6.021/Notes/2006-11-13

Cable model

experimental data from lobster: $\lambda_c \approx 1.3$ mm
Thus, infinitesimal electrode means much smaller than 1 mm and remote electrode means much greater than 1 mm
The distance a signal can travel without Hodgkin-Huxley regenerative mechanism is quite small
Look at dynamics of stimulus pulse
- Pulse in space and time
- Solution of form: $v_m(z,t)=w(z,t) e^{-t/\tau_m}$
- where
  - This is the Diffusion Equation with $D=\frac{\lambda_c^2}{\tau_m}$
- The effect of the stimulus diffuses down according to w but also dissipates equally across the membrane
In decrement free conduction (HH), space/time relationship follows wave equation whereas in decremental conduction in cable model, it's diffusion-like