Abstract
The equation for the quantum transitions (spontaneous and stimulated) of membrane dipoles is solved for the various forms of time-varying stimulation in nerve. From the condition of ever-increasing dipole population in the upper state, the threshold for excitation is determined in each case. The results obtained are in agreement with the established facts. The optimum frequency for stimulation is given asv 0=0.0615/T 2 whereT 2 is the dipole relaxation time. The feature of the theory is that the mathematical formulation is based upon a physical mechanism and the results can thus provide some understanding in the observed phenomena.
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Literature
Hill, A. V. 1936. “Excitation and Accommodation in Nerve.”Proc. Roy. Soc. (London),B119, 305–355.
Hill, A. V., B. Katz and D. Y. Solandt. 1936. “Nerve Excitation by Alternating Current.” —Ibid. 121, 74–133.
Lengyel, B. A. 1971.Lasers. New York: Wiley.
Rashevsky, N. 1960.Mathematical Biophysics. Vol. 1 Chapters XXXII and XXXIII. New York: Dover Publications.
Solandt, D. Y. 1936. “A Comparison of Various Methods of Measuring the Time Constants of Accommodation of Nerve.”Proc. Roy. Soc. (London),B120, 389–408.
Wei, L. Y. 1969. “Molecular Mechanisms of Nerve Excitation and Conduction.”Bull. Math. Biophysics,31, 39–58.
— 1971. “Quantum Theory of Nerve Excitation.” —Ibid.,33, 187–194.
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Wei, L.Y. Quantum theory of time-varying stimulation in nerve. Bltn Mathcal Biology 35, 359–374 (1973). https://doi.org/10.1007/BF02458343
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DOI: https://doi.org/10.1007/BF02458343