Electroencephalographic field influence on calcium momentum waves

Macroscopic EEG fields can be an explicit top-down neocortical mechanism that directly drives bottom-up processes that describe memory, attention, and other neuronal processes. The top-down mechanism considered are macrocolumnar EEG firings in neocortex, as described by a statistical mechanics of neocortical interactions (SMNI), developed as a magnetic vector potential $mathbf{A}$. The bottom-up process considered are $mathrm{Ca}^{2+}$ waves prominent in synaptic and extracellular processes that are considered to greatly influence neuronal firings. Here, the complimentary effects are considered, i.e., the influence of $mathbf{A}$ on $mathrm{Ca}^{2+}$ momentum, $mathbf{p}$. The canonical momentum of a charged particle in an electromagnetic field, $mathbf{Pi} = mathbf{p} + q mathbf{A}$ (SI units), is calculated, where the charge of $mathrm{Ca}^{2+}$ is $q = - 2 e$, $e$ is the magnitude of the charge of an electron. Calculations demonstrate that macroscopic EEG $mathbf{A}$ can be quite influential on the momentum $mathbf{p}$ of $mathrm{Ca}^{2+}$ ions, in both classical and quantum mechanics. Molecular scales of $mathrm{Ca}^{2+}$ wave dynamics are coupled with $mathbf{A}$ fields developed at macroscopic regional scales measured by coherent neuronal firing activity measured by scalp EEG. The project has three main aspects: fitting $mathbf{A}$ models to EEG data as reported here, building tripartite models to develop $mathbf{A}$ models, and studying long coherence times of $mathrm{Ca}^{2+}$ waves in the presence of $mathbf{A}$ due to coherent neuronal firings measured by scalp EEG. The SMNI model supports a mechanism wherein the $mathbf{p} + q mathbf{A}$ interaction at tripartite synapses, via a dynamic centering mechanism (DCM) to control background synaptic activity, acts to maintain short-term memory (STM) during states of selective attention.