Dynamic causal modeling with neural fields

Phase slips extracted from derivatives of EEG data provide a deeper insight into the formation of cortical phase transitions

The phase slips are generally extracted from the EEG using Hilbert transforms but could also be extracted from the derivatives of EEG, providing additional information about the formation of cortical phase transitions. We examined this from the 30 s long, 256-channel resting state, eyes open EEG data of a 30-year-old male subject. The phase slip rates, PSR1 from EEG, PSR2 from the first-order derivative of EEG, and PSR3 from the second-order derivative of EEG, respectively, were extracted. The study was performed in the alpha (7-12 Hz) band only. The spatiotemporal plots of the EEG and phase slip rates over a 3.0 s period with a 0.5 s resolution were made with a montage layout of the 256 electrode positions. The spatiotemporal patterns of EEG and its derivatives exhibited shifting activity from posterior visual areas to the central and frontal regions over the 3.0 s period. The PSR1, PSR2, and PSR3 activity areas were different from the EEG and were distributed in larger areas as compared with the EEG and its derivatives. Also, the PSR2 and PSR3 activity areas and magnitudes were significantly different as compared with the PSR1 alone. This was also confirmed (p < 0.01) by the one-way ANOVA analysis of the means of PSR1, PSR2, and PSR3. These results show that PSR2 and PSR3 carry additional information that could potentially be biomarkers for studying the rate of formation of phase slips and the related cortical activity from the derivatives of EEG data.

A cortical field theory - dynamics and symmetries

We characterise cortical dynamics using partial differential equations (PDEs), analysing various connectivity patterns within the cortical sheet. This exploration yields diverse dynamics, encompassing wave equations and limit cycle activity. We presume balanced equations between excitatory and inhibitory neuronal units, reflecting the ubiquitous oscillatory patterns observed in electrophysiological measurements. Our derived dynamics comprise lowest-order wave equations (i.e., the Klein-Gordon model), limit cycle waves, higher-order PDE formulations, and transitions between limit cycles and near-zero states. Furthermore, we delve into the symmetries of the models using the Lagrangian formalism, distinguishing between continuous and discontinuous symmetries. These symmetries allow for mathematical expediency in the analysis of the model and could also be useful in studying the effect of symmetrical input from distributed cortical regions. Overall, our ability to derive multiple constraints on the fields - and predictions of the model - stems largely from the underlying assumption that the brain operates at a critical state. This assumption, in turn, drives the dynamics towards oscillatory or semi-conservative behaviour. Within this critical state, we can leverage results from the physics literature, which serve as analogues for neural fields, and implicit construct validity. Comparisons between our model predictions and electrophysiological findings from the literature - such as spectral power distribution across frequencies, wave propagation speed, epileptic seizure generation, and pattern formation over the cortical surface - demonstrate a close match. This study underscores the importance of utilizing symmetry preserving PDE formulations for further mechanistic insights into cortical activity.

Decrease in phase slip rates and phase cone structures during seizure evolution and epileptogenic activities derived from microgrid ECoG data

Sudden phase changes are related to cortical phase transitions, which likely change in frequency and spatial distribution as epileptogenic activity evolves. A 100 s long section of micro-ECoG data obtained before and during a seizure was selected and analyzed. In addition, nine other short-duration epileptic events were also examined. The data was collected at 420 Hz, imported into MATLAB, downsampled to 200 Hz, and filtered in the 1-50 Hz band. The Hilbert transform was applied to compute the analytic phase, which was then unwrapped, and detrended to look for sudden phase changes. The phase slip rate (counts/s) and its acceleration (counts/s2) were computed with a stepping window of 1-s duration and with a step size of 5 ms. The analysis was performed for theta (3-7 Hz), alpha (7-12 Hz), and beta (12-30 Hz) bands. The phase slip rate on all electrodes in the theta band decreased while it increased for the alpha and beta bands during the seizure period. Similar patterns were observed for isolated epileptogenic events. Spatiotemporal contour plots of the phase slip rates were also constructed using a montage layout of 8 × 8 electrode positions. These plots exhibited dynamic and oscillatory formation of phase cone-like structures which were higher in the theta band and lower in the alpha and beta bands during the seizure period and epileptogenic events. These results indicate that the formation of phase cones might be an excellent biomarker to study the evolution of a seizure and also the cortical dynamics of isolated epileptogenic events.

Bayesian inference of a spectral graph model for brain oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which cannot be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Language network self-inhibition and semantic similarity in first-episode schizophrenia: A computational-linguistic and effective connectivity approach

INTRODUCTION

A central feature of schizophrenia is the disorganization and impoverishment of language. Recently, we observed higher semantic similarity in first-episode-schizophrenia (FES) patients. In this study, we investigate if this aberrant similarity relates to the 'causal' connectivity between two key nodes of the word production system: inferior frontal gyrus (IFG) and the semantic-hub at the ventral anterior temporal lobe (vATL).

METHODS

Resting-state fMRI scans were collected from 60 participants (30 untreated FES and 30 healthy controls). The semantic distance was measured with the CoVec semantic tool based on GloVe. A spectral dynamic causal model with Parametrical Empirical Bayes was constructed modelling the intrinsic self-inhibitory and extrinsic-excitatory connections within the brain regions. We estimated the parameters of a fully connected model with the semantic distance as a covariate.

RESULTS

FES patients chose words with higher semantic similarity when describing the pictures compared to the HC group. Among patients, an increased semantic similarity was related with an increase in intrinsic connections within both the vATL and IFG, suggesting that reduced 'synaptic gain' in these regions likely contribute to aberrant sampling of the semantic space during discourse in schizophrenia.

CONCLUSIONS

Lexical impoverishment relates to increased self-inhibition in both the IFG and vATL. The associated reduction in synaptic gain may relate to reduced precision of locally generated neural activity, forcing the choice of words that are already 'activated' in a lexical network. One approach to improve word sampling may be via promoting synaptic gain via supra-physiological stimulation within the Broca's-vATL network; this proposal needs verification.

