The study of brain activity spans diverse scales and levels of description and requires the development of computational models alongside experimental investigations to explore integrations across scales. The high dimensionality of spiking networks presents challenges for understanding their dynamics. To tackle this, a mean-field formulation offers a potential approach for dimensionality reduction while retaining essential elements. Here, we focus on a previously developed mean-field model of adaptive exponential integrate and fire (AdEx) networks used in various research work. We observe qualitative similarities in the bifurcation structure but quantitative differences in mean firing rates between the mean-field model and AdEx spiking network simulations. Even if the mean-field model does not accurately predict phase shift during transients and oscillatory input, it generally captures the qualitative dynamics of the spiking network's response to both constant and varying inputs. Finally, we offer an overview of the dynamical properties of the AdExMF to assist future users in interpreting their results of simulations.

Epilepsy is a prevalent brain disorder, characterized by sudden, abnormal brain activity, making it difficult to live with. One-third of people with epilepsy do not respond to anti-epileptic drugs. Drug-resistant epilepsy is treated with brain surgery. Successful surgical treatment relies on identifying brain regions responsible for seizure onset, known as epileptogenic zones (EZ). Despite various methods for EZ estimation, evaluating their efficacy remains challenging due to a lack of ground truth for empirical data. To address this, we generated and evaluated a cohort of 30 virtual epilepsy patients, using patient-specific anatomical and functional data from 30 real drug-resistant epilepsy patients. This personalized modeling approach, based on each patient's brain data, is called a virtual brain twin. For each virtual patient, we provided data that included anatomically parcellated brain regions, structural connectivity, reconstructed intracranial electrodes, simulated brain activity at both the brain region and electrode levels, and key parameters of the virtual brain twin. These key parameters, which include the EZ hypothesis, serve as the ground truth for simulated brain activity. For each virtual brain twin, we generated synthetic spontaneous seizures, stimulation-induced seizures and interictal activity. We systematically evaluated these simulated brain signals by quantitatively comparing them against their corresponding empirical intracranial recordings. Simulated signals based on patient-specific EZ captured spatio-temporal seizure generation and propagation. Through in-silico exploration of stimulation parameters, we also demonstrated the role of patient-specific stimulation location and amplitude in reproducing empirically stimulated seizures. The virtual epileptic cohort is openly available, and can be used to systematically evaluate methods for the estimation of EZ or source localization using ground truth EZ parameters and source signals.

Transcranial direct current stimulation (tDCS) has shown promise in treating neurological disorders, particularly through dorsolateral prefrontal cortex (DLPFC) targeting. However, the effects of DLPFC-tDCS on brain functional networks and the underlying propagation mechanisms remain poorly understood. We present a novel tDCS hybrid brain model (tDCS-HBM) that incorporates tDCS-induced gray matter electric fields into a large-scale brain network model, considering their relationship with membrane potential to effectively predict spatiotemporal dynamics. Using this model, we simulated brain activity in response to tDCS over the left (F3-Fp2) and right DLPFC (F4-Fp1). Our results demonstrate that tDCS enhances brain complexity and flexibility, leading to increased functional connectivity (FC) across the whole brain and an improvement in global network efficiency. Dynamic analysis reveals an initial FC decline, followed by widespread enhancement originating from inferior and orbital frontal regions. Importantly, right DLPFC-tDCS induces strong FC associated with the ventral attention network. These changes in topological metrics and spatiotemporal patterns are consistent with prior modeling and empirical findings, validating the utility of our tDCS-HBM in understanding propagation mechanisms. Our hybrid model holds the potential to predict the stimulation effects of modulation protocols, providing precise guidance for clinical neuromodulation interventions.

The Virtual Epileptic Patient (VEP) refers to a computer-based representation of a patient with epilepsy that combines personalized anatomical data with dynamical models of abnormal brain activities. It is capable of generating spatio-temporal seizure patterns that resemble those recorded with invasive methods such as stereoelectro EEG data, allowing for the evaluation of clinical hypotheses before planning surgery. This study highlights the effectiveness of calibrating VEP models using a global optimization approach. The approach utilizes SaCeSS, a cooperative metaheuristic algorithm capable of parallel computation, to yield high-quality solutions without requiring excessive computational time. Through extensive benchmarking on synthetic data, our proposal successfully solved a set of different configurations of VEP models, demonstrating better scalability and superior performance against other parallel solvers. These results were further enhanced using a Bayesian optimization framework for hyperparameter tuning, with significant gains in terms of both accuracy and computational cost. Additionally, we added a scalable uncertainty quantification phase after model calibration, and used it to assess the variability in estimated parameters across different problems. Overall, this study has the potential to improve the estimation of pathological brain areas in drug-resistant epilepsy, thereby to inform the clinical decision-making process.

