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 $$\frac{\partial w}{\partial t} = \frac{\lambda_c^2}{\tau_m} \frac{\partial^2 w}{\partial z^2}$$
 * 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