The mechanism of seizure emergence and the role of brief interictal epileptiform discharges (IEDs) in seizure generation are two of the most important unresolved issues in modern epilepsy research. We found that the transition to seizure is not a sudden phenomenon, but is instead a slow process that is characterized by the progressive loss of neuronal network resilience. From a dynamical perspective, the slow transition is governed by the principles of critical slowing, a robust natural phenomenon that is observable in systems characterized by transitions between dynamical regimes. In epilepsy, this process is modulated by synchronous synaptic input from IEDs. IEDs are external perturbations that produce phasic changes in the slow transition process and exert opposing effects on the dynamics of a seizure-generating network, causing either anti-seizure or pro-seizure effects. We found that the multifaceted nature of IEDs is defined by the dynamical state of the network at the moment of the discharge occurrence.
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This study was supported by grants of the Czech Science Foundation GACR 14-02634S (to P.J.), Neuron Fund for Support of Science (to P.J.), the Ministry of Health of the Czech Republic AZV 15-29835A (to P.J.), 17-28427A (to P.J.), the Medical Research Council G0802162 (to J.G.R.J.), and the James Lewis Foundation through Epilepsy Research UK P1402 (to J.G.R.J.).
Integrated supplementary information
(a) The laminar profile of an averaged HFA cycle in the isolated CA1 is characterized by maximal field potential negativity at the stratum pyramidale. (b) Current source density profile and its contour plot (c) reveal that the HFA cycle is accompanied by an initial current sink at the pyramidal layer, which then back-propagates along the dendritic region. On a cellular level, the current source density profile corresponds to dendritic back-propagation of action potentials generated at the soma. (d) Current source density profile for an episode of HFA with superimposed band-passed (100-300 Hz) filtered signal recorded in the stratum pyramidale. (e-h) Laminar profile and current source density of HFA in intact hippocampal preparations display similar features (n=10 slices).
(a) Averaged normalized power spectra of interictal signals in the isolated CA1 demonstrate a clear peak in the high-frequency band due to the presence of HFA. (b) Recording with multiple electrodes demonstrated that HFA was present across the entire CA1. Normalized power spectra in each region were color-coded to display the spatial properties of the spectral profile. (c) Mean power spectra of the signal recorded in CA1 of the intact hippocampus between seizures. (d) Spatial analysis of the spectral profile also demonstrates the presence of HFA in the entire CA1 region. The HFA peak is around 180 Hz, while lower frequency peaks correspond to spectral components of IEDs. (n=10 isolated CA1 slices, and n=10 intact hippocampal slices).
Supplementary Figure 3 Seizures are preceded by an increased sensitivity to external perturbations and delayed recovery from them.
(a) Regular stimulation of constant intensity was delivered to Schaffer collaterals to explore the dynamical state of the CA1 network. (b) The properties of evoked responses were quantified using the line length parameter, which combines information about changes in amplitude, morphology and duration of the response. Seizures are preceded by an increase in the line length – due to increasing sensitivity to stimulation (perturbation) in advance of a seizure. It is reflected by increased amplitude, the occurrence of multiple population spikes and a longer duration of the response (c-e). Delayed recovery from perturbation and increased sensitivity are the main markers of losing resilience and critical slowing in the dynamical system.
(a) IEDs triggered in the CA3 propagate to the CA1 where they induce IEDs. (b,c) Current source density analysis reveals that CA1 IEDs are due to a current sink at the region of the middle apical dendrites and basal dendrites flanked by sources in the distal radiatum as well as the pyramidale. The slow wave following the IEDs is characterized by sources in the same regions with a passive sink in the somatic region. Observed current source density profile suggests that at the cellular level the IEDs in CA1 are due to postsynaptic excitation at the middle part of apical dendrites.
(a) Transitions between interictal state and seizure were modeled as a slow-fast process, where the slow variable represents a change in excitability and the fast variable is a mean population firing rate. For extremely low or high values of excitability only one equilibrium state exists; either the interictal (low firing) or the seizure (high-firing) state, respectively. For intermediate values of excitability, the system has two equilibrium states separated by unstable fixed (tipping) points. (b) If the excitability is dynamically changing, then the system periodically oscillates between these two states and in a phase portrait it has a character of a limit cycle. If the interictal excitability crosses the catastrophic bifurcation F1 the system undergoes a rapid and large shift to a seizure regime. The reverse situation occurs if the excitability during seizure reaches the second catastrophic bifurcation F2 when the seizure suddenly terminates. (c) The corresponding time series demonstrates a repeated transition between the contrasting dynamical regimes, i.e. interictal and seizure states.
Supplementary Figure 6 The complex effect of interictal perturbations on the transition to seizure in the modified Epileptor model.
(a) The transition between interictal state and seizure in the Epileptor model is characterized by a saddle-node bifurcation. (b) The Epileptor model captures both slow processes and faster dynamics, replicating local field potentials during seizure respectively. (c,d) Introduction of less frequent but stronger interictal perturbations increases the probability of the transition to seizure. (e,f) Increasing the frequency of perturbations decreases the probability of the transition to seizure, or it can result in complete cessation of seizures (g,h). (i) Map of combinations of perturbation parameters, i.e. frequency and amplitude and their resulting impact on ictogenesis.
(a) Multi-day intercluster recording from the right hippocampus, which was injected with the tetanus toxin. (b) Bursts originate in the injected right hippocampus. They are characterized by initial high-amplitude discharges followed by a burst of rhythmic activity. (c,d) With the approaching next cluster of seizures, the duration and rate of bursts increases, as well as, propagation to the contralateral hippocampus and motor cortices of both hemispheres (n = 6/6 intercluster periods/animals; 1041.3±149.2 bursts per cluster). MCxL – left motor cortex, MCxR – right motor cortex, HippL – left hippocampus, HippR – right hippocampus.
Supplementary Figure 8 Temporal profiles of the variance derived from intracranial recordings in 12 patients implanted with seizure prediction devices.
The temporal evolution of signal variance three hours before a seizure, is shown. The dashed line marks 30 minutes before the seizure during which the variance was analyzed. In two patients significant pre-seizure increases in variance were observed. In five patients, the variance significantly decreased. N denotes the number of recorded seizures in each patient. P marks the value of Wilcoxon sign-rank test. The sign after the p-value indicates whether right-tailed (+) or left-tailed (–) Wilcoxon sign-rank test was significant. Lines and shaded lines represent mean and s.e.m. respectively.
Supplementary Figures 1–8
The dynamics of the slow–fast process in the absence of perturbations.
The dynamics of the slow–fast process in the presence of frequent low-amplitude perturbations. Perturbations increased the distance from the catastrophic bifurcation and slowed the transition to seizure. If the system is approaching the tipping point, even small perturbations can initiate the seizure.
The dynamics of the slow–fast process in the presence of sparse large-amplitude perturbations. Large amplitude perturbations had a stronger seizure inducing capacity, and they could initiate seizures far in advance of the catastrophic bifurcation.
The dynamics of the slow–fast process in the presence of frequent large-amplitude perturbations. The presence of perturbations results in complete abolition of seizures.