Description
Epilepor5D (E5D) is a phenomenological, coupled, nonlinear five-dimensional (i.e., five state-variables ('x1', 'y1', 'z', 'x2', 'y2')) neural mass model able to realistically reproduce the temporal dynamics of epileptic seizures and the alternating sequence of seizures (ictal and interictal state; Jirsa et al.,2014; El Houssaini et al., 2015, 2020).
Epileptor5D comprises three different time scales interacting together and accounting for various electrographic patterns:
- the fastest and intermediate time scales are two coupled oscillators ((x1, y1) and (x2, y2)), accounting respectively for the low-voltage fast discharges (i.e., very fast oscillations) and spike-and-wave discharges.
- the slowest time scale is responsible for leading the autonomous switch between interictal and ictal states and is driven by a slow-permittivity variable z. This switching is accompanied by a direct current (DC) shift that has been recorded in vitro and in vivo.
The main output of the model: -x1+ x2, bears analogy with the field potential, while the precise biophysical equivalent of the z variable is unknown and will be likely complex.
Note:
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- Equations and default parameters are taken from (Jirsa et al.,2014 & El Houssaini et al., 2015),
- The integral coupling function g(x1) can be rewritten as an ordinary differential equation, which is technically introduced, here, as a sixth state-variable (see Jirsa et al.,2014),
- The slow permittivity state-variable (z_E5D) can be modified to account for the time difference between the interictal (between seizures) and ictal (during seizure) states (see Proix et al., 2014).