A multi-layer mean-field model of the cerebellum embedding microstructure and population-specific dynamics

Mean-field (MF) models are computational formalism used to summarize in a few statistical parameters the salient biophysical properties of an inter-wired neuronal network. Their formalism normally incorporates different types of neurons and synapses along with their topological organization. MFs are crucial to efficiently implement the computational modules of large-scale models of brain function, maintaining the specificity of local cortical microcircuits. While MFs have been generated for the isocortex, they are still missing for other parts of the brain. Here we have designed and simulated a multi-layer MF of the cerebellar microcircuit (including Granule Cells, Golgi Cells, Molecular Layer Interneurons, and Purkinje Cells) and validated it against experimental data and the corresponding spiking neural network (SNN) microcircuit model. The cerebellar MF was built using a system of equations, where properties of neuronal populations and topological parameters are embedded in inter-dependent transfer functions. The model time constant was optimised using local field potentials recorded experimentally from acute mouse cerebellar slices as a template. The MF reproduced the average dynamics of different neuronal populations in response to various input patterns and predicted the modulation of the Purkinje Cells firing depending on cortical plasticity, which drives learning in associative tasks, and the level of feedforward inhibition. The cerebellar MF provides a computationally efficient tool for future investigations of the causal relationship between microscopic neuronal properties and ensemble brain activity in virtual brain models addressing both physiological and pathological conditions.

In vivo ephaptic coupling allows memory network formation

It is increasingly clear that memories are distributed across multiple brain areas. Such "engram complexes" are important features of memory formation and consolidation. Here, we test the hypothesis that engram complexes are formed in part by bioelectric fields that sculpt and guide the neural activity and tie together the areas that participate in engram complexes. Like the conductor of an orchestra, the fields influence each musician or neuron and orchestrate the output, the symphony. Our results use the theory of synergetics, machine learning, and data from a spatial delayed saccade task and provide evidence for in vivo ephaptic coupling in memory representations.

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.

Accurate and Efficient Simulation of Very High-Dimensional Neural Mass Models with Distributed-Delay Connectome Tensors

This paper introduces methods and a novel toolbox that efficiently integrates high-dimensional Neural Mass Models (NMMs) specified by two essential components. The first is the set of nonlinear Random Differential Equations (RDEs) of the dynamics of each neural mass. The second is the highly sparse three-dimensional Connectome Tensor (CT) that encodes the strength of the connections and the delays of information transfer along the axons of each connection. To date, simplistic assumptions prevail about delays in the CT, often assumed to be Dirac-delta functions. In reality, delays are distributed due to heterogeneous conduction velocities of the axons connecting neural masses. These distributed-delay CTs are challenging to model. Our approach implements these models by leveraging several innovations. Semi-analytical integration of RDEs is done with the Local Linearization (LL) scheme for each neural mass model, ensuring dynamical fidelity to the original continuous-time nonlinear dynamic. This semi-analytic LL integration is highly computationally-efficient. In addition, a tensor representation of the CT facilitates parallel computation. It also seamlessly allows modeling distributed delays CT with any level of complexity or realism. This ease of implementation includes models with distributed-delay CTs. Consequently, our algorithm scales linearly with the number of neural masses and the number of equations they are represented with, contrasting with more traditional methods that scale quadratically at best. To illustrate the toolbox's usefulness, we simulate a single Zetterberg-Jansen-Rit (ZJR) cortical column, a single thalmo-cortical unit, and a toy example comprising 1000 interconnected ZJR columns. These simulations demonstrate the consequences of modifying the CT, especially by introducing distributed delays. The examples illustrate the complexity of explaining EEG oscillations, e.g., split alpha peaks, since they only appear for distinct neural masses. We provide an open-source Script for the toolbox.

Uncovering the organization of neural circuits with Generalized Phase Locking Analysis

Despite the considerable progress of in vivo neural recording techniques, inferring the biophysical mechanisms underlying large scale coordination of brain activity from neural data remains challenging. One obstacle is the difficulty to link high dimensional functional connectivity measures to mechanistic models of network activity. We address this issue by investigating spike-field coupling (SFC) measurements, which quantify the synchronization between, on the one hand, the action potentials produced by neurons, and on the other hand mesoscopic "field" signals, reflecting subthreshold activities at possibly multiple recording sites. As the number of recording sites gets large, the amount of pairwise SFC measurements becomes overwhelmingly challenging to interpret. We develop Generalized Phase Locking Analysis (GPLA) as an interpretable dimensionality reduction of this multivariate SFC. GPLA describes the dominant coupling between field activity and neural ensembles across space and frequencies. We show that GPLA features are biophysically interpretable when used in conjunction with appropriate network models, such that we can identify the influence of underlying circuit properties on these features. We demonstrate the statistical benefits and interpretability of this approach in various computational models and Utah array recordings. The results suggest that GPLA, used jointly with biophysical modeling, can help uncover the contribution of recurrent microcircuits to the spatio-temporal dynamics observed in multi-channel experimental recordings.

Bayesian Inference of a Spectral Graph Model for Brain Oscillations

The relationship between brain functional connectivity and structural connectivity has caught extensive attention of the neuroscience community, commonly inferred using mathematical modeling. Among many modeling approaches, spectral graph model (SGM) is distinctive as it has a closed-form solution of the wide-band frequency spectra of brain oscillations, requiring only global biophysically interpretable parameters. While SGM is parsimonious in parameters, the determination of SGM parameters is non-trivial. Prior works on SGM determine the parameters through a computational intensive annealing algorithm, which only provides a point estimate with no confidence intervals for parameter estimates. To fill this gap, we incorporate the simulation-based inference (SBI) algorithm and develop a Bayesian procedure for inferring the posterior distribution of the SGM parameters. Furthermore, using SBI dramatically reduces the computational burden for inferring the SGM parameters. We evaluate the proposed SBI-SGM framework on the resting-state magnetoencephalography recordings from healthy subjects and show that the proposed procedure has similar performance to the annealing algorithm in recovering power spectra and the spatial distribution of the alpha frequency band. In addition, we also analyze the correlations among the parameters and their uncertainty with the posterior distribution which can not be done with annealing inference. These analyses provide a richer understanding of the interactions among biophysical parameters of the SGM. In general, the use of simulation-based Bayesian inference enables robust and efficient computations of generative model parameter uncertainties and may pave the way for the use of generative models in clinical translation applications.

Toward biophysical markers of depression vulnerability

A major difficulty with treating psychiatric disorders is their heterogeneity: different neural causes can lead to the same phenotype. To address this, we propose describing the underlying pathophysiology in terms of interpretable, biophysical parameters of a neural model derived from the electroencephalogram. We analyzed data from a small patient cohort of patients with depression and controls. Using DCM, we constructed biophysical models that describe neural dynamics in a cortical network activated during a task that is used to assess depression state. We show that biophysical model parameters are biomarkers, that is, variables that allow subtyping of depression at a biological level. They yield a low dimensional, interpretable feature space that allowed description of differences between individual patients with depressive symptoms. They could capture internal heterogeneity/variance of depression state and achieve significantly better classification than commonly used EEG features. Our work is a proof of concept that a combination of biophysical models and machine learning may outperform earlier approaches based on classical statistics and raw brain data.

