Abstract
Starting with the spatially extended non-linear node model (Reilly et al., 1985), which incorporates Frankenhaeuser-Huxley non-linearities at each of several nodes in a row, a model is developed to describe many aspects of the behaviour of mammalian nerve fibres in a quantitative way. By taking into account the effects of temperature and by introducing a realistic nerve morphology, a good fit is obtained between the shape, duration and conduction velocity of simulated and in vivo action potentials in mammals. The resulting model correctly predicts the influence of physiological variations of body temperature on various aspects of nerve behaviour. It is shown that the absolute refractory period predicted by the model is within physiological ranges. Both in vivo and in the model, the spike amplitude and the spike conduction velocity are reduced in the relative refractory period. It is concluded that single-node models (although widely used) cannot replace this multiple nonlinear node model, as the stimulus repetition rates that can be followed by the simulated nerve fibre are limited by impulse conduction properties, rather than by the frequency following behaviour of a single node.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Boyd, I. A., andKalu, K. U. (1979): ‘Scaling factor relating conduction velocity and diameter for myelinated afferent nerve fibres in the cat hind limb’,J. Physiol. Lond.,289, pp. 277–297
Brismar, T. (1980): ‘Potential clamp analysis of membrane currents in rat myelinated nerve fibres’, ——Ibid.,298, pp. 171–184
Chu, S. Y., Ritchie, J. M., Rogart, R. B., andStagg, D. (1979): ‘A quantitative description of membrane currents in rabbit myelinated nerve’, ——Ibid.,292, pp. 149–166.
Colombo, J., andParkins, C. W. (1987): ‘A model of electrical excitation of the mammalian auditory-nerve neuron,Hear. Res.,31, pp. 287–312
Frankenhaeuser, B., andMoore, L. E. (1963): ‘The effect of temperature on sodium and potassium permeability changes in myelinated nerve fibres of Xenopus Laevis,’J. Physiol. Lond.,169, pp. 431–437
Frankenhaeuser, B., andHuxley, A. F. (1964): ‘The action potential in the myelinated nerve fibre of Xenopus laevis as computed on the basis of voltage clamp data’, ——ibid.,171, pp. 302–315
Fruns, J. H. M., andSchoonhoven, R. (1992): ‘Refractoriness and Frequency Following Behavior in a Model of Electrical Stimulation of Mammalian Myelinated Nerve Fibres,’Proc. Ann. Conf. IEEE-EMBS,14, pp. 1372–1373
Gaumond, R. P., Molnar, C. E., andKim, D. O. (1982): ‘Stimulus and recovery dependence of cat cochlear nerve fibre spike discharge probability,’J. Neurophysiol.,48, pp. 856–873
Gorman, P. H., andMortimer, J. T. (1983): ‘The effect of stimulus parameters on the recruitment characteristics of direct nerve stimulation,”IEEE Trans.,BME-60, pp. 407–414
Guyton, A. C. (1981): ‘Textbook of medical physiology’, (W. B. Saunders Company, Philadelphia) pp. 41–54
Halter, J. A., andClark, J. W. Jr. (1991): ‘A distributed-parameter model of the myelinated nerve fibre.J. Theor. Biol.,148, pp. 345–382
Hess, A., andYoung, J. Z. (1949): ‘Correlation of internodal length and fibre diameter in the central nervous system,’Nature,164, pp. 490–491
Hursh, J. B. (1939): ‘Conduction velocity and diameter of nerve fibres,’Am. J. Physiol.,127, pp. 131–139
McNeal, D. R. (1976): ‘Analysis of a model for excitation of myelinated nerve,’IEEE Trans.,BME-23, pp. 329–337
Meier, J. H., Rutten, W. L. C., Zoutman, A. E., Boom, H. B. K., andBergveld, P. (1992): ‘Simulation of multipolar fibre selective neural stimulation using intrafascicular electrodes’,IEEE Trans.,BME-39, pp. 122–134
