in cortical networks.

Emergence of multiple spontaneous coherent subnetworks from a single configuration of human connectome coupled oscillators model

Multi-state metastability in neuroimaging signals reflects the brain's flexibility to transition between network configurations in response to changing environments or tasks. We modeled these dynamics with a Kuramoto network of 90 nodes oscillating at an intrinsic frequency of 40 Hz, interconnected using human brain structural connectivity strengths and delays. We simulated this model for 30 min to generate multi-state metastability. We identified global coupling and delay parameters that maximize spectral entropy, a proxy for multi-state metastability. At this operational point, multiple frequency-specific coherent sub-networks spontaneously emerge across oscillatory modes, persisting for periods between 140 and 4300 ms, reflecting flexible and sustained dynamic states. The topography of these sub-networks aligns with empirical resting-state neuroimaging data. Additionally, periodic components of the EEG spectra from young healthy participants correlate with maximal multi-state metastability, while dynamics away from this point correlate with sleep and anesthesia spectra. Our findings suggest that multi-state metastable functional dynamics observed in empirical data emerge from specific interactions of structural topography and connection delays, providing a platform to study mechanisms underlying flexible dynamics of cognition.

Different oscillatory mechanisms of dementia-related diseases with cognitive impairment in closed-eye state

The escalating global trend of aging has intensified the focus on health concerns prevalent among the elderly. Notably, Dementia related diseases, including Alzheimer's disease (AD) and frontotemporal dementia (FTD), significantly impair the quality of life for both affected seniors and their caregivers. However, the underlying neural mechanisms of these diseases remain incompletely understood, especially in terms of neural oscillations. In this study, we leveraged an open dataset containing 36 CE, 23 FTD, and 29 healthy controls (HC) to investigate these mechanisms. We accurately and clearly identified three stable oscillation targets (theta, ∼5 Hz, alpha, ∼10 Hz, and beta, ∼18 Hz) that facilitate differentiation between AD, FTD, and HC both statistically and through classification using machine learning algorithms. Overall, the differences between AD and HC were the most pronounced, with FTD exhibiting intermediate characteristics. The differences in the theta and alpha bands showed a global pattern, whereas the differences in the beta band were localized to the central-temporal region. Moreover, our analysis revealed that the relative theta power was significantly and negatively correlated with the Mini Mental State Examination (MMSE) scores, while the relative alpha and beta power showed a significant positive correlation. This study is the first to pinpoint multiple robust and effective neural oscillation targets to distinguish AD, offering a simple and convenient method that holds promise for future applications in the early screening of large-scale dementia-related diseases.

Transcranial ultrasound stimulation effect in the redundant and synergistic networks consistent across macaques

Low-intensity transcranial ultrasound stimulation (TUS) is a noninvasive technique that safely alters neural activity, reaching deep brain areas with good spatial accuracy. We investigated the effects of TUS in macaques using a recent metric, the synergy minus redundancy rank gradient, which quantifies different kinds of neural information processing. We analyzed this high-order quantity on the fMRI data after TUS in two targets: the supplementary motor area (SMA-TUS) and the frontal polar cortex (FPC-TUS). The TUS produced specific changes at the limbic network at FPC-TUS and the motor network at SMA-TUS and altered the sensorimotor, temporal, and frontal networks in both targets, mostly consistent across macaques. Moreover, there was a reduction in the structural and functional coupling after both stimulations. Finally, the TUS changed the intrinsic high-order network topology, decreasing the modular organization of the redundancy at SMA-TUS and increasing the synergistic integration at FPC-TUS.