Structure-function models of temporal, spatial, and spectral characteristics of non-invasive whole brain functional imaging

We review recent advances in using mathematical models of the relationship between the brain structure and function that capture features of brain dynamics. We argue the need for models that can jointly capture temporal, spatial, and spectral features of brain functional activity. We present recent work on spectral graph theory based models that can accurately capture spectral as well as spatial patterns across multiple frequencies in MEG reconstructions.

Beyond dimension reduction: Stable electric fields emerge from and allow representational drift

It is known that the exact neurons maintaining a given memory (the neural ensemble) change from trial to trial. This raises the question of how the brain achieves stability in the face of this representational drift. Here, we demonstrate that this stability emerges at the level of the electric fields that arise from neural activity. We show that electric fields carry information about working memory content. The electric fields, in turn, can act as "guard rails" that funnel higher dimensional variable neural activity along stable lower dimensional routes. We obtained the latent space associated with each memory. We then confirmed the stability of the electric field by mapping the latent space to different cortical patches (that comprise a neural ensemble) and reconstructing information flow between patches. Stable electric fields can allow latent states to be transferred between brain areas, in accord with modern engram theory.

Conductance-based dynamic causal modeling: A mathematical review of its application to cross-power spectral densities

Dynamic Causal Modeling (DCM) is a Bayesian framework for inferring on hidden (latent) neuronal states, based on measurements of brain activity. Since its introduction in 2003 for functional magnetic resonance imaging data, DCM has been extended to electrophysiological data, and several variants have been developed. Their biophysically motivated formulations make these models promising candidates for providing a mechanistic understanding of human brain dynamics, both in health and disease. However, due to their complexity and reliance on concepts from several fields, fully understanding the mathematical and conceptual basis behind certain variants of DCM can be challenging. At the same time, a solid theoretical knowledge of the models is crucial to avoid pitfalls in the application of these models and interpretation of their results. In this paper, we focus on one of the most advanced formulations of DCM, i.e. conductance-based DCM for cross-spectral densities, whose components are described across multiple technical papers. The aim of the present article is to provide an accessible exposition of the mathematical background, together with an illustration of the model's behavior. To this end, we include step-by-step derivations of the model equations, point to important aspects in the software implementation of those models, and use simulations to provide an intuitive understanding of the type of responses that can be generated and the role that specific parameters play in the model. Furthermore, all code utilized for our simulations is made publicly available alongside the manuscript to allow readers an easy hands-on experience with conductance-based DCM.

Computational Models in Electroencephalography

Computational models lie at the intersection of basic neuroscience and healthcare applications because they allow researchers to test hypotheses in silico and predict the outcome of experiments and interactions that are very hard to test in reality. Yet, what is meant by “computational model” is understood in many different ways by researchers in different fields of neuroscience and psychology, hindering communication and collaboration. In this review, we point out the state of the art of computational modeling in Electroencephalography (EEG) and outline how these models can be used to integrate findings from electrophysiology, network-level models, and behavior. On the one hand, computational models serve to investigate the mechanisms that generate brain activity, for example measured with EEG, such as the transient emergence of oscillations at different frequency bands and/or with different spatial topographies. On the other hand, computational models serve to design experiments and test hypotheses in silico. The final purpose of computational models of EEG is to obtain a comprehensive understanding of the mechanisms that underlie the EEG signal. This is crucial for an accurate interpretation of EEG measurements that may ultimately serve in the development of novel clinical applications.

Pairwise maximum entropy model explains the role of white matter structure in shaping emergent co-activation states

A major challenge in neuroscience is determining a quantitative relationship between the brain's white matter structural connectivity and emergent activity. We seek to uncover the intrinsic relationship among brain regions fundamental to their functional activity by constructing a pairwise maximum entropy model (MEM) of the inter-ictal activation patterns of five patients with medically refractory epilepsy over an average of ~14 hours of band-passed intracranial EEG (iEEG) recordings per patient. We find that the pairwise MEM accurately predicts iEEG electrodes' activation patterns' probability and their pairwise correlations. We demonstrate that the estimated pairwise MEM's interaction weights predict structural connectivity and its strength over several frequencies significantly beyond what is expected based solely on sampled regions' distance in most patients. Together, the pairwise MEM offers a framework for explaining iEEG functional connectivity and provides insight into how the brain's structural connectome gives rise to large-scale activation patterns by promoting co-activation between connected structures.

Noise induced quiescence of epileptic spike generation in patients with epilepsy

Clinical scalp electroencephalographic recordings from patients with epilepsy are distinguished by the presence of epileptic discharges i.e. spikes or sharp waves. These often occur randomly on a background of fluctuating potentials. The spike rate varies between different brain states (sleep and awake) and patients. Epileptogenic tissue and regions near these often show increased spike rates in comparison to other cortical regions. Several studies have shown a relation between spike rate and background activity although the underlying reason for this is still poorly understood. Both these processes, spike occurrence and background activity show evidence of being at least partly stochastic processes. In this study we show that epileptic discharges seen on scalp electroencephalographic recordings and background activity are driven at least partly by a common biological noise. Furthermore, our results indicate noise induced quiescence of spike generation which, in analogy with computational models of spiking, indicate spikes to be generated by transitions between semi-stable states of the brain, similar to the generation of epileptic seizure activity. The deepened physiological understanding of spike generation in epilepsy that this study provides could be useful in the electrophysiological assessment of different therapies for epilepsy including the effect of different drugs or electrical stimulation.

Differences in visually induced MEG oscillations reflect differences in deep cortical layer activity

Neural activity is organized at multiple scales, ranging from the cellular to the whole brain level. Connecting neural dynamics at different scales is important for understanding brain pathology. Neurological diseases and disorders arise from interactions between factors that are expressed in multiple scales. Here, we suggest a new way to link microscopic and macroscopic dynamics through combinations of computational models. This exploits results from statistical decision theory and Bayesian inference. To validate our approach, we used two independent MEG datasets. In both, we found that variability in visually induced oscillations recorded from different people in simple visual perception tasks resulted from differences in the level of inhibition specific to deep cortical layers. This suggests differences in feedback to sensory areas and each subject's hypotheses about sensations due to differences in their prior experience. Our approach provides a new link between non-invasive brain imaging data, laminar dynamics and top-down control.

