Neural Mass Research Articles

Probabilistic delay differential equation modeling of event-related potentials

“Dynamic causal models” (DCMs) are a promising approach in the analysis of functional neuroimaging data due to their biophysical interpretability and their consolidation of functional-segregative and functional-integrative propositions. In this theoretical note we are concerned with the DCM framework for electroencephalographically recorded event-related potentials (ERP-DCM). Intuitively, ERP-DCM combines deterministic dynamical neural mass models with dipole-based EEG forward models to describe the event-related scalp potential time-series over the entire electrode space. Since its inception, ERP-DCM has been successfully employed to capture the neural underpinnings of a wide range of neurocognitive phenomena. However, in spite of its empirical popularity, the technical literature on ERP-DCM remains somewhat patchy. A number of previous communications have detailed certain aspects of the approach, but no unified and coherent documentation exists. With this technical note, we aim to close this gap and to increase the technical accessibility of ERP-DCM. Specifically, this note makes the following novel contributions: firstly, we provide a unified and coherent review of the mathematical machinery of the latent and forward models constituting ERP-DCM by formulating the approach as a probabilistic latent delay differential equation model. Secondly, we emphasize the probabilistic nature of the model and its variational Bayesian inversion scheme by explicitly deriving the variational free energy function in terms of both the likelihood expectation and variance parameters. Thirdly, we detail and validate the estimation of the model with a special focus on the explicit form of the variational free energy function and introduce a conventional nonlinear optimization scheme for its maximization. Finally, we identify and discuss a number of computational issues which may be addressed in the future development of the approach.

Modeling the effect of sleep regulation on a neural mass model.

In mammals, sleep is categorized by two main sleep stages, rapid eye movement (REM) and non-REM (NREM) sleep that are known to fulfill different functional roles, the most notable being the consolidation of memory. While REM sleep is characterized by brain activity similar to wakefulness, the EEG activity changes drastically with the emergence of K-complexes, sleep spindles and slow oscillations during NREM sleep. These changes are regulated by circadian and ultradian rhythms, which emerge from an intricate interplay between multiple neuronal populations in the brainstem, forebrain and hypothalamus and the resulting varying levels of neuromodulators. Recently, there has been progress in the understanding of those rhythms both from a physiological as well as theoretical perspective. However, how these neuromodulators affect the generation of the different EEG patterns and their temporal dynamics is poorly understood. Here, we build upon previous work on a neural mass model of the sleeping cortex and investigate the effect of those neuromodulators on the dynamics of the cortex and the corresponding transition between wakefulness and the different sleep stages. We show that our simplified model is sufficient to generate the essential features of human EEG over a full day. This approach builds a bridge between sleep regulatory networks and EEG generating neural mass models and provides a valuable tool for model validation.

Neural mass model-based tracking of anesthetic brain states

Neural mass model-based tracking of brain states from electroencephalographic signals holds the promise of simultaneously tracking brain states while inferring underlying physiological changes in various neuroscientific and clinical applications. Here, neural mass model-based tracking of brain states using the unscented Kalman filter applied to estimate parameters of the Jansen–Rit cortical population model is evaluated through the application of propofol-based anesthetic state monitoring. In particular, 15 subjects underwent propofol anesthesia induction from awake to anesthetised while behavioral responsiveness was monitored and frontal electroencephalographic signals were recorded. The unscented Kalman filter Jansen–Rit model approach applied to frontal electroencephalography achieved reasonable testing performance for classification of the anesthetic brain state (sensitivity: 0.51; chance sensitivity: 0.17; nearest neighbor sensitivity 0.75) when compared to approaches based on linear (autoregressive moving average) modeling (sensitivity 0.58; nearest neighbor sensitivity: 0.91) and a high performing standard depth of anesthesia monitoring measure, Higuchi Fractal Dimension (sensitivity: 0.50; nearest neighbor sensitivity: 0.88). Moreover, it was found that the unscented Kalman filter based parameter estimates of the inhibitory postsynaptic potential amplitude varied in the physiologically expected direction with increases in propofol concentration, while the estimates of the inhibitory postsynaptic potential rate constant did not. These results combined with analysis of monotonicity of parameter estimates, error analysis of parameter estimates, and observability analysis of the Jansen–Rit model, along with considerations of extensions of the Jansen–Rit model, suggests that the Jansen–Rit model combined with unscented Kalman filtering provides a valuable reference point for future real-time brain state tracking studies. This is especially true for studies of more complex, but still computationally efficient, neural models of anesthesia that can more accurately track the anesthetic brain state, while simultaneously inferring underlying physiological changes that can potentially provide useful clinical information.

