Skip to main content
Biophysical Journal logoLink to Biophysical Journal
. 1991 Sep;60(3):538–555. doi: 10.1016/S0006-3495(91)82084-7

Analytical theory for extracellular electrical stimulation of nerve with focal electrodes. II. Passive myelinated axon.

J T Rubinstein 1
PMCID: PMC1260098  PMID: 1932546

Abstract

The cable model of a passive, myelinated fiber is derived using the theory of electromagnetic propagation in periodic structures. The cable may be excited by an intracellular source or by an arbitrary, time-varying, applied extracellular field. When the cable is stimulated by a distant source, its properties are qualitatively similar to an unmyelinated fiber. Under these conditions relative threshold is proportional to the cube of the source distance and inversely proportional to the square of the fiber diameter. Electrical parameters of the model are chosen where possible, from mammalian peripheral nerve and anatomic parameters from cat auditory nerve. Several anatomic representations of the paranodal region are analyzed for their effects on the length and time constants of the fibers. Sensitivity of the model to parameter changes is studied. The linear model reliably predicts the effects of fiber size and electrode-fiber separation on threshold of cat dorsal column fibers to extracellular electrical stimulation.

Full text

PDF
538

Images in this article

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Altman K. W., Plonsey R. Analysis of the longitudinal and radial resistivity measurements of the nerve trunk. Ann Biomed Eng. 1989;17(4):313–324. doi: 10.1007/BF02368054. [DOI] [PubMed] [Google Scholar]
  2. Altman K. W., Plonsey R. Development of a model for point source electrical fibre bundle stimulation. Med Biol Eng Comput. 1988 Sep;26(5):466–475. doi: 10.1007/BF02441913. [DOI] [PubMed] [Google Scholar]
  3. Andrietti F., Bernardini G. Segmented and "equivalent" representation of the cable equation. Biophys J. 1984 Nov;46(5):615–623. doi: 10.1016/S0006-3495(84)84060-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  4. Arnesen A. R., Osen K. K. The cochlear nerve in the cat: topography, cochleotopy, and fiber spectrum. J Comp Neurol. 1978 Apr 15;178(4):661–678. doi: 10.1002/cne.901780405. [DOI] [PubMed] [Google Scholar]
  5. Barrett E. F., Barrett J. N. Intracellular recording from vertebrate myelinated axons: mechanism of the depolarizing afterpotential. J Physiol. 1982 Feb;323:117–144. doi: 10.1113/jphysiol.1982.sp014064. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. BeMent S. L., Ranck J. B., Jr A model for electrical stimulation of central myelinated fibers with monopolar electrodes. Exp Neurol. 1969 Jun;24(2):171–186. doi: 10.1016/0014-4886(69)90013-2. [DOI] [PubMed] [Google Scholar]
  7. BeMent S. L., Ranck J. B., Jr A quantitative study of electrical stimulation of central myelinated fibers. Exp Neurol. 1969 Jun;24(2):147–170. doi: 10.1016/0014-4886(69)90012-0. [DOI] [PubMed] [Google Scholar]
  8. Black J. A., Kocsis J. D., Waxman S. G. Ion channel organization of the myelinated fiber. Trends Neurosci. 1990 Feb;13(2):48–54. doi: 10.1016/0166-2236(90)90068-l. [DOI] [PubMed] [Google Scholar]
  9. Bostock H. The strength-duration relationship for excitation of myelinated nerve: computed dependence on membrane parameters. J Physiol. 1983 Aug;341:59–74. doi: 10.1113/jphysiol.1983.sp014792. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Brismar T. Electrical properties of isolated demyelinated rat nerve fibres. Acta Physiol Scand. 1981 Oct;113(2):161–166. doi: 10.1111/j.1748-1716.1981.tb06877.x. [DOI] [PubMed] [Google Scholar]
  11. Brismar T. Potential clamp analysis of membrane currents in rat myelinated nerve fibres. J Physiol. 1980 Jan;298:171–184. doi: 10.1113/jphysiol.1980.sp013074. [DOI] [PMC free article] [PubMed] [Google Scholar]
  12. Colombo J., Parkins C. W. A model of electrical excitation of the mammalian auditory-nerve neuron. Hear Res. 1987 Dec 31;31(3):287–311. doi: 10.1016/0378-5955(87)90197-3. [DOI] [PubMed] [Google Scholar]