The Epileptor is a phenomenological model for seizure activity that is used in a personalized large-scale brain modeling framework, the Virtual Epileptic Patient, with the aim of improving surgery outcomes for drug-resistant epileptic patients. Transitions between interictal and ictal states are modeled as bifurcations, enabling the definition of seizure classes in terms of onset/offset bifurcations. This establishes a taxonomy of seizures grounded in their essential underlying dynamics and the Epileptor replicates the activity of the most common class, as observed in patients with focal epilepsy, which is characterized by square-wave bursting properties. The Epileptor also encodes an additional mechanism to account for interictal spikes and spike and wave discharges. Here we use insights from a more generic model for square-wave bursting, based on the Unfolding Theory approach, to guide the bifurcation analysis of the Epileptor and gain a deeper understanding of the model and the role of its parameters. We show how the Epileptor's parameters can be modified to produce activities for other seizures classes of the taxonomy, as observed in patients, so that the large-scale brain models could be further personalized. Some of these classes have already been described in the literature in the Epileptor, others, predicted by the generic model, are new. Finally, we unveil how the interaction with the additional mechanism for spike and wave discharges alters the bifurcation structure of the main burster.

Whole-brain modeling of epilepsy combines personalized anatomical data with dynamical models of abnormal activities to generate spatio-temporal seizure patterns as observed in brain imaging data. Such a parametric simulator is equipped with a stochastic generative process, which itself provides the basis for inference and prediction of the local and global brain dynamics affected by disorders. However, the calculation of likelihood function at whole-brain scale is often intractable. Thus, likelihood-free algorithms are required to efficiently estimate the parameters pertaining to the hypothetical areas, ideally including the uncertainty. In this study, we introduce the simulation-based inference for the virtual epileptic patient model (SBI-VEP), enabling us to amortize the approximate posterior of the generative process from a low-dimensional representation of whole-brain epileptic patterns. The state-of-the-art deep learning algorithms for conditional density estimation are used to readily retrieve the statistical relationships between parameters and observations through a sequence of invertible transformations. We show that the SBI-VEP is able to efficiently estimate the posterior distribution of parameters linked to the extent of the epileptogenic and propagation zones from sparse intracranial electroencephalography recordings. The presented Bayesian methodology can deal with non-linear latent dynamics and parameter degeneracy, paving the way for fast and reliable inference on brain disorders from neuroimaging modalities.

Individualized anatomical information has been used as prior knowledge in Bayesian inference paradigms of whole-brain network models. However, the actual sensitivity to such personalized information in priors is still unknown. In this study, we introduce the use of fully Bayesian information criteria and leave-one-out cross-validation technique on the subject-specific information to assess different epileptogenicity hypotheses regarding the location of pathological brain areas based on a priori knowledge from dynamical system properties. The Bayesian Virtual Epileptic Patient (BVEP) model, which relies on the fusion of structural data of individuals, a generative model of epileptiform discharges, and a self-tuning Monte Carlo sampling algorithm, is used to infer the spatial map of epileptogenicity across different brain areas. Our results indicate that measuring the out-of-sample prediction accuracy of the BVEP model with informative priors enables reliable and efficient evaluation of potential hypotheses regarding the degree of epileptogenicity across different brain regions. In contrast, while using uninformative priors, the information criteria are unable to provide strong evidence about the epileptogenicity of brain areas. We also show that the fully Bayesian criteria correctly assess different hypotheses about both structural and functional components of whole-brain models that differ across individuals. The fully Bayesian information-theory based approach used in this study suggests a patient-specific strategy for epileptogenicity hypothesis testing in generative brain network models of epilepsy to improve surgical outcomes.