Annealed Importance Sampling for Neural Mass Models.

Neural Mass Models provide a compact description of the dynamical activity of cell populations in neocortical regions. Moreover, models of regional activity can be connected together into networks, and inferences made about the strength of connections, using M/EEG data and Bayesian inference. To date, however, Bayesian methods have been largely restricted to the Variational Laplace (VL) algorithm which assumes that the posterior distribution is Gaussian and finds model parameters that are only locally optimal. This paper explores the use of Annealed Importance Sampling (AIS) to address these restrictions. We implement AIS using proposals derived from Langevin Monte Carlo (LMC) which uses local gradient and curvature information for efficient exploration of parameter space. In terms of the estimation of Bayes factors, VL and AIS agree about which model is best but report different degrees of belief. Additionally, AIS finds better model parameters and we find evidence of non-Gaussianity in their posterior distribution.

Identification of Glioblastoma Subpopulations by Flim

Glioblastoma multiforme (GBM) is one of the most aggressive forms of brain cancer. The tumor is known to be composed of heterogeneous subpopulations of cells, potentially playing a role in therapeutic resistance. Therefore, an understanding of the tumor heterogeneity is essential for the development of effective therapies. To further study the tumor heterogeneity, a culture method was developed to isolate distinct subpopulations from an established glioma cell line. These subpopulations include neural stem-like cells and tumor mass cells.

Model selection for identifying power-law scaling

Long-range temporal and spatial correlations have been reported in a remarkable number of studies. In particular power-law scaling in neural activity raised considerable interest. We here provide a straightforward algorithm not only to quantify power-law scaling but to test it against alternatives using (Bayesian) model comparison. Our algorithm builds on the well-established detrended fluctuation analysis (DFA). After removing trends of a signal, we determine its mean squared fluctuations in consecutive intervals. In contrast to DFA we use the values per interval to approximate the distribution of these mean squared fluctuations. This allows for estimating the corresponding log-likelihood as a function of interval size without presuming the fluctuations to be normally distributed, as is the case in conventional DFA. We demonstrate the validity and robustness of our algorithm using a variety of simulated signals, ranging from scale-free fluctuations with known Hurst exponents, via more conventional dynamical systems resembling exponentially correlated fluctuations, to a toy model of neural mass activity. We also illustrate its use for encephalographic signals. We further discuss confounding factors like the finite signal size. Our model comparison provides a proper means to identify power-law scaling including the range over which it is present.

Detection of Coupling in Short Physiological Series by a Joint Distribution Entropy Method.

In this study, we developed a joint distribution entropy (JDistEn) method to robustly estimate the coupling in short physiological series. The JDistEn method is derived from a joint distance matrix which is constructed from a combination of the distance matrix corresponding to each individual data channel using a geometric mean calculation. A coupled Rössler system and a coupled dual-kinetics neural mass model were used to examine how well JDistEn performed, specifically, its sensitivity for detecting weak coupling, its consistency in gauging coupling strength, and its reliability in processing input of decreased data length. Performance of JDistEn in estimating physiological coupling was further examined with bivariate electroencephalography data from rats and RR interval and diastolic time interval series from human beings. Cross-sample entropy (XSampEn), cross-conditional entropy (XCE), and Shannon entropy of diagonal lines in the joint recurrence plots (JENT) were applied for purposes of comparison. Simulation results suggest that JDistEn showed markedly higher sensitivity than XSampEn, XCE, and JENT for dynamics in weak coupling, although as the simulation models were more intensively coupled, JDistEn performance was comparable to the three others. In addition, this improved sensitivity was much more pronounced for short datasets. Experimental results further confirmed that JDistEn outperformed XSampEn, XCE, and JENT for detecting weak coupling, especially for short physiological data. This study suggested that our proposed JDistEn could be useful for continuous and even real-time coupling analysis for physiological signals in clinical practice.

