Ephaptic Coupling in White Matter Fibre Bundles: A Generative Model for EEG/MEG Spectral Densities

1986 

Abstract Submission 

PK Douglas¹

¹IACS, Los Angeles, CA

PK Douglas  
IACS
Los Angeles, CA

Axons are generally regarded as isolated units that faithfully transmit neural signals to the synapse. In the 1940s, seminal experiments (Katz and Schmitt 1940) (Arvanitaki 1942) demonstrated that signals traveling along parallel axons could interact with each other by changing the electric potential of the extracellular medium. Notably, these experiments showed that axons in a bundle that began firing with an initial offset, would resynchronize, by slowing down neighboring spike propagation velocities. However, this ephaptic coupling, or axonal cross-talk, was only observed in when axons were immersed in a highly resistive medium. In cortex, extracellular resistivity is low (isotropic), and ephaptic coupling is typically thought to be negligible.
Recently, novel fixation techniques have revealed that unmyelinated neurons are present in significant quantities in white matter fiber bundles. Thus, densely packed (anisotropic) white matter tracts have a higher packing density and resistivity (Logothetis, Kayser et al. 2007), when the presence of unmyelinated neurons is taken into account. Thus, it is possible that axon potentials traveling along parallel axons in white matter tracts may exert subtle effects on their neighbors (Schmidt, Hahn et al. 2021).
Here, we explore a novel theoretical and generative framework, the white matter ephaptic coupling model (WMEC), and test its ability to explain the relationship between white matter morphology, spike propagation dynamics, and log-linear spectral densities observed in brain activity data.

We developed a computational modelling framework, based on cable theoretic principles including contributions from both myelinated (Liewald, Miller et al. 2014) and unmyelinated neurons (Wang, Shultz et al. 2008) across a range of axonal calibers, (Figure 1). To model bi-directional communication in the form of "recursive spike volleys" propagating along axonal fibre bundles, we embedded the canonical microcircuit (CMC) model within the white matter cable model.
To generate time-frequency estimates, we extracted white matter geometric properties from diffusion MRI (dMRI) data from a subset of 95 subjects in the HCP 1200 data set, where both structure (dMRI) and functional data (MEG) were available. We used DSI Studio to perform tractography analysis on these data using the JHU White Matter Atlas. Derived measures (number of tracts, mean path length (mm), curl, diameter, and volume) were used as inputs into our generative model (Figure 2 a, b). The model was used to furnishing estimates of spike propagation velocities across fiber caliber and myelination for all white matter tracts for each subject. These estimates were used to generate time series and spectral density predictions for each subject.

Superposition of spectral predictions across all white matter tracts, produced time series and spectral decompositions across a range of ephaptic coupling strengths. Ephaptic coupling at a strengths of 10 or higher showed log-linear characteristics (Figure 2 c-h). A kappa of 12.5 had the maximum cross-correlation with the empirical MEG distribution. At a kappa of 15, there is a diminution in the higher frequency power, though the "alpha peak" appears to be correlate with the empirical data.

The subtle effect of ephaptic coupling may play an influential role in entraining neuronal signaling. Here, we showed that signaling along white matter fiber bundles may show 1/f characteristics, should the effects of ephaptic coupling be significant. While this phenomena is widely studied in the peripheral nervous system, it is unclear how prominent its effects are in brain. Further work and perturbation studies are needed to better understand ephaptic coupling, lead field embedding, and the potential for white matter signaling to contribute to EEG/MEG recordings.

EEG/MEG Modeling and Analysis ²

Other Methods ¹

Electroencephaolography (EEG)

MEG

Modeling