Cortical beta oscillations reflect the contextual gating of visual action feedback

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We decouple seen and felt hand postures during action via virtual reality.

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Vision of the hand is either task-relevant or a distractor.

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Task-relevance of vision is reflected by in- or decreases of occipital beta power.

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DCM suggests underlying changes in cortical (visual) excitability.

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Occipital beta may indicate the contextual gating of visual action feedback.

In sensorimotor integration, the brain needs to decide how its predictions should accommodate novel evidence by ‘gating’ sensory data depending on the current context. Here, we examined the oscillatory correlates of this process by recording magnetoencephalography (MEG) data during a new task requiring action under intersensory conflict. We used virtual reality to decouple visual (virtual) and proprioceptive (real) hand postures during a task in which the phase of grasping movements tracked a target (in either modality). Thus, we rendered visual information either task-relevant or a (to-be-ignored) distractor. Under visuo-proprioceptive incongruence, occipital beta power decreased (relative to congruence) when vision was task-relevant but increased when it had to be ignored. Dynamic causal modeling (DCM) revealed that this interaction was best explained by diametrical, task-dependent changes in visual gain. These results suggest a crucial role for beta oscillations in the contextual gating (i.e., gain or precision control) of visual vs proprioceptive action feedback, depending on current behavioral demands.

Thalamocortical inhibitory dynamics support conscious perception

Whether thalamocortical interactions play a decisive role in conscious perception remains an open question. We presented rapid red/green color flickering stimuli, which induced the mental perception of either an illusory orange color or non-fused red and green colors. Using magnetoencephalography, we observed 6-Hz thalamic activity associated with thalamocortical inhibitory coupling only during the conscious perception of the illusory orange color. This sustained thalamic disinhibition was temporally coupled with higher visual cortical activation during the conscious perception of the orange color, providing neurophysiological evidence of the role of thalamocortical synchronization in conscious awareness of mental representation. Bayesian model comparison consistently supported the thalamocortical model in conscious perception. Taken together, experimental and theoretical evidence established the thalamocortical inhibitory network as a gateway to conscious mental representations.

Statistical decision theory and multiscale analyses of human brain data

BACKGROUND

In the era of Big Data, large scale electrophysiological data from animal and human studies are abundant. These data contain information at multiple spatiotemporal scales. However, current approaches for the analysis of electrophysiological data often focus on a single spatiotemporal scale only.

NEW METHOD

We discuss a multiscale approach for the analysis of electrophysiological data. This is based on combining neural models that describe brain data at different scales. It allows us to make laminar-specific inferences about neurobiological properties of cortical sources using non invasive human electrophysiology data.

RESULTS

We provide a mathematical proof of this approach using statistical decision theory. We also consider its extensions to brain imaging studies including data from the same subjects performing different tasks. As an illustration, we show that changes in gamma oscillations between different people might originate from differences in recurrent connection strengths of inhibitory interneurons in layers 5/6.

COMPARISON WITH EXISTING METHODS

This is a new approach that follows up on our recent work. It is different from other approaches where the scale of spatiotemporal dynamics is fixed.

CONCLUSIONS

We discuss a multiscale approach for the analysis of human MEG data. This uses a neural mass model that includes constraints informed by a compartmental model. This has two advantages. First, it allows us to find differences in cortical laminar dynamics and understand neurobiological properties like neuromodulation, excitation to inhibition balance etc. using non invasive data. Second, it allows us to validate macroscale models by exploiting animal data.

Effects of physiological parameter evolution on the dynamics of tonic-clonic seizures

The temporal and spectral characteristics of tonic-clonic seizures are investigated using a neural field model of the corticothalamic system in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into ∼ 10 Hz seizure oscillations once a threshold is passed and a subcritical Hopf bifurcation occurs. In this study, the spectral and temporal characteristics of tonic-clonic seizures are explored as functions of the relevant properties of physiological connection strengths, such as maximum strength, time above threshold, and the ramp rate at which the strength increases or decreases. Analysis shows that the seizure onset time decreases with the maximum connection strength and time above threshold, but increases with the ramp rate. Seizure duration and offset time increase with maximum connection strength, time above threshold, and rate of change. Spectral analysis reveals that the power of nonlinear harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. A secondary limit cycle at ∼ 18 Hz, termed a saddle-cycle, is also seen during seizure onset and becomes more prominent and robust with increasing ramp rate. If the time above the threshold is too small, the system does not reach the 10 Hz limit cycle, and only exhibits 18 Hz saddle-cycle oscillations. It is also seen that the time to reach the saturated large amplitude limit-cycle seizure oscillation from both the instability threshold and from the end of the saddle-cycle oscillations is inversely proportional to the square root of the ramp rate.

Structure learning in coupled dynamical systems and dynamic causal modelling

Identifying a coupled dynamical system out of many plausible candidates, each of which could serve as the underlying generator of some observed measurements, is a profoundly ill-posed problem that commonly arises when modelling real-world phenomena. In this review, we detail a set of statistical procedures for inferring the structure of nonlinear coupled dynamical systems (structure learning), which has proved useful in neuroscience research. A key focus here is the comparison of competing models of network architectures-and implicit coupling functions-in terms of their Bayesian model evidence. These methods are collectively referred to as dynamic causal modelling. We focus on a relatively new approach that is proving remarkably useful, namely Bayesian model reduction, which enables rapid evaluation and comparison of models that differ in their network architecture. We illustrate the usefulness of these techniques through modelling neurovascular coupling (cellular pathways linking neuronal and vascular systems), whose function is an active focus of research in neurobiology and the imaging of coupled neuronal systems. This article is part of the theme issue 'Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences'.

Neural field models for latent state inference: Application to large-scale neuronal recordings

Large-scale neural recording methods now allow us to observe large populations of identified single neurons simultaneously, opening a window into neural population dynamics in living organisms. However, distilling such large-scale recordings to build theories of emergent collective dynamics remains a fundamental statistical challenge. The neural field models of Wilson, Cowan, and colleagues remain the mainstay of mathematical population modeling owing to their interpretable, mechanistic parameters and amenability to mathematical analysis. Inspired by recent advances in biochemical modeling, we develop a method based on moment closure to interpret neural field models as latent state-space point-process models, making them amenable to statistical inference. With this approach we can infer the intrinsic states of neurons, such as active and refractory, solely from spiking activity in large populations. After validating this approach with synthetic data, we apply it to high-density recordings of spiking activity in the developing mouse retina. This confirms the essential role of a long lasting refractory state in shaping spatiotemporal properties of neonatal retinal waves. This conceptual and methodological advance opens up new theoretical connections between mathematical theory and point-process state-space models in neural data analysis.