Mechanisms underlying different onset patterns of focal seizures

Event Abstract Back to Event Mechanisms underlying different onset patterns of focal seizures Yujiang Wang1* 1 Newcastle University, School of Computing Science, United Kingdom Focal seizures typically begin with an electrographic onset pattern that is highly stereotyped in individual patients. Qualitative classifications of these onset patterns describe two frequently occurring waveforms – low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Interestingly, only the former of the patterns is associated with a good surgical outcome. Given the importance of this clinical distinction, we therefore explored whether these two patterns arise from fundamentally different spatio-temporal dynamics. We used a previously established computational model of neocortical tissue, and validated it as an adequate model using clinical recordings of focal seizures. Using this model we then investigated the possible mechanisms underlying the different focal seizure onset patterns. We show that the two patterns are associated with different mechanisms at the spatial scale of a single ECoG electrode. The LAF onset is initiated by independent patches of localised activity, which slowly invade the surrounding tissue and coalesce over time (see Fig. 1A). In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event (see Fig. 1B). We find that such a global transition is enabled by an increase in excitability of the surrounding tissue, essentially creating a seizure supporting surrounding. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically observed difference in surgical outcomes. Finally, we demonstrate how changes in tissue excitability could be elucidated in principle using active stimulation. We conclude that the excitability of the tissue surrounding the seizure core plays a determining role in the seizure onset pattern, as well as in the surgical outcome. Figure 1 Keywords: Epilepsy, neural mass model, Seizures, Seizure onset pattern, cortical excitability Conference: Neuroinformatics 2016, Reading, United Kingdom, 3 Sep - 4 Sep, 2016. Presentation Type: Investigator presentations Topic: Brain disorders Citation: Wang Y (2016). Mechanisms underlying different onset patterns of focal seizures. Front. Neuroinform. Conference Abstract: Neuroinformatics 2016. doi: 10.3389/conf.fninf.2016.20.00016 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 26 Apr 2016; Published Online: 18 Jul 2016. * Correspondence: Dr. Yujiang Wang, Newcastle University, School of Computing Science, Newcastle upon Tyne, NE1 7RU, United Kingdom, Yujiang.Wang@newcastle.ac.uk Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Yujiang Wang Google Yujiang Wang Google Scholar Yujiang Wang PubMed Yujiang Wang Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

A Pharmacokinetics-Neural Mass Model (PK-NMM) for the Simulation of EEG Activity during Propofol Anesthesia.

Modeling the effects of anesthetic drugs on brain activity is very helpful in understanding anesthesia mechanisms. The aim of this study was to set up a combined model to relate actual drug levels to EEG dynamics and behavioral states during propofol-induced anesthesia. We proposed a new combined theoretical model based on a pharmacokinetics (PK) model and a neural mass model (NMM), which we termed PK-NMM—with the aim of simulating electroencephalogram (EEG) activity during propofol-induced general anesthesia. The PK model was used to derive propofol effect-site drug concentrations (C eff) based on the actual drug infusion regimen. The NMM model took C eff as the control parameter to produce simulated EEG-like (sEEG) data. For comparison, we used real prefrontal EEG (rEEG) data of nine volunteers undergoing propofol anesthesia from a previous experiment. To see how well the sEEG could describe the dynamic changes of neural activity during anesthesia, the rEEG data and the sEEG data were compared with respect to: power-frequency plots; nonlinear exponent (permutation entropy (PE)); and bispectral SynchFastSlow (SFS) parameters. We found that the PK-NMM model was able to reproduce anesthesia EEG-like signals based on the estimated drug concentration and patients’ condition. The frequency spectrum indicated that the frequency power peak of the sEEG moved towards the low frequency band as anesthesia deepened. Different anesthetic states could be differentiated by the PE index. The correlation coefficient of PE was 0.80±0.13 (mean±standard deviation) between rEEG and sEEG for all subjects. Additionally, SFS could track the depth of anesthesia and the SFS of rEEG and sEEG were highly correlated with a correlation coefficient of 0.77±0.13. The PK-NMM model could simulate EEG activity and might be a useful tool for understanding the action of propofol on brain activity.