Surgical interventions in epileptic patients aimed at the removal of the epileptogenic zone have success rates at only 60-70%. This failure can be partly attributed to the insufficient spatial sampling by the implanted intracranial electrodes during the clinical evaluation, leading to an incomplete picture of spatio-temporal seizure organization in the regions that are not directly observed. Utilizing the partial observations of the seizure spreading through the brain network, complemented by the assumption that the epileptic seizures spread along the structural connections, we infer if and when are the unobserved regions recruited in the seizure. To this end we introduce a data-driven model of seizure recruitment and propagation across a weighted network, which we invert using the Bayesian inference framework. Using a leave-one-out cross-validation scheme on a cohort of 45 patients we demonstrate that the method can improve the predictions of the states of the unobserved regions compared to an empirical estimate that does not use the structural information, yet it is on the same level as the estimate that takes the structure into account. Furthermore, a comparison with the performed surgical resection and the surgery outcome indicates a link between the inferred excitable regions and the actual epileptogenic zone. The results emphasize the importance of the structural connectome in the large-scale spatio-temporal organization of epileptic seizures and introduce a novel way to integrate the patient-specific connectome and intracranial seizure recordings in a whole-brain computational model of seizure spread.

Intracranial electroencephalography is a standard tool in clinical evaluation of patients with focal epilepsy. Various early electrographic seizure patterns differing in frequency, amplitude, and waveform of the oscillations are observed. The pattern most common in the areas of seizure propagation is the so-called theta-alpha activity (TAA), whose defining features are oscillations in the θ - α range and gradually increasing amplitude. A deeper understanding of the mechanism underlying the generation of the TAA pattern is however lacking. In this work we evaluate the hypothesis that the TAA patterns are caused by seizures spreading across the cortex. To do so, we perform simulations of seizure dynamics on detailed patient-derived cortical surfaces using the spreading seizure model as well as reference models with one or two homogeneous sources. We then detect the occurrences of the TAA patterns both in the simulated stereo-electroencephalographic signals and in the signals of recorded epileptic seizures from a cohort of fifty patients, and we compare the features of the groups of detected TAA patterns to assess the plausibility of the different models. Our results show that spreading seizure hypothesis is qualitatively consistent with the evidence available in the seizure recordings, and it can explain the features of the detected TAA groups best among the examined models.

Studies to improve the efficacy of epilepsy surgery have focused on better refining the localization of the epileptogenic zone (EZ) with the aim of effectively resecting it. However, in a considerable number of patients, EZs are distributed across multiple brain regions and may involve eloquent areas that cannot be removed due to the risk of neurological complications. There is a clear need for developing alternative approaches to induce seizure relief, but minimal impact on normal brain functions. Here, we develop a personalized in-silico network approach, that suggests effective and safe surgical interventions for each patient. Based on the clinically identified EZ, we employ modularity analysis to identify target brain regions and fiber tracts involved in seizure propagation. We then construct and simulate a patient-specific brain network model comprising phenomenological neural mass models at the nodes, and patient-specific structural brain connectivity using the neuroinformatics platform The Virtual Brain (TVB), in order to evaluate effectiveness and safety of the target zones (TZs). In particular, we assess safety via electrical stimulation for pre- and post-surgical condition to quantify the impact on the signal transmission properties of the network. We demonstrate the existence of a large repertoire of efficient surgical interventions resulting in reduction of degree of seizure spread, but only a small subset of them proves safe. The identification of novel surgical interventions through modularity analysis and brain network simulations may provide exciting solutions to the treatment of inoperable epilepsies.

Information transmission in the human brain is a fundamentally dynamic network process. In partial epilepsy, this process is perturbed and highly synchronous seizures originate in a local network, the so-called epileptogenic zone (EZ), before recruiting other close or distant brain regions. We studied patient-specific brain network models of 15 drug-resistant epilepsy patients with implanted stereotactic electroencephalography (SEEG) electrodes. Each personalized brain model was derived from structural data of magnetic resonance imaging (MRI) and diffusion tensor weighted imaging (DTI), comprising 88 nodes equipped with region specific neural mass models capable of demonstrating a range of epileptiform discharges. Each patient's virtual brain was further personalized through the integration of the clinically hypothesized EZ. Subsequent simulations and connectivity modulations were performed and uncovered a finite repertoire of seizure propagation patterns. Across patients, we found that (i) patient-specific network connectivity is predictive for the subsequent seizure propagation pattern; (ii) seizure propagation is characterized by a systematic sequence of brain states; (iii) propagation can be controlled by an optimal intervention on the connectivity matrix; (iv) the degree of invasiveness can be significantly reduced via the proposed seizure control as compared to traditional resective surgery. To stop seizures, neurosurgeons typically resect the EZ completely. We showed that stability analysis of the network dynamics, employing structural and dynamical information, estimates reliably the spatiotemporal properties of seizure propagation. This suggests novel less invasive paradigms of surgical interventions to treat and manage partial epilepsy.

