Dynamic mechanisms of neocortical focal seizure onset

The vitals for steady nucleation maps of spontaneous spiking coherence in autonomous two-dimensional neuronal networks

Thin pancake-like neuronal networks cultured on top of a planar microelectrode array have been extensively tried out in neuroengineering, as a substrate for the mobile robot's control unit, i.e., as a cyborg's brain. Most of these attempts failed due to intricate self-organizing dynamics in the neuronal systems. In particular, the networks may exhibit an emergent spatial map of steady nucleation sites ("n-sites") of spontaneous population spikes. Being unpredictable and independent of the surface electrode locations, the n-sites drastically change local ability of the network to generate spikes. Here, using a spiking neuronal network model with generative spatially-embedded connectome, we systematically show in simulations that the number, location, and relative activity of spontaneously formed n-sites ("the vitals") crucially depend on the samplings of three distributions: (1) the network distribution of neuronal excitability, (2) the distribution of connections between neurons of the network, and (3) the distribution of maximal amplitudes of a single synaptic current pulse. Moreover, blocking the dynamics of a small fraction (about 4%) of non-pacemaker neurons having the highest excitability was enough to completely suppress the occurrence of population spikes and their n-sites. This key result is explained theoretically. Remarkably, the n-sites occur taking into account only short-term synaptic plasticity, i.e., without a Hebbian-type plasticity. As the spiking network model used in this study is strictly deterministic, all simulation results can be accurately reproduced. The model, which has already demonstrated a very high richness-to-complexity ratio, can also be directly extended into the three-dimensional case, e.g., for targeting peculiarities of spiking dynamics in cerebral (or brain) organoids. We recommend the model as an excellent illustrative tool for teaching network-level computational neuroscience, complementing a few benchmark models.

Mechanism of an Intrinsic Oscillation in Rat Geniculate Interneurons

Depolarizing current injections produced a rhythmic bursting of action potentials - a bursting oscillation - in a set of local interneurons in the lateral geniculate nucleus (LGN) of rats. The current dynamics underlying this firing pattern have not been determined, though this cell type constitutes an important cellular component of thalamocortical circuitry, and contributes to both pathologic and non-pathologic brain states. We thus investigated the source of the bursting oscillation using pharmacological manipulations in LGN slices in vitro and in silico. 1. Selective blockade of calcium channel subtypes revealed that high-threshold calcium currentsI L andI P contributed strongly to the oscillation. 2. Increased extracellular K+ concentration (decreased K+currents) eliminated the oscillation. 3. Selective blockade of K+ channel subtypes demonstrated that the calcium-sensitive potassium current (I A H P ) was of primary importance. A morphologically simplified, multicompartment model of the thalamic interneuron characterized the oscillation as follows: 1. The low-threshold calcium currentI T provided the strong initial burst characteristic of the oscillation. 2. Alternating fluxes through high-threshold calcium channels andI A H P then provided the continuing oscillation's burst and interburst periods respectively. This interplay betweenI L andI A H P contrasts with the current dynamics underlying oscillations in thalamocortical and reticularis neurons, which primarily involveI T andI H , orI T andI A H P respectively. These findings thus point to a novel electrophysiological mechanism for generating intrinsic oscillations in a major thalamic cell type. Because local interneurons can sculpt the behavior of thalamocortical circuits, these results suggest new targets for the manipulation of ascending thalamocortical network activity.

Bifurcations and bursting in the Epileptor

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.

Spatial organisation of the mesoscale connectome: A feature influencing synchrony and metastability of network dynamics

Significant research has investigated synchronisation in brain networks, but the bulk of this work has explored the contribution of brain networks at the macroscale. Here we explore the effects of changing network topology on functional dynamics in spatially constrained random networks representing mesoscale neocortex. We use the Kuramoto model to simulate network dynamics and explore synchronisation and critical dynamics of the system as a function of topology in randomly generated networks with a distance-related wiring probability and no preferential attachment term. We show networks which predominantly make short-distance connections smooth out the critical coupling point and show much greater metastability, resulting in a wider range of coupling strengths demonstrating critical dynamics and metastability. We show the emergence of cluster synchronisation in these geometrically-constrained networks with functional organisation occurring along structural connections that minimise the participation coefficient of the cluster. We show that these cohorts of internally synchronised nodes also behave en masse as weakly coupled nodes and show intra-cluster desynchronisation and resynchronisation events related to inter-cluster interaction. While cluster synchronisation appears crucial to healthy brain function, it may also be pathological if it leads to unbreakable local synchronisation which may happen at extreme topologies, with implications for epilepsy research, wider brain function and other domains such as social networks.

Temporal stability of intracranial electroencephalographic abnormality maps for localizing epileptogenic tissue

OBJECTIVE

Identifying abnormalities on interictal intracranial electroencephalogram (iEEG), by comparing patient data to a normative map, has shown promise for the localization of epileptogenic tissue and prediction of outcome. The approach typically uses short interictal segments of approximately 1 min. However, the temporal stability of findings has not been established.

METHODS

Here, we generated a normative map of iEEG in nonpathological brain tissue from 249 patients. We computed regional band power abnormalities in a separate cohort of 39 patients for the duration of their monitoring period (.92-8.62 days of iEEG data, mean = 4.58 days per patient, >4800 hours recording). To assess the localizing value of band power abnormality, we computedD RS -a measure of how different the surgically resected and spared tissue was in terms of band power abnormalities-over time.