Metastable Oscillatory Modes as a Signature of Entropy Management in the Brain

Entropy management, central to the Free Energy Principle, requires a process that temporarily shifts brain activity toward states of lower or higher entropy. Metastable synchronization is a process by which a system achieves entropy fluctuations by intermittently transitioning between states of collective order and disorder. Previous work has shown that collective oscillations, similar to those recorded from the brain, emerge spontaneously from weakly stable synchronization in critically coupled oscillator systems. However, direct evidence linking the formation of collective oscillations to entropy fluctuations is lacking. In this short communication, we demonstrate how the emergence of Metastable Oscillatory Modes (MOMs) is directly associated with a temporary reduction in entropy in the ongoing dynamics. We apply Shannon entropy to the distribution of eigenvalues of phase covariance over sliding time windows, capturing the temporal evolution of entropy at the level of the entire dynamical system. By demonstrating how the formation of MOMs impacts a system's entropy levels, we bridge theoretical works on the physics of coupled oscillators with the FEP framework, supporting the hypothesis that brain rhythms recorded experimentally are a signature of entropy management.

Toward a more comprehensive understanding of network centrality disruption in amnestic mild cognitive impairment: a MEG multilayer approach

BACKGROUND

Alzheimer's Disease (AD) is the most common form of dementia. Its early stage, amnestic Mild Cognitive Impairment (aMCI), is characterized by disrupted information flow in the brain. Previous studies have yielded inconsistent results when using electrophysiological techniques to investigate functional connectivity changes in AD, and a contributing factor may be the study of brain activity divided into frequencies.

METHODS

Our study aimed to address this issue by employing a cross-frequency approach to compare the functional networks of 172 healthy subjects and 105 aMCI patients. Using magnetoencephalography, we constructed source-based multilayer graphs considering both intra- and inter-frequency functional connectivity. We then assessed changes in network organization through three centrality measures, and combined them into a unified centrality score to provide a comprehensive assessment of centrality disruption in aMCI.

RESULTS

The results revealed a noteworthy shift in centrality distribution in aMCI patients, both in terms of spatial distribution and frequency. Posterior brain regions decrease synchrony between their high-frequency oscillations and other regions' activity across all frequencies, while anterior regions increase synchrony between their low-frequency oscillations and other regions' activity across all frequencies. Thus, posterior regions reduce their relative importance in favor of anterior regions.

CONCLUSIONS

Our findings provide valuable insights into the intricate changes that occur in functional brain networks during the early stages of AD, demonstrating that considering the interplays between different frequency bands enhances our understanding of AD network dynamics and setting a precedent for the study of functional networks using a multilayer approach.

Exploring nonlinear dynamics in brain functionality through phase portraits and fuzzy recurrence plots

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

Analyzing asymmetry in brain hierarchies with a linear state-space model of resting-state fMRI data

This study challenges the traditional focus on zero-lag statistics in resting-state functional magnetic resonance imaging (rsfMRI) research. Instead, it advocates for considering time-lag interactions to unveil the directionality and asymmetries of the brain hierarchy. Effective connectivity (EC), the state matrix in dynamical causal modeling (DCM), is a commonly used metric for studying dynamical properties and causal interactions within a linear state-space system description. Here, we focused on how time-lag statistics are incorporated within the framework of DCM resulting in an asymmetric EC matrix. Our approach involves decomposing the EC matrix, revealing a steady-state differential cross-covariance matrix that is responsible for modeling information flow and introducing time-irreversibility. Specifically, the system's dynamics, influenced by the off-diagonal part of the differential covariance, exhibit a curl steady-state flow component that breaks detailed balance and diverges the dynamics from equilibrium. Our empirical findings indicate that the EC matrix's outgoing strengths correlate with the flow described by the differential cross covariance, while incoming strengths are primarily driven by zero-lag covariance, emphasizing conditional independence over directionality.

Network connectivity underlying information processing speed in children: Application of a pediatric brain tumor survivor injury model

Elucidating how adaptive and maladaptive changes to the structural connectivity of brain networks influences neural synchrony, and how this structure-function coupling impacts cognition is an important question in human neuroscience. This study assesses these links in the default mode and executive control networks during resting state, a visual-motor task, and through computational modeling in the developing brain and in acquired brain injuries. Pediatric brain tumor survivors were used as an injury model as they are known to exhibit cognitive deficits, structural connectivity compromise, and perturbations in neural communication. Focusing on information processing speed to assess cognitive performance, we demonstrate that during the presence and absence of specific task demands, structural connectivity of these critical brain networks directly influences neural communication and information processing speed, and white matter compromise has an indirect adverse impact on reaction time via perturbed neural synchrony. Further, when our experimentally acquired structural connectomes simulated neural activity, the resulting functional simulations aligned with our empirical results and accurately predicted cognitive group differences. Overall, our synergistic findings further our understanding of the neural underpinnings of cognition and when it is perturbed. Further establishing alterations in structural-functional coupling as biomarkers of cognitive impairments could facilitate early intervention and monitoring of these deficits.

