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Home/Biophysics, Fluids & Geoscience/Cable Equation on an Axon

Cable Equation on an Axon

1D passive cable ∂V/∂t = D∂²V/∂x² − (V−V_r)/τ + I; compare uniform fiber vs myelinated (higher D in internodes).

Cable parameters

0.35
2.8
12
8
1.2

Discrete passive cable: ∂V/∂t = ∂/∂x(D(x)∂V/∂x) − V/τ + I. Higher D in yellow “internode” bands mimics faster effective propagation along myelinated axons (qualitative, not cable equation with lumped nodes).

Measured values

V at far end0.0000

About this model

The passive cable equation linearizes membrane dynamics near rest: ∂V/∂t = ∂/∂x(D(x)∂V/∂x) − V/τ + I, where D bundles axial resistance and membrane capacitance in these teaching units. Piecewise larger D mimics lower loss in myelinated internodes, giving faster apparent propagation than a uniform fiber at the same mean parameters.

Who it's for: Students linking compartment models to saltatory conduction phenomenology.

Key terms

  • Cable equation
  • Myelin
  • Diffusion
  • Leak time constant

How it works

Finite-difference cable with piecewise diffusion coefficient: saltatory conduction cartoon by alternating low-D “node” and high-D myelinated stretches.

Frequently asked questions

Is this a full myelinated cable with explicit nodes of Ranvier?
No. It is a coarse finite-difference cartoon: periodically elevated D stands in for reduced leakage per unit length between excitable nodes.