RESULTS

In each patient, theD RS value was relatively consistent over time. The medianD RS of the entire recording period separated seizure-free (International League Against Epilepsy [ILAE] = 1) and not-seizure-free (ILAE> 1) patients well (area under the curve [AUC] = .69). This effect was similar interictally (AUC = .69) and peri-ictally (AUC = .71).

SIGNIFICANCE

Our results suggest that band power abnormality D_RS, as a predictor of outcomes from epilepsy surgery, is a relatively robust metric over time. These findings add further support for abnormality mapping of neurophysiology data during presurgical evaluation.

Closed-loop optogenetic control of the dynamics of neural activity in non-human primates

Electrical neurostimulation is effective in the treatment of neurological disorders, but associated recording artefacts generally limit its applications to open-loop stimuli. Real-time and continuous closed-loop control of brain activity can, however, be achieved by pairing concurrent electrical recordings and optogenetics. Here we show that closed-loop optogenetic stimulation with excitatory opsins enables the precise manipulation of neural dynamics in brain slices from transgenic mice and in anaesthetized non-human primates. The approach generates oscillations in quiescent tissue, enhances or suppresses endogenous patterns in active tissue and modulates seizure-like bursts elicited by the convulsant 4-aminopyridine. A nonlinear model of the phase-dependent effects of optical stimulation reproduced the modulation of cycles of local-field potentials associated with seizure oscillations, as evidenced by the systematic changes in the variability and entropy of the phase-space trajectories of seizures, which correlated with changes in their duration and intensity. We also show that closed-loop optogenetic neurostimulation could be delivered using intracortical optrodes incorporating light-emitting diodes. Closed-loop optogenetic approaches may be translatable to therapeutic applications in humans.

Noise-modulated multistable synapses in a Wilson-Cowan-based model of plasticity

Frequency-dependent plasticity refers to changes in synaptic strength in response to different stimulation frequencies. Resonance is a factor known to be of importance in such frequency dependence, however, the role of neural noise in the process remains elusive. Considering the brain is an inherently noisy system, understanding its effects may prove beneficial in shaping therapeutic interventions based on non-invasive brain stimulation protocols. The Wilson-Cowan (WC) model is a well-established model to describe the average dynamics of neural populations and has been shown to exhibit bistability in the presence of noise. However, the important question of how the different stable regimes in the WC model can affect synaptic plasticity when cortical populations interact has not yet been addressed. Therefore, we investigated plasticity dynamics in a WC-based model of interacting neural populations coupled with activity-dependent synapses in which a periodic stimulation was applied in the presence of noise of controlled intensity. The results indicate that for a narrow range of the noise variance, synaptic strength can be optimized. In particular, there is a regime of noise intensity for which synaptic strength presents a triple-stable state. Regulating noise intensity affects the probability that the system chooses one of the stable states, thereby controlling plasticity. These results suggest that noise is a highly influential factor in determining the outcome of plasticity induced by stimulation.

Functional network connectivity imprint in febrile seizures

Complex febrile seizures (CFS), a subset of paediatric febrile seizures (FS), have been studied for their prognosis, epileptogenic potential and neurocognitive outcome. We evaluated their functional connectivity differences with simple febrile seizures (SFS) in children with recent-onset FS. Resting-state fMRI (rs-fMRI) datasets of 24 children with recently diagnosed FS (SFS-n = 11; CFS-n = 13) were analysed. Functional connectivity (FC) was estimated using time series correlation of seed region–to-whole-brain-voxels and network topology was assessed using graph theory measures. Regional connectivity differences were correlated with clinical characteristics (FDR corrected p < 0.05). CFS patients demonstrated increased FC of the bilateral middle temporal pole (MTP), and bilateral thalami when compared to SFS. Network topology study revealed increased clustering coefficient and decreased participation coefficient in basal ganglia and thalamus suggesting an inefficient-unbalanced network topology in patients with CFS. The number of seizure recurrences negatively correlated with the integration of Left Thalamus (r = − 0.58) and FC of Left MTP to 'Right Supplementary Motor and left Precentral' gyrus (r = − 0.53). The FC of Right MTP to Left Amygdala, Putamen, Parahippocampal, and Orbital Frontal Cortex (r = 0.61) and FC of Left Thalamus to left Putamen, Pallidum, Caudate, Thalamus Hippocampus and Insula (r 0.55) showed a positive correlation to the duration of the longest seizure. The findings of the current study report altered connectivity in children with CFS proportional to the seizure recurrence and duration. Regardless of the causal/consequential nature, such observations demonstrate the imprint of these disease-defining variables of febrile seizures on the developing brain.

Spontaneous transitions to focal-onset epileptic seizures: A dynamical study

Given the complex temporal evolution of epileptic seizures, understanding their dynamic nature might be beneficial for clinical diagnosis and treatment. Yet, the mechanisms behind, for instance, the onset of seizures are still unknown. According to an existing classification, two basic types of dynamic onset patterns plus a number of more complex onset waveforms can be distinguished. Here, we introduce a basic three-variable model with two time scales to study potential mechanisms of spontaneous seizure onset. We expand the model to demonstrate how coupling of oscillators leads to more complex seizure onset waveforms. Finally, we test the response to pulse perturbation as a potential biomarker of interictal changes.

