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Stimulation of a myelinated nerve axon by electromagnetic induction

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Abstract

A model of electromagnetic stimulation predicts the transmembrane potential distribution along a myelinated nerve axon and the volume of stimulated tissue within a limb. Threshold stimulus stregth is shown to be inversely proportional to the square of the axon diameter. It is inversely proportional to pulse duration for short pulses and independent of pulse duration for long ones. These results are also predicted by dimensional analysis. Two dimensionless numbers, Sem, the ratio of the induced transmembrane potential to the axon's threshold potential, and Tc/T, the ratio of the pulse duration to the membrane time constant, summarise the dependence of threshold stimulus strength on pulse duration and axon diameter.

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References

  • Altman, K. W. andPlonsey, R. (1988) Development of a model for point source electrical fibre bundle stimulation.Med. & Biol. Eng. & Comput.,26, 466–475.

    Article  Google Scholar 

  • Andrietti, F. andBernardini, G. (1984) Segmented and ‘equivalent’ representation of the cable equation.Biophys. J.,46, 615–623.

    Google Scholar 

  • Barker, A. T., Jalinous, R. andFreeston, I. L. (1985) Noninvasive magnetic stimulation of human motor cortex.Lancet,1, 1106–1107.

    Article  Google Scholar 

  • Bickford, R. G. andFremming, B. D. (1965) Neuronal stimulation by pulsed magnetic fields in animals and man. Dig. 6th Int. Conf. Med. Electronics Biol. Eng., 112.

  • Chiu, S. Y., Ritchie, J. M., Rogart, R. B. andStagg, D. (1979) A quantitative description of membrane currents in rabbit myelinated nerve.Lond. J. Physiol.,292, 149–166.

    Google Scholar 

  • Chiu, S. Y. andRitchie, J. M. (1984) On the physiological role of internodal potassium channels and the security of conduction in myelinated nerve fibres.Proc. R. Soc. Lond. B,220, 415–422.

    Google Scholar 

  • Chokroverty, S. (1989) Magnetic stimulation of the human peripheral nerves.Electromyogr. Clin. Neurophysiol.,29, 409–416.

    Google Scholar 

  • Cohen, L. G., Roth, B. J., Nilsson, J., Dang, N., Panizza, M., Bandinelli, S., Friauf, W. andHallett, M. (1990a) Effect of coil design on delivery of focal magnetic stimulation. I. Technical considerations.Electroenceph. Clin. Neutrophysiol.,75, 350–357.

    Article  Google Scholar 

  • Cohen, M. S., Weisskopf, R. O., Rzedzian, H. L. andKantor, H. L. (1990b) Sensory stimulation by time-varying magnetic fields.Magn. Reson. Med.,14, 409–414.

    Google Scholar 

  • Evans, B. A., Litchy, W. J. andDaube, J. R. (1988) The utility of magnetic stimulation for routine peripheral nerve conduction studies.Muscle & Nerve,11, 1074–1078.

    Article  Google Scholar 

  • Fitzhugh, R. (1962) Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber.Biophys. J.,2, 11–21.

    MathSciNet  Google Scholar 

  • Fitzhugh, R. (1969) Mathematical models of excitation and propagation in nerve. InBiological engineering.Schwan, H. (Ed.), McGraw-Hill, 1–83.

  • Geddes, L. A. (1988) Optimal stimulus duration for extracranial cortical stimulation.Neurosurg.,20, 94–99.

    Google Scholar 

  • Goldman, L. andAlbus, J. S. (1968) Computation of impulse conduction in myelinated fibers: theoretical basis of the velocity-diameter relation.Biophys. J.,8, 596–607.

    Article  Google Scholar 

  • Hallett, M. andCohen, L. G. (1989) Magnetism: a new method for stimulation of nerve and brain.JAMA,262, 538–541.

    Article  Google Scholar 

  • Kelier, J. B. (1977) Effective behavior of heterogeneous media, InStatistical mechanics and statistical methods. InTheory and applications.Landman, U. (Ed.) Plenum Press, New York, 631–644.

    Google Scholar 

  • Keller, J. B. (1980) Darcy's law for flow in porous media and the two-space method. InNonlinear partial equations. InEngineering and applied science,Sternberg,R. L.,Kalinowski,A. J. andPapadakis,J. S. (Eds.), Marcel Dekker, New York, 429–443.

    Google Scholar 

  • Plonsey, R. (1969)Bioelectric phenomena. McGraw-Hill, New York.

    Google Scholar 

  • Polson, M. J. R., Barker, A. T. andFreeston, I. L. (1982) Stimulation of nerve trunks with time-varying magnetic fields.Med. & Biol. Eng. & Comput.,20, 243–244.

    Article  Google Scholar 

  • Rattay, F. (1986) Analysis of models for external stimulation of axons.IEEE Trans.,BME-33, 974–977.

    Google Scholar 

  • Rattay, F. (1987) Ways to approximate current-distance relations for electrically stimulated fibers.J. Theor. Biol.,125, 339–349.

    Article  Google Scholar 

  • Rattay, F. (1988) Modeling the excitation of fibers under surface electrodes.IEEE Trans.,BME-35, 199–202.

    Google Scholar 

  • Ritchie, J. M. (1982) On the relation between fibre diameter and conduction velocity in myelinated nerve fibres.Proc. R. Soc. Lond. B,217, 29–35.

    Article  Google Scholar 

  • Roth, B. J. andBasser, P. J. (1990) A model of the stimulation of a nerve fiber by electromagnetic induction.IEEE Trans.,BME-37, 588–597.

    Google Scholar 

  • Roth, B. J., Cohen, L. G., Hallett, M., Friauf, W. andBasser, P. J. (1990) A theoretical calculation of the electric field induced by magnetic stimulation of a peripheral nerve.Muscle & Nerve,13, 734–741.

    Article  Google Scholar 

  • Rushton, W. A. H. (1951) A theory of the effects of fibre size in medullated nerve.J. Physiol. (London),115, 101–122.

    Google Scholar 

  • Sweeney, J. D., Mortimer, J. T. andDurand, D. (1987) Modeling of mammalian myelinated nerve for functional neuromuscular stimulation. In Proc. of the 9th Ann. Conf. of IEEE EMBS, 1577–1578.

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Basser, P.J., Roth, B.J. Stimulation of a myelinated nerve axon by electromagnetic induction. Med. Biol. Eng. Comput. 29, 261–268 (1991). https://doi.org/10.1007/BF02446708

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  • DOI: https://doi.org/10.1007/BF02446708

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