The Dynamic Dielectric at a Brain Functional Site and an EM Wave Approach to Functional Brain Imaging

Abstract

Functional brain imaging has tremendous applications. The existing methods for functional brain imaging include functional Magnetic Resonant Imaging (fMRI), scalp electroencephalography (EEG), implanted EEG, magnetoencephalography (MEG) and Positron Emission Tomography (PET), which have been widely and successfully applied to various brain imaging studies. To develop a new method for functional brain imaging, here we show that the dielectric at a brain functional site has a dynamic nature, varying with local neuronal activation as the permittivity of the dielectric varies with the ion concentration of the extracellular fluid surrounding neurons in activation. Therefore, the neuronal activation can be sensed by a radiofrequency (RF) electromagnetic (EM) wave propagating through the site as the phase change of the EM wave varies with the permittivity. Such a dynamic nature of the dielectric at a brain functional site provides the basis for an RF EM wave approach to detecting and imaging neuronal activation at brain functional sites, leading to an RF EM wave approach to functional brain imaging.

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

“…where (for ε = 0) σ (1) represents the conductivity tensor used in analytical solution of Eqs. (10), i.e., currents only in the z direction, σ (2) represents different orientation, where currents are allowed in the direction of 45 • relative to all axis, and σ (3) represents more complicated current anisotropy, with crossing currents flowing in the x and z directions, but with no currents in the y direction. Parameters n, r 0 , and r 1 used to control the thickness of the inhomogeneous "cortical" layer (r 0 = 0.5, r 1 = 0.9, α ∞ = 500, and n = 0, 2, 14, and 25 used for Figs.…”

“…The same σ (1) , σ (2) , and σ (3) fixed (location-independent) anisotropic tensors as in the spherical shell cortex model Eq. (A2) were assigned to every location in the brain.…”

“…Similarly to the previous case the diffusion tensor D i j was estimated for each voxel, and eigenvector d (1) with the largest eigenvalue λ (1) d was used to define the anisotropy tensor major axis. The position-dependent anisotropy value was defined by introducing parameter ε as either λ (2) d /λ (1) d or (λ (2) d + λ (3) d )/2/λ (1) d (in both cases resulting in an axisymmetric form of the conductivity tensor) and using two different values λ (2) d /λ (1) d and λ (3) d /λ (1) d for σ 22 and σ 11 .…”

“…13. An example of complete wave trajectory (a) and emergent loop pattern (b) for the spherical shell cortex model with 45 • orientation single-fiber anisotropy tensor σ (2) and intermediately wide inhomogeneity layer (n = 14, r 0 = 0.5, and r 1 = 0.9). The trajectory was initialized with wave vector k = (−0.1/ √ 2, 0.1/ √ 2, −0.1) inside the inhomogeneous layer with voxel coordinates r = (141, 141, 141).…”

“…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. Experimentally, data on which this assumption is employed range from high temporal resolu-tion neural oscillations detected at low spatial resolution by EEG/MEG [1] to high spatial resolution functional MRI resting state modes oscillation detected at low temporal resolution [2]. As a consequence, a great deal of research activity is directed at the construction of connectivity maps between different brain regions (e.g., the Human Connectome Project [3]) and using those maps to study dynamical network properties with the help of different models of signal communication through this network along structurally aligned pathways [4], i.e., by allowing input from different scales or introducing axon propagation delays [5].…”