Ionic waves in animal tissues

A proof is given that self-sustaining ionic-wave propagations—heuristically inferred by the author in a previous paper [Phys. Rev. A 32, 3618 (1985)] concerning a new holographic theory of animal memory—are possible in animal tissues at normal physiological conditions. The proof is obtained by standard electrochemical methods purely on the basis of well-known properties of cell membranes and of molecular devices found in them. It is shown that interstitial pockets filled with extracellular fluid, when viewed as functional units dispersed all over the cell tissue, promote ion currents proportionally to linear combinations of macroscopic sodium and potassium concentration gradients. Oscillations of sodium and potassium macroscopic concentrations prove to be possible thanks to the voltage-driven amplification function for ion fluxes exerted by ${\mathrm{Na}}^{+}$-${\mathrm{K}}^{+}$-ATPase (adenosinetriphosphatase) pumps and to the feedback control role exerted by the (${\mathrm{Na}}^{+}$ antiports ${\mathrm{Ca}}^{2+}$)→(${\mathrm{Ca}}^{2+}$ activates ${\mathrm{K}}^{+}$) channel system. All steps in deriving the wave equations are coarse-graining invariant; this ensures the correctness of the macroscopic view in treating the problem. Theoretical wave patterns and their general features are in excellent agreement with EEG (electroencephalogram) patterns detected on brain cortices and on scalps. Epileptic foci artificially generated by injection of ${\mathrm{Na}}^{+}$ ions into glial tissue and inhibition of EEG by ${\mathrm{K}}^{+}$ superfusion of brain cortex, are correctly accounted for by the theory.