Skip to main content
Log in

Modelling the effects of electric fields on nerve fibres: Influence of the myelin sheath

  • Published:
Medical and Biological Engineering and Computing Aims and scope Submit manuscript

Abstract

The excitation and conduction properties of computer-based cable models of mammalian motor nerve fibres, incorporating three different myelin representations, are compared. The three myelin representations are a perfectly insulating single cable (model A), a finite impedance single cable (model B) and a finite impedance double cable (model C). Extracellular stimulation of the three models is used to study their strength-duration and current0distance (I–X) relationships, conduction velocity (CV) and action potential shape. All three models have a chronaxie time that is within the experimental range. Models B and C have increased threshold currents compared with model A, but each model has a slope to the I–X relationship that matches experimental results. Model B has a CV that matches experimental data, whereas the CV of models A and C are above and below the experimental range, respectively. Model C is able to produce a depolarising afterpotential (DAP), whereas models A and B exhibit hyperpolarising afterpotentials. Models A and B are determined to be the preferred models when low-frequency stimulation (<∼25Hz) is used, owing to their efficiency and accurate excitation and conduction properties. For high frequency stimulation (∼25Hz and greater), model C, with its ability to produce a DAP, is necessary accurately to simulate excitation behaviour.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Google Scholar 

  • Arbuthnott, E. R., Boyd, I. A., andKalu, K. U. (1980): ‘Ultrasimetural dimensions of myelinated peripheral nerve fibers in the eat and their relation to conduction velocity’,J. Physiol.,308, pp. 125–157

    Google Scholar 

  • Awiszus, F. (1990): ‘Effects of paranodal potassium permeability on repetitive activity of mammalian myelinated nerve fiber models’,Biol. Cybern.,64, pp. 69–76

    Article  Google Scholar 

  • Baker, M., Bostock, H., Grafe, P., andMartius, P. (1987): ‘Function and distribution of three types of rectifying channel in rat spinal root myelinated axons’,J. Physiol.,383, pp. 45–67

    Google Scholar 

  • Barrett, J. N., andCrill, W. E. (1974): ‘Specific membrane properties of cat motoneurones’,J. Physiol. (Lond.),239, pp. 301–324

    Google Scholar 

  • Barrett, E. F., andBarrett, J. N. (1982): ‘Intracellular recording from myelinated axons: mechanism of the depolarizing afterpotential’,J. Physiol. (Lond.),323, pp. 117–144

    Google Scholar 

  • Basser, P. J. (1993): ‘Cable equation for a myelinated axon derived from its microstructure’,Med. Biol. Eng. Comput.,31, pp. S87-S92

    Google Scholar 

  • BeMent, S. L., andRanck, J. B. (1969): ‘A quantitative study of electrical stimulation of central myelinated fibers’,Exp. Neurol.,24, pp. 147–170

    Google Scholar 

  • Berthold, C. H., Nilsson, I., andRydmark, M. (1983): ‘Axon diameter and myelin sheath thickness in nerve fibers of the ventral spinal root of the seventh lumbar nerve of the adult and developing cat’,J. Anat.,136, pp. 483–508

    Google Scholar 

  • Blaght, A. R. (1985): ‘Computer simulation of action potentials and afrepotentials in mammalian myelinated axons: the case for a lower resistance myelin sheath’,Neurosci.,15, pp. 13–31

    Google Scholar 

  • Blaght, A. R., andSomeya, S. (1985): ‘Depolarizing afterpotentials in myelinated axons of mammalian spinal cord’,Neurosci.,15, pp. 1–12

    Google Scholar 

  • Bostock, H., andSears, T.A. (1977): ‘The internodal axon membrane: electrical excitability and continuous conduction in segmental demyelination’,J. Physiol.,280, pp. 273–301

    Google Scholar 

  • Bostock, H., Baker, M., andReid, G. (1991): ‘Changes in excitability of human motor axons underlying post-ischaemic fasciculations: evidence for two stable states’,J. Physiol.,441, pp. 537–557