Exploring Nonlinear Dynamics In Brain Functionality Through Phase Portraits And Fuzzy Recurrence Plots

Much of the complexity and diversity found in nature is driven by nonlinear phenomena, and this holds true for the brain. Nonlinear dynamics theory has been successfully utilized in explaining brain functions from a biophysics standpoint, and the field of statistical physics continues to make substantial progress in understanding brain connectivity and function. This study delves into complex brain functional connectivity using biophysical nonlinear dynamics approaches. We aim to uncover hidden information in high-dimensional and nonlinear neural signals, with the hope of providing a useful tool for analyzing information transitions in functionally complex networks. By utilizing phase portraits and fuzzy recurrence plots, we investigated the latent information in the functional connectivity of complex brain networks. Our numerical experiments, which include synthetic linear dynamics neural time series and a biophysically realistic neural mass model, showed that phase portraits and fuzzy recurrence plots are highly sensitive to changes in neural dynamics and can also be used to predict functional connectivity based on structural connectivity. Furthermore, the results showed that phase trajectories of neuronal activity encode low-dimensional dynamics, and the geometric properties of the limit-cycle attractor formed by the phase portraits can be used to explain the neurodynamics. Additionally, our results showed that the phase portrait and fuzzy recurrence plots can be used as functional connectivity descriptors, and both metrics were able to capture and explain nonlinear dynamics behavior during specific cognitive tasks. In conclusion, our findings suggest that phase portraits and fuzzy recurrence plots could be highly effective as functional connectivity descriptors, providing valuable insights into nonlinear dynamics in the brain.

Emergence of metastability in frustrated oscillatory networks: the key role of hierarchical modularity

Oscillatory complex networks in the metastable regime have been used to study the emergence of integrated and segregated activity in the brain, which are hypothesised to be fundamental for cognition. Yet, the parameters and the underlying mechanisms necessary to achieve the metastable regime are hard to identify, often relying on maximising the correlation with empirical functional connectivity dynamics. Here, we propose and show that the brain's hierarchically modular mesoscale structure alone can give rise to robust metastable dynamics and (metastable) chimera states in the presence of phase frustration. We construct unweighted 3-layer hierarchical networks of identical Kuramoto-Sakaguchi oscillators, parameterized by the average degree of the network and a structural parameter determining the ratio of connections between and within blocks in the upper two layers. Together, these parameters affect the characteristic timescales of the system. Away from the critical synchronization point, we detect the emergence of metastable states in the lowest hierarchical layer coexisting with chimera and metastable states in the upper layers. Using the Laplacian renormalization group flow approach, we uncover two distinct pathways towards achieving the metastable regimes detected in these distinct layers. In the upper layers, we show how the symmetry-breaking states depend on the slow eigenmodes of the system. In the lowest layer instead, metastable dynamics can be achieved as the separation of timescales between layers reaches a critical threshold. Our results show an explicit relationship between metastability, chimera states, and the eigenmodes of the system, bridging the gap between harmonic based studies of empirical data and oscillatory models.

The virtual multiple sclerosis patient

Multiple sclerosis (MS) diagnosis typically involves assessing clinical symptoms, MRI findings, and ruling out alternative explanations. While myelin damage broadly affects conduction speeds, traditional tests focus on specific white-matter tracts, which may not reflect overall impairment accurately. In this study, we integrate diffusion tensor immaging (DTI) and magnetoencephalography (MEG) data into individualized virtual brain models to estimate conduction velocities for MS patients and controls. Using Bayesian inference, we demonstrated a causal link between empirical spectral changes and inferred slower conduction velocities in patients. Remarkably, these velocities proved superior predictors of clinical disability compared to structural damage. Our findings underscore a nuanced relationship between conduction delays and large-scale brain dynamics, suggesting that individualized velocity alterations at the whole-brain level contribute causatively to clinical outcomes in MS.

