Abstract
An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non-evanescent (weakly damped) wave-like modes propagating in the thin cortex layers transverse to both the mean neural fiber direction and to 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 non-resonant 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 damped to 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 new mechanism for understanding the nature of spiking behavior, 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.
Highlights
The majority of approaches to characterizing brain dynamical behavior are based on the assumption that signal propagation along well-known anatomically defined pathways, such as major neural fiber bundles, tracts, or groups of axons, should be sufficient to deduce the dynamical characteristics of brain activity at different spatiotemporal scales
All wave simulations were initialized with wave packets of random parameters, but clearly show an emergence of localized persistent closed loop patterns at different spatial and temporal scales, from scales as large as the whole brain where rotational wave activity has been experimentally detected in Ref. [6] to as small as the resolution used for the cortical layer thickness detection
Contrary to this and rather unexpectedly, Eq (29) is obtained through an integration of a large number of oscillatory brain wave modes nonresonantly interacting in an inhomogeneous anisotropic media and shows spiking pattern solutions emerging as a result of this nonresonant multimode interaction rather than as a consequence of empirical fitting of a nonlinear model to several locally measured parameters
Summary
The majority of approaches to characterizing brain dynamical behavior are based on the assumption that signal propagation along well-known anatomically defined pathways, such as major neural fiber bundles, tracts, or groups of axons (down to a single axon connectivity), should be sufficient to deduce the dynamical characteristics of brain activity at different spatiotemporal scales. In order to describe this complex behavior we show for the first time that the inverse proportionality of frequency and wave number in brain wave dispersion relation permits the characterization of a limiting form for the signals in terms of a large number of wave modes as a summation of nonresonant wave harmonics, allowing a closed analytical form of a nonlinear equation that integrates and includes the collective nonresonant input from multiple wave modes This general mechanism explains the emergence of synchronized spiking from an elegant perspective of nonlinear wave physics, rather than relying on empirical fitting of a single measured quantity to a set of ad hoc multiparametric differential equations using 20 or more dimensional and dimensionless fitting parameters, as is typically employed by a multitude of single-neuron spiking models [10,12].
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