Domino-like transient dynamics at seizure onset in epilepsy

The International League Against Epilepsy (ILAE) groups seizures into "focal", "generalized" and "unknown" based on whether the seizure onset is confined to a brain region in one hemisphere, arises in several brain region simultaneously, or is not known, respectively. This separation fails to account for the rich diversity of clinically and experimentally observed spatiotemporal patterns of seizure onset and even less so for the properties of the brain networks generating them. We consider three different patterns of domino-like seizure onset in Idiopathic Generalized Epilepsy (IGE) and present a novel approach to classification of seizures. To understand how these patterns are generated on networks requires understanding of the relationship between intrinsic node dynamics and coupling between nodes in the presence of noise, which currently is unknown. We investigate this interplay here in the framework of domino-like recruitment across a network. In particular, we use a phenomenological model of seizure onset with heterogeneous coupling and node properties, and show that in combination they generate a range of domino-like onset patterns observed in the IGE seizures. We further explore the individual contribution of heterogeneous node dynamics and coupling by interpreting in-vitro experimental data in which the speed of onset can be chemically modulated. This work contributes to a better understanding of possible drivers for the spatiotemporal patterns observed at seizure onset and may ultimately contribute to a more personalized approach to classification of seizure types in clinical practice.

Computer modelling of connectivity change suggests epileptogenesis mechanisms in idiopathic generalised epilepsy

Patients with idiopathic generalised epilepsy (IGE) typically have normal conventional magnetic resonance imaging (MRI), hence diagnosis based on MRI is challenging. Anatomical abnormalities underlying brain dysfunctions in IGE are unclear and their relation to the pathomechanisms of epileptogenesis is poorly understood.

In this study, we applied connectometry, an advanced quantitative neuroimaging technique for investigating localised changes in white-matter tissues in vivo. Analysing white matter structures of 32 subjects we incorporated our in vivo findings in a computational model of seizure dynamics to suggest a plausible mechanism of epileptogenesis.

Patients with IGE have significant bilateral alterations in major white-matter fascicles. In the cingulum, fornix, and superior longitudinal fasciculus, tract integrity is compromised, whereas in specific parts of tracts between thalamus and the precentral gyrus, tract integrity is enhanced in patients. Combining these alterations in a logistic regression model, we computed the decision boundary that discriminated patients and controls. The computational model, informed with the findings on the tract abnormalities, specifically highlighted the importance of enhanced cortico-reticular connections along with impaired cortico-cortical connections in inducing pathological seizure-like dynamics.

We emphasise taking directionality of brain connectivity into consideration towards understanding the pathological mechanisms; this is possible by combining neuroimaging and computational modelling. Our imaging evidence of structural alterations suggest the loss of cortico-cortical and enhancement of cortico-thalamic fibre integrity in IGE. We further suggest that impaired connectivity from cortical regions to the thalamic reticular nucleus offers a therapeutic target for selectively modifying the brain circuit for reversing the mechanisms leading to epileptogenesis.

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Significant focal alterations along major white-matter fascicles in IGE patients are characterised.

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Increased white matter integrity found in thalamo-cortical connections.

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Decreased white matter integrity found in cortico-cortical connections.

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Disease mechanism is investigated by combining the neuroimaging findings with a dynamical model of seizure activity.

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Model implicates cortical projections to the thalamic reticular nucleus in IGE.

Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications

The quantification of brain dynamics is essential to its understanding. However, the brain is a system operating on multiple time scales, and characterization of dynamics across time scales remains a challenge. One framework to study such dynamics is that of fractal geometry; and currently there exist several methods for the study of brain dynamics using fractal geometry. We aim to highlight some of the practical challenges of applying fractal geometry to brain dynamics—and as a putative feature for machine learning applications, and propose solutions to enable its wider use in neuroscience. Using intracranially recorded electroencephalogram (EEG) and simulated data, we compared monofractal and multifractal methods with regards to their sensitivity to signal variance. We found that both monofractal and multifractal properties correlate closely with signal variance, thus not being a useful feature of the signal. However, after applying an epoch-wise standardization procedure to the signal, we found that multifractal measures could offer non-redundant information compared to signal variance, power (in different frequency bands) and other established EEG signal measures. We also compared different multifractal estimation methods to each other in terms of reliability, and we found that the Chhabra-Jensen algorithm performed best. Finally, we investigated the impact of sampling frequency and epoch length on the estimation of multifractal properties. Using epileptic seizures as an example event in the EEG, we show that there may be an optimal time scale (i.e., combination of sampling frequency and epoch length) for detecting temporal changes in multifractal properties around seizures. The practical issues we highlighted and our suggested solutions should help in developing robust methods for the application of fractal geometry in EEG signals. Our analyses and observations also aid the theoretical understanding of the multifractal properties of the brain and might provide grounds for new discoveries in the study of brain signals. These could be crucial for the understanding of neurological function and for the developments of new treatments.

