×

zbMATH — the first resource for mathematics

Quadratic binary programming and dynamical system approach to determine the predictability of epileptic seizures. (English) Zbl 1050.92031
Epilepsy is one of the most common disorders of the nervous system. The progressive entrainment between an epileptogenic focus and normal brain areas results in transitions of the brain from chaotic to less chaotic spatiotemporal states, the epileptic seizures. The entrainment between two brain sites can be quantified by the T-index from the measures of chaos (e.g., Lyapunov exponents) of the electrical activity (EEG) of the brain. By applying optimization theory, in particular quadratic zero-one programming, we were able to select the most entrained brain sites 10 minutes before seizures and subsequently follow their entrainment over 2 hours before seizures. In five patients with 3–24 seizures, we found that over 90 % of the seizures are predictable by the optimal selection of electrode sites. This procedure, which is applied to epilepsy research for the first time, shows the possibility of prediction of epileptic seizures well in advance (19.8 to 42.9 minutes) of their occurrence.

MSC:
92C50 Medical applications (general)
90C20 Quadratic programming
92C20 Neural biology
90C90 Applications of mathematical programming
92C55 Biomedical imaging and signal processing
PDF BibTeX XML Cite
Full Text: DOI