Modeling noninvasive neurostimulation in epilepsy as stochastic interference in brain networks

Abstract

Noninvasive brain stimulation is one of very few potential therapies for medically refractory epilepsy. However, its efficacy remains suboptimal and its therapeutic value has not been consistently assessed. This is in part due to the nonoptimized spatio-temporal application of stimulation protocols for seizure prevention or arrest, and incomplete knowledge of the neurodynamics of seizure evolution. Through simulations, this study investigated electroencephalography (EEG)-guided, stochastic interference with aberrantly coordinated neuronal networks, to prevent seizure onset or interrupt a propagating partial seizure, and prevent it from spreading to large areas of the brain. Brain stimulation was modeled as additive white or band-limited noise, and simulations using real EEGs and data generated from a network of integrate-and-fire neuronal ensembles were used to quantify spatio-temporal noise effects. It was shown that additive stochastic signals (noise) may destructively interfere with network dynamics and decrease or abolish synchronization associated with progressively coupled networks. Furthermore, stimulation parameters, particularly amplitude and spatio-temporal application, may be optimized based on patient-specific neurodynamics estimated directly from noninvasive EEGs.

Fig. 1

EEG signal segmentation for estimation of 1) preictal network coordination and 2) ictal propagation (from ictal segment (shaded).

Fig. 2

Time delays (in s) as a function of EEG channels, using T3 as the reference channel.

Fig. 3

Simulated EEG spectrum (black) and superimposed real scalp EEG spectrum (red). Both signals were sampled at 500 Hz.

Fig. 4

Nonictal CMI for one patient with seizures originating in the left temporal lobe. CMI between channel T3 and all others, at frequencies ≤100 Hz (left plots) and >100 Hz (right plots) is shown. Corresponding parameters following addition of white noise are shown in the bottom plots.

Fig. 5

Preictal CMI for one patient with seizures originating in the left temporal lobe. CMI between channel T3 and all other, at frequencies ≤100 Hz (left plots) and >100 Hz (right plots) is shown. Corresponding parameters following noise perturbation at time 50–55s are shown in bottom plots.

Fig. 6

Preictal conditional mutual information (CMI, top plots) and interaction information (II, bottom plots) as a function of channels, at frequencies ≤100 Hz (left plots) and >100 Hz (right plots) is shown. For each channel, information parameters were averaged over all pairwise values between that channel and all others. Inter-patient variability is superimposed. Values prior to noise perturbation (black dashed line), and following addition of white noise with amplitudes 0.1 (red), 0.5 (cyan), 1 (green), 2 (blue), 4(black) times the maximum amplitude of the signal are superimposed. Noise was added to each signal at the time interval of maximum mean CMI.

Fig. 7

Mean conditional (CMI, top plots) and interaction (II, bottom plots) ictal information as a function of channels, at frequencies ≤100 Hz (left plots) and >100 Hz (right plots) is shown. Inter-patient variability is superimposed to averaged parameters over patients. Values prior to noise perturbation (black dashed line), and following addition of white noise with amplitudes 10% (red), 50% (cyan), 100% (green), 200% (blue), 400% (black) the amplitude of the EEG are superimposed.

Fig. 8

Preictal conditional and interaction information (CMI, II) as a function of the noise bandwidth: white noise (black), bandlimited at frequencies ≤100 Hz (green), bandlimited at >100 (blue). The unperturbed CMI and II are superimposed (red). Parameters are shown in the two frequency ranges (left: ≤100 Hz, right:>100 Hz).

Fig. 9

Simulated network in which propagation is limited to nodes 1–5 (top left panel). There is also limited propagation in adjacent nodes (6,7) due to connectivity between nodes 5–6 and 6–7, but the remaining nodes are only weakly coupled (the baseline), with CMI≤0.3. Top right panel corresponds to the network response to a white noise perturbation at node 2, at time t=5s from the beginning of the simulation. Bottom left and right panels correspond to perturbations at times t = 20 s and t = 50 s, respectively.

Fig. 10

Simulated larger network with delayed neural propagation from nodes 1 to 15 (top left panel). The top right panel corresponds to the network response to white noise perturbation at node 2, at time t = 5 s. Bottom left and right panels correspond to perturbations at times t = 50s also at node 2, and at t = 50 s at node 16 (outside the sub-network involved in propagation).

Fig. 11

Simulated network with delayed neural propagation from nodes 1 to 9 (top left panel). The modulated network when white noise was added every 10s in node 5, for the entire duration of the stimulation (top right panel), every 20s in node 5 (bottom left panel), and every 500 ms in the first 5s (bottom right panel), are also shown.