Dynamics underlying interictal to ictal transition in temporal lobe epilepsy: insights from a neural mass model

We propose an approach that combines a neural mass model and clinical intracranial electroencephalographic (iEEG) recordings to explore the potential pathophysiological mechanisms (at the neuronal population level) of ictogenesis. Thirty iEEG recordings from 10 temporal lobe epilepsy (TLE) patients around seizure onset were investigated. Physiologically meaningful parameters [average excitatory (A_e ), slow (B), and fast (G) inhibitory synaptic gain] were identified during interictal to ictal transition. Four ratios (A_e /G, A_e /B, A_e /(B + G), and B/G) were derived from these parameters, and their evolution over time was analyzed. The excitation/inhibition ratio increased around seizure onset and decreased before seizure offset, indicating the impairment and re-emergence of excitation/inhibition balance around seizure onset and before seizure offset, respectively. Moreover, the slow inhibition may have an earlier effect on excitation/inhibition imbalance. We confirm the decrease in excitation/inhibition ratio upon seizure termination in human temporal lobe epilepsy, as revealed by optogenetic approaches both in vivo in animal models and in vitro. The increase in excitation/inhibition ratio around seizure occurrence could be an indicator to detect seizures.

Evidence for frequency-dependent cortical plasticity in the human brain

Frequency-dependent plasticity (FDP) describes adaptation at the synapse in response to stimulation at different frequencies. Its consequence on the structure and function of cortical networks is unknown. We tested whether cortical "resonance," favorable stimulation frequencies at which the sensory cortices respond maximally, influenced the impact of FDP on perception, functional topography, and connectivity of the primary somatosensory cortex using psychophysics and functional imaging (fMRI). We costimulated two digits on the hand synchronously at, above, or below the resonance frequency of the somatosensory cortex, and tested subjects' accuracy and speed on tactile localization before and after costimulation. More errors and slower response times followed costimulation at above- or below-resonance, respectively. Response times were faster after at-resonance costimulation. In the fMRI, the cortical representations of the two digits costimulated above-resonance shifted closer, potentially accounting for the poorer performance. Costimulation at-resonance did not shift the digit regions, but increased the functional coupling between them, potentially accounting for the improved response time. To relate these results to synaptic plasticity, we simulated a network of oscillators incorporating Hebbian learning. Two neighboring patches embedded in a cortical sheet, mimicking the two digit regions, were costimulated at different frequencies. Network activation outside the stimulated patches was greatest at above-resonance frequencies, reproducing the spread of digit representations seen with fMRI. Connection strengths within the patches increased following at-resonance costimulation, reproducing the increased fMRI connectivity. We show that FDP extends to the cortical level and is influenced by cortical resonance.

A Spiking Neural Network Model of the Lateral Geniculate Nucleus on the SpiNNaker Machine

We present a spiking neural network model of the thalamic Lateral Geniculate Nucleus (LGN) developed on SpiNNaker, which is a state-of-the-art digital neuromorphic hardware built with very-low-power ARM processors. The parallel, event-based data processing in SpiNNaker makes it viable for building massively parallel neuro-computational frameworks. The LGN model has 140 neurons representing a "basic building block" for larger modular architectures. The motivation of this work is to simulate biologically plausible LGN dynamics on SpiNNaker. Synaptic layout of the model is consistent with biology. The model response is validated with existing literature reporting entrainment in steady state visually evoked potentials (SSVEP)-brain oscillations corresponding to periodic visual stimuli recorded via electroencephalography (EEG). Periodic stimulus to the model is provided by: a synthetic spike-train with inter-spike-intervals in the range 10-50 Hz at a resolution of 1 Hz; and spike-train output from a state-of-the-art electronic retina subjected to a light emitting diode flashing at 10, 20, and 40 Hz, simulating real-world visual stimulus to the model. The resolution of simulation is 0.1 ms to ensure solution accuracy for the underlying differential equations defining Izhikevichs neuron model. Under this constraint, 1 s of model simulation time is executed in 10 s real time on SpiNNaker; this is because simulations on SpiNNaker work in real time for time-steps dt ⩾ 1 ms. The model output shows entrainment with both sets of input and contains harmonic components of the fundamental frequency. However, suppressing the feed-forward inhibition in the circuit produces subharmonics within the gamma band (>30 Hz) implying a reduced information transmission fidelity. These model predictions agree with recent lumped-parameter computational model-based predictions, using conventional computers. Scalability of the framework is demonstrated by a multi-node architecture consisting of three "nodes," where each node is the "basic building block" LGN model. This 420 neuron model is tested with synthetic periodic stimulus at 10 Hz to all the nodes. The model output is the average of the outputs from all nodes, and conforms to the above-mentioned predictions of each node. Power consumption for model simulation on SpiNNaker is ≪1 W.

Mechanisms underlying different onset patterns of focal seizures

Focal seizures are episodes of pathological brain activity that appear to arise from a localised area of the brain. The onset patterns of focal seizure activity have been studied intensively, and they have largely been distinguished into two types-low amplitude fast oscillations (LAF), or high amplitude spikes (HAS). Here we explore whether these two patterns arise from fundamentally different mechanisms. Here, we use a previously established computational model of neocortical tissue, and validate it as an adequate model using clinical recordings of focal seizures. We then reproduce the two onset patterns in their most defining properties and investigate the possible mechanisms underlying the different focal seizure onset patterns in the model. 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. In contrast, the HAS onset is a global, systemic transition to a coexisting seizure state triggered by a local event. We find that such a global transition is enabled by an increase in the excitability of the "healthy" surrounding tissue, which by itself does not generate seizures, but can support seizure activity when incited. In our simulations, the difference in surrounding tissue excitability also offers a simple explanation of the clinically reported difference in surgical outcomes. Finally, we demonstrate in the model how changes in tissue excitability could be elucidated, in principle, using active stimulation. Taken together, our modelling results suggest that the excitability of the tissue surrounding the seizure core may play a determining role in the seizure onset pattern, as well as in the surgical outcome.

