A Model for the Propagation of Seizure Activity in Normal Brain Tissue

Cartoon of the modeled scenarios.

a–f, Firing rate of the network populations in response to a perturbation (blue, the incoming perturbation; green, excitatory and in red inhibitory populations): propagative and non-propagative scenarios (respectively, left and right columns) for AdEx model (a, b), with amplitude of perturbation α=80Hz and τon/off=100ms ; CAdEx model (c, d) with α=70Hz and τon/off=80ms ; HH model with α=60Hz and (e), and with α=140Hz and τon/off=60ms (f). For each model, the networks are the same in the propagative or non-propagative scenarios; the only difference comes from the incoming input with different realizations.

Grid search on the amplitude and slope of the incoming perturbation for each network. a, b, The percentage of realizations that propagate (Prop.), respectively, for AdEx (a) and CAdEx (b) networks. c, d, For HH networks, the means and SDs (over realizations) of the difference in firing rates between excitatory (c) and Poisson (d) populations (Δ firing rate = ν_e − ν_Pois), averaged over the length of the plateau.

Influence of connectivity on single neurons firing rates. a, Influence of Poissonian ( NinpPois ), excitatory ( NinpExc ), and inhibitory ( NinpInh ) in-degree on the firing rates of excitatory neurons ( νENP ), and inhibitory neurons ( νINP ) in the non-propagative scenario of the AdEx network. The standard Pearson correlation coefficient ρ is estimated. b, Time-averaged single-neuron firing rates and differences in propagative versus non-propagative regimes, as a function of both inhibitory and Poissonian in-degrees.

Grid search on the in-degree inhibitory probability of connection for the AdEx network. a, b, Percentage of propagation (Prop.) with parameters, as follows: α=70Hz and τ=70ms (a); and α=95Hz and τ=70ms (b), where for both figures Pie is the probability of connection from inhibitory to excitatory neurons and Pii is the probability of connection from inhibitory neurons to inhibitory neurons. Decreasing the probability of connection from inhibitory to excitatory neurons or increasing the probability of connection from inhibitory to inhibitory neurons tends to decrease the overall inhibition in the network and thus facilitates propagative behavior.

Dynamics in the propagative scenario (AdEx). a, In a raster plot of a simulation with propagative behavior, neuron indices are sorted according to the number of spikes during the simulation. A “cascade” phenomenon can be observed when zooming on the onset of the perturbation propagation in the excitatory population. b, The same cascade phenomenon is observed when neuron indices are sorted as a function of the number of inhibitory inputs received. Note that the absence of excitatory activity after the perturbation is because of a strong adaptation current (Eqs. 1, 2).

Dynamics in the propagative scenario (CAdEx and HH). a–d, Same plot as previously shown but for the CAdEx network (spike sorting, a; inhibitory in-degree sorting, b) and HH network (spike sorting, c; inhibitory in-degree sorting, d). Cascade phenomena are still observable in a, b, and d, hence showing its robustness, but not in c, where propagation takes a slightly different form, highlighting the contrast induced by different perspectives on a single-complex dynamics.

Mean membrane potential over subgroups of neurons (same network connectivity, different noise realizations) for each group defined as a function of their incoming inhibitory connections, averaged over 50 noise realizations (17 non-propagative and 33 propagative). a, b, Color maps correspond for each group to the average membrane potential (top) and SD (bottom) across noise realizations in the propagative situations (a) and non-propagative situations (b) for both excitatory (RS) and inhibitory (FS) populations. The blue rectangle highlights the (time) region where the system either switches to a propagative regime or remains stable.

Mean membrane potential over subgroups of neurons (different network connectivities) for each group defined as a function of their incoming inhibitory connections. Here, we averaged over 50 network connectivities, for which we found a couple of noise realizations corresponding to propagative and non-propagative scenarios. a, b, Color maps correspond for each group to the average membrane potential (top) and SD (bottom) across different connectivities in the propagative (a) and non-propagative scenarios (b) for both excitatory (RS) and inhibitory (FS) populations. The blue rectangle highlight the (time) region where the system either switches to a propagative regime or remains stable.

Kuramoto R of membrane potentials over subgroups of neurons (same network connectivity, different noise realizations) for each group defined as a function of their incoming inhibitory connections, averaged over 50 noise realizations (17 non-propagative and 33 propagative). a, b, Color maps correspond for each group to the average Kuramoto parameter (top) and SD (bottom) across noise realizations in the propagative (a) and non-propagative (b) scenarios for both excitatory (RS) and inhibitory (FS) populations. The blue rectangle highlights the (time) region where the system either switches to a propagative regime or remains stable.

Kuramoto R of membrane potentials over subgroups of neurons (different connectivities) for each group defined as a function of their incoming inhibitory connections. Here, we averaged over 50 network connectivities for which we found a couple of noise realizations corresponding to propagative and non-propagative scenarios. a, b, Color maps correspond for each group to the average membrane potential (top) and SD (bottom) across different connectivities in the propagative (a) and non-propagative scenarios (b) for both excitatory (RS) and inhibitory (FS) populations. The blue rectangle highlights the (time) region where the system either switches to a propagative regime or remains stable.