The critical dynamics of hippocampal seizures

Abstract

Epilepsy is defined by the abrupt emergence of harmful seizures, but the nature of these regime shifts remains enigmatic. From the perspective of dynamical systems theory, such critical transitions occur upon inconspicuous perturbations in highly interconnected systems and can be modeled as mathematical bifurcations between alternative regimes. The predictability of critical transitions represents a major challenge, but the theory predicts the appearance of subtle dynamical signatures on the verge of instability. Whether such dynamical signatures can be measured before impending seizures remains uncertain. Here, we verified that predictions on bifurcations applied to the onset of hippocampal seizures, providing concordant results from in silico modeling, optogenetics experiments in male mice and intracranial EEG recordings in human patients with epilepsy. Leveraging pharmacological control over neural excitability, we showed that the boundary between physiological excitability and seizures can be inferred from dynamical signatures passively recorded or actively probed in hippocampal circuits. Of importance for the design of future neurotechnologies, active probing surpassed passive recording to decode underlying levels of neural excitability, notably when assessed from a network of propagating neural responses. Our findings provide a promising approach for predicting and preventing seizures, based on a sound understanding of their dynamics.

Fig. 1. Probing seizure resilience and neural excitability.

A Intracranial EEG (iEEG) electrodes implanted in a patient with epilepsy undergoing pre-surgical evaluation. The hippocampus is highlighted in red, the amygdala in orange. B Corresponding examples of iEEG signals from one unprovoked (spontaneous) and one provoked seizure (electrical stimulation in the entorhinal cortex, 2 s at 60 Hz), recorded for clinical localization of the seizure onset zone. The provoked seizure recapitulates most of the electrographical and semiological characteristics of the unprovoked seizure. C The ‘Epileptor’ models the brain as a bistable dynamical system. Therein, the brain can be represented as stability landscapes (top, green to red), where the ictal (light red shading in the lower pannel) and non-ictal regimes (white background) form basins of attraction, separated by a threshold (dashed line). Bidirectional changes in neural excitability (the system’s control parameter) modulate the stability landscape with lower (yellow) or heightened resilience (green double arrow). When excitability reaches the critical point (empty red dot), the non-ictal regime disappears and the system is forced to transition into the ictal regime. D For a given level of neural excitability (black ball), resilience to seizure can be measured as the amount of external perturbation (here, stimulations, blue arrows) necessary to cross the threshold and transition to the seizure regime (provoked seizure). When the system is close to the critical point (empty red dot, resilience tends to zero), ictal transitions can occur in the absence of external excitation (unprovoked seizure). E1–3 Experimentally, trains of stimulation of increasing duration were used to measure seizure resilience. Example in silico using the Epileptor model (E1, 20 Hz, 3 ms pulse-width), in mice Using optogenetic stimulation on the entorhinal cortex in mice (E2, 20 Hz, 3 ms pulse-width on Channelrhodopsin-transfected pyramidal neurons) and in humans using electrical stimulation on the entorhinal cortex (E3, 60 Hz, 1 ms pulse-width). The time of train stimulation necessary to provoke a seizure is indicative of the distance to the seizure threshold. F1–3 Smaller perturbations (here, single pulses) can be used to probe neural excitability without inducing a seizure. Dynamically, they correspond to an excursion contained within the non-ictal regime (circle arrows in D, see Supplementary Fig. 2). Experimentally, to probe the dynamic range of physiological neural excitability, we used a range of single-pulse stimulations of varying intensity (dark to bright red) leading to increasing responses in silico (F1, 3 ms pulse), as well as in vivo in mice (F2, iEEG response to single 3 ms laser pulses between ~0−50 mW) and human patients (F3, iEEG response to single 1 ms electrical pulses between 0.2−10 mA). G1–3 For a given perturbation, the induced response can be quantified as the line length of the iEEG signal over a 250 ms window, which intuitively reflects the excursion length in state-space (Supplementary Fig. 2). E1–3 created with BioRender.com released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license https://creativecommons.org/licenses/by-nc-nd/4.0/deed.en.

Fig. 2. Probing variable neural resilience.