Understanding Epileptiform After-Discharges as Rhythmic Oscillatory Transients

Electro-cortical activity in patients with epilepsy may show abnormal rhythmic transients in response to stimulation. Even when using the same stimulation parameters in the same patient, wide variability in the duration of transient response has been reported. These transients have long been considered important for the mapping of the excitability levels in the epileptic brain but their dynamic mechanism is still not well understood. To investigate the occurrence of abnormal transients dynamically, we use a thalamo-cortical neural population model of epileptic spike-wave activity and study the interaction between slow and fast subsystems. In a reduced version of the thalamo-cortical model, slow wave oscillations arise from a fold of cycles (FoC) bifurcation. This marks the onset of a region of bistability between a high amplitude oscillatory rhythm and the background state. In vicinity of the bistability in parameter space, the model has excitable dynamics, showing prolonged rhythmic transients in response to suprathreshold pulse stimulation. We analyse the state space geometry of the bistable and excitable states, and find that the rhythmic transient arises when the impending FoC bifurcation deforms the state space and creates an area of locally reduced attraction to the fixed point. This area essentially allows trajectories to dwell there before escaping to the stable steady state, thus creating rhythmic transients. In the full thalamo-cortical model, we find a similar FoC bifurcation structure. Based on the analysis, we propose an explanation of why stimulation induced epileptiform activity may vary between trials, and predict how the variability could be related to ongoing oscillatory background activity. We compare our dynamic mechanism with other mechanisms (such as a slow parameter change) to generate excitable transients, and we discuss the proposed excitability mechanism in the context of stimulation responses in the epileptic cortex.

Human seizures couple across spatial scales through travelling wave dynamics

Epilepsy—the propensity toward recurrent, unprovoked seizures—is a devastating disease affecting 65 million people worldwide. Understanding and treating this disease remains a challenge, as seizures manifest through mechanisms and features that span spatial and temporal scales. Here we address this challenge through the analysis and modelling of human brain voltage activity recorded simultaneously across microscopic and macroscopic spatial scales. We show that during seizure large-scale neural populations spanning centimetres of cortex coordinate with small neural groups spanning cortical columns, and provide evidence that rapidly propagating waves of activity underlie this increased inter-scale coupling. We develop a corresponding computational model to propose specific mechanisms—namely, the effects of an increased extracellular potassium concentration diffusing in space—that support the observed spatiotemporal dynamics. Understanding the multi-scale, spatiotemporal dynamics of human seizures—and connecting these dynamics to specific biological mechanisms—promises new insights to treat this devastating disease.

The authors record both local and long-range neural activity during human epileptic seizures to study the underlying multi-scale dynamics. They find that coupling of activity across spatial scales increases during seizures through propagating waves that are fit by a model that combines neural activity and potassium concentration dynamics.

Neural mass models as a tool to investigate neural dynamics during seizures

Epilepsy is one of the most common neurological disorders and is characterized by recurrent seizures. We use theoretical neuroscience tools to study brain dynamics during seizures. We derive and simulate a computational model of a network of hippocampal neuronal populations. Each population within the network is based on a model that has been shown to replicate the electrophysiological dynamics observed during seizures. The results provide insights into possible mechanisms for seizure spread. We observe that epileptiform activity remains localized to a pathological region when a global connectivity parameter is less than a critical value. After establishing the critical value for seizure spread, we explored how to correct the effect by altering particular synaptic gains. The spreading of seizures is quantified using numerical methods for seizure detection. The results from this study provide a new avenue of exploration for seizure control.

Within brain area tractography suggests local modularity using high resolution connectomics

Previous structural brain connectivity studies have mainly focussed on the macroscopic scale of around 1,000 or fewer brain areas (network nodes). However, it has recently been demonstrated that high resolution structural connectomes of around 50,000 nodes can be generated reproducibly. In this study, we infer high resolution brain connectivity matrices using diffusion imaging data from the Human Connectome Project. With such high resolution we are able to analyse networks within brain areas in a single subject. We show that the global network has a scale invariant topological organisation, which means there is a hierarchical organisation of the modular architecture. Specifically, modules within brain areas are spatially localised. We find that long range connections terminate between specific modules, whilst short range connections via highly curved association fibers terminate within modules. We suggest that spatial locations of white matter modules overlap with cytoarchitecturally distinct grey matter areas and may serve as the structural basis for function specialisation within brain areas. Future studies might elucidate how brain diseases change this modular architecture within brain areas.

Predicting neurosurgical outcomes in focal epilepsy patients using computational modelling

See Eissa and Schevon (doi:10.1093/aww332) for a scientific commentary on this article.