How to design optimal brain stimulation to modulate phase-amplitude coupling?

Objective.Phase-amplitude coupling (PAC), the coupling of the amplitude of a faster brain rhythm to the phase of a slower brain rhythm, plays a significant role in brain activity and has been implicated in various neurological disorders. For example, in Parkinson's disease, PAC between the beta (13-30 Hz) and gamma (30-100 Hz) rhythms in the motor cortex is exaggerated, while in Alzheimer's disease, PAC between the theta (4-8 Hz) and gamma rhythms is diminished. Modulating PAC (i.e. reducing or enhancing PAC) using brain stimulation could therefore open new therapeutic avenues. However, while it has been previously reported that phase-locked stimulation can increase PAC, it is unclear what the optimal stimulation strategy to modulate PAC might be. Here, we provide a theoretical framework to narrow down the experimental optimisation of stimulation aimed at modulating PAC, which would otherwise rely on trial and error.Approach.We make analytical predictions using a Stuart-Landau model, and confirm these predictions in a more realistic model of coupled neural populations.Main results.Our framework specifies the critical Fourier coefficients of the stimulation waveform which should be tuned to optimally modulate PAC. Depending on the characteristics of the amplitude response curve of the fast population, these components may include the slow frequency, the fast frequency, combinations of these, as well as their harmonics. We also show that the optimal balance of energy between these Fourier components depends on the relative strength of the endogenous slow and fast rhythms, and that the alignment of fast components with the fast rhythm should change throughout the slow cycle. Furthermore, we identify the conditions requiring to phase-lock stimulation to the fast and/or slow rhythms.Significance.Together, our theoretical framework lays the foundation for guiding the development of innovative and more effective brain stimulation aimed at modulating PAC for therapeutic benefit.

Human connectome topology directs cortical traveling waves and shapes frequency gradients

Traveling waves and neural oscillation frequency gradients are pervasive in the human cortex. While the direction of traveling waves has been linked to brain function and dysfunction, the factors that determine this direction remain elusive. We hypothesized that structural connectivity instrength gradients - defined as the gradually varying sum of incoming connection strengths across the cortex - could shape both traveling wave direction and frequency gradients. We confirm the presence of instrength gradients in the human connectome across diverse cohorts and parcellations. Using a cortical network model, we demonstrate how these instrength gradients direct traveling waves and shape frequency gradients. Our model fits resting-state MEG functional connectivity best in a regime where instrength-directed traveling waves and frequency gradients emerge. We further show how structural subnetworks of the human connectome generate opposing wave directions and frequency gradients observed in the alpha and beta bands. Our findings suggest that structural connectivity instrength gradients affect both traveling wave direction and frequency gradients.

Biophysical modulation and robustness of itinerant complexity in neuronal networks

Transient synchronization of bursting activity in neuronal networks, which occurs in patterns of metastable itinerant phase relationships between neurons, is a notable feature of network dynamics observed in vivo. However, the mechanisms that contribute to this dynamical complexity in neuronal circuits are not well understood. Local circuits in cortical regions consist of populations of neurons with diverse intrinsic oscillatory features. In this study, we numerically show that the phenomenon of transient synchronization, also referred to as metastability, can emerge in an inhibitory neuronal population when the neurons' intrinsic fast-spiking dynamics are appropriately modulated by slower inputs from an excitatory neuronal population. Using a compact model of a mesoscopic-scale network consisting of excitatory pyramidal and inhibitory fast-spiking neurons, our work demonstrates a relationship between the frequency of pyramidal population oscillations and the features of emergent metastability in the inhibitory population. In addition, we introduce a method to characterize collective transitions in metastable networks. Finally, we discuss potential applications of this study in mechanistically understanding cortical network dynamics.

