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.
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Andrietti, F., andBernardini, G. (1984): ‘Segmented and ‘equivalent’ representation of the cable equation’,Biophys. J.,46, pp. 615–623
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
Awiszus, F. (1990): ‘Effects of paranodal potassium permeability on repetitive activity of mammalian myelinated nerve fiber models’,Biol. Cybern.,64, pp. 69–76
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
Barrett, J. N., andCrill, W. E. (1974): ‘Specific membrane properties of cat motoneurones’,J. Physiol. (Lond.),239, pp. 301–324
Barrett, E. F., andBarrett, J. N. (1982): ‘Intracellular recording from myelinated axons: mechanism of the depolarizing afterpotential’,J. Physiol. (Lond.),323, pp. 117–144
Basser, P. J. (1993): ‘Cable equation for a myelinated axon derived from its microstructure’,Med. Biol. Eng. Comput.,31, pp. S87-S92
BeMent, S. L., andRanck, J. B. (1969): ‘A quantitative study of electrical stimulation of central myelinated fibers’,Exp. Neurol.,24, pp. 147–170
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
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
Blaght, A. R., andSomeya, S. (1985): ‘Depolarizing afterpotentials in myelinated axons of mammalian spinal cord’,Neurosci.,15, pp. 1–12
Bostock, H., andSears, T.A. (1977): ‘The internodal axon membrane: electrical excitability and continuous conduction in segmental demyelination’,J. Physiol.,280, pp. 273–301
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
Bostock, H., andRothwell, J.C. (1997): ‘Latent addition in motor and sensory fibers of human peripheral nerve’,J. Physiol.,313, pp. 277–294
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
Brink, E. E., andMackel, R. G. (1993): ‘Time course of action potentials recorded from single human afferents’,Brain,116, pp. 415–432
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
Fitzhugh, R. (1962): ‘Computation of impulse initiation and saltatory conduction in a myelinated nerve fiber’,Biophys. J.,2, pp. 11–21
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
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
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
Goldman, L., andAlbus, J. (1968): ‘Computation of impulse conduction in myelinated fibers: theoretical basis of the velocitydiameter relation’,Biophys. J.,8, pp. 596–607
Halter, J., andClark, J. (1991): ‘A distributed-parameter model of the myelinated nerve fiber’,J. Theor. Biol.,148, pp. 345–382
Hines, M. L., andCarnevale, N. T. (1997): ‘The NEURON simulation environment’,Neural Comput.,9, pp 1179–1209
Huxley, A. F., andStampeli, R. (1949): ‘Evidence for saltatory conduction in peripheral myelinated nerve fibers’,J. Physiol.,108, pp. 315–339
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
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
McIntyre, C. C., andGrill, W. M. (1998a): ‘Sensitivity analysis of a model of mammalian neural membrane’,Biol. Cybern.,79, pp. 29–37
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
McNeal, D. R. (1976): ‘Analysis of a model for excitation of myelinated nerve’.IEEE Trans.,BME-23, pp. 329–337
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
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
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
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
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
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
Rydmark, M. (1981): ‘Nodal axon diameter correlates linearly with internodal axon diameter in spinal roots of the cat’,Neurosci. Lett.,24, pp. 247–250
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
Safronov, B. V., Kampe, K., andVogel, W. (1993): ‘Single voltage dependent potassium channels in rat peripheral nerve membrane’,J. Physiol.,460, pp. 675–691
Scholz, A., Reid, G., Vogel, W., andBostock, H. (1993): ‘Ion channels in human axons’,J. Neurophys.,70, pp. 1274–1279
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
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
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
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
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
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
Waxman, S. G., andRitchie, J. M. (1985): ‘Organization of ion channels in the myelinated nerve fiber’,Science,228, pp. 1502–1507
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)
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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
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DOI: https://doi.org/10.1007/BF02345014