Marc Goodfellow

Intermittent spike-wave dynamics in a heterogeneous, spatially extended neural mass model.

Generalised epileptic seizures are frequently accompanied by sudden, reversible transitions from low amplitude, irregular background activity to high amplitude, regular spike-wave discharges (SWD) in the EEG. The underlying mechanisms responsible for SWD generation and for the apparently spontaneous transitions to SWD and back again are still not fully understood. Specifically, the role of spatial cortico-cortical interactions in ictogenesis is not well studied. We present a macroscopic, neural mass model of a cortical column which includes two distinct time scales of inhibition. This model can produce both an oscillatory background and a pathological SWD rhythm. We demonstrate that coupling two of these cortical columns can lead to a bistability between out-of-phase, low amplitude background dynamics and in-phase, high amplitude SWD activity. Stimuli can cause state-dependent transitions from background into SWD. In an extended local area of cortex, spatial heterogeneities in a model parameter can lead to spontaneous reversible transitions from a desynchronised background to synchronous SWD due to intermittency. The deterministic model is therefore capable of producing absence seizure-like events without any time dependent adjustment of model parameters. The emergence of such mechanisms due to spatial coupling demonstrates the importance of spatial interactions in modelling ictal dynamics, and in the study of ictogenesis.

Self-organised transients in a neural mass model of epileptogenic tissue dynamics

Stimulation of human epileptic tissue can induce rhythmic, self-terminating responses on the EEG or ECoG. These responses play a potentially important role in localising tissue involved in the generation of seizure activity, yet the underlying mechanisms are unknown. However, in vitro evidence suggests that self-terminating oscillations in nervous tissue are underpinned by non-trivial spatio-temporal dynamics in an excitable medium. In this study, we investigate this hypothesis in spatial extensions to a neural mass model for epileptiform dynamics. We demonstrate that spatial extensions to this model in one and two dimensions display propagating travelling waves but also more complex transient dynamics in response to local perturbations. The neural mass formulation with local excitatory and inhibitory circuits, allows the direct incorporation of spatially distributed, functional heterogeneities into the model. We show that such heterogeneities can lead to prolonged reverberating responses to a single pulse perturbation, depending upon the location at which the stimulus is delivered. This leads to the hypothesis that prolonged rhythmic responses to local stimulation in epileptogenic tissue result from repeated self-excitation of regions of tissue with diminished inhibitory capabilities. Combined with previous models of the dynamics of focal seizures this macroscopic framework is a first step towards an explicit spatial formulation of the concept of the epileptogenic zone. Ultimately, an improved understanding of the pathophysiologic mechanisms of the epileptogenic zone will help to improve diagnostic and therapeutic measures for treating epilepsy.

A Computational Study of Stimulus Driven Epileptic Seizure Abatement

Active brain stimulation to abate epileptic seizures has shown mixed success. In spike-wave (SW) seizures, where the seizure and background state were proposed to coexist, single-pulse stimulations have been suggested to be able to terminate the seizure prematurely. However, several factors can impact success in such a bistable setting. The factors contributing to this have not been fully investigated on a theoretical and mechanistic basis. Our aim is to elucidate mechanisms that influence the success of single-pulse stimulation in noise-induced SW seizures. In this work, we study a neural population model of SW seizures that allows the reconstruction of the basin of attraction of the background activity as a four dimensional geometric object. For the deterministic (noise-free) case, we show how the success of response to stimuli depends on the amplitude and phase of the SW cycle, in addition to the direction of the stimulus in state space. In the case of spontaneous noise-induced seizures, the basin becomes probabilistic introducing some degree of uncertainty to the stimulation outcome while maintaining qualitative features of the noise-free case. Additionally, due to the different time scales involved in SW generation, there is substantial variation between SW cycles, implying that there may not be a fixed set of optimal stimulation parameters for SW seizures. In contrast, the model suggests an adaptive approach to find optimal stimulation parameters patient-specifically, based on real-time estimation of the position in state space. We discuss how the modelling work can be exploited to rationally design a successful stimulation protocol for the abatement of SW seizures using real-time SW detection.

Estimation of brain network ictogenicity predicts outcome from epilepsy surgery

Surgery is a valuable option for pharmacologically intractable epilepsy. However, significant post-operative improvements are not always attained. This is due in part to our incomplete understanding of the seizure generating (ictogenic) capabilities of brain networks. Here we introduce an in silico, model-based framework to study the effects of surgery within ictogenic brain networks. We find that factors conventionally determining the region of tissue to resect, such as the location of focal brain lesions or the presence of epileptiform rhythms, do not necessarily predict the best resection strategy. We validate our framework by analysing electrocorticogram (ECoG) recordings from patients who have undergone epilepsy surgery. We find that when post-operative outcome is good, model predictions for optimal strategies align better with the actual surgery undertaken than when post-operative outcome is poor. Crucially, this allows the prediction of optimal surgical strategies and the provision of quantitative prognoses for patients undergoing epilepsy surgery.

The importance of modeling epileptic seizure dynamics as spatio-temporal patterns

The occurrence of seizures is the common feature across the spectrum of epileptic disorders. We describe how the use of mechanistic neural population models leads to novel insight into the dynamic mechanisms underlying two important types of epileptic seizures. We specifically stress the need for a spatio-temporal description of the rhythms to deal with the complexity of the pathophenotype. Adapted to functional and structural patient data, the macroscopic models may allow a patient-specific description of seizures and prediction of treatment outcome.