Does the brain behave like a (complex) network? I. Dynamics

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network structure does not entail that the brain actually works as a network. Asking whether the brain behaves as a network means asking whether network properties count. From the viewpoint of neurophysiology and, possibly, of brain physics, the most substantial issues a network structure may be instrumental in addressing relate to the influence of network properties on brain dynamics and to whether these properties ultimately explain some aspects of brain function. Here, we address the dynamical implications of complex network, examining which aspects and scales of brain activity may be understood to genuinely behave as a network. To do so, we first define the meaning of networkness, and analyse some of its implications. We then examine ways in which brain anatomy and dynamics can be endowed with a network structure and discuss possible ways in which network structure may be shown to represent a genuine organisational principle of brain activity, rather than just a convenient description of its anatomy and dynamics.

Exploring global and local processes underlying alterations in resting-state functional connectivity and dynamics in schizophrenia

Introduction

We examined changes in large-scale functional connectivity and temporal dynamics and their underlying mechanisms in schizophrenia (ScZ) through measurements of resting-state functional magnetic resonance imaging (rs-fMRI) data and computational modelling.

Methods

The rs-fMRI measurements from patients with chronic ScZ (n=38) and matched healthy controls (n=43), were obtained through the public schizConnect repository. Computational models were constructed based on diffusion-weighted MRI scans and fit to the experimental rs-fMRI data.

Results

We found decreased large-scale functional connectivity across sensory and association areas and for all functional subnetworks for the ScZ group. Additionally global synchrony was reduced in patients while metastability was unaltered. Perturbations of the computational model revealed that decreased global coupling and increased background noise levels both explained the experimentally found deficits better than local changes to the GABAergic or glutamatergic system.

Discussion

The current study suggests that large-scale alterations in ScZ are more likely the result of global rather than local network changes.

The Hopf whole-brain model and its linear approximation

Whole-brain models have proven to be useful to understand the emergence of collective activity among neural populations or brain regions. These models combine connectivity matrices, or connectomes, with local node dynamics, noise, and, eventually, transmission delays. Multiple choices for the local dynamics have been proposed. Among them, nonlinear oscillators corresponding to a supercritical Hopf bifurcation have been used to link brain connectivity and collective phase and amplitude dynamics in different brain states. Here, we studied the linear fluctuations of this model to estimate its stationary statistics, i.e., the instantaneous and lagged covariances and the power spectral densities. This linear approximation-that holds in the case of heterogeneous parameters and time-delays-allows analytical estimation of the statistics and it can be used for fast parameter explorations to study changes in brain state, changes in brain activity due to alterations in structural connectivity, and modulations of parameter due to non-equilibrium dynamics.

Bridging functional and anatomical neural connectivity through cluster synchronization

The dynamics of the brain results from the complex interplay of several neural populations and is affected by both the individual dynamics of these areas and their connection structure. Hence, a fundamental challenge is to derive models of the brain that reproduce both structural and functional features measured experimentally. Our work combines neuroimaging data, such as dMRI, which provides information on the structure of the anatomical connectomes, and fMRI, which detects patterns of approximate synchronous activity between brain areas. We employ cluster synchronization as a tool to integrate the imaging data of a subject into a coherent model, which reconciles structural and dynamic information. By using data-driven and model-based approaches, we refine the structural connectivity matrix in agreement with experimentally observed clusters of brain areas that display coherent activity. The proposed approach leverages the assumption of homogeneous brain areas; we show the robustness of this approach when heterogeneity between the brain areas is introduced in the form of noise, parameter mismatches, and connection delays. As a proof of concept, we apply this approach to MRI data of a healthy adult at resting state.

Efficient, Formal, Material, and Final Causes in Biology and Technology

This paper considers how a classification of causal effects as comprising efficient, formal, material, and final causation can provide a useful understanding of how emergence takes place in biology and technology, with formal, material, and final causation all including cases of downward causation; they each occur in both synchronic and diachronic forms. Taken together, they underlie why all emergent levels in the hierarchy of emergence have causal powers (which is Noble's principle of biological relativity) and so why causal closure only occurs when the upwards and downwards interactions between all emergent levels are taken into account, contra to claims that some underlying physics level is by itself causality complete. A key feature is that stochasticity at the molecular level plays an important role in enabling agency to emerge, underlying the possibility of final causation occurring in these contexts.