Using the time-to-seizure, neural resilience can be probed bidirectionally in conditions of higher and lower levels of neural excitability. A1–A2 Prediction that bidirectional changes in neural excitability lead to measurable changes in resilience to seizure (number of pulses, blue arrows). B1 The prediction was modelled in silico by measuring the time-to-seizure upon changing the control parameter (x₀) in the Epileptor model. C1–D1 The prediction was tested in vivo, by measuring the time-to-seizure in the presence of an agonist (benzodiazepine, BZD) or an antagonist (Pentylenetetrazol, PTZ) of the GABA-A receptor. B2–C2 Zoom in on the stimulation train leading to the onset of a seizure. C3 Average changes in time-to-seizure (mean ± bootstrapped 95% CI difference to the NaCl control session) with increasing doses of BZD and a subconvulsive dose of PTZ across mice and sessions.

Fig. 3. Probing variable neural excitability.

Using the line length of evoked responses, recovery can be probed bidirectionally in conditions of higher and lower levels of neural excitability. A1–A2 Prediction that bidirectional changes in neural excitability lead to different recovery rates (line length, circle arrows in A1, white double arrow in A2) upon the same perturbation (single-pulse, blue arrow in A2). B1–D1 Modulation of excitability (same as in Fig. 2) results in detectable changes in iEEG responses and their recovery to single-pulse stimulation in silico (B1, response at half-maximum intensity), in mice (C1, iEEG response at maximum intensity), and humans (D1, iEEG response at 3 mA). Thick lines are the mean across sessions, shading the standard deviation. B2–D2 Measured iEEG responses (line length, ‘output’) to a range of single-pulse stimulations of varying intensity (‘input’) resulting in an ‘input-output curve’ under variable excitability in silico (B2), in mice (C2, N = 9–17) and in one participant (D2, group result in Fig. 5). C3 Magnitude of the iEEG responses across mice, quantified as the line length of the signal over a 250 ms window and normalized to the baseline (NaCl). Half-violin plot shows mean differences with bootstrapped 95% CI across respectively 23 (PTZ) or 40 (BZD) sessions among 9 or 17 mice. C4 Quantification of the area under the input-output curve (IOC) as a function of changes in excitability. Half-violin plot shows mean differences with bootstrapped 95% CI across respectively 23 (PTZ) or 40 (BZD) sessions among 9 or 17 mice.

Fig. 4. Passive signatures of neural excitability.

Passive dynamical signatures are found in bidirectional changes in univariate statistics (line length, autocorrelation, variance, and skewness) in conditions of higher and lower levels of neural excitability. A1–A2 Prediction that endogenous stochastic perturbations result in trajectories of increasing length and asymmetry with increasing excitability. B1–D1 Example of recorded signals (4 s) in the absence of stimulation at different levels of excitability in silico, (B1, x₁ + x₂ in the Epileptor in presence of stochastic noise) as well as in vivo from iEEG in the hippocampus in mice (C1) and participants (D1). B2–D2 Corresponding autocorrelation function of the signal with calculation of the lag value at half-maximum. B3–D3 Corresponding histogram of the signal’s values across conditions. B4–B7 For each passive signature, quantification of the changes when excitability is varied, expressed in difference to baseline condition and calculated on 790 simulated iEEG samples. Half-violin plot on the right shows mean differences with bootstrapped 95% CI. C4–C7 Mean (±bootstrapped 95% CI) change in passive signatures in presence of BZD (N = 17) or PTZ (N = 9) across 103 sessions in mice, normalized to the control session (NaCl). D4–D7 Mean (±bootstrapped 95% CI) change in passive makers in presence of BZD across 36 hippocampal electrodes in 6 participants.

Fig. 5. Network dynamics in humans.

Probing network responses to single-pulse stimulations uncovers changes in network dynamics. A For a representative participant (EL014), matrix of mean difference in Pearson correlation between all pairs of hippocampal electrodes compared to the control condition (baseline pre-BZD i.v.). B Mean (± bootstrapped 95% CI) spatial correlation across participants (n = 6). C In a representative participant, two examples of sub-networks responding to stimulation, respectively in the right hippocampus and the right superior temporal gyrus, identified by NMF and projected to the cortical surface. D Mean (± bootstrapped 95% CI) decrease in excitability with BZD across 16 sub-networks identified among 7 participants (colored dots). Full lines are for stimulation sites in the hippocampal circuits (limbic), dashed lines for stimulation in the extra-limbic neocortex. Supplementary Table 1 shows further clinical characteristics of the participants. mTLE and nTLE mesio and neocortical temporal lobe epilepsy, FLE frontal lobe epilepsy.