Towards a large-scale model of patient-specific epileptic spike-wave discharges

Clinical electroencephalographic (EEG) recordings of the transition into generalised epileptic seizures show a sudden onset of spike-wave dynamics from a low-amplitude irregular background. In addition, non-trivial and variable spatio-temporal dynamics are widely reported in combined EEG/fMRI studies on the scale of the whole cortex. It is unknown whether these characteristics can be accounted for in a large-scale mathematical model with fixed heterogeneous long-range connectivities. Here, we develop a modelling framework with which to investigate such EEG features. We show that a neural field model composed of a few coupled compartments can serve as a low-dimensional prototype for the transition between irregular background dynamics and spike-wave activity. This prototype then serves as a node in a large-scale network with long-range connectivities derived from human diffusion-tensor imaging data. We examine multivariate properties in 42 clinical EEG seizure recordings from 10 patients diagnosed with typical absence epilepsy and 50 simulated seizures from the large-scale model using 10 DTI connectivity sets from humans. The model can reproduce the clinical feature of stereotypy where seizures are more similar within a patient than between patients, essentially creating a patient-specific fingerprint. We propose the approach as a feasible technique for the investigation of patient-specific large-scale epileptic features in space and time.

Dynamic mechanisms of neocortical focal seizure onset.

Recent experimental and clinical studies have provided diverse insight into the mechanisms of human focal seizure initiation and propagation. Often these findings exist at different scales of observation, and are not reconciled into a common understanding. Here we develop a new, multiscale mathematical model of cortical electric activity with realistic mesoscopic connectivity. Relating the model dynamics to experimental and clinical findings leads us to propose three classes of dynamical mechanisms for the onset of focal seizures in a unified framework. These three classes are: (i) globally induced focal seizures; (ii) globally supported focal seizures; (iii) locally induced focal seizures. Using model simulations we illustrate these onset mechanisms and show how the three classes can be distinguished. Specifically, we find that although all focal seizures typically appear to arise from localised tissue, the mechanisms of onset could be due to either localised processes or processes on a larger spatial scale. We conclude that although focal seizures might have different patient-specific aetiologies and electrographic signatures, our model suggests that dynamically they can still be classified in a clinically useful way. Additionally, this novel classification according to the dynamical mechanisms is able to resolve some of the previously conflicting experimental and clinical findings.

A Critical Role for Network Structure in Seizure Onset: A Computational Modeling Approach

Recent clinical work has implicated network structure as critically important in the initiation of seizures in people with idiopathic generalized epilepsies. In line with this idea, functional networks derived from the electroencephalogram (EEG) at rest have been shown to be significantly different in people with generalized epilepsy compared to controls. In particular, the mean node degree of networks from the epilepsy cohort was found to be statistically significantly higher than those of controls. However, the mechanisms by which these network differences can support recurrent transitions into seizures remain unclear. In this study, we use a computational model of the transition into seizure dynamics to explore the dynamic consequences of these differences in functional networks. We demonstrate that networks with higher mean node degree are more prone to generating seizure dynamics in the model and therefore suggest a mechanism by which increased mean node degree of brain networks can cause heightened ictogenicity.

A Systems-Level Approach to Human Epileptic Seizures

Epileptic seizures are due to the pathological collective activity of large cellular assemblies. A better understanding of this collective activity is integral to the development of novel diagnostic and therapeutic procedures. In contrast to reductionist analyses, which focus solely on small-scale characteristics of ictogenesis, here we follow a systems-level approach, which combines both small-scale and larger-scale analyses. Peri-ictal dynamics of epileptic networks are assessed by studying correlation within and between different spatial scales of intracranial electroencephalographic recordings (iEEG) of a heterogeneous group of patients suffering from pharmaco-resistant epilepsy. Epileptiform activity as recorded by a single iEEG electrode is determined objectively by the signal derivative and then subjected to a multivariate analysis of correlation between all iEEG channels. We find that during seizure, synchrony increases on the smallest and largest spatial scales probed by iEEG. In addition, a dynamic reorganization of spatial correlation is observed on intermediate scales, which persists after seizure termination. It is proposed that this reorganization may indicate a balancing mechanism that decreases high local correlation. Our findings are consistent with the hypothesis that during epileptic seizures hypercorrelated and therefore functionally segregated brain areas are re-integrated into more collective brain dynamics. In addition, except for a special sub-group, a highly significant association is found between the location of ictal iEEG activity and the location of areas of relative decrease of localised EEG correlation. The latter could serve as a clinically important quantitative marker of the seizure onset zone (SOZ).

microRNA input into a neural ultradian oscillator controls emergence and timing of alternative cell states

Progenitor maintenance, timed differentiation and the potential to enter quiescence are three fundamental processes that underlie the development of any organ system. In the nervous system, progenitor cells show short-period oscillations in the expression of the transcriptional repressor Hes1, while neurons and quiescent progenitors show stable low and high levels of Hes1, respectively. Here we use experimental data to develop a mathematical model of the double-negative interaction between Hes1 and a microRNA, miR-9, with the aim of understanding how cells transition from one state to another. We show that the input of miR-9 into the Hes1 oscillator tunes its oscillatory dynamics, and endows the system with bistability and the ability to measure time to differentiation. Our results suggest that a relatively simple and widespread network of cross-repressive interactions provides a unifying framework for progenitor maintenance, the timing of differentiation and the emergence of alternative cell states.