Breathing in waves: Understanding respiratory-brain coupling as a gradient of predictive oscillations

Breathing plays a crucial role in shaping perceptual and cognitive processes by regulating the strength and synchronisation of neural oscillations. Numerous studies have demonstrated that respiratory rhythms govern a wide range of behavioural effects across cognitive, affective, and perceptual domains. Additionally, respiratory-modulated brain oscillations have been observed in various mammalian models and across diverse frequency spectra. However, a comprehensive framework to elucidate these disparate phenomena remains elusive. In this review, we synthesise existing findings to propose a neural gradient of respiratory-modulated brain oscillations and examine recent computational models of neural oscillations to map this gradient onto a hierarchical cascade of precision-weighted prediction errors. By deciphering the computational mechanisms underlying respiratory control of these processes, we can potentially uncover new pathways for understanding the link between respiratory-brain coupling and psychiatric disorders.

Mental Gravity: Depression as Spacetime Curvature of the Self, Mind, and Brain

The principle of mental gravity contends that the mind uses physical gravity as a mental model or simulacrum to express the relation between the inner self and the outer world in terms of "UP"-ness and "DOWN"-ness. The simulation of increased gravity characterises a continuum of mental gravity which states includes depression as the paradigmatic example of being down, low, heavy, and slow. The physics of gravity can also be used to model spacetime curvature in depression, particularly gravitational time dilation as a property of MG analogous to subjective time dilation (i.e., the slowing of temporal flow in conscious experience). The principle has profound implications for the Temporo-spatial Theory of Consciousness (TTC) with regard to temporo-spatial alignment that establishes a "world-brain relation" that is centred on embodiment and the socialisation of conscious states. The principle of mental gravity provides the TTC with a way to incorporate the structure of the world into the structure of the brain, conscious experience, and thought. In concert with other theories of cognitive and neurobiological spacetime, the TTC can also work towards the "common currency" approach that also potentially connects the TTC to predictive processing frameworks such as free energy, neuronal gauge theories, and active inference accounts of depression. It gives the up/down dimension of space, as defined by the gravitational field, a unique status that is connected to both our embodied interaction with the physical world, and also the inverse, reflective, emotional but still embodied experience of ourselves.

Multi-modal and multi-model interrogation of large-scale functional brain networks

Existing whole-brain models are generally tailored to the modelling of a particular data modality (e.g., fMRI or MEG/EEG). We propose that despite the differing aspects of neural activity each modality captures, they originate from shared network dynamics. Building on the universal principles of self-organising delay-coupled nonlinear systems, we aim to link distinct features of brain activity - captured across modalities - to the dynamics unfolding on a macroscopic structural connectome. To jointly predict connectivity, spatiotemporal and transient features of distinct signal modalities, we consider two large-scale models - the Stuart Landau and Wilson and Cowan models - which generate short-lived 40 Hz oscillations with varying levels of realism. To this end, we measure features of functional connectivity and metastable oscillatory modes (MOMs) in fMRI and MEG signals - and compare them against simulated data. We show that both models can represent MEG functional connectivity (FC), functional connectivity dynamics (FCD) and generate MOMs to a comparable degree. This is achieved by adjusting the global coupling and mean conduction time delay and, in the WC model, through the inclusion of balance between excitation and inhibition. For both models, the omission of delays dramatically decreased the performance. For fMRI, the SL model performed worse for FCD and MOMs, highlighting the importance of balanced dynamics for the emergence of spatiotemporal and transient patterns of ultra-slow dynamics. Notably, optimal working points varied across modalities and no model was able to achieve a correlation with empirical FC higher than 0.4 across modalities for the same set of parameters. Nonetheless, both displayed the emergence of FC patterns that extended beyond the constraints of the anatomical structure. Finally, we show that both models can generate MOMs with empirical-like properties such as size (number of brain regions engaging in a mode) and duration (continuous time interval during which a mode appears). Our results demonstrate the emergence of static and dynamic properties of neural activity at different timescales from networks of delay-coupled oscillators at 40 Hz. Given the higher dependence of simulated FC on the underlying structural connectivity, we suggest that mesoscale heterogeneities in neural circuitry may be critical for the emergence of parallel cross-modal functional networks and should be accounted for in future modelling endeavours.