Architecture of phase relationships among neural oscillations is central for their functional significance but has remained theoretically poorly understood. We use phenomenological model of delay-coupled oscillators with increasing degree of topological complexity to identify underlying principles by which the spatio-temporal structure of the brain governs the phase lags between oscillatory activity at distant regions. Phase relations and their regions of stability are derived and numerically confirmed for two oscillators and for networks with randomly distributed or clustered bimodal delays, as a first approximation for the brain structural connectivity. Besides in-phase, clustered delays can induce anti-phase synchronization for certain frequencies, while the sign of the lags is determined by the natural frequencies and by the inhomogeneous network interactions. For in-phase synchronization faster oscillators always phase lead, while stronger connected nodes lag behind the weaker during frequency depression, which consistently arises for in-silico results. If nodes are in anti-phase regime, then a distance π is added to the in-phase trends. The statistics of the phases is calculated from the phase locking values (PLV), as in many empirical studies, and we scrutinize the method's impact. The choice of surrogates do not affects the mean of the observed phase lags, but higher significance levels that are generated by some surrogates, cause decreased variance and might fail to detect the generally weaker coherence of the interhemispheric links. These links are also affected by the non-stationary and intermittent synchronization, which causes multimodal phase lags that can be misleading if averaged. Taken together, the results describe quantitatively the impact of the spatio-temporal connectivity of the brain to the synchronization patterns between brain regions, and to uncover mechanisms through which the spatio-temporal structure of the brain renders phases to be distributed around 0 and π. TRIAL REGISTRATION: South African Clinical Trials Register: http://www.sanctr.gov.za/SAClinicalbrnbspTrials/tabid/169/Default.aspx, then link to respiratory tract then link to tuberculosis, pulmonary; and TASK Applied Sciences Clinical Trials, AP-TB-201-16 (ALOPEXX): https://task.org.za/clinical-trials/.

Oscillations are ubiquitous phenomena in the animal and human brain. Among them, the alpha rhythm in human EEG is one of the most prominent examples. However, its precise mechanisms of generation are still poorly understood. It was mainly this lack of knowledge that motivated a number of simultaneous electroencephalography (EEG) - functional magnetic resonance imaging (fMRI) studies. This approach revealed how oscillatory neuronal signatures such as the alpha rhythm are paralleled by changes of the blood oxygenation level dependent (BOLD) signal. Several such studies revealed a negative correlation between the alpha rhythm and the hemodynamic BOLD signal in visual cortex and a positive correlation in the thalamus. In this study we explore the potential generative mechanisms that lead to those observations. We use a bursting capable Stefanescu-Jirsa 3D (SJ3D) neural-mass model that reproduces a wide repertoire of prominent features of local neuronal-population dynamics. We construct a thalamo-cortical network of coupled SJ3D nodes considering excitatory and inhibitory directed connections. The model suggests that an inverse correlation between cortical multi-unit activity, i.e. the firing of neuronal populations, and narrow band local field potential oscillations in the alpha band underlies the empirically observed negative correlation between alpha-rhythm power and fMRI signal in visual cortex. Furthermore the model suggests that the interplay between tonic and bursting mode in thalamus and cortex is critical for this relation. This demonstrates how biophysically meaningful modelling can generate precise and testable hypotheses about the underpinnings of large-scale neuroimaging signals.

Noise driven exploration of a brain network's dynamic repertoire has been hypothesized to be causally involved in cognitive function, aging and neurodegeneration. The dynamic repertoire crucially depends on the network's capacity to store patterns, as well as their stability. Here we systematically explore the capacity of networks derived from human connectomes to store attractor states, as well as various network mechanisms to control the brain's dynamic repertoire. Using a deterministic graded response Hopfield model with connectome-based interactions, we reconstruct the system's attractor space through a uniform sampling of the initial conditions. Large fixed-point attractor sets are obtained in the low temperature condition, with a bigger number of attractors than ever reported so far. Different variants of the initial model, including (i) a uniform activation threshold or (ii) a global negative feedback, produce a similarly robust multistability in a limited parameter range. A numerical analysis of the distribution of the attractors identifies spatially-segregated components, with a centro-medial core and several well-delineated regional patches. Those different modes share similarity with the fMRI independent components observed in the "resting state" condition. We demonstrate non-stationary behavior in noise-driven generalizations of the models, with different meta-stable attractors visited along the same time course. Only the model with a global dynamic density control is found to display robust and long-lasting non-stationarity with no tendency toward either overactivity or extinction. The best fit with empirical signals is observed at the edge of multistability, a parameter region that also corresponds to the highest entropy of the attractors.