Surgery can be a last resort for patients with intractable, medically refractory epilepsy. For many of these patients, however, there is substantial risk that the surgery will be ineffective. The prediction of who is likely to benefit from a surgical approach is crucial for being able to inform patients better, conduct principled prospective clinical trials, and ultimately tailor therapeutic approaches to these patients more effectively. Dynamical computational models, informed with patient data, can be used to make predictions and give mechanistic insight. In this study, we develop patient-specific dynamical network models of epileptogenic cortex. We infer the network connectivity matrix from non-seizure electrographic recordings of patients and use these connectivity matrices as the network structure in our model. The model simulates the dynamics of a bi-stable switch at every node in this network, meaning that every node starts in a background state, but has the ability to transit to a co-existing seizure state. Whether a transition happens in a node is partly determined by the stochastic nature of the input to the node, but also by the input the node receives from other connected nodes in the network. By conducting simulations with such a model, we can detect the average transition time for nodes in a given network, and therefore define nodes with a short transition time as highly epileptogenic. In a retrospective study, we found that in some patients the regions with high epileptogenicity in the model overlap with those identified clinically as the seizure onset zone. Moreover, it was found that the resection of these regions in the model reduces the overall likelihood of a seizure. Following removal of these regions in the model, we predicted surgical outcomes and compared these to actual patient outcomes. Our predictions were found to be 81.3% accurate on a dataset of 16 patients with intractable epilepsy. Intriguingly, in patients with unsuccessful outcomes, the proposed computational approach is able to suggest alternative resection sites. The model presented here gives mechanistic insight as to why surgery may be unsuccessful in some patients. This may aid clinicians in presurgical evaluation by providing a tool to explore various surgical options, offering complementary information to existing clinical techniques.

Causal Role of Thalamic Interneurons in Brain State Transitions: A Study Using a Neural Mass Model Implementing Synaptic Kinetics

Experimental studies on the Lateral Geniculate Nucleus (LGN) of mammals and rodents show that the inhibitory interneurons (IN) receive around 47.1% of their afferents from the retinal spiking neurons, and constitute around 20–25% of the LGN cell population. However, there is a definite gap in knowledge about the role and impact of IN on thalamocortical dynamics in both experimental and model-based research. We use a neural mass computational model of the LGN with three neural populations viz. IN, thalamocortical relay (TCR), thalamic reticular nucleus (TRN), to study the causality of IN on LGN oscillations and state-transitions. The synaptic information transmission in the model is implemented with kinetic modeling, facilitating the linking of low-level cellular attributes with high-level population dynamics. The model is parameterized and tuned to simulate alpha (8–13 Hz) rhythm that is dominant in both Local Field Potential (LFP) of LGN and electroencephalogram (EEG) of visual cortex in an awake resting state with eyes closed. The results show that: First, the response of the TRN is suppressed in the presence of IN in the circuit; disconnecting the IN from the circuit effects a dramatic change in the model output, displaying high amplitude synchronous oscillations within the alpha band in both TCR and TRN. These observations conform to experimental reports implicating the IN as the primary inhibitory modulator of LGN dynamics in a cognitive state, and that reduced cognition is achieved by suppressing the TRN response. Second, the model validates steady state visually evoked potential response in humans corresponding to periodic input stimuli; however, when the IN is disconnected from the circuit, the output power spectra do not reflect the input frequency. This agrees with experimental reports underpinning the role of IN in efficient retino-geniculate information transmission. Third, a smooth transition from alpha to theta band is observed by progressive decrease of neurotransmitter concentrations in the synaptic clefts; however, the transition is abrupt with removal of the IN circuitry in the model. The results imply a role of IN toward maintaining homeostasis in the LGN by suppressing any instability that may arise due to anomalous synaptic attributes.

Interaction between synaptic inhibition and glial-potassium dynamics leads to diverse seizure transition modes in biophysical models of human focal seizures

How focal seizures initiate and evolve in human neocortex remains a fundamental problem in neuroscience. Here, we use biophysical neuronal network models of neocortical patches to study how the interaction between inhibition and extracellular potassium ([K (+)] o ) dynamics may contribute to different types of focal seizures. Three main types of propagated focal seizures observed in recent intracortical microelectrode recordings in humans were modelled: seizures characterized by sustained (∼30-60 Hz) gamma local field potential (LFP) oscillations; seizures where the onset in the propagated site consisted of LFP spikes that later evolved into rhythmic (∼2-3 Hz) spike-wave complexes (SWCs); and seizures where a brief stage of low-amplitude fast-oscillation (∼10-20 Hz) LFPs preceded the SWC activity. Our findings are fourfold: (1) The interaction between elevated [K (+)] o (due to abnormal potassium buffering by glial cells) and the strength of synaptic inhibition plays a predominant role in shaping these three types of seizures. (2) Strengthening of inhibition leads to the onset of sustained narrowband gamma seizures. (3) Transition into SWC seizures is obtained either by the weakening of inhibitory synapses, or by a transient strengthening followed by an inhibitory breakdown (e.g. GABA depletion). This reduction or breakdown of inhibition among fast-spiking (FS) inhibitory interneurons increases their spiking activity and leads them eventually into depolarization block. Ictal spike-wave discharges in the model are then sustained solely by pyramidal neurons. (4) FS cell dynamics are also critical for seizures where the evolution into SWC activity is preceded by low-amplitude fast oscillations. Different levels of elevated [K (+)] o were important for transitions into and maintenance of sustained gamma oscillations and SWC discharges. Overall, our modelling study predicts that the interaction between inhibitory interneurons and [K (+)] o glial buffering under abnormal conditions may explain different types of ictal transitions and dynamics during propagated seizures in human focal epilepsy.

