Fig 1.
Single neuron activity during ictal discharges in simulation with the orignal Epileptor-2 model (left) and experiment (right).
Two ictal discharges as bursts of clustered interictal-like short bursts are seen in the membrane voltage. In the experiment, the ictal discharges were recorded in a pyramidal neuron from a rat entorhinal cortex using an in vitro 4-AP model of epileptic activity. Modified from [21].
Table 1.
Basic parameter values are from [25], except the modified values that are given in bold.
Fig 2.
Computational domain includes a 6mm by 6mm piece of the cortical tissue.
The central circular domain with R = 0.3 mm (red) is a center of excitation due to higher synaptic conductance Gsyn than outside the circle (blue).
Fig 3.
Diffusion mechanism (Model 1).
A: Repeated IDs recorded in the center of the cortical domain (Fig 2). B: An ictal discharge recorded in the center of the cortical domain. a: The representative neuron membrane depolarization U. The inset is a magnification of the first burst. b: The total input current u. c: The ionic concentrations [K]o and [Na]i, and the Na+/K+ pump current Ipump. d: The somatic firing rate ν and the synaptic resource xD. C: Potassium concentration spatial-temporal patterns during generation of two IDs. Two sites of “recordings” are marked as “S1” and “S2”, remote at a distance of 2mm. D: A comparative plot of [K]o at two points S1 and S2. E: A comparative plot of U at the sites S1 and S2. F: The dependence of the front wave speed on the diffusion coefficient (obtained with a narrow computational domain).
Fig 4.
A: Repeated IDs recorded in the center of the cortical domain(Fig 2). B: A single ictal discharge recorded in the center of the cortical domain. a: The representative neuron membrane depolarization U. The inset is a magnification of the first burst. b: The total input current u. c: The ionic concentrations [K]o and [Na]i, and the Na+/K+ pump current Ipump. d: The somatic firing rate ν and the synaptic resource xD. e: The presynaptic firing rate φ. C: Potassium concentration spatial-temporal patterns during generation of two IDs. D: A comparative plot of [K]o at two different points. E: A comparative plot of U at two different points. F: The dependence of the front wave speed on the connection length (obtained with a narrow computational domain).
Fig 5.
A. The membrane potential V at the 163rd second of the simulation. The red bar marks the region of interest (ROI) for spatial-temporal analysis. B. Propagation pattern of the ROI within the interval of 400 ms since the time moment at 163s. The stripes-bursts constituting the pattern are rather vertical, which means that the speed of the bursts is much larger (or infinite) in comparison to that of the ictal wave.
Fig 6.
Preictal events at different points are highly correlated, whereas the onsets of ID are delayed.
The firing rate φ is plotted at different points with the distance 1 mm between them.
Fig 7.
Model 2: Domain with a lesion.
Potassium concentration spatial-temporal patterns during generation of two IDs.
Fig 8.
Model 3: Domain with a partial lesion.
Potassium concentration spatial-temporal patterns during generation of a single ID.
Fig 9.
Model 3: Domain with a complete lesion.
A. The schematic of the computational domain. B and C. The evolution of the extracellular potassium concentration at the three sites of the domain, S1, S2 and S3, in simulations with (C) and without (B) the diffusion. D and E. The spatial-temporal patterns of the extracellular potassium concentration during generation of two discharges in the left domain. The discharge in the right domain originates due to the potassium diffusion. Specific parameters were: τK = 10s, gK,leak/gL = 3, Kbath = 4mM and Gsyn/gL = 1mV⋅s in the periphery, Kbath = 7mM and Gsyn/gL = 5mV⋅s in the central zone, a spatially nonhomogeneous noise, DK = 2 ⋅ 10−5cm2/s.