Moore, J. W., Joyner, R. W., Brill, M. H., Waxman, S. D., andNajar-Joa, M. (1978): ‘Simulations of conduction in uniform myelinted fibres: relative sensitivity to changes in nodal and internodal parameters,’Biophys. J.,21, pp. 147–160
Motz, H., andRattay, F. (1986): ‘A study of the application of the Hodgkin-Huxley and the Frankenhaeuser-Huxley model for electrostimulation of the acoustic nerve,’Neursci.,18, pp. 699–712
Paintal, A. S. (1966): ‘The influence of diameter of medullated nerve fibres of cat on the rising and falling phase of the spike and its recovery,’J. Physiol. Lond.,184, pp. 791–811
Paintal, A. S. (1973): ‘Conduction in mammalian nerve fibres’in Desmedt, J. E. (Ed.): New developments in electromyography and clinical neurophysiology’ (Karger, Basel) pp. 19–41
Press, W. H., Flannery, B. P., Teukolsky, S. A., andVetterling, W. T. (1988): ‘Numerical recipes: the art of scientific computing’ (Cambridge University Press, Cambridge) pp. 547–560
Panck, J. B. Jr. (1975): ‘Which elements are excited in electrical stimulation of mammalian central nervous system: a review,’Brain Res.,98, pp. 417–440
Reilly, J. P., Freeman, V. T., andLarkin, W. D. (1985): ‘Sensory effects of transient electrical stimulation: evaluation with a neuroelectrical model,’IEEE Trans.,BME-32, pp. 1001–1011
Reilly, J. P., andBauer, R. H. (1987). ‘Application of a neuroelectric model to electrocutaneous sensory sensitivity: parameter variation study,’IEEE Trans.,BME-34, pp. 752–754
Reilly, J. P. (1989): ‘Peripheral nerve stimulation by induced electrical currents: exposure to time-varying magnetic fields,’Med. Biol. Eng. Comput.,27, (2), pp. 101–110
Schoepfle, G. M., andErlanger, J. (1941): ‘The action of temperature on the excitability, spike height and configuration, and the refractory period observed in the responses of single medullated nerve fibres,’Am. J. Physiol.,134, pp. 694–704
Schwarz, J. R., andEikhof, G. (1987): ‘Na currents and action potentials in rat myelinated nerve fibres at 20 and 37°C”,Pflügers Arch.,409, pp. 569–577
Stegeman, D. F., De Weerd, J. P. C., andNotermans, S. L. H. (1983): ‘Modelling compound action potential of peripheral nerves in situ III: nerve propagation in the refractory period”,Electroenceph. Clin. Neurophysiol.,55, pp. 668–679
Struijk, J. J., Holsheimer, J., van der Heide, G. G., andBoom, H. B. K. (1992): ‘Recruitment of dorsal column fibres in spinal cord stimulation: influence of collateral branching’,IEEE Trans.,BME-9, pp. 903–912
Sweeney, J. D., Mortimer, J. T., andDurand, D. (1987): ‘Modelling of mammalian myelinated nerve for functional neuromuscular stimulation’,Proc. Ann. Conf. IEEE-EMBS,9, pp. 1577–1578
Tasaki, I. (1982): ‘Physiology and electrochemistry of nerve fibres’ (Academic Press, New York)
Tyler, R. S., Moore, B. C. J., andKuk, F. K. (1989): ‘Performance of some of the better cochlear-implant patients,’J. Speech. Hear. Res.,32, pp. 887–911
Veltink, P. H., van Alste, J. A., andBoom, H. B. K. (1989): ‘Multielectrode intrafascicular and extraneural stimulation’,Med. Biol. Eng. Comput.,27, (1), pp. 19–24
Warman, E. N., Grill, W. M., andDurand, D. (1992): ‘Modeling the effects of electric fields on nerve fibres: determination of excitation thresholds’,IEEE Trans.,BME-39, pp. 1244–1254
Waxman, S. G. (1978): ‘Variations in axonal morphology and their functional significance’ inWaxman, S. G. (Ed.), Physiology and pathobiology of axons’, (Raven Press, New York) pp. 169–174
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Frijns, J.H.M., ten Kate, J.H. A model of myelinated nerve fibres for electrical prosthesis design. Med. Biol. Eng. Comput. 32, 391–398 (1994). https://doi.org/10.1007/BF02524690
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02524690