Approaching Electroencephalographic Pathological Spikes in Terms of Solitons

Abstract

A delicate balance between dissipative and nonlinear forces allows traveling waves termed solitons to preserve their shape and energy for long distances without steepening and flattening out. Solitons are so widespread that they can generate both destructive waves on oceans’ surfaces and noise-free message propagation in silica optic fibers. They are naturally observed or artificially produced in countless physical systems at very different coarse-grained scales, from solar winds to Bose–Einstein condensates. We hypothesize that some of the electric oscillations detectable by scalp electroencephalography (EEG) could be assessed in terms of solitons. A nervous spike must fulfill strict mathematical and physical requirements to be termed a soliton. They include the proper physical parameters like wave height, horizontal distance and unchanging shape; the appropriate nonlinear wave equations’ solutions and the correct superposition between sinusoidal and non-sinusoidal waves. After a thorough analytical comparison with the EEG traces available in the literature, we argue that solitons bear striking similarities with the electric activity recorded from medical conditions like epilepsies and encephalopathies. Emerging from the noisy background of the normal electric activity, high-amplitude, low-frequency EEG soliton-like pathological waves with relatively uniform morphology and duration can be observed, characterized by repeated, stereotyped patterns propagating on the hemispheric surface of the brain over relatively large distances. Apart from the implications for the study of cognitive activities in the healthy brain, the theoretical possibility to treat pathological brain oscillations in terms of solitons has powerful operational implications, suggesting new therapeutical options to counteract their detrimental effects.