# 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. e lectrodes; critically ill patients; juvenile absence epilepsy; nonlinear Schrodinger equation; Korteweg-de Vries equation; Peregrine soliton +
Footnote †: journal: Medical Imaging  
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Footnote †: journal: Medical Imaging  
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Footnote 1: email: {[[https://www.mdpi.com/journal/signals/2009](https://www.mdpi.com/journal/signals/2009)]([https://www.mdpi.com/journal/signals/2009](https://www.mdpi.com/journal/signals/2009))  
solids and nematic liquid crystals [14] suggests a role for solitons in the physical properties of solids at high temperatures [11]. It has been conjectured that soliton-like mechanisms could also underlie biological phenomena like electron/proton transport along proteins' helices [15; 16] as well as cardiac action potentials [17]. Still, attempts have been made to describe the MICROSCOPIC nervous activity of the central nervous system in terms of solitons [18]. It has been conjectured that the standard Hodgkin-Huxley model of the neurons' action potential could be piezoelectrically coupled with synchronized soliton pressure pulses generated inside the lipids of biological membranes [19] and influenced by thermodynamic variables like voltage, temperature, pressure, chemical potentials [17]. According to this controversial model, the traveling solitons are localized in the membrane, do not spread out in the surrounding medium, do not release heat, and can modify the local membrane density and thickness [20; 21]. Here, we take a different turn, suggesting another potential approach to assess the nervous electric spikes in the context of solitary waves. Looking at the central nervous system's nervous activity at the MACROSCOPIC scale, we argue that some of the brain electric oscillations detected by electroencephalography (EEG) could be mathematically and biophysically approached in terms of solitons' motion. We contend that the electric oscillation spikes attained by scalp EEG monitoring techniques resemble, in many respects, solitary waves.