    Google Scholar 

  • Bostock, H., andRothwell, J.C. (1997): ‘Latent addition in motor and sensory fibers of human peripheral nerve’,J. Physiol.,313, pp. 277–294

    Google Scholar 

  • Boyd, I. A., andKalu, K. U. (1978): ‘Scaling factor relating conduction velocity and diameter for myelinated afferent nerve fibers in the cat hind limb’,J. Physiol.,289, pp. 277–297

    Google Scholar 

  • Brink, E. E., andMackel, R. G. (1993): ‘Time course of action potentials recorded from single human afferents’,Brain,116, pp. 415–432

    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 fibers’,Proc. R. Soc. Lond., B,220, pp. 415–422

    Google Scholar 

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

    MathSciNet  Google Scholar 

  • Frankenhaeuser, B., andHuxley, A. F. (1964): ‘The action potential in the myelinated nerve fiber ofXenopus Laevis as computed on the basis of voltage clamp data’,J. Physiol.,171, pp. 302–315

    Google Scholar 

  • Frijns, J. H. M., andten Kate, J. H. (1994): ‘A model of myelinated nerve fibers for electrical prosthesis design’,Med. Biol. Eng. Comput.,32, pp. 391–398

    Google Scholar 

  • Frijns, J. H. M., Mooij, J., andten Kate, J. H. (1994): ‘A quantitative approach to modeling mammalian myelinated nerve fibers for electrical prosthesis design’,IEEE Trans.,BME41, pp. 556–566

    Google Scholar 

  • Goldman, L., andAlbus, J. (1968): ‘Computation of impulse conduction in myelinated fibers: theoretical basis of the velocitydiameter relation’,Biophys. J.,8, pp. 596–607

    Google Scholar 

  • Halter, J., andClark, J. (1991): ‘A distributed-parameter model of the myelinated nerve fiber’,J. Theor. Biol.,148, pp. 345–382

    Google Scholar 

  • Hines, M. L., andCarnevale, N. T. (1997): ‘The NEURON simulation environment’,Neural Comput.,9, pp 1179–1209

    Google Scholar 

  • Huxley, A. F., andStampeli, R. (1949): ‘Evidence for saltatory conduction in peripheral myelinated nerve fibers’,J. Physiol.,108, pp. 315–339

    Google Scholar 

  • Jankowska, E., andRoberts, W. J. (1972): ‘An electrophysiological demonstration of the axonal projections of single spinal interneurones in the cat’,J. Physiol.,222, pp. 597–622

    Google Scholar 

  • Kocsis, J. D., Eng, D. L., Gordon, T. R., andWaxman, S. G. (1987): ‘Functional differences between 4-aminopyridine and tetraethylammonium-sensitive potassium channels in myelinated axons’,Neurosci. Lett.,75, pp. 193–198

    Article  Google Scholar 

  • McIntyre, C. C., andGrill, W. M. (1998a): ‘Sensitivity analysis of a model of mammalian neural membrane’,Biol. Cybern.,79, pp. 29–37

    Article  Google Scholar 

  • McIntyre, C. C., andGrill, W. M. (1998b): ‘Models of mammalian peripheral nerve: strength duration properties and anode break excitation’,Ann. Biomed. Eng.,26, pp. S103

    Google Scholar 

  • McNeal, D. R. (1976): ‘Analysis of a model for excitation of myelinated nerve’.IEEE Trans.,BME-23, pp. 329–337

    Google Scholar 

  • Moore, J. W., Joyner, R. W., Brill, M. H., Waxman, S., andNajar-Joa, M. (1978): ‘Simulations of conduction in uniform myelinated fibers. Relative sensitivity to changes in nodal and internodal parameters’,Biophys. J.,21, pp. 147–160

    Google Scholar 

  • Nilsson, I., andBerthold, C. H. (1988): ‘Axon classes and internodal growth in the ventral spinal root L7 of adult and developing cats’,J. Anat.,156, pp. 71–96

    Google Scholar 

  • Panizza, M., Nilsson, J., Roth, B. J., Rothwell, J., andHallett, M. (1994): ‘The time constant of motor and sensory peripheral nerve fibers measured with the method of latent addition’,Electroenceph. Clin. Neurophysiol.,93, pp. 147–154

