Universal theory of brain waves: From linear loops to nonlinear synchronized spiking and collective brain rhythms

Abstract

An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of nonevanescent (weakly damped) wavelike modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and the cortex spatial gradient. Although the amplitude of these modes stays below the typically observed axon spiking potential, the lifetime of these modes may significantly exceed the spiking potential inverse decay constant. Full brain numerical simulations based on parameters extracted from diffusion and structural MRI confirm the existence and extended duration of these wave modes. Contrary to the standard paradigm that the neural fibers determine the pathways for signal propagation in the brain, the signal propagation due to the cortex wave modes in highly folded areas will exhibit no apparent correlation with the fiber directions. The results are consistent with numerous recent experimental animal and human brain studies demonstrating the existence of electrostatic field activity in the form of traveling waves (including studies where neuronal connections were severed) and with wave-loop-induced peaks observed in EEG spectra. In addition, we demonstrate that the resonant and nonresonant terms of the nonlinear coupling between multiple modes produce both synchronous spiking-like high-frequency wave activity as well as low-frequency wave rhythms as a result of their unique dispersion properties. Numerical simulation of forced multiple mode dynamics shows that as forcing increases there is a transition from a damped to an oscillatory regime that subsequently decays away as over-excitation is reached. The resonant nonlinear coupling results in the emergence of low-frequency rhythms with frequencies that are several orders of magnitude below the linear frequencies of modes taking part in the coupling. The localization and persistence of these cortical wave modes, and this mechanism of their collective input to the generation of synchronized spiking and low-frequency rhythms, have significant implications in particular for neuroimaging methods that detect electromagnetic physiological activity, such as EEG and MEG, and in general for the understanding of brain activity, including mechanisms of memory.

Information, Thermodynamics and Life: A Narrative Review

“…Hence, similar early works attempted to reduce this irregularity by accounting for the average of multiple signals. Although, this reduced the noise it is now known that even slight irregularities in brain signals still carry out messages [68]. The same was hypothesized for molecular signals in the cellular environment, which has been found that the most important differences were those that took place in infinitesimal ranges.…”

“…The same was hypothesized for molecular signals in the cellular environment, which has been found that the most important differences were those that took place in infinitesimal ranges. Finally, it is possible that irregularities in neural signaling may actually represent the actual information transmission [67,68]. Overall, neuroscience stated two hypotheses, about the nature of neural information processing.…”

Critical brain wave physics of neuronal avalanches without sandpiles of self organized criticality

“…This equilibrium solution provides the locus of the bifurcation point at where the nonlinear spiking oscillations occur (as was shown both in 1,2 and in 33 ).…”

“…evanescent cortical wave (WETCOW) modes 1,2 . The Hamiltonian framework developed for these WETCOW modes in 33 is advantageous in that it explicitly uncovers the reciprocity of the temporal and the spatial dynamics of the evolutionary equations.…”

“…In this paper we show that our recently described theory of weakly evanescent brain waves (WETCOW) originally developed in 1,2 and then reformulated in a general Hamiltonian framework 33 provides a physical theory, based on the propagation of electromagnetic fields through the highly complex geometry of inhomogeneous and anisotropic domain of real brain tissues, that explains the broad range of observed seemingly disparate brain wave characteristics. This theory produces a set of nonlinear equations for both the temporal and spatial evolution of brain wave modes that includes all possible nonlinear interaction between propagating modes at multiple spatial and temporal scales and degrees of nonlinearity.…”