Qualitative resonance in networks of chaotic oscillators: A modeling framework for focal and multi-focal epilepsy

We propose a modeling framework for (multi-) focal epilepsy aimed at identifying the most probable epileptic foci, the neuronal masses driving the epileptic response. We model the brain as an ensemble of macro-anatomically defined regions, each with electrical activity described by a chaotic oscillator. The connection strengths are normalized to obtain an asynchronous, complex (chaotic and high-dimensional) seizure-free activity. Seizures manifest as a resonance phenomenon, in which one (or more) oscillator receives a periodic stimulus (the elaboration of an external stimulus in reflex epilepsies, or the result of functional disorders or lesions), resonates with it, thus lowering the complexity of its behavior by following the stimulus, and passes the stimulus through the connections. As a result, part or the entire network tends to synchronize on a less complex (periodic-like and low-dimensional) regime, and by stimulating different oscillators one can identify the possible epileptic foci. We exploit the ``qualitative resonance'' typical of oscillators with chaotic behavior organized by a homoclinic bifurcation (Shil'nikov-like chaos, as observed in reconstructed and modeled epileptic attractors). We test our framework on a simple network of Colpitts oscillators. Although further testing, with different oscillators and networks, seems promising, we here provide only qualitative results. Future developments will make use of EEG, MEG, or fMRI connectivity information and will be tested against clinical data.