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Dipole theory of interactions of nerve signals

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Abstract

Based upon the transition rate equation of dipoles in the membrane, we deal with two important aspects of interaction of nerve signals: (1) conditions for nerve excitation and (2) frequency spectrum analysis of nerve impulse. Interrelations between signal amplitudes and frequencies are formulated in detail. There are several important conclusions which can be drawn from our calculations. First, toexcite the nerve, low frequencies are generally more effective than high frequencies. Second, tosedate the nerve (i.e. to suppress undesired activities), high frequencies would suit better. Third, harmonics produced through interactions of nerve signals are not necessarily weaker than the fundamental frequencies. The great significance of our theory is that it indicates in principle the feasibility to alter or rewrite the information contents of a nerve message in our body by applying stimulations of appropriate strengths and frequencies. Thus, the theory provides a physical basis and hence some understanding for a new branch of medicine—neuro therapy such as Nogier's auriculotherapy, Lamy's phonophoresis, Voll's electroacupuncture and the fast rising TENS (transcutaneous electro-neuro stimulation).

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Literature

  • Agin, D., L. Hersh and D. Holtzman. 1965. “The action of anesthetics on excitable membranes: A quantum chemical analysis”.Proc. Natn Acad. Sci. U.S.A.,53, 952–958.

    Article  Google Scholar 

  • Blaustein, M. P. and D. E. Goldman. 1966. “Action of anionic and cationic nerve-blocking agents: Experimental and interpretation”.Science,153, 429–432.

    Google Scholar 

  • Burton, C. and D. D. Maurer. 1974. “Pain suppression by transcutaneous electronics stimulation”.IEEE Trans. BME,21, 81–88.

    Google Scholar 

  • Chiang, C. 1978. “On the nerve impulse equation: The dynamical responses of nerve impulse.Bull. Math. Biol.,40, 247–256.

    Article  MathSciNet  Google Scholar 

  • Frankenhaeuser, B. and A. L. Hodgkin. 1957. “The action of calcium on the electrical properties of squid axon”.J. Physiol. Lond.,137, 218–244.

    Google Scholar 

  • Frazee, J. S. 1975. “Experimental harmonic progression and simultaneous dual frequency stimulation”.Am. J. Acup.,3, 315–324.

    Google Scholar 

  • Gilbert, D. L. and G. Ehrenstein, 1969. “Effect of divalent cations on potassium conductance of squid axons: Determination of surface charge”.Biophys. J.,9, 447–463.

    Google Scholar 

  • Hill, A. V. 1936. “Excitation and accommodation in nerve”.Proc. R. Soc. Lond., B119, 305–355.

    Google Scholar 

  • Hodson, C. and L. Y. Wei. 1976. “Comparative evaluation of quantum theory of nerve excitation”.Bull. Math. Biol.,38, 277–293.

    Article  MATH  Google Scholar 

  • Kittel, C. 1963.Quantum Theory of Solids, pp. 69–70. New York, John Wiley.

    Google Scholar 

  • Lamy, J. 1967. 1969.Acupuncture Phonophorèse-Technique, Clinique. Tome I; Tome II. Librairie Maloine. S.A. Paris.

    Google Scholar 

  • Lee, C. Y. and C. Chiang. 1976. “Nerve excitations by the coupling of dipoles and the membrane matrix”.Bull. Math. Biol.,38, 59–70.

    Article  MATH  Google Scholar 

  • Loeser, J. D.,et al. 1975. “Relief of pain by transcutaneous stimulation”.J. Neurosurg.,42, 308–314.

    Article  Google Scholar 

  • Narahashi, T. 1971. “Neurophysiological basis for drug action: Ionic mechanism, site of action and active form in nerve fibres”. InBiophysics and Physiology of Excitable Membranes, Ed. W. J. Adelman, Jr., pp. 423–462. New York: Van Nostrand Reinhold.

    Google Scholar 

  • Nogier, P. F. M. 1972.Treatise of Auriculo-therapy. Maisonneuve, Moulins-Les-Metz, France.

    Google Scholar 

  • Rashevsky, N. 1933. “Outline of a physico-mathematical theory of excitation and inhibition”.Protoplasma,20, 42–56.

    Google Scholar 

  • Singer, J. R. 1959.Masers. New York: John Wiley.

    Google Scholar 

  • Solandt, D. Y.. 1936. “The measurement of accommodation in nerve”.Proc. R. Soc. Lond.,B119, 355–379.

    Article  Google Scholar 

  • Tany, M. and S. Sawatsuga. 1975. “New development: electromagnetic acupuncture”.Am. J. Acup.,3, 58–66.

    Google Scholar 

  • Veale, J. R. 1976.Report on Transcutaneous electrical nerve stimulation for pain relief. Food and Drug Adm., Washington, D.C..

    Google Scholar 

  • Voll, R. 1974.Kopf herde-Diagnostik und Therapie Mittels Elektroakupunktur. Uelzen. Germany: ML. Verlag.

    Google Scholar 

  • — 1975. “Twenty years of electroacupuncture therapy using low-frequency current pulses”.Am. J. Acup.,3, 291–314.

    Google Scholar 

  • Wei, L. Y., 1969a. “Role of surface dipoles on axon membrane.”Science,163, 280–282.

    Google Scholar 

  • —. 1969b. “Molecular mechanisms of nerve excitation and conduction”.Bull. Math. Biophys.,31, 39–58.

    Google Scholar 

  • —. 1971a. “Quantum theory of nerve excitation”.Bull. Math. Biophys.,33, 187–194.

    Google Scholar 

  • —. 1971b. “Possible origin of action potential and birefringence change in nerve axon”.Bull. Math. Biophys.,33, 521–537.

    Google Scholar 

  • — 1972. “Dipole theory of heat production and absorption in nerve axon”.Biophys. J.,12, 1159–1170.

    Article  Google Scholar 

  • — 1973. Quantum theory of time-varying stimulation in nerve.Bull. Math. Biol.,35, 359–374.

    MATH  Google Scholar 

  • — 1974. “Dipole mechanisms of electrical, optical and thermal energy transductions in nerve membrane”.Ann. N. Y. Acad. Sci.,272, 285–293.

    Google Scholar 

  • —, and C. Hodson. 1977. “Nerve transmission and acupuncture mechanism”.Am. J. Acup.,5, 69–83.

    Google Scholar 

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Wei, L.Y. Dipole theory of interactions of nerve signals. Bltn Mathcal Biology 42, 79–94 (1980). https://doi.org/10.1007/BF02462367

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  • DOI: https://doi.org/10.1007/BF02462367

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