Cable Equation on an Axon
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.
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