Seizure Prediction: Science Fiction or Soon to Become Reality?

This review highlights recent developments in the field of epileptic seizure prediction. We argue that seizure prediction is possible; however, most previous attempts have used data with an insufficient amount of information to solve the problem. The review discusses four methods for gaining more information above standard clinical electrophysiological recordings. We first discuss developments in obtaining long-term data that enables better characterisation of signal features and trends. Then, we discuss the usage of electrical stimulation to probe neural circuits to obtain robust information regarding excitability. Following this, we present a review of developments in high-resolution micro-electrode technologies that enable neuroimaging across spatial scales. Finally, we present recent results from data-driven model-based analyses, which enable imaging of seizure generating mechanisms from clinical electrophysiological measurements. It is foreseeable that the field of seizure prediction will shift focus to a more probabilistic forecasting approach leading to improvements in the quality of life for the millions of people who suffer uncontrolled seizures. However, a missing piece of the puzzle is devices to acquire long-term high-quality data. When this void is filled, seizure prediction will become a reality.

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.

Interictal spikes and epileptic seizures: their relationship and underlying rhythmicity

We report on a quantitative analysis of electrocorticography data from a study that acquired continuous ambulatory recordings in humans over extended periods of time. The objectives were to examine patterns of seizures and spontaneous interictal spikes, their relationship to each other, and the nature of periodic variation. The recorded data were originally acquired for the purpose of seizure prediction, and were subsequently analysed in further detail. A detection algorithm identified potential seizure activity and a template matched filter was used to locate spikes. Seizure events were confirmed manually and classified as either clinically correlated, electroencephalographically identical but not clinically correlated, or subclinical. We found that spike rate was significantly altered prior to seizure in 9 out of 15 subjects. Increased pre-ictal spike rate was linked to improved predictability; however, spike rate was also shown to decrease before seizure (in 6 out of the 9 subjects). The probability distribution of spikes and seizures were notably similar, i.e. at times of high seizure likelihood the probability of epileptic spiking also increased. Both spikes and seizures showed clear evidence of circadian regulation and, for some subjects, there were also longer term patterns visible over weeks to months. Patterns of spike and seizure occurrence were highly subject-specific. The pre-ictal decrease in spike rate is not consistent with spikes promoting seizures. However, the fact that spikes and seizures demonstrate similar probability distributions suggests they are not wholly independent processes. It is possible spikes actively inhibit seizures, or that a decreased spike rate is a secondary symptom of the brain approaching seizure. If spike rate is modulated by common regulatory factors as seizures then spikes may be useful biomarkers of cortical excitability.

Predicting Surgery Targets in Temporal Lobe Epilepsy through Structural Connectome Based Simulations

Temporal lobe epilepsy (TLE) is a prevalent neurological disorder resulting in disruptive seizures. In the case of drug resistant epilepsy resective surgery is often considered. This is a procedure hampered by unpredictable success rates, with many patients continuing to have seizures even after surgery. In this study we apply a computational model of epilepsy to patient specific structural connectivity derived from diffusion tensor imaging (DTI) of 22 individuals with left TLE and 39 healthy controls. We validate the model by examining patient-control differences in simulated seizure onset time and network location. We then investigate the potential of the model for surgery prediction by performing in silico surgical resections, removing nodes from patient networks and comparing seizure likelihood post-surgery to pre-surgery simulations. We find that, first, patients tend to transit from non-epileptic to epileptic states more often than controls in the model. Second, regions in the left hemisphere (particularly within temporal and subcortical regions) that are known to be involved in TLE are the most frequent starting points for seizures in patients in the model. In addition, our analysis also implicates regions in the contralateral and frontal locations which may play a role in seizure spreading or surgery resistance. Finally, the model predicts that patient-specific surgery (resection areas chosen on an individual, model-prompted, basis and not following a predefined procedure) may lead to better outcomes than the currently used routine clinical procedure. Taken together this work provides a first step towards patient specific computational modelling of epilepsy surgery in order to inform treatment strategies in individuals.

Temporal lobe epilepsy (TLE) is a disorder characterised by unpredictable seizures, where surgical removal of brain tissue is often the final treatment option. In roughly 30% of cases surgery procedures are unsuccessful at preventing future seizures. This paper shows the application of a computational model which uses patient derived brain connectivity to predict the success rates of surgery in people with TLE. We consider the brains of 22 patients as networks, with brain regions as nodes and the white matter connections between them as edges. The brain network is unique to each subject and produced from brain imaging scans of 22 patients and 39 controls. Seizures are simulated before and after surgery, where surgery in the model is the removal of nodes from the network. The model successfully identifies regions known to be involved in TLE, and its predicted success rates for surgery are close to the results found in reality. The model additionally provides patient specific recommendations for surgical procedures, which in simulations show improved results compared to standard surgery in every case. This is a first step towards designing personalised surgery procedures in order to improve surgery success rates.