Using the connectome to predict epileptic seizure propagation in the human brain

Partial seizures in epileptic patients are generated in localized networks, so-called Epileptogenic Zone (EZ), before recruiting other regions, so-called Propagation Zone (PZ) [1]. For drug-resistant patients, surgical resection is sometimes possible. Correctly delineating the extent of the EZ and PZ is critical for a successful surgical resection, in order to remove enough of the epileptogenic tissue to prevent seizures while minimizing the cognitive collateral damages. EZ and PZ extents are evaluated using imaging tools such as M/EEG, MRI, PET and stereotaxic EEG (sEEG). In this modelisation work, we used the large-scale connectome to build a network of neural masses in order to reproduce seizure propagation through the human brain. In particular, we aimed at predicting the propagation of epileptic seizures, i.e. the PZ, using the localization of the EZ. We preprocessed data obtained from 18 different patients with different types of partial epilepsy. Using MRI and diffusion MRI data, we generated patient-specific connectomes along with cortical surfaces, using different parcellation resolutions. Epileptic dynamics of a single region was based on the Epileptor, a neural mass model able to autonomously generate epileptic seizures [2]. The different regions interacted via a permittivity coupling allowing to reproduce seizures propagation such as observed in sEEG [3]. Using a reduced Epileptor model, we performed a stability analysis at the edge of the seizure onset. We confirmed our results with simulations of the network of Epileptors using The Virtual Brain, a neuroinformatics platform to simulate large-scale dynamics [4]. The analytical prediction of seizure spatial extent correctly reproduces seizure simulations. We systematically predicted the spatial spread of the seizure, i.e. the PZ, for each patient, according to the spatial extent and localization of the EZ such as observed with sEEG, using different global connectivity and excitability parameters. An example of an EZ and PZ along with a simulation of the forward calculation on sEEG electrodes are shown in Figure ​Figure1.1. Our results show a good agreement with clinician predictions, surgery results, and sEEG signals. To confirm the determinant role of the connectome in spatial seizure propagation, we performed several surrogate analysis with other neural mass models (e.g. FitzHugh-Nagumo model), connectivity of control subjects and generic connectivities such as shuffled connectivities, random and small-world networks, again evaluated against clinical data. Real connectomes always performed better than generic connectivities. The connectome particular structure of a patient was often but not always better to predict seizure propagation than connectome of controls. Figure 1 A. Example of the EZ (red) and the calculated PZ (yellow) displayed on the patient cortical surface, along with sEEG electrodes (small spheres). B. Corresponding simulated time series. In conclusion, our results show that large-scale white matter tracts play an important role in the propagation of epileptic seizures. Better understanding of their exact role can help to significantly improve the success rate of surgical resections for epileptic patients.

The dynamics of resting fluctuations in the brain

The grand average functional connectivity (FC) of a resting brain captures properly the well- structured spatial correlations between different brain areas. Whole-brain-models explicitly linking spontaneous local neuronal dynamics with the tractography based anatomical structure of the brain are able to explain the emergence of those spatial resting correlations. Nevertheless, resting activity is not only spatially structured but also shows a very stereotypical temporal structure which is characterized by rapid transitions switching between a few discrete FC states across time. In this talk, we introduce a powerful theoretical framework, which allows us to demonstrate that resting functional connectivity FC dynamics (FCD) constrains more strongly the dynamical working point of whole-brain models. Furthermore, using a very general neural mass model based on the normal form of a Hopf bifurcation we are able to demonstrate that the temporal dynamics of resting state fluctuations emerges at the edge of the transition between asynchronous to oscillatory behavior. Even more importantly, at that particular working point the global metastability of the whole brain is maximized. By optimizing the spectral characteristics of each local brain node, we discover the dynamical core of the brain, i.e., the set of nodes, which drives the rest of the whole brain by oscillations.

Are rich club regions masters or slaves of brain network dynamics?

Anatomical networks of brain systems emphasize their inherent hierarchical structure, in which the rich club (most inner core of the brain) is highlighted because it promotes topological efficiency and integrates communication between regions [1]. The hierarchical structure is fundamental and also observed in the neuronal dynamics: Cortical anatomy is thought to recapitulate the temporal hierarchy that is inherent in the dynamics of environmental states and human behavior [2]. According to this classical view the caudal-rostral arrangement maps the fast-slow gradient of neuronal time scales [3]. Here we ask whether the topological arrangement of the networks can provide a scaffold on which a hierarchy of time scales including slow and stable dynamics emerges. We modeled neuronal dynamics unfolding on an anatomical network reconstructed from primate cortex that has a set of rich-club regions at the core of the network that are surrounded by their feeders and peripheral areas [4]. We utilized a conductance-based neural mass model [5], which gives rise to node dynamics with two time scales. The system synchronizes at the fast time scale and exhibits rich phase relations at the slow rhythm (~10Hz). We then characterized and compared the oscillatory dynamics of nodes and the synchronization between pairs of nodes. Our results show that highly connected regions, such as rich-club members, exhibit a more regular dynamics, and larger stability of phase relation with respective to other regions [6]. Owing to the dynamics of the local connectivity and network-motif structure [7,8], central nodes also catalyze better local zero-lag synchronization between their neighbors. Together our results show how the topology of this constellation of brain regions supports stable, slowly fluctuating patterns of synchronization. In contrast, the topology of the surrounding feeder cortical regions shows unstable, rapidly fluctuating dynamics. Hence, assuming the interaction of identical dynamical elements coupled via the structural connectome of primate cortex [4], we already find an emerging hierarchy of time scales due to the network structure. We thus propose that the network properties of central cortical regions are the structural determinants of slow neuronal fluctuations in these brain regions. Although the traditional caudal-rostral hierarchical cortical mapping exhibited an unprecedented success, our dynamic-based study aligned with recent observations indicates that the cortical organizing principle may be best described by a periphery-core axis. Intriguingly, as a metaphor to social networks, rich-club members could be seen to be slaves of their own power. The richness of these brain regions comes from their large in-degree. However, for this very reason, their dynamics are consequently more regular because larger in-degree guarantees larger regularity. In other words, the autonomous dynamics of connectome hubs are largely enslaved to the strong, rhythmic output of the entire connectome. Therefore, rich-club regions cannot behave very differently from what is expected in contrast to the peripheral nodes, which have the most freedom to explore the dynamical landscape.

