Cable Equation — Dendritic Propagation

Space constant λ = 300 µm

Time constant τ = 10 ms

Dendrite length = 800 µm

Stimulus amplitude = 20 mV

Stimulus width = 50 µm

Inject position = 0%

Cable Equation:
λ² ∂²V/∂x² = τ ∂V/∂t + V

Space constant: λ = √(r_m/r_i)
Electrotonic distance: X = x/λ

Steady-state solution:
V(x) = V₀ · e^(-|x|/λ)

λ = 300 µm
At X=1: 37% amplitude
At X=2: 14% amplitude

Color = voltage (orange=high)