Bifurcation analysis of the Poincaré map function of intracranial EEG signals in temporal lobe epilepsy patients

In this paper, the Poincaré map function as a one-dimensional first-return map is obtained by approximating the scatter plots of inter-peak interval (IPI) during preictal and postictal periods from invasive EEG recordings of nine patients suffering from medically intractable focal epilepsy. Evolutionary Algorithm (EA) is utilized for parameter estimation of the Poincaré map. Bifurcation analyses of the iterated map reveal that as the neuronal activity progresses from preictal state toward the ictal event, the parameter values of the Poincaré map move toward the bifurcation points. However, following the seizure occurrence and in the postictal period, these parameter values move away from the bifurcation points. Both flip and fold bifurcations are analyzed and it is demonstrated that in some cases the flip bifurcation and in other cases the fold bifurcation are the dynamical regime underlying epileptiform events. This information can offer insights into the dynamical nature and variability of the brain signals and consequently could help to predict and control seizure events.