Stimulus induced resonance in a neural mass model driven with a temporally correlated noise

determine the model’s activity. Furthermore, we show that this dependence has non-trivial, non-monotonous characteristics. We find that experimental results obtained in the absence of a stimulus are best reproduced when the model operates close to a bifurcation. In the presence of the stimulus, computational results recapitulate the experimental observations when the alpha resonance is not fully developed. The emergence of resonance depends on the driving signal amplitude, properties of the noise, and it relies on collective synchronization, which in turn depends on the coupling between the network elements. The model allows us to make predictions for driving with frequencies greater than the one used in the experiment. Our results indicate that the cross-frequency transfer observed experimentally may occur only for slow driving: for faster input the alpha peak does not increase and might even be suppressed. In summary, our results show that a 1/f b realistic power spectrum with an embedded alpha peak can be obtained from a neural mass model driven by a temporally correlated noise. The model’s dynamics depend in a nonmonotonous way on the correlation time of the noise. Slow oscillatory driving of this model operating close to a bifurcation facilitates development of a resonance in the alpha band, giving rise to a cross-frequency power transfer, which reproduces experimental observations [1].

Large-scale brain dynamics: effect of connectivity resolution

Large-scale brain dynamics recently started to be modeled numerically based on both heterogeneous large-scale networks build from diffusion MRI, that is, a connectome, and local homogeneous connectivity kernel representing intracortical synaptic connections. However, topological properties of a connectome can significantly change with resolution and parcellation [1]. Furthermore, the sampling of the cerebral surfaces, resulting in a geometric model, and, in this way, the local connectivity kernel play crucial roles in the formation of spatial patterns on the cerebral surfaces as well as on the sensor level (e.g., EEG electrodes) by a forward calculation [2]. However, the effect of sampling and parcellation on modeling brain dynamics has not been studied so far. Here, we investigate qualitatively and quantitatively: (i) how different parcellation resolutions affect the dynamics of the network; and (ii) how the local connectivity affects the network dynamics. To do so, we used the neuroinformatics platform for large-scale brain simulations, called The Virtual Brain (TVB) [3] and developed a preprocessing pipeline to incorporate experimental data (e.g., structural MRI, diffusion-weighted MRI) in TVB [4]. We prepared ten individual models based on ten randomly selected subjects from the Human Connectome Project dataset [5]. For each individual model we performed simulations under two conditions during rest: (i) noise driven, using a bistable neural mass model, and (ii) after stimulation, using an excitable neural mass model. We investigated the effect of heterogeneous and homogeneous connectivity on large-scale brain dynamics by different numbers of regions in the parcellation (70 to 2240) and by varying the local connectivity coupling strength. To introduce experimental data (i.e., structural and diffusion MRI) into TVB we tackled issues such as surface downsampling (for achieving moderate simulation times) and mapping between surface and parcellation (to consistently use heterogeneous and homogeneous connectivity) by developing the Surface and Connectivity Reconstruction with an Imaging Pipeline for TVB Simulations, short SCRIPTS [4]. When considering slow dynamics, the major fiber bundles best reflected in the coarsest parcellation appeared to be mainly responsible for the emergence of the network attractors with limited changes over different parcellations and different local coupling strengths. For fast dynamics, new qualitative solutions appeared, but only in the presence of delays. Figure 1 A. Spatial attractors. For each value of the global (G) or local (G_local) coupling parameter, correlation with in-strength (blue points) and with s-core (red points) for ten different initial conditions. The blue square indicates the critical interval. ...