Developing statistical tools to connect single-neuron activity to emergent collective dynamics is vital for building interpretable models of neural activity. Neural field models relate single-neuron activity to emergent collective dynamics in neural populations, but integrating them with data remains challenging. Recently, latent state-space models have emerged as a powerful tool for constructing phenomenological models of neural population activity. The advent of high-density multi-electrode array recordings now enables us to examine large-scale collective neural activity. We show that classical neural field approaches can yield latent state-space equations and demonstrate that this enables inference of the intrinsic states of neurons from recorded spike trains in large populations.

Optimal Model Parameter Estimation from EEG Power Spectrum Features Observed during General Anesthesia

Mathematical modeling is a powerful tool that enables researchers to describe the experimentally observed dynamics of complex systems. Starting with a robust model including model parameters, it is necessary to choose an appropriate set of model parameters to reproduce experimental data. However, estimating an optimal solution of the inverse problem, i.e., finding a set of model parameters that yields the best possible fit to the experimental data, is a very challenging problem. In the present work, we use different optimization algorithms based on a frequentist approach, as well as Monte Carlo Markov Chain methods based on Bayesian inference techniques to solve the considered inverse problems. We first probe two case studies with synthetic data and study models described by a stochastic non-delayed linear second-order differential equation and a stochastic linear delay differential equation. In a third case study, a thalamo-cortical neural mass model is fitted to the EEG spectral power measured during general anesthesia induced by anesthetics propofol and desflurane. We show that the proposed neural mass model fits very well to the observed EEG power spectra, particularly to the power spectral peaks within δ - (0 - 4 Hz) and α - (8 - 13 Hz) frequency ranges. Furthermore, for each case study, we perform a practical identifiability analysis by estimating the confidence regions of the parameter estimates and interpret the corresponding correlation and sensitivity matrices. Our results indicate that estimating the model parameters from analytically computed spectral power, we are able to accurately estimate the unknown parameters while avoiding the computational costs due to numerical integration of the model equations.

Propofol-induced unresponsiveness is associated with impaired feedforward connectivity in cortical hierarchy

BACKGROUND

Impaired consciousness has been associated with impaired cortical signal propagation after transcranial magnetic stimulation (TMS). We hypothesised that the reduced current propagation under propofol-induced unresponsiveness is associated with changes in both feedforward and feedback connectivity across the cortical hierarchy.

METHODS

Eight subjects underwent left occipital TMS coupled with high-density EEG recordings during wakefulness and propofol-induced unconsciousness. Spectral analysis was applied to responses recorded from sensors overlying six hierarchical cortical sources involved in visual processing. Dynamic causal modelling (DCM) of induced time-frequency responses and evoked response potentials were used to investigate propofol's effects on connectivity between regions.

RESULTS

Sensor space analysis demonstrated that propofol reduced both induced and evoked power after TMS in occipital, parietal, and frontal electrodes. Bayesian model selection supported a DCM with hierarchical feedforward and feedback connections. DCM of induced EEG responses revealed that the primary effect of propofol was impaired feedforward responses in cross-frequency theta/alpha-gamma coupling and within frequency theta coupling (F contrast, family-wise error corrected P<0.05). An exploratory analysis (thresholded at uncorrected P<0.001) also suggested that propofol impaired feedforward and feedback beta band coupling. Post hoc analyses showed impairments in all feedforward connections and one feedback connection from parietal to occipital cortex. DCM of the evoked response potential showed impaired feedforward connectivity between left-sided occipital and parietal cortex (T contrast P=0.004, Bonferroni corrected).

CONCLUSIONS

Propofol-induced loss of consciousness is associated with impaired hierarchical feedforward connectivity assessed by EEG after occipital TMS.

Generic dynamic causal modelling: An illustrative application to Parkinson's disease

We present a technical development in the dynamic causal modelling of electrophysiological responses that combines qualitatively different neural mass models within a single network. This affords the option to couple various cortical and subcortical nodes that differ in their form and dynamics. Moreover, it enables users to implement new neural mass models in a straightforward and standardized way. This generic framework hence supports flexibility and facilitates the exploration of increasingly plausible models. We illustrate this by coupling a basal ganglia-thalamus model to a (previously validated) cortical model developed specifically for motor cortex. The ensuing DCM is used to infer pathways that contribute to the suppression of beta oscillations induced by dopaminergic medication in patients with Parkinson's disease. Experimental recordings were obtained from deep brain stimulation electrodes (implanted in the subthalamic nucleus) and simultaneous magnetoencephalography. In line with previous studies, our results indicate a reduction of synaptic efficacy within the circuit between the subthalamic nucleus and external pallidum, as well as reduced efficacy in connections of the hyperdirect and indirect pathway leading to this circuit. This work forms the foundation for a range of modelling studies of the synaptic mechanisms (and pathophysiology) underlying event-related potentials and cross-spectral densities.

Dependence of absence seizure dynamics on physiological parameter evolution

A neural field model of the corticothalamic system is applied to investigate the temporal and spectral characteristics of absence seizures in the presence of a temporally varying connection strength between the cerebral cortex and thalamus. Increasing connection strength drives the system into an absence seizure-like state once a threshold is passed and a supercritical Hopf bifurcation occurs. The dynamics and spectral characteristics of the resulting model seizures are explored as functions of maximum connection strength, time above threshold, and the rate at which the connection strength increases (ramp rate). Our results enable spectral and temporal characteristics of seizures to be related to changes in the underlying physiological evolution of connections via nonlinear dynamics and neural field theory. Spectral analysis reveals that the power of the harmonics and the duration of the oscillations increase as the maximum connection strength and the time above threshold increase. It is also found that the time to reach the stable limit-cycle seizure oscillation from the instability threshold decreases with the square root of the ramp rate.

