Theoretical basis for the hypothesis of white-matter resonance as a background of spike-wave discharges

It remains unclear how spike-wave discharges (SWDs) in electroencephalograms (EEGs) arise, although some researchers believe that there is some focus in the deep brain and others have pointed out the importance of the interaction between the thalami and cortices. My previous work hypothesized that possible resonance in white matter may induce extremely large amplitude discharges in an EEG, which are associated with SWDs. The visual evoked potential (VEP) technique revealed a resonance phenomenon that supports this hypothesis. In this research, I theoretically reconsidered the resonance phenomenon based on the cable theory modified by considering dielectric dispersion. If both the resistive and capacitive currents in the dielectric material contribute to conduction along an axon, we can show that the current amplitude has a single maximum at a certain frequency and this amplitude depends on the geometrical ratio of capacitance to resistance. The frequency can be common for any axon in a wide white-matter area. We can infer that SWDs will arise, when the frequency generated by the thalamic reticular nucleus neurons coincides with the resonance frequency of the white matter. The resonance frequency predicted by the modified theory is close to the known frequency of the SWDs.