Active paradigms of seizure anticipation: Computer model evidence for necessity of stimulation

It has been shown that the analysis of electroencephalographic (EEG) signals submitted to an appropriate external stimulation (active paradigm) is efficient with respect to anticipating epileptic seizures [S. Kalitzin et al., Clin. Neurophysiol. 116, 718 (2005)]. To better understand how an active paradigm is able to detect properties of EEG signals by means of which proictal states can be identified, we performed a simulation study using a computational model of seizure generation of a hippocampal network. Applying the active stimulation methodology, we investigated (i) how changes in model parameters that lead to a transition from the normal ongoing EEG to an ictal pattern are reflected in the properties of the simulated EEG output signals and (ii) how the evolution of neuronal excitability towards seizures can be reconstructed from EEG data using an active paradigm, rather than passively, using only ongoing EEG signals. The simulations indicate that a stimulation paradigm combined with appropriate analytical tools, as proposed here, may yield information about the change in excitability that precedes the transition to a seizure. Such information is apparently not fully reflected in the ongoing EEG activity. These findings give strong support to the development and application of active paradigms with the aim of predicting the occurrence of a transition to an epileptic seizure.

Figure 1

Neuronal population model based on the cellular organization of the hippocampus (CA1 subfield). (a). Structure of model which represents a cluster of neurons composed of three subpopulations: main cells (i.e., pyramidal cells) and local interneurons (i.e., O-LM or basket cells). Pyramidal cells receive excitatory input from other pyramidal cells (collateral excitation) and inhibitory input from interneurons. (b). Block diagram representation of the model. $S\left(v\right)$ denote “wave-to-pulse” functions (asymmetric sigmoid curve), while $h_{EXC}\left(t\right)$, $h_{SDI}\left(t\right)$, and $h_{FSI}\left(t\right)$ denote “pulse-to-wave” functions (see text). The external stimulation was represented by an additive model between the output of “pulse-to-wave” functions and the potential difference induced by the extracellular bipolar stimulation electrode “Stim.”

Figure 2

(Color online) Dependence of the model properties ($z$ axis and color) on SDI ($x$ axis) and EXC ($y$ axis) parameters. In all four plots the color scale corresponds to the value of the seizure threshold. (a) Dependence of the seizure threshold [in pulses per second (pps)] and a color bar showing the color scale used. (b) Dependence of the standard deviation of spontaneous activity $S_0$. One can see that this measure is sensitive only to a change of the EXC, but not to a change of the SDI parameter. (c) Dependence of the system’s triggered response $D_1$. One can see that this measure is sensitive only to a change of the SDI, but not to a change of the EXC parameter. (d) Dependence of the rPCI showing that this measure is sensitive to a change of both the EXC and SDI parameters.

Figure 3

(a), (b), (c) Scatter plots of the seizure threshold [pulses per second (pps)] and measurable quantities ($S_0$, $D_1$, and rPCI, respectively) obtained for all pairs of the EXC and SDI parameters in the model. In each graph, the value of nonlinear association measure $h^2$ is used to quantify the correlation between the respective variables. The $h^2$ values show that the rPCI measure is best correlated with the seizure threshold, while its scatter-plot hyperbolic shape resembles that of the real data. (d) Scatter plot of the time to next seizure and rPCI value in a TLE patient (patient 3 described in [3]).

Figure 4

Examples of time evolution of the $S_0$, $D_1$, and rPCI in two TLE patients. Points denote measurements, while the vertical bars denote seizures. The inhomogeneous structure of the plots is due to the fact that data were collected in these cases mainly during the night. In patient 3, the $S_0$ does not change towards seizures, while there is a marked decrease of the $D_1$ parameter and increase of the rPCI parameter. In patient 4, there is an increase of the $S_0$ parameter toward seizures. The $D_1$ parameter initially decreases, but starts to increase after the first seizure. The rPCI parameter initially increases up to few hours after first seizure and starts to decrease afterwards.

Figure 5

(Color online) Model-based interpretation of the relationship between the PCI and the level of excitability. In each part (a), (b), (c), and (d) of this figure, different variables are plotted for four different conditions. Simulations of normal conditions (“normal”) were performed with $\mathrm{EXC}=2.5\mathrm{mV}$ and $\mathrm{SDI}=50\mathrm{mV}$; increased excitability due to increased excitation (“high Exc”) was simulated using $\mathrm{EXC}=4.75\mathrm{mV}$ and $\mathrm{SDI}=50\mathrm{mV}$; increased excitability due to decreased inhibition (“low Inh”) was simulated using $\mathrm{EXC}=2.5\mathrm{mV}$ and $\mathrm{SDI}=22\mathrm{mV}$; and highest excitability (“high Exc, low Inh”) was simulated using $\mathrm{EXC}=4.75\mathrm{mV}$ and $\mathrm{SDI}=22\mathrm{mV}$. In all simulations the external stimulation input was a $10\text{−}\mathrm{Hz}$ sequence of 60 monophasic pulses of $1\mathrm{ms}$ duration. (a) Spontaneous model output for different excitability conditions. Different parameter settings result in different DC offsets of the signals; “normal,” $-9.45\mathrm{mV}$; “high Exc,” $-7\mathrm{mV}$; “low Inh,” $-3\mathrm{mV}$; “high Exc, low Inh,” $-0.52\mathrm{mV}$. Increased excitation (upper right panel) leads to increased signal variance, while lowered inhibition (lower left side panel) has no significant influence on the signal variance. (b) Average power spectra of spontaneous and triggered activity. In both cases the spectra were computed by dividing the signal (in the spontaneous case artificial “triggers” were introduced) into segments corresponding to single response epochs $\left(100\mathrm{ms}\right)$ and removing the DC offset of each epoch. For spontaneous spectra the magnitudes obtained from discrete Fourier transform of the epochs were averaged across all epochs and plotted along a logarithmic (dB) scale. For triggered spectra, the average of complex amplitudes of Fourier-transformed triggered responses over all epochs was computed and its magnitude was plotted. In each panel, spectra corresponding to different excitability conditions are plotted with different colors and markers: “normal,” blue crosses; “high Exc,” green squares; “low Inh,” yellow circles; “high Exc, low Inh,” red dots. Spontaneous spectra of “normal” and “low Inh” as well as those of “high Exc” and “high Exc, low Inh” overlap with each other, implying that level of inhibition has no influence on spectral power of background activity at any frequency. The spectra of triggered responses are distinct for changes of excitation and inhibition. (c) Spectrum of phase clustering index. Phase coherencies at a given frequency were computed directly from the spread of phases of complex amplitudes obtained by Fourier transform of triggered responses (blue bars) and using Eq. (2) (black dashed line). Values of the PCI at the driving frequency $\left({\mathrm{PCI}}_1\right)$ and at the frequency at which the PCI has maximal value $\left({\mathrm{PCI}}_{\max }\right)$ are marked with horizontal lines of colors corresponding to the color code used in spectral plots in part (b). The distance between the lines corresponds to the value of rPCI. The rPCI values increase for increasing DC levels of the output signals shown in part (a). (d) Complex amplitudes. Polar plots of amplitudes of Fourier-transformed triggered responses at the driving frequency and at which the PCI is maximal. Color of the arrows corresponds to the color code used in parts (b) and (c). Only amplitudes from the first 25 triggered responses are shown for clarity. While the spread of phases—i.e., the variability of the arrow directions—is small for ${\mathrm{PCI}}_{\max }$ for all four conditions, the degree of phase scattering at the driving frequency, as quantified by ${\mathrm{PCI}}_1$, differs between the conditions studied.