Epileptic seizure dynamics span multiple scales in space and time. Understanding seizure mechanisms requires identifying the relations between seizure components within and across these scales, together with the analysis of their dynamical repertoire. Mathematical models have been developed to reproduce seizure dynamics across scales ranging from the single neuron to the neural population. In this study, we develop a network model of spiking neurons and systematically investigate the conditions, under which the network displays the emergent dynamic behaviors known from the Epileptor, which is a well-investigated abstract model of epileptic neural activity. This approach allows us to study the biophysical parameters and variables leading to epileptiform discharges at cellular and network levels. Our network model is composed of two neuronal populations, characterized by fast excitatory bursting neurons and regular spiking inhibitory neurons, embedded in a common extracellular environment represented by a slow variable. By systematically analyzing the parameter landscape offered by the simulation framework, we reproduce typical sequences of neural activity observed during status epilepticus. We find that exogenous fluctuations from extracellular environment and electro-tonic couplings play a major role in the progression of the seizure, which supports previous studies and further validates our model. We also investigate the influence of chemical synaptic coupling in the generation of spontaneous seizure-like events. Our results argue towards a temporal shift of typical spike waves with fast discharges as synaptic strengths are varied. We demonstrate that spike waves, including interictal spikes, are generated primarily by inhibitory neurons, whereas fast discharges during the wave part are due to excitatory neurons. Simulated traces are compared with in vivo experimental data from rodents at different stages of the disorder. We draw the conclusion that slow variations of global excitability, due to exogenous fluctuations from extracellular environment, and gap junction communication push the system into paroxysmal regimes. We discuss potential mechanisms underlying such machinery and the relevance of our approach, supporting previous detailed modeling studies and reflecting on the limitations of our methodology.

Traditional approaches to cognitive modelling generally portray cognitive events in terms of 'discrete' states (point attractor dynamics) rather than in terms of processes, thereby neglecting the time structure of cognition. In contrast, more recent approaches explicitly address this temporal dimension, but typically provide no entry points into cognitive categorization of events and experiences. With the aim to incorporate both these aspects, we propose a framework for functional architectures. Our approach is grounded in the notion that arbitrary complex (human) behaviour is decomposable into functional modes (elementary units), which we conceptualize as low-dimensional dynamical objects (structured flows on manifolds). The ensemble of modes at an agent's disposal constitutes his/her functional repertoire. The modes may be subjected to additional dynamics (termed operational signals), in particular, instantaneous inputs, and a mechanism that sequentially selects a mode so that it temporarily dominates the functional dynamics. The inputs and selection mechanisms act on faster and slower time scales then that inherent to the modes, respectively. The dynamics across the three time scales are coupled via feedback, rendering the entire architecture autonomous. We illustrate the functional architecture in the context of serial behaviour, namely cursive handwriting. Subsequently, we investigate the possibility of recovering the contributions of functional modes and operational signals from the output, which appears to be possible only when examining the output phase flow (i.e., not from trajectories in phase space or time).

The cortex is a complex system, characterized by its dynamics and architecture, which underlie many functions such as action, perception, learning, language, and cognition. Its structural architecture has been studied for more than a hundred years; however, its dynamics have been addressed much less thoroughly. In this paper, we review and integrate, in a unifying framework, a variety of computational approaches that have been used to characterize the dynamics of the cortex, as evidenced at different levels of measurement. Computational models at different space-time scales help us understand the fundamental mechanisms that underpin neural processes and relate these processes to neuroscience data. Modeling at the single neuron level is necessary because this is the level at which information is exchanged between the computing elements of the brain; the neurons. Mesoscopic models tell us how neural elements interact to yield emergent behavior at the level of microcolumns and cortical columns. Macroscopic models can inform us about whole brain dynamics and interactions between large-scale neural systems such as cortical regions, the thalamus, and brain stem. Each level of description relates uniquely to neuroscience data, from single-unit recordings, through local field potentials to functional magnetic resonance imaging (fMRI), electroencephalogram (EEG), and magnetoencephalogram (MEG). Models of the cortex can establish which types of large-scale neuronal networks can perform computations and characterize their emergent properties. Mean-field and related formulations of dynamics also play an essential and complementary role as forward models that can be inverted given empirical data. This makes dynamic models critical in integrating theory and experiments. We argue that elaborating principled and informed models is a prerequisite for grounding empirical neuroscience in a cogent theoretical framework, commensurate with the achievements in the physical sciences.