  13. Dun F. T. The length and diameter of the node of Ranvier. IEEE Trans Biomed Eng. 1970 Jan;17(1):21–24. doi: 10.1109/tbme.1970.4502680. [DOI] [PubMed] [Google Scholar]
  14. FITZHUGH R. Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber. Biophys J. 1962 Jan;2:11–21. doi: 10.1016/s0006-3495(62)86837-4. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. FitzHugh R. Dimensional analysis of nerve models. J Theor Biol. 1973 Aug 22;40(3):517–541. doi: 10.1016/0022-5193(73)90008-8. [DOI] [PubMed] [Google Scholar]
  16. Goldman L., Albus J. S. Computation of impulse conduction in myelinated fibers; theoretical basis of the velocity-diameter relation. Biophys J. 1968 May;8(5):596–607. doi: 10.1016/S0006-3495(68)86510-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Liberman M. C., Oliver M. E. Morphometry of intracellularly labeled neurons of the auditory nerve: correlations with functional properties. J Comp Neurol. 1984 Feb 20;223(2):163–176. doi: 10.1002/cne.902230203. [DOI] [PubMed] [Google Scholar]
  18. McNeal D. R. Analysis of a model for excitation of myelinated nerve. IEEE Trans Biomed Eng. 1976 Jul;23(4):329–337. doi: 10.1109/tbme.1976.324593. [DOI] [PubMed] [Google Scholar]
  19. Neumcke B., Stämpfli R. Sodium currents and sodium-current fluctuations in rat myelinated nerve fibres. J Physiol. 1982 Aug;329:163–184. doi: 10.1113/jphysiol.1982.sp014296. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Noble D., Stein R. B. The threshold conditions for initiation of action potentials by excitable cells. J Physiol. 1966 Nov;187(1):129–162. doi: 10.1113/jphysiol.1966.sp008079. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Paintal A. S. The influence of diameter of medullated nerve fibres of cats on the rising and falling phases of the spike and its recovery. J Physiol. 1966 Jun;184(4):791–811. doi: 10.1113/jphysiol.1966.sp007948. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Parkins C. W., Colombo J. Auditory-nerve single-neuron thresholds to electrical stimulation from scala tympani electrodes. Hear Res. 1987 Dec 31;31(3):267–285. doi: 10.1016/0378-5955(87)90196-1. [DOI] [PubMed] [Google Scholar]
  23. Plonsey R., Barr R. C. A critique of impedance measurements in cardiac tissue. Ann Biomed Eng. 1986;14(4):307–322. doi: 10.1007/BF02367405. [DOI] [PubMed] [Google Scholar]
  24. RANCK J. B., Jr, BEMENT S. L. THE SPECIFIC IMPEDANCE OF THE DORSAL COLUMNS OF CAT: AN INISOTROPIC MEDIUM. Exp Neurol. 1965 Apr;11:451–463. doi: 10.1016/0014-4886(65)90059-2. [DOI] [PubMed] [Google Scholar]
  25. Rattay F. Analysis of models for extracellular fiber stimulation. IEEE Trans Biomed Eng. 1989 Jul;36(7):676–682. doi: 10.1109/10.32099. [DOI] [PubMed] [Google Scholar]
  26. Reilly J. P., Freeman V. T., Larkin W. D. Sensory effects of transient electrical stimulation--evaluation with a neuroelectric model. IEEE Trans Biomed Eng. 1985 Dec;32(12):1001–1011. doi: 10.1109/TBME.1985.325509. [DOI] [PubMed] [Google Scholar]
  27. Rubinstein J. T., Spelman F. A. Analytical theory for extracellular electrical stimulation of nerve with focal electrodes. I. Passive unmyelinated axon. Biophys J. 1988 Dec;54(6):975–981. doi: 10.1016/S0006-3495(88)83035-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  28. SCOTT A. C. ANALYSIS OF A MYELINATED NERVE MODEL. Bull Math Biophys. 1964 Sep;26:247–254. doi: 10.1007/BF02479046. [DOI] [PubMed] [Google Scholar]
  29. Scott A. C. More on myelinated nerve model analysis. Bull Math Biophys. 1967 Jun;29(2):363–371. doi: 10.1007/BF02476907. [DOI] [PubMed] [Google Scholar]
  30. TASAKI I. 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. 1955 Jun;181(3):639–650. doi: 10.1152/ajplegacy.1955.181.3.639. [DOI] [PubMed] [Google Scholar]
  31. Veltink P. H., van Alsté J. A., Boom H. B. Simulation of intrafascicular and extraneural nerve stimulation. IEEE Trans Biomed Eng. 1988 Jan;35(1):69–75. doi: 10.1109/10.1338. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES