Abstracts

Rationale: Encephalopathic brain lacks the diverse and complex dynamics responsible for the higher-level information processing and demonstrates more stereotypical response patterns. One of such patterns frequently observed in critically ill patients is ictal-interictal continuum activity. We demonstrate that a basic rule governing its dynamics can be described with a simple bifurcation model. Methods: An 11-hour long electroencephalogram(EEG) was obtained from a forty-one years old male patient status post cardiac arrest. The recorded EEG activity consisted mostly of generalized epileptiform discharges with variable periodicity of 1-3Hz superimposed on background activity predominantly of theta and delta frequency at the beginning of the recording at 9:00AM. The epileptiform discharges gradually became less frequent over the next six hours and by 3:00PM lost its periodicity.Wavelet transformation was used for localization of epileptiform discharges as well as extraction of phase and power of background delta and theta activity. A minimal model based on dynamical systems theory was developed to explain the relationship between the background rhythm and epileptiform discharges. Results: The epileptiform discharges were found to occur at the intersections of the trough of delta activity and peak of theta activity (Fig. 1). The mean phase was 1.07p for delta activity and 0.09p for theta activity. Also identified was an increase in the ratio of the powers at discharges to that at intersections with progression of EEG activity towards interictal end of the continuum, from 1.17 to 1.95 for delta and from 1.26 to 2.30 for theta (Fig. 2). It was discovered that above findings can be replicated with a phase model of an epileptic neural mass near a saddle-node bifurcation on an invariant circle, where the limit cycle represents the trajectory of an epileptiform discharge. The increase in periodicity and frequency of epileptiform discharges during the transition from interictal to ictal phase corresponds to decrease in the distance between the two equilibria in the model. Conclusions: A minimal model based on saddle-node bifurcation on an invariant circle capable of reproducing electrographic activity of an encephalopathic brain was developed. Funding: Self-funded