Microscale spatiotemporal dynamics during neocortical propagation of human focal seizures

Some of the most clinically consequential aspects of focal epilepsy, e.g. loss of consciousness, arise from the generalization or propagation of seizures through local and large-scale neocortical networks. Yet, the dynamics of such neocortical propagation remain poorly understood. Here, we studied the microdynamics of focal seizure propagation in neocortical patches (4×4 mm) recorded via high-density microelectrode arrays (MEAs) implanted in people with pharmacologically resistant epilepsy. Our main findings are threefold: (1) a newly developed stage segmentation method, applied to local field potentials (LFPs) and multiunit activity (MUA), revealed a succession of discrete seizure stages, each lasting several seconds. These different stages showed characteristic evolutions in overall activity and spatial patterns, which were relatively consistent across seizures within each of the 5 patients studied. Interestingly, segmented seizure stages based on LFPs or MUA showed a dissociation of their spatiotemporal dynamics, likely reflecting different contributions of non-local synaptic inputs and local network activity. (2) As previously reported, some of the seizures showed a peak in MUA that happened several seconds after local seizure onset and slowly propagated across the MEA. However, other seizures had a more complex structure characterized by, for example, several MUA peaks, more consistent with the succession of discrete stages than the slow propagation of a simple wavefront of increased MUA. In both cases, nevertheless, seizures characterized by spike-wave discharges (SWDs, ~2-3 Hz) eventually evolved into patterns of phase-locked MUA and LFPs. (3) Individual SWDs or gamma oscillation cycles (25-60 Hz), characteristic of two different types of recorded seizures, tended to propagate with varying degrees of directionality, directions of propagation and speeds, depending on the identified seizure stage. However, no clear relationship was observed between the MUA peak onset time (in seizures where such peak onset occurred) and changes in MUA or LFP propagation patterns. Overall, our findings indicate that the recruitment of neocortical territories into ictal activity undergoes complex spatiotemporal dynamics evolving in slow discrete states, which are consistent across seizures within each patient. Furthermore, ictal states at finer spatiotemporal scales (individual SWDs or gamma oscillations) are organized by slower time scale network dynamics evolving through these discrete stages.

Computational modeling of neurostimulation in brain diseases

Neurostimulation as a therapeutic tool has been developed and used for a range of different diseases such as Parkinson's disease, epilepsy, and migraine. However, it is not known why the efficacy of the stimulation varies dramatically across patients or why some patients suffer from severe side effects. This is largely due to the lack of mechanistic understanding of neurostimulation. Hence, theoretical computational approaches to address this issue are in demand. This chapter provides a review of mechanistic computational modeling of brain stimulation. In particular, we will focus on brain diseases, where mechanistic models (e.g., neural population models or detailed neuronal models) have been used to bridge the gap between cellular-level processes of affected neural circuits and the symptomatic expression of disease dynamics. We show how such models have been, and can be, used to investigate the effects of neurostimulation in the diseased brain. We argue that these models are crucial for the mechanistic understanding of the effect of stimulation, allowing for a rational design of stimulation protocols. Based on mechanistic models, we argue that the development of closed-loop stimulation is essential in order to avoid inference with healthy ongoing brain activity. Furthermore, patient-specific data, such as neuroanatomic information and connectivity profiles obtainable from neuroimaging, can be readily incorporated to address the clinical issue of variability in efficacy between subjects. We conclude that mechanistic computational models can and should play a key role in the rational design of effective, fully integrated, patient-specific therapeutic brain stimulation.

Modeling focal epileptic activity in the Wilson-cowan model with depolarization block

Measurements of neuronal signals during human seizure activity and evoked epileptic activity in experimental models suggest that, in these pathological states, the individual nerve cells experience an activity driven depolarization block, i.e. they saturate. We examined the effect of such a saturation in the Wilson-Cowan formalism by adapting the nonlinear activation function; we substituted the commonly applied sigmoid for a Gaussian function. We discuss experimental recordings during a seizure that support this substitution. Next we perform a bifurcation analysis on the Wilson-Cowan model with a Gaussian activation function. The main effect is an additional stable equilibrium with high excitatory and low inhibitory activity. Analysis of coupled local networks then shows that such high activity can stay localized or spread. Specifically, in a spatial continuum we show a wavefront with inhibition leading followed by excitatory activity. We relate our model simulations to observations of spreading activity during seizures.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1186/s13408-015-0019-4) contains supplementary material 1.

Structural connectivity based whole brain modelling in epilepsy

Epilepsy is a neurological condition characterised by the recurrence of seizures. During seizures multiple brain areas can behave abnormally. Rather than considering each abnormal area in isolation, one can consider them as an interconnected functional 'network'. Recently, there has been a shift in emphasis to consider epilepsy as a disorder involving more widespread functional brain networks than perhaps was previously thought. The basis for these functional networks is proposed to be the static structural brain network established through the connectivity of the white matter. Additionally, it has also been argued that time varying aspects of epilepsy are of crucial importance and as such computational models of these dynamical properties have recently advanced. We describe how dynamic computer models can be combined with static human in vivo connectivity obtained through diffusion weighted magnetic resonance imaging. We predict that in future the use of these two methods in concert will lead to predictions for optimal surgery and brain stimulation sites for epilepsy and other neurological disorders.