A model of myelinated nerve fibres for electrical prosthesis design

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.

[1]  J. Schwarz,et al.  Na currents and action potentials in rat myelinated nerve fibres at 20 and 37° C , 1987, Pflügers Archiv.

[2]  F K Kuk,et al.  Performance of some of the better cochlear-implant patients. , 1989, Journal of speech and hearing research.

[3]  I. A. Boyd,et al.  Scaling factor relating conduction velocity and diameter for myelinated afferent nerve fibres in the cat hind limb. , 1979, The Journal of physiology.

[4]  A. Huxley,et al.  The action potential in the myelinated nerve fibre of Xenopus laevis as computed on the basis of voltage clamp data , 1964, The Journal of physiology.

[5]  P. Veltink,et al.  Multielectrode intrafascicular and extraneural stimulation , 2006, Medical and Biological Engineering and Computing.

[6]  T Brismar,et al.  Potential clamp analysis of membrane currents in rat myelinated nerve fibres. , 1980, The Journal of physiology.

[7]  J. Erlanger,et al.  THE ACTION OF TEMPERATURE ON THE EXCITABILITY, SPIKE HEIGHT AND CONFIGURATION, AND THE REFRACTORY PERIOD OBSERVED IN THE RESPONSES OF SINGLE MEDULLATED NERVE FIBERS , 1941 .

[8]  John W. Clark,et al.  A distributed-parameter model of the myelinated nerve fiber. , 1991 .

[9]  J. B. Ranck,et al.  Which elements are excited in electrical stimulation of mammalian central nervous system: A review , 1975, Brain Research.

[10]  D F Stegeman,et al.  Modelling compound action potentials of peripheral nerves in situ. III. Nerve propagation in the refractory period. , 1983, Electroencephalography and clinical neurophysiology.

[11]  Charles W. Parkins,et al.  A model of electrical excitation of the mammalian auditory-nerve neuron , 1987, Hearing Research.

[12]  J. E. Glynn,et al.  Numerical Recipes: The Art of Scientific Computing , 1989 .

[13]  J.S.T. Huang,et al.  Flat-band voltage dependence on channel length in short-channel threshold model , 1985, IEEE Transactions on Electron Devices.

[14]  J. M. Ritchie,et al.  A quantitative description of membrane currents in rabbit myelinated nerve. , 1979, The Journal of physiology.

[15]  J W Moore,et al.  Simulations of conduction in uniform myelinated fibers. Relative sensitivity to changes in nodal and internodal parameters. , 1978, Biophysical journal.

[16]  J. Z. YOUNG,et al.  Correlation of Internodal Length and Fibre Diameter in the Central Nervous System , 1949, Nature.

[17]  Ichiji Tasaki,et al.  Physiology and electrochemistry of nerve fibers , 1982 .

[18]  A. Paintal.  Conduction in Mammalian Nerve Fibres , 1973 .

[19]  J.H. Meier,et al.  Simulation of multipolar fiber selective neural stimulation using intrafascicular electrodes , 1992, IEEE Transactions on Biomedical Engineering.

[20]  J. Patrick Reilly,et al.  Application of a Neuroelectric Model to Electrocutaneous Sensory Sensitivity: Parameter Variation Study , 1987, IEEE Transactions on Biomedical Engineering.

[21]  J. Reilly.  Peripheral nerve stimulation by induced electric currents: Exposure to time-varying magnetic fields , 1989, Medical and Biological Engineering and Computing.

[22]  J. Hursh.  CONDUCTION VELOCITY AND DIAMETER OF NERVE FIBERS , 1939 .

[23]  J. Patrick Reilly,et al.  Sensory Effects of Transient Electrical Stimulation - Evaluation with a Neuroelectric Model , 1985, IEEE Transactions on Biomedical Engineering.

[24]  J. Mortimer,et al.  The Effect of Stimulus Parameters on the Recruitment Characteristics of Direct Nerve Stimulation , 1983, IEEE Transactions on Biomedical Engineering.

[25]  Johan H. M. Frijns,et al.  Refractoriness and frequency following behavior in a model of electrical stimulation of mammalian myelinated nerve fibers , 1992, 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[26]  A. Guyton,et al.  Textbook of Medical Physiology , 1961 .

[27]  F. Rattay,et al.  A study of the application of the Hodgkin-Huxley and the Frankenhaeuser-Huxley model for electrostimulation of the acoustic nerve , 1986, Neuroscience.

[28]  D. Mcneal.  Analysis of a Model for Excitation of Myelinated Nerve , 1976, IEEE Transactions on Biomedical Engineering.

[29]  B. Frankenhaeuser,et al.  The effect of temperature on the sodium and potassium permeability changes in myelinated nerve fibres of Xenopus laevis , 1963, The Journal of physiology.

[30]  A. Paintal,et al.  The influence of diameter of medullated nerve fibres of cats on the rising and falling phases of the spike and its recovery , 1966, The Journal of physiology.

[31]  J. Holsheimer,et al.  Recruitment of dorsal column fibers in spinal cord stimulation: influence of collateral branching , 1992, IEEE Transactions on Biomedical Engineering.

[32]  D. Durand,et al.  Modeling the effects of electric fields on nerve fibers: Determination of excitation thresholds , 1992, IEEE Transactions on Biomedical Engineering.

[33]  C. E. Molnar,et al.  Stimulus and recovery dependence of cat cochlear nerve fiber spike discharge probability. , 1982, Journal of neurophysiology.