A universal description of stochastic oscillators

Many systems in physics, chemistry, and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example, linear dynamics of a stable focus with fluctuations, limit-cycle systems perturbed by noise, or excitable systems in which random inputs lead to a train of pulses. Despite their diverse origins, the phenomenology of random oscillations can be strikingly similar. Here, we introduce a nonlinear transformation of stochastic oscillators to a complex-valued function [Formula: see text](x) that greatly simplifies and unifies the mathematical description of the oscillator's spontaneous activity, its response to an external time-dependent perturbation, and the correlation statistics of different oscillators that are weakly coupled. The function [Formula: see text] (x) is the eigenfunction of the Kolmogorov backward operator with the least negative (but nonvanishing) eigenvalue λ1 = μ1 + iω1. The resulting power spectrum of the complex-valued function is exactly given by a Lorentz spectrum with peak frequency ω1 and half-width μ1; its susceptibility with respect to a weak external forcing is given by a simple one-pole filter, centered around ω1; and the cross-spectrum between two coupled oscillators can be easily expressed by a combination of the spontaneous power spectra of the uncoupled systems and their susceptibilities. Our approach makes qualitatively different stochastic oscillators comparable, provides simple characteristics for the coherence of the random oscillation, and gives a framework for the description of weakly coupled oscillators.

Multiscale effects of excitatory-inhibitory homeostasis in lesioned cortical networks: A computational study

Stroke-related disruptions in functional connectivity (FC) often spread beyond lesioned areas and, given the localized nature of lesions, it is unclear how the recovery of FC is orchestrated on a global scale. Since recovery is accompanied by long-term changes in excitability, we propose excitatory-inhibitory (E-I) homeostasis as a driving mechanism. We present a large-scale model of the neocortex, with synaptic scaling of local inhibition, showing how E-I homeostasis can drive the post-lesion restoration of FC and linking it to changes in excitability. We show that functional networks could reorganize to recover disrupted modularity and small-worldness, but not network dynamics, suggesting the need to consider forms of plasticity beyond synaptic scaling of inhibition. On average, we observed widespread increases in excitability, with the emergence of complex lesion-dependent patterns related to biomarkers of relevant side effects of stroke, such as epilepsy, depression and chronic pain. In summary, our results show that the effects of E-I homeostasis extend beyond local E-I balance, driving the restoration of global properties of FC, and relating to post-stroke symptomatology. Therefore, we suggest the framework of E-I homeostasis as a relevant theoretical foundation for the study of stroke recovery and for understanding the emergence of meaningful features of FC from local dynamics.

Interacting spiral wave patterns underlie complex brain dynamics and are related to cognitive processing

The large-scale activity of the human brain exhibits rich and complex patterns, but the spatiotemporal dynamics of these patterns and their functional roles in cognition remain unclear. Here by characterizing moment-by-moment fluctuations of human cortical functional magnetic resonance imaging signals, we show that spiral-like, rotational wave patterns (brain spirals) are widespread during both resting and cognitive task states. These brain spirals propagate across the cortex while rotating around their phase singularity centres, giving rise to spatiotemporal activity dynamics with non-stationary features. The properties of these brain spirals, such as their rotational directions and locations, are task relevant and can be used to classify different cognitive tasks. We also demonstrate that multiple, interacting brain spirals are involved in coordinating the correlated activations and de-activations of distributed functional regions; this mechanism enables flexible reconfiguration of task-driven activity flow between bottom-up and top-down directions during cognitive processing. Our findings suggest that brain spirals organize complex spatiotemporal dynamics of the human brain and have functional correlates to cognitive processing.

