Perturbations both trigger and delay seizures due to generic properties of slow-fast relaxation oscillators

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.

Personalized dynamic network models of the human brain as a future tool for planning and optimizing epilepsy therapy

Epilepsy is a common neurological disorder, with one third of patients not responding to currently available antiepileptic drugs. The proportion of pharmacoresistant epilepsies has remained unchanged for many decades. To cure epilepsy and control seizures requires a paradigm shift in the development of new approaches to epilepsy diagnosis and treatment. Contemporary medicine has benefited from the exponential growth of computational modeling, and the application of network dynamics theory to understanding and treating human brain disorders. In epilepsy, the introduction of these approaches has led to personalized epileptic network modeling that can explore the patient's seizure genesis and predict the functional impact of resection on its individual network's propensity to seize. The application of the dynamic systems approach to neurostimulation therapy of epilepsy allows designing stimulation strategies that consider the patient's seizure dynamics and long-term fluctuations in the stability of their epileptic networks. In this article, we review, in a nontechnical fashion suitable for a broad neuroscientific audience, recent progress in personalized dynamic brain network modeling that is shaping the future approach to the diagnosis and treatment of epilepsy.

Computational modeling allows unsupervised classification of epileptic brain states across species

Current advances in epilepsy treatment aim to personalize and responsively adjust treatment parameters to overcome patient heterogeneity in treatment efficiency. For tailoring treatment to the individual and the current brain state, tools are required that help to identify the patient- and time-point-specific parameters of epilepsy. Computational modeling has long proven its utility in gaining mechanistic insight. Recently, the technique has been introduced as a diagnostic tool to predict individual treatment outcomes. In this article, the Wendling model, an established computational model of epilepsy dynamics, is used to automatically classify epileptic brain states in intracranial EEG from patients (n = 4) and local field potential recordings from in vitro rat data (high-potassium model of epilepsy, n = 3). Five-second signal segments are classified to four types of brain state in epilepsy (interictal, preonset, onset, ictal) by comparing a vector of signal features for each data segment to four prototypical feature vectors obtained by Wendling model simulations. The classification result is validated against expert visual assessment. Model-driven brain state classification achieved a classification performance significantly above chance level (mean sensitivity 0.99 on model data, 0.77 on rat data, 0.56 on human data in a four-way classification task). Model-driven prototypes showed similarity with data-driven prototypes, which we obtained from real data for rats and humans. Our results indicate similar electrophysiological patterns of epileptic states in the human brain and the animal model that are well-reproduced by the computational model, and captured by a key set of signal features, enabling fully automated and unsupervised brain state classification in epilepsy.

Optogenetic stimulation reveals a latent tipping point in cortical networks during ictogenesis

Brain-state transitions are readily apparent from changes in brain rhythms,1 but are difficult to predict, suggestive that the underlying cause is latent to passive recording methods. Among the most important transitions, clinically, are the starts of seizures. We here show that an 'active probing' approach may have several important benefits for epileptic management, including by helping predict these transitions. We used mice expressing the optogenetic actuator, channelrhodopsin, in pyramidal cells, allowing this population to be stimulated in isolation. Intermittent stimulation at frequencies as low as 0.033 Hz (period = 30 s) delayed the onset of seizure-like events in an acute brain slice model of ictogenesis, but the effect was lost if stimulation was delivered at even lower frequencies (1/min). Notably, active probing additionally provides advance indication of when seizure-like activity is imminent, revealed by monitoring the postsynaptic response to stimulation. The postsynaptic response, recorded extracellularly, showed an all-or-nothing change in both amplitude and duration, a few hundred seconds before seizure-like activity began-a sufficient length of time to provide a helpful warning of an impending seizure. The change in the postsynaptic response then persisted for the remainder of the recording, indicative of a state change from a pre-epileptic to a pro-epileptic network. This occurred in parallel with a large increase in the stimulation-triggered Ca2+ entry into pyramidal dendrites, and a step increase in the number of evoked postsynaptic action potentials, both consistent with a reduction in the threshold for dendritic action potentials. In 0 Mg2+ bathing media, the reduced threshold was not associated with changes in glutamatergic synaptic function, nor of GABAergic release from either parvalbumin or somatostatin interneurons, but simulations indicate that the step change in the optogenetic response can instead arise from incremental increases in intracellular [Cl-]. The change in the response to stimulation was replicated by artificially raising intracellular [Cl-], using the optogenetic chloride pump, halorhodopsin. By contrast, increases in extracellular [K+] cannot account for the firing patterns in the response to stimulation, although this, and other cellular changes, may contribute to ictal initiation in other circumstances. We describe how these various cellular changes form a synergistic network of positive feedback mechanisms, which may explain the precipitous nature of seizure onset. This model of seizure initiation draws together several major lines of epilepsy research as well as providing an important proof-of-principle regarding the utility of open-loop brain stimulation for clinical management of the condition.

Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators

Seminal work by A. Winfree and J. Guckenheimer showed that a deterministic phase variable can be defined either in terms of Poincaré sections or in terms of the asymptotic (long-time) behaviour of trajectories approaching a stable limit cycle. However, this equivalence between the deterministic notions of phase is broken in the presence of noise. Different notions of phase reduction for a stochastic oscillator can be defined either in terms of mean-return-time sections or as the argument of the slowest decaying complex eigenfunction of the Kolmogorov backwards operator. Although both notions of phase enjoy a solid theoretical foundation, their relationship remains unexplored. Here, we quantitatively compare both notions of stochastic phase. We derive an expression relating both notions of phase and use it to discuss differences (and similarities) between both definitions of stochastic phase for (i) a spiral sink motivated by stochastic models for electroencephalograms, (ii) noisy limit-cycle systems-neuroscience models, and (iii) a stochastic heteroclinic oscillator inspired by a simple motor-control system.