    Google Scholar 

  • Panizza, M., Nilsson, J., Roth, B. J., Grill, S. E., Demirci, M., andHallett, M. (1998): ‘Differences between the time constant of sensory and motor peripheral nerve fibers: further studies and considerations’,Muscle Nerve.,21, pp. 48–54

    Article  Google Scholar 

  • Roberts, W. J., andSmith, D. O. (1973): ‘Analysis of threshold currents during microstimulation of fibers in the spinal cord’,Acta Physiol. Scand.,89, pp. 384–394

    Google Scholar 

  • Rubinstein, J. T. (1991): ‘Analytical theory for extracellular electrical stimulation of nerve with focal electrodes: II. Passive myelinated axon’,Biophys. J.,60, pp. 538–555

    Google Scholar 

  • Rydmark, M. (1981): ‘Nodal axon diameter correlates linearly with internodal axon diameter in spinal roots of the cat’,Neurosci. Lett.,24, pp. 247–250

    Article  Google Scholar 

  • Rydmark, M., andBerthold, C.-H. (1983): ‘Electron microscopic serial section analysis of nodes of Ranvier in lumbar spinal roots of the cat: a morphometric study of nodal compartments in fibers of different sizes’,J. Neurocyt.,12, pp. 537–565

    Google Scholar 

  • Safronov, B. V., Kampe, K., andVogel, W. (1993): ‘Single voltage dependent potassium channels in rat peripheral nerve membrane’,J. Physiol.,460, pp. 675–691

    Google Scholar 

  • Scholz, A., Reid, G., Vogel, W., andBostock, H. (1993): ‘Ion channels in human axons’,J. Neurophys.,70, pp. 1274–1279

    Google Scholar 

  • Schwarz, J. R., Reid, G., andBostock, H. (1995): ‘Action potentials and membrane currents in the human node of Ranvier’,Pflugers Arch.,430, pp. 283–292

    Article  Google Scholar 

  • Stephanova, D. I., andBostock, H. (1995): ‘A distributed-parameter model of the myelinated human motor nerve fiber: temporal and spatial distributions of action potentials and ionic currents’,Biol. Cybern.,73, pp. 275–280

    Google Scholar 

  • Stoney, S. D. Jr.,Thompson, W. D., andAsanuma, H. (1968): ‘Excitation of pyramidal tract cells by intracortical microstimulation: effective extent of stimulating current’,J. Neurophysiol.,31, pp. 659–69

    Google Scholar 

  • Sweeney, J. D., Durand, D., andMortimer, J. T. (1987): ‘Modeling of mammalian myelinated nerve for functional neuromuscular stimulation’, Proc. 9th Int. Conf.IEEE-EMBS,9, pp. 1577–1578

    Google Scholar 

  • Tasaki, I. (1955): ‘New measurements of the capacity and the resistance of the myelin sheath and the nodal membrane of the isolated frog nerve fiber’,Am. J. Physiol.,181, pp. 639–650

    Google Scholar 

  • Warman, E. N., Grill, W. M., andDurand, D. (1992): ‘Modeling the effects of electric fields on nerve fibers: determination of excitation the sholds’,IEEE Trans. Biomed. Eng.,39, pp. 1244–1254

    Article  Google Scholar 

  • Waxman, S. G., andRitchie, J. M. (1985): ‘Organization of ion channels in the myelinated nerve fiber’,Science,228, pp. 1502–1507

    Google Scholar 

  • Weiss, G. (1901): ‘Sur la possibilité de rendre comparables entre eux les appareils servant a l'excitation électrique’,Arch. Ital. Biol.,35, pp. 413–446 (ascited inBostock, H. (1983)J. Physiol.,341, pp. 59–74)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to W. M. Grill.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Richardson, A.G., McIntyre, C.C. & Grill, W.M. Modelling the effects of electric fields on nerve fibres: Influence of the myelin sheath. Med. Biol. Eng. Comput. 38, 438–446 (2000). https://doi.org/10.1007/BF02345014

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02345014

Keywords

Navigation