Moving from phenomenological to predictive modelling: Progress and pitfalls of modelling brain stimulation in-silico

Brain stimulation is an increasingly popular neuromodulatory tool used in both clinical and research settings; however, the effects of brain stimulation, particularly those of non-invasive stimulation, are variable. This variability can be partially explained by an incomplete mechanistic understanding, coupled with a combinatorial explosion of possible stimulation parameters. Computational models constitute a useful tool to explore the vast sea of stimulation parameters and characterise their effects on brain activity. Yet the utility of modelling stimulation in-silico relies on its biophysical relevance, which needs to account for the dynamics of large and diverse neural populations and how underlying networks shape those collective dynamics. The large number of parameters to consider when constructing a model is no less than those needed to consider when planning empirical studies. This piece is centred on the application of phenomenological and biophysical models in non-invasive brain stimulation. We first introduce common forms of brain stimulation and computational models, and provide typical construction choices made when building phenomenological and biophysical models. Through the lens of four case studies, we provide an account of the questions these models can address, commonalities, and limitations across studies. We conclude by proposing future directions to fully realise the potential of computational models of brain stimulation for the design of personalized, efficient, and effective stimulation strategies.

Intrinsic macroscale oscillatory modes driving long range functional connectivity in female rat brains detected by ultrafast fMRI

Spontaneous fluctuations in functional magnetic resonance imaging (fMRI) signals correlate across distant brain areas, shaping functionally relevant intrinsic networks. However, the generative mechanism of fMRI signal correlations, and in particular the link with locally-detected ultra-slow oscillations, are not fully understood. To investigate this link, we record ultrafast ultrahigh field fMRI signals (9.4 Tesla, temporal resolution = 38 milliseconds) from female rats across three anesthesia conditions. Power at frequencies extending up to 0.3 Hz is detected consistently across rat brains and is modulated by anesthesia level. Principal component analysis reveals a repertoire of modes, in which transient oscillations organize with fixed phase relationships across distinct cortical and subcortical structures. Oscillatory modes are found to vary between conditions, resonating at faster frequencies under medetomidine sedation and reducing both in number, frequency, and duration with the addition of isoflurane. Peaking in power within clear anatomical boundaries, these oscillatory modes point to an emergent systemic property. This work provides additional insight into the origin of oscillations detected in fMRI and the organizing principles underpinning spontaneous long-range functional connectivity.

Dynamic sensitivity analysis: Defining personalised strategies to drive brain state transitions via whole brain modelling

Traditionally, in neuroimaging, model-free analyses are used to find significant differences between brain states via signal detection theory. Depending on the a priori assumptions about the underlying data, different spatio-temporal features can be analysed. Alternatively, model-based techniques infer features from the data and compare significance from model parameters. However, to assess transitions from one brain state to another remains a challenge in current paradigms. Here, we introduce a "Dynamic Sensitivity Analysis" framework that quantifies transitions between brain states in terms of stimulation ability to rebalance spatio-temporal brain activity towards a target state such as healthy brain dynamics. In practice, it means building a whole-brain model fitted to the spatio-temporal description of brain dynamics, and applying systematic stimulations in-silico to assess the optimal strategy to drive brain dynamics towards a target state. Further, we show how Dynamic Sensitivity Analysis extends to various brain stimulation paradigms, ultimately contributing to improving the efficacy of personalised clinical interventions.

How critical is brain criticality?

Criticality is the singular state of complex systems poised at the brink of a phase transition between order and randomness. Such systems display remarkable information-processing capabilities, evoking the compelling hypothesis that the brain may itself be critical. This foundational idea is now drawing renewed interest thanks to high-density data and converging cross-disciplinary knowledge. Together, these lines of inquiry have shed light on the intimate link between criticality, computation, and cognition. Here, we review these emerging trends in criticality neuroscience, highlighting new data pertaining to the edge of chaos and near-criticality, and making a case for the distance to criticality as a useful metric for probing cognitive states and mental illness. This unfolding progress in the field contributes to establishing criticality theory as a powerful mechanistic framework for studying emergent function and its efficiency in both biological and artificial neural networks.