Using reissner-nordstrom solution for modeling epileptic seizures

Abstract

Modeling of the brainstorm of epileptic seizure is to find and follow paths of clusters of charges carried by ions from epileptic foci to the scalp area of the brain. This will also estimate the location of the epileptic foci or onset of the seizures. The foci may be located in a small volume of brain tissue due to unusually large accumulation of ionic charges. As a seizure begins, the electrostatic repulsive force among these ions throws the ions outward in all directions along 100 billions neurons inside the brain. These charges of electric pulses arrive finally at the scalps, and are recorded as electroencephalography (EEG) voltage signals. Modeling this event poses challenges since seizures might start at other locations at the same instant. Hence, the mixture of paths from different foci is unavoidable which resulted in a very chaotic trace of EEG signals. Sporadic ionic burst of the epileptic brainstorm is very similar to the event of the Big Bang. The tremendous explosion originated from a point of singularity, threw all matters and space outwards, and started the expansion of the universe. The journey of the matters along with this expansion provides a good model for the journey of the charges to the scalp during brainstorm epileptic seizure. General relativity states that the fundamental force of gravitation can be described as a curved space-time caused by the presence of matter and energy. Thus, matters move along this curve space-time, during the expansion of the universe. Likewise, electrostatic field of charges curved space provides path for the charges’ journey during epilepsy attack. Exact solution to the Einstein Field equation of fluid which describes the expansion of the universe may also give exact solution to Einstein field equation of electromagnetic field which describes the path of the ions during epilepsy attack. The electrovacuum solution of Reissner-Nordström metric of a charged, non-rotating black hole is suited to the variables of the model. Results obtained were then compared to another result that was obtained by using pixel image method of flat EEG. The percentage agreement is around 56.3% and was determined by the number of pixel dots that actually resides in the spherical domains of the charges’ paths. Significantly and interestingly enough, 33% of the lengths of the paths are less than 4 mm while 67% are much deeper inside the brain. This value totally agrees with the percentage of folded cortex deep inside the brain and far from the scalp.