Generative models for clinical applications in computational psychiatry

Despite the success of modern neuroimaging techniques in furthering our understanding of cognitive and pathophysiological processes, translation of these advances into clinically relevant tools has been virtually absent until now. Neuromodeling represents a powerful framework for overcoming this translational deadlock, and the development of computational models to solve clinical problems has become a major scientific goal over the last decade, as reflected by the emergence of clinically oriented neuromodeling fields like Computational Psychiatry, Computational Neurology, and Computational Psychosomatics. Generative models of brain physiology and connectivity in the human brain play a key role in this endeavor, striving for computational assays that can be applied to neuroimaging data from individual patients for differential diagnosis and treatment prediction. In this review, we focus on dynamic causal modeling (DCM) and its use for Computational Psychiatry. DCM is a widely used generative modeling framework for functional magnetic resonance imaging (fMRI) and magneto-/electroencephalography (M/EEG) data. This article reviews the basic concepts of DCM, revisits examples where it has proven valuable for addressing clinically relevant questions, and critically discusses methodological challenges and recent methodological advances. We conclude this review with a more general discussion of the promises and pitfalls of generative models in Computational Psychiatry and highlight the path that lies ahead of us. This article is categorized under: Neuroscience > Computation Neuroscience > Clinical Neuroscience.

Variational Bayesian Parameter Estimation Techniques for the General Linear Model

Variational Bayes (VB), variational maximum likelihood (VML), restricted maximum likelihood (ReML), and maximum likelihood (ML) are cornerstone parametric statistical estimation techniques in the analysis of functional neuroimaging data. However, the theoretical underpinnings of these model parameter estimation techniques are rarely covered in introductory statistical texts. Because of the widespread practical use of VB, VML, ReML, and ML in the neuroimaging community, we reasoned that a theoretical treatment of their relationships and their application in a basic modeling scenario may be helpful for both neuroimaging novices and practitioners alike. In this technical study, we thus revisit the conceptual and formal underpinnings of VB, VML, ReML, and ML and provide a detailed account of their mathematical relationships and implementational details. We further apply VB, VML, ReML, and ML to the general linear model (GLM) with non-spherical error covariance as commonly encountered in the first-level analysis of fMRI data. To this end, we explicitly derive the corresponding free energy objective functions and ensuing iterative algorithms. Finally, in the applied part of our study, we evaluate the parameter and model recovery properties of VB, VML, ReML, and ML, first in an exemplary setting and then in the analysis of experimental fMRI data acquired from a single participant under visual stimulation.

Bayesian population receptive field modelling

We introduce a probabilistic (Bayesian) framework and associated software toolbox for mapping population receptive fields (pRFs) based on fMRI data. This generic approach is intended to work with stimuli of any dimension and is demonstrated and validated in the context of 2D retinotopic mapping. The framework enables the experimenter to specify generative (encoding) models of fMRI timeseries, in which experimental stimuli enter a pRF model of neural activity, which in turns drives a nonlinear model of neurovascular coupling and Blood Oxygenation Level Dependent (BOLD) response. The neuronal and haemodynamic parameters are estimated together on a voxel-by-voxel or region-of-interest basis using a Bayesian estimation algorithm (variational Laplace). This offers several novel contributions to receptive field modelling. The variance/covariance of parameters are estimated, enabling receptive fields to be plotted while properly representing uncertainty about pRF size and location. Variability in the haemodynamic response across the brain is accounted for. Furthermore, the framework introduces formal hypothesis testing to pRF analysis, enabling competing models to be evaluated based on their log model evidence (approximated by the variational free energy), which represents the optimal tradeoff between accuracy and complexity. Using simulations and empirical data, we found that parameters typically used to represent pRF size and neuronal scaling are strongly correlated, which is taken into account by the Bayesian methods we describe when making inferences. We used the framework to compare the evidence for six variants of pRF model using 7 T functional MRI data and we found a circular Difference of Gaussians (DoG) model to be the best explanation for our data overall. We hope this framework will prove useful for mapping stimulus spaces with any number of dimensions onto the anatomy of the brain.

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We introduce a Bayesian toolbox for population receptive field (pRF) mapping.

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Neuronal and haemodynamic parameters are estimated per voxel or per region.

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Hypotheses can be tested by comparing pRF models based on their evidence.

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The uncertainty over parameters (such as pRF size) is estimated and visualised.

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We establish face validity using simulations and test-rest reliability with 7 T fMRI.

On memories, neural ensembles and mental flexibility

Memories are assumed to be represented by groups of co-activated neurons, called neural ensembles. Describing ensembles is a challenge: complexity of the underlying micro-circuitry is immense. Current approaches use a piecemeal fashion, focusing on single neurons and employing local measures like pairwise correlations. We introduce an alternative approach that identifies ensembles and describes the effective connectivity between them in a holistic fashion. It also links the oscillatory frequencies observed in ensembles with the spatial scales at which activity is expressed. Using unsupervised learning, biophysical modeling and graph theory, we analyze multi-electrode LFPs from frontal cortex during a spatial delayed response task. We find distinct ensembles for different cues and more parsimonious connectivity for cues on the horizontal axis, which may explain the oblique effect in psychophysics. Our approach paves the way for biophysical models with learned parameters that can guide future Brain Computer Interface development.

Abnormal frontoparietal synaptic gain mediating the P300 in patients with psychotic disorder and their unaffected relatives

The "dysconnection hypothesis" of psychosis suggests that a disruption of functional integration underlies cognitive deficits and clinical symptoms. Impairments in the P300 potential are well documented in psychosis. Intrinsic (self-)connectivity in a frontoparietal cortical hierarchy during a P300 experiment was investigated. Dynamic Causal Modeling was used to estimate how evoked activity results from the dynamics of coupled neural populations and how neural coupling changes with the experimental factors. Twenty-four patients with psychotic disorder, twenty-four unaffected relatives, and twenty-five controls underwent EEG recordings during an auditory oddball paradigm. Sixteen frontoparietal network models (including primary auditory, superior parietal, and superior frontal sources) were analyzed and an optimal model of neural coupling, explaining diagnosis and genetic risk effects, as well as their interactions with task condition were identified. The winning model included changes in connectivity at all three hierarchical levels. Patients showed decreased self-inhibition-that is, increased cortical excitability-in left superior frontal gyrus across task conditions, compared with unaffected participants. Relatives had similar increases in excitability in left superior frontal and right superior parietal sources, and a reversal of the normal synaptic gain changes in response to targets relative to standard tones. It was confirmed that both subjects with psychotic disorder and their relatives show a context-independent loss of synaptic gain control at the highest hierarchy levels. The relatives also showed abnormal gain modulation responses to task-relevant stimuli. These may be caused by NMDA-receptor and/or GABAergic pathologies that change the excitability of superficial pyramidal cells and may be a potential biological marker for psychosis. Hum Brain Mapp 38:3262-3276, 2017. © 2017 Wiley Periodicals, Inc.

