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<p>The classical Hodgkin–Huxley model describes the propagation of an action potential (AP) in unmyelinated axons. In many cases, the axons have a myelin sheath and the experimental studies have then revealed significant changes in the velocity of APs. In this paper, a theoretical model is proposed describing the AP propagation in myelinated axons. As far as the velocity of an AP is affected, the basis of the model is taken after Lieberstein, who included the possible effect of inductance that might influence velocity, into the governing equation. The proposed model includes the structural properties of the myelin sheath: the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mu\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>μ</mi> </math></EquationSource> </InlineEquation>-ratio (the ratio of the length of the myelin sheath and the node of Ranvier) and g-ratio (the ratio of the inner-to-outer diameter of a myelinated axon) through parameter <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma\)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>. The Lieberstein model can describe all the essential effects characteristic to the formation and propagation of an AP in an unmyelinated axon. Then a phenomenological model (a wave-type equation) for a myelinated axon is described including the influence of the structural properties of the myelin sheath and the radius of an axon. The numerical simulation using the physical variables demonstrates the changes in the velocity of an AP. These results match well the known effects from experimental studies.</p>

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The modelling of the action potentials in myelinated nerve fibres

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Kert Tamm,
  • Tanel Peets,
  • Jüri Engelbrecht

摘要

The classical Hodgkin–Huxley model describes the propagation of an action potential (AP) in unmyelinated axons. In many cases, the axons have a myelin sheath and the experimental studies have then revealed significant changes in the velocity of APs. In this paper, a theoretical model is proposed describing the AP propagation in myelinated axons. As far as the velocity of an AP is affected, the basis of the model is taken after Lieberstein, who included the possible effect of inductance that might influence velocity, into the governing equation. The proposed model includes the structural properties of the myelin sheath: the \(\mu\) μ -ratio (the ratio of the length of the myelin sheath and the node of Ranvier) and g-ratio (the ratio of the inner-to-outer diameter of a myelinated axon) through parameter \(\gamma\) γ . The Lieberstein model can describe all the essential effects characteristic to the formation and propagation of an AP in an unmyelinated axon. Then a phenomenological model (a wave-type equation) for a myelinated axon is described including the influence of the structural properties of the myelin sheath and the radius of an axon. The numerical simulation using the physical variables demonstrates the changes in the velocity of an AP. These results match well the known effects from experimental studies.