Traditionally brain function is studied through measuring physiological responses in controlled sensory, motor, and cognitive paradigms. However, even at rest, in the absence of overt goal-directed behavior, collections of cortical regions consistently show temporally coherent activity. In humans, these resting state networks have been shown to greatly overlap with functional architectures present during consciously directed activity, which motivates the interpretation of rest activity as day dreaming, free association, stream of consciousness, and inner rehearsal. In monkeys, it has been shown though that similar coherent fluctuations are present during deep anesthesia when there is no consciousness. Here, we show that comparable resting state networks emerge from a stability analysis of the network dynamics using biologically realistic primate brain connectivity, although anatomical information alone does not identify the network. We specifically demonstrate that noise and time delays via propagation along connecting fibres are essential for the emergence of the coherent fluctuations of the default network. The spatiotemporal network dynamics evolves on multiple temporal scales and displays the intermittent neuroelectric oscillations in the fast frequency regimes, 1-100 Hz, commonly observed in electroencephalographic and magnetoencephalographic recordings, as well as the hemodynamic oscillations in the ultraslow regimes, <0.1 Hz, observed in functional magnetic resonance imaging. The combination of anatomical structure and time delays creates a space-time structure in which the neural noise enables the brain to explore various functional configurations representing its dynamic repertoire.

The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems) to accomplish varying behavioral functions such as speed constraints.

Neural networks consisting of globally coupled excitatory and inhibitory nonidentical neurons may exhibit a complex dynamic behavior including synchronization, multiclustered solutions in phase space, and oscillator death. We investigate the conditions under which these behaviors occur in a multidimensional parametric space defined by the connectivity strengths and dispersion of the neuronal membrane excitability. Using mode decomposition techniques, we further derive analytically a low dimensional description of the neural population dynamics and show that the various dynamic behaviors of the entire network can be well reproduced by this reduced system. Examples of networks of FitzHugh-Nagumo and Hindmarsh-Rose neurons are discussed in detail.

Dynamic systems have proven to be well suited to describe a broad spectrum of human coordination behavior such synchronization with auditory stimuli. Simultaneous measurements of the spatiotemporal dynamics of electroencephalographic (EEG) and magnetoencephalographic (MEG) data reveals that the dynamics of the brain signals is highly ordered and also accessible by dynamic systems theory. However, models of EEG and MEG dynamics have typically been formulated only in terms of phenomenological modeling such as fixed-current dipoles or spatial EEG and MEG patterns. In this paper, it is our goal to connect three levels of organization, that is the level of coordination behavior, the level of patterns observed in the EEG and MEG and the level of neuronal network dynamics. To do so, we develop a methodological framework, which defines the spatiotemporal dynamics of neural ensembles, the neural field, on a sphere in three dimensions. Using magnetic resonance imaging we map the neural field dynamics from the sphere onto the folded cortical surface of a hemisphere. The neural field represents the current flow perpendicular to the cortex and, thus, allows for the calculation of the electric potentials on the surface of the skull and the magnetic fields outside the skull to be measured by EEG and MEG, respectively. For demonstration of the dynamics, we present the propagation of activation at a single cortical site resulting from a transient input. Finally, a mapping between finger movement profile and EEG/MEG patterns is obtained using Volterra integrals.

For the paradigmatic case of bimanual coordination, we review levels of organization of behavioral dynamics and present a description in terms of modes of behavior. We briefly review a recently developed model of spatiotemporal brain activity that is based on short- and long-range connectivity of neural ensembles. This model is specified for the case of motor and sensorimotor units embedded in the neural sheet. Focusing on the cortical left-right symmetry, we derive a bimodal description of the brain activity that is connected to behavioral dynamics. We make predictions of global features of brain dynamics during coordination tasks and test these against experimental magnetoencephalogram (MEG) results. A key feature of our approach is that phenomenological laws at the behavioral level can be connected to a field-theoretical description of cortical dynamics.