Linking canonical microcircuits and neuronal activity: Dynamic causal modelling of laminar recordings

Neural models describe brain activity at different scales, ranging from single cells to whole brain networks. Here, we attempt to reconcile models operating at the microscopic (compartmental) and mesoscopic (neural mass) scales to analyse data from microelectrode recordings of intralaminar neural activity. Although these two classes of models operate at different scales, it is relatively straightforward to create neural mass models of ensemble activity that are equipped with priors obtained after fitting data generated by detailed microscopic models. This provides generative (forward) models of measured neuronal responses that retain construct validity in relation to compartmental models. We illustrate our approach using cross spectral responses obtained from V1 during a visual perception paradigm that involved optogenetic manipulation of the basal forebrain. We find that the resulting neural mass model can distinguish between activity in distinct cortical layers - both with and without optogenetic activation - and that cholinergic input appears to enhance (disinhibit) superficial layer activity relative to deep layers. This is particularly interesting from the perspective of predictive coding, where neuromodulators are thought to boost prediction errors that ascend the cortical hierarchy.

Estimating Fast Neural Input Using Anatomical and Functional Connectivity

In the last 20 years there has been an increased interest in estimating signals that are sent between neurons and brain areas. During this time many new methods have appeared for measuring those signals. Here we review a wide range of methods for which connected neurons can be identified anatomically, by tracing axons that run between the cells, or functionally, by detecting if the activity of two neurons are correlated with a short lag. The signals that are sent between the neurons are represented by the activity in the neurons that are connected to the target population or by the activity at the corresponding synapses. The different methods not only differ in the accuracy of the signal measurement but they also differ in the type of signal being measured. For example, unselective recording of all neurons in the source population encompasses more indirect pathways to the target population than if one selectively record from the neurons that project to the target population. Infact, this degree of selectivity is similar to that of optogenetic perturbations; one can perturb selectively or unselectively. Thus it becomes possible to match a given signal measurement method with a signal perturbation method, something that allows for an exact input control to any neuronal population.

Intersubject variability and induced gamma in the visual cortex: DCM with empirical Bayes and neural fields

This article describes the first application of a generic (empirical) Bayesian analysis of between‐subject effects in the dynamic causal modeling (DCM) of electrophysiological (MEG) data. It shows that (i) non‐invasive (MEG) data can be used to characterize subject‐specific differences in cortical microcircuitry and (ii) presents a validation of DCM with neural fields that exploits intersubject variability in gamma oscillations. We find that intersubject variability in visually induced gamma responses reflects changes in the excitation‐inhibition balance in a canonical cortical circuit. Crucially, this variability can be explained by subject‐specific differences in intrinsic connections to and from inhibitory interneurons that form a pyramidal‐interneuron gamma network. Our approach uses Bayesian model reduction to evaluate the evidence for (large sets of) nested models—and optimize the corresponding connectivity estimates at the within and between‐subject level. We also consider Bayesian cross‐validation to obtain predictive estimates for gamma‐response phenotypes, using a leave‐one‐out procedure. Hum Brain Mapp 37:4597–4614, 2016. © The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Cortical Resonance Frequencies Emerge from Network Size and Connectivity

Neural oscillations occur within a wide frequency range with different brain regions exhibiting resonance-like characteristics at specific points in the spectrum. At the microscopic scale, single neurons possess intrinsic oscillatory properties, such that is not yet known whether cortical resonance is consequential to neural oscillations or an emergent property of the networks that interconnect them. Using a network model of loosely-coupled Wilson-Cowan oscillators to simulate a patch of cortical sheet, we demonstrate that the size of the activated network is inversely related to its resonance frequency. Further analysis of the parameter space indicated that the number of excitatory and inhibitory connections, as well as the average transmission delay between units, determined the resonance frequency. The model predicted that if an activated network within the visual cortex increased in size, the resonance frequency of the network would decrease. We tested this prediction experimentally using the steady-state visual evoked potential where we stimulated the visual cortex with different size stimuli at a range of driving frequencies. We demonstrate that the frequency corresponding to peak steady-state response inversely correlated with the size of the network. We conclude that although individual neurons possess resonance properties, oscillatory activity at the macroscopic level is strongly influenced by network interactions, and that the steady-state response can be used to investigate functional networks.

When entrained using repetitive stimulation, sensory cortices appear to respond maximally, or resonate, at different driving frequencies: 10Hz in visual cortex; 20Hz and 40Hz in somatosensory and auditory cortices, respectively. The resonance frequencies are inversely correlated to the cortical volume of the respective regions, but it is unclear what drives this relationship. Here we used both computational and empirical data to demonstrate that resonance frequencies are emergent properties of the connectivity parameters of the underlying networks. The experimental paradigm stimulated large and small areas of visual cortex with different size objects made of flickering dots, and varied the driving frequency. Larger cortical areas exhibited maximum response at lower frequency than smaller areas, suggesting the inverse relationship between cortical size and resonance frequency holds, even within the same sensory modality. Computationally, we simulated cortical patches of different sizes and varied their connectivity parameters. We demonstrate that the size of the activated network is inversely related to its resonance frequency and that this change is due to the increased transmission delay and greater node degree within the larger network. The results are important for understanding the functional significance of oscillatory processes, and as a tool for probing changes in functional connectivity.