Fig. 6. Decoding network dynamics in mice.

Probing network responses to single-pulse stimulations highlights changes in network dynamics and enables better decoding of the underlying level of neural excitability. A Mean (±bootstrapped 95% CI) difference in Pearson correlation between all pairs of electrodes compared to the control condition (NaCl) across 103 sessions among 17 mice. B Representative example in one mouse of the GABAergic modulation of the average normalized spatial correlation between all recording electrodes (no probing). C Representative example in one mouse of the GABAergic modulation of the average iEEG response to optogenetic single-pulse stimulation (active probing, down-pointing arrow in the right entorhinal cortex) and ensuing propagation across hippocampal circuits. D Mean GABAergic modulation of response to single-pulse stimulation at maximal intensity in each recording channel (dots) across mice (N = 17), compared to the NaCl condition after bootstrapping (values within 95% confidence intervals were left blank). E Changes in IOC (±bootstrapped 95% CI) compared to the control condition (NaCl) for conjoint network responses to stimulation computed across electrodes, stimulation intensities, and pharmacological conditions using NMF (see Supplementary Fig. 8). Half-violin plot shows mean differences with bootstrapped 95% CI, N are reported in the figure. F Differences in resilience inversely correlates with differences in single-pulse network responses in the same session. The thick line shows the linear regression and shading the 95% CI. R2 is Pearson’s correlation coefficient and p the two-sided p value. G–I Average (±SD, N = 8) accuracy (unseen test data) and comparison of different single-trial multilabel classifiers (three balanced excitability levels: low, normal, high) based on the raw iEEG response to single pulses (active probing, 0–0.25 s, G, H) or multisite iEEG passive recordings (multiple (H) or single (I) passive signatures, 4 s as in Fig. 4) or the combination of these features (combined, H). Mean ± SD chance-level shown in gray (100 label one-sided permutations test, see methods) with significant timepoints as horizontal black bars. Each dot (N = 8) corresponds to one mouse that received both BZD and PTZ in different sessions, filled if significant (p < 0.05, one-sided permutations test, see methods). * shows significant differences between classifiers (p < 0.05, two-sided paired Wilcoxon rank-test). D created with BioRender.com, released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license https://creativecommons.org/licenses/by-nc-nd/4.0/deed.en.

Fig. 7. Warning signs of ictal transitions.

The system’s response gradually increases for the same probing stimulus at the approach of the critical point. A Prediction that a progressive increase in neural excitability results in a loss of resilience close to the critical point, where minimal perturbations can tip the system into an ictal transition. B In silico probing with single-pulse stimulations during an increase in excitability up to the critical point. In chronological order, early stimulation pulses (cyan tick) yield habitual responses (dark blue), whereas later pulses yield exaggerated responses (redder colors), until the last pulse provokes a seizure. C Corresponding responses to single-pulse stimulation, quantified as line length as a function of the distance to the critical point, measured in state space. D In vivo (N = 8) single-pulse stimulations during increasing excitability up to the critical point over the 5–20 min following the injection of a single convulsive dose of PTZ (25–35 mg/kg). E Example of single-pulse stimulation (cyan ticks, every 8–12 s) and recording in the right CA1 hippocampus at baseline and after injection of PTZ. F Individual (thin lines) and average (thick line) NMF coefficients (see methods) of the network response to single pulses with increasing excitability (PTZ, red) and in control conditions (NaCl, gray). G Mean differences in single-pulse responses (line length, left blank if non-significant after bootstrapping) compared to baseline for each electrode 10 and 2 min before seizure, across 18 sessions among N = 8 mice. H Zoom in on the network response to single-pulse at baseline (H1) and increasing levels of excitability (H2 to H4). In this example, the last pulse induces a seizure but seizures could also start between simulations. D and G created with BioRender.com released under a Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International license https://creativecommons.org/licenses/by-nc-nd/4.0/deed.en.