Internetwork and intranetwork communications during bursting dynamics: Applications to seizure prediction

We use a simple dynamical model of two interacting networks of integrate-and-fire neurons to explain a seemingly paradoxical result observed in epileptic patients indicating that the level of phase synchrony declines below normal levels during the state preceding seizures (preictal state). We model the transition from the seizure free interval (interictal state) to the seizure (ictal state) as a slow increase in the mean depolarization of neurons in a network corresponding to the epileptic focus. We show that the transition from the interictal to preictal and then to the ictal state may be divided into separate dynamical regimes: the formation of slow oscillatory activity due to resonance between the two interacting networks observed during the interictal period, structureless activity during the preictal period when the two networks have different properties, and bursting dynamics driven by the network corresponding to the epileptic focus. Based on this result, we hypothesize that the beginning of the preictal period marks the beginning of the transition of the epileptic network from normal activity toward seizing.

Figure 1

Examples of the different types of behavior of the collective current trace of a single, uncoupled network. (a) Random firing behavior seen below the bursting threshold, $E=0.85$. (b) Fast oscillatory modulation just before the transition to bursting, $E=0.95$. (c) Bursting behavior observed above the bursting threshold, $E=1.1$.

Figure 2

(Color online) (a) Relationship between the excitability parameter of a single network and the average firing rate of five different neurons within the network. Increasing the excitability of the network causes the neurons to fire more rapidly and to synchronize. (b) The average total current in a single network as a function of the excitability. As the excitability is increased, the total synaptic current in the network will rise. The dotted line denotes the bursting threshold.

Figure 3

Plots of the average phase coherence and maximum cross correlation coefficient as a function of the mismatch between the excitability parameters in the networks. Values were averaged over 100 simulations as described in the text. Sample current traces are shown for the different types of behavior seen during the resonance (A), random firing (B), and bursting regimes (C).

Figure 4

(a, c, e) Average synchronization as a function of the coupling parameters during two regimes: $\Delta E=0$—upper lines, and $\Delta E=0.1$—lower lines. (b, d, f) Difference between the level of synchronization between the two regimes. (a) and (b) Calculated as a function $B$, with $m=15$. (c) and (d) Calculated as a function of the number of connections between networks $m$ with $B=0.4$. (e) and (f) Calculated as a function of internetwork synaptic delay with $B=0.4$ and $m=15$ with a constant intranetwork delay of 0.6 ms.

Figure 5

Panels (a)–(c) show the analysis for $N1$, panels (d)–(f) show the analysis for $N2$. (a) and (d) Interspike interval (ISI) histograms for each neuron shown for four levels of excitability mismatch. (b) and (e) Samples of corresponding collective signals. (c) and (f) Interburst interval (IBI) histograms of the collective signal during the same intervals as in (a) and (c). Histograms were created by running a peak detection program on the collective signal to determine population spikes. Note that the ISI and IBI histograms do not necessarily correspond, indicating that the phase of the neuron plays a large role in the behavior of the network as a whole.

Figure 6

Measures of synchronization. The vertical dashed line represents the bursting threshold. (a) Excitability parameters as a function of time. N1—black, N2—gray. (b) Phase coherence $R$ as a function of time. (c) Maximum cross correlation coefficient $C_{\text{max}}$ as a function of time. High levels of synchronization occur during the region of parameter matching and during bursting behavior, while other regions exhibit low levels of synchronization.

Figure 7

Profile of the mean phase coherence $R$ for a pair of intrahippocampal EEG recordings from a patient suffering from mesial temporal lobe epilepsy. Seizure onset is at $t=0$.

Figure 8

Calculated preictal lengths for 12 different realizations of a network. Four simulations were run for each network realization and the preictal length was calculated as described in the text.