Impaired prefrontal synaptic gain in people with psychosis and their relatives during the mismatch negativity

The mismatch negativity (MMN) evoked potential, a preattentive brain response to a discriminable change in auditory stimulation, is significantly reduced in psychosis. Glutamatergic theories of psychosis propose that hypofunction of NMDA receptors (on pyramidal cells and inhibitory interneurons) causes a loss of synaptic gain control. We measured changes in neuronal effective connectivity underlying the MMN using dynamic causal modeling (DCM), where the gain (excitability) of superficial pyramidal cells is explicitly parameterised. EEG data were obtained during a MMN task—for 24 patients with psychosis, 25 of their first‐degree unaffected relatives, and 35 controls—and DCM was used to estimate the excitability (modeled as self‐inhibition) of (source‐specific) superficial pyramidal populations. The MMN sources, based on previous research, included primary and secondary auditory cortices, and the right inferior frontal gyrus. Both patients with psychosis and unaffected relatives (to a lesser degree) showed increased excitability in right inferior frontal gyrus across task conditions, compared to controls. Furthermore, in the same region, both patients and their relatives showed a reversal of the normal response to deviant stimuli; that is, a decrease in excitability in comparison to standard conditions. Our results suggest that psychosis and genetic risk for the illness are associated with both context‐dependent (condition‐specific) and context‐independent abnormalities of the excitability of superficial pyramidal cell populations in the MMN paradigm. These abnormalities could relate to NMDA receptor hypofunction on both pyramidal cells and inhibitory interneurons, and appear to be linked to the genetic aetiology of the illness, thereby constituting potential endophenotypes for psychosis. Hum Brain Mapp 37:351–365, 2016. © 2015 The Authors Human Brain Mapping Published by Wiley Periodicals, Inc.

Neural field simulator: two-dimensional spatio-temporal dynamics involving finite transmission speed

Neural Field models (NFM) play an important role in the understanding of neural population dynamics on a mesoscopic spatial and temporal scale. Their numerical simulation is an essential element in the analysis of their spatio-temporal dynamics. The simulation tool described in this work considers scalar spatially homogeneous neural fields taking into account a finite axonal transmission speed and synaptic temporal derivatives of first and second order. A text-based interface offers complete control of field parameters and several approaches are used to accelerate simulations. A graphical output utilizes video hardware acceleration to display running output with reduced computational hindrance compared to simulators that are exclusively software-based. Diverse applications of the tool demonstrate breather oscillations, static and dynamic Turing patterns and activity spreading with finite propagation speed. The simulator is open source to allow tailoring of code and this is presented with an extension use case.

Relating Granger causality to long-term causal effects

In estimation of causal couplings between observed processes, it is important to characterize coupling roles at various time scales. The widely used Granger causality reflects short-term effects: it shows how strongly perturbations of a current state of one process affect near future states of another process, and it quantifies that via prediction improvement (PI) in autoregressive models. However, it is often more important to evaluate the effects of coupling on long-term statistics, e.g., to find out how strongly the presence of coupling changes the variance of a driven process as compared to an uncoupled case. No general relationships between Granger causality and such long-term effects are known. Here, we pose the problem of relating these two types of coupling characteristics, and we solve it for a class of stochastic systems. Namely, for overdamped linear oscillators, we rigorously derive that the above long-term effect is proportional to the short-term effects, with the proportionality coefficient depending on the prediction interval and relaxation times. We reveal that this coefficient is typically considerably greater than unity so that small normalized PI values may well correspond to quite large long-term effects of coupling. The applicability of the derived relationship to wider classes of systems, its limitations, and its value for further research are discussed. To give a real-world example, we analyze couplings between large-scale climatic processes related to sea surface temperature variations in equatorial Pacific and North Atlantic regions.

How the cortico-thalamic feedback affects the EEG power spectrum over frontal and occipital regions during propofol-induced sedation

Increasing concentrations of the anaesthetic agent propofol initially induces sedation before achieving full general anaesthesia. During this state of anaesthesia, the observed specific changes in electroencephalographic (EEG) rhythms comprise increased activity in the δ- (0.5-4 Hz) and α- (8-13 Hz) frequency bands over the frontal region, but increased δ- and decreased α-activity over the occipital region. It is known that the cortex, the thalamus, and the thalamo-cortical feedback loop contribute to some degree to the propofol-induced changes in the EEG power spectrum. However the precise role of each structure to the dynamics of the EEG is unknown. In this paper we apply a thalamo-cortical neuronal population model to reproduce the power spectrum changes in EEG during propofol-induced anaesthesia sedation. The model reproduces the power spectrum features observed experimentally both in frontal and occipital electrodes. Moreover, a detailed analysis of the model indicates the importance of multiple resting states in brain activity. The work suggests that the α-activity originates from the cortico-thalamic relay interaction, whereas the emergence of δ-activity results from the full cortico-reticular-relay-cortical feedback loop with a prominent enforced thalamic reticular-relay interaction. This model suggests an important role for synaptic GABAergic receptors at relay neurons and, more generally, for the thalamus in the generation of both the δ- and the α- EEG patterns that are seen during propofol anaesthesia sedation.

Physiologically based arousal state estimation and dynamics

A neural field model of the brain is used to represent brain states using physiologically based parameters rather than arbitrary, discrete sleep stages. Each brain state is represented as a point in a physiologically parametrized space. Over time, changes in brain state cause these points to trace continuous trajectories, unlike the artificial discrete jumps in sleep stage that occur with traditional sleep staging. The discrete Rechtschaffen and Kales sleep stages are associated with regions in the physiological parameter space based on their electroencephalographic features, which enables interpretation of traditional sleep stages in terms of physiological trajectories. Wake states are found to be associated with strong positive corticothalamic feedback compared to sleep. The existence of physiologically valid trajectories between brain states in the model is demonstrated. Actual trajectories for an individual can be determined by fitting the model using EEG alone, and enable analysis of the physiological differences between subjects.

Modeling fMRI signals can provide insights into neural processing in the cerebral cortex

Every stimulus or task activates multiple areas in the mammalian cortex. These distributed activations can be measured with functional magnetic resonance imaging (fMRI), which has the best spatial resolution among the noninvasive brain imaging methods. Unfortunately, the relationship between the fMRI activations and distributed cortical processing has remained unclear, both because the coupling between neural and fMRI activations has remained poorly understood and because fMRI voxels are too large to directly sense the local neural events. To get an idea of the local processing given the macroscopic data, we need models to simulate the neural activity and to provide output that can be compared with fMRI data. Such models can describe neural mechanisms as mathematical functions between input and output in a specific system, with little correspondence to physiological mechanisms. Alternatively, models can be biomimetic, including biological details with straightforward correspondence to experimental data. After careful balancing between complexity, computational efficiency, and realism, a biomimetic simulation should be able to provide insight into how biological structures or functions contribute to actual data processing as well as to promote theory-driven neuroscience experiments. This review analyzes the requirements for validating system-level computational models with fMRI. In particular, we study mesoscopic biomimetic models, which include a limited set of details from real-life networks and enable system-level simulations of neural mass action. In addition, we discuss how recent developments in neurophysiology and biophysics may significantly advance the modelling of fMRI signals.