Epileptogenic zone localization and seizure control in coupled neural mass models.

Exact localization of the epileptogenic zone (EZ) is the first priority for ensuring epilepsy treatments and reducing side effects. The results of traditional visual methods for localizing the origin of seizures are far from satisfactory in some cases. Signal processing methods could extract substantial information that may complement visual inspection of EEG signals. In this study, EZ localization is changed into a driver identification problem, and a nonlinear interdependence measure, the weighted rank interdependence, is proposed and used as a driver indicator because it can detect coupling information, especially directionality, from EEG signals. A proportional integral derivative (PID) controller is then explored, using simulations, to establish its suitability for seizure control. The seizure control we propose rests on identifying the EZ using nonlinear interdependence measures of directed functional connectivity. Two directionally coupled neural mass models are employed for simulation investigation. Two parameters can adjust the sensitivity and completeness of the weighted rank interdependence for different applications, and their effect is discussed in the context of neural mass models. Simulation results demonstrate that use of the weighted rank interdependence for EZ identification can be applied to different EZ types, and the approach achieves an overall identification rate of 98.84 % for several EZ types. Simulations also indicate that PID control can effectively regulate synchronization between neural masses.

The enhanced information flow from visual cortex to frontal area facilitates SSVEP response: evidence from model-driven and data-driven causality analysis.

The neural mechanism of steady-state visual evoked potentials (SSVEP) is still not clearly understood. Especially, only certain frequency stimuli can evoke SSVEP. Our previous network study reveals that 8 Hz stimulus that can evoke strong SSVEP response shows the enhanced linkage strength between frontal and visual cortex. To further probe the directed information flow between the two cortex areas for various frequency stimuli, this paper develops a causality analysis based on the inversion of double columns model using particle swarm optimization (PSO) to characterize the directed information flow between visual and frontal cortices with the intracranial rat electroencephalograph (EEG). The estimated model parameters demonstrate that the 8 Hz stimulus shows the enhanced directional information flow from visual cortex to frontal lobe facilitates SSVEP response, which may account for the strong SSVEP response for 8 Hz stimulus. Furthermore, the similar finding is replicated by data-driven causality analysis. The inversion of neural mass model proposed in this study may be helpful to provide the new causality analysis to link the physiological model and the observed datasets in neuroscience and clinical researches.

Suppression of seizures based on the multi-coupled neural mass model.

Epilepsy is one of the most common serious neurological disorders, which affects approximately 1% of population in the world. In order to effectively control the seizures, we propose a novel control methodology, which combines the feedback linearization control (FLC) with the underlying mechanism of epilepsy, to achieve the suppression of seizures. The three coupled neural mass model is constructed to study the property of the electroencephalographs (EEGs). Meanwhile, with the model we research on the propagation of epileptiform waves and the synchronization of populations, which are taken as the foundation of our control method. Results show that the proposed approach not only yields excellent performances in clamping the pathological spiking patterns to the reference signals derived under the normal state but also achieves the normalization of the pathological parameter, where the parameters are estimated from EEGs with Unscented Kalman Filter. The specific contribution of this paper is to treat the epilepsy from its pathogenesis with the FLC, which provides critical theoretical basis for the clinical treatment of neurological disorders.

Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.

Relating Alpha Power and Phase to Population Firing and Hemodynamic Activity Using a Thalamo-cortical Neural Mass Model.

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.

Synchronization-based computation through networks of coupled oscillators.

The mesoscopic activity of the brain is strongly dynamical, while at the same time exhibits remarkable computational capabilities. In order to examine how these two features coexist, here we show that the patterns of synchronized oscillations displayed by networks of neural mass models, representing cortical columns, can be used as substrates for Boolean-like computations. Our results reveal that the same neural mass network may process different combinations of dynamical inputs as different logical operations or combinations of them. This dynamical feature of the network allows it to process complex inputs in a very sophisticated manner. The results are reproduced experimentally with electronic circuits of coupled Chua oscillators, showing the robustness of this kind of computation to the intrinsic noise and parameter mismatch of the coupled oscillators. We also show that the information-processing capabilities of coupled oscillations go beyond the simple juxtaposition of logic gates.