Solving the Cable Equation

G

m

(mS/cm

2

)

C

m

(μF/cm

2

)

R

i

(Ωcm)

I

max

(nA)

current duration (ms)

injection position(μm)

time (ms)

0

10

20

30

40

x(μm)

5

10

15

20

25

30

V

m

(mV)

A fundamental equation in mathematical biophysics is the cable equation, whose solution gives the time-dependent distribution of voltage along the length of a biological membrane, such as a neuronal axon. The voltage distribution depends upon a number of variables, such as membrane conductance

(G

m

)

, membrane capacitance

(C

m

)

, intracellular resistivity

(R

i

)

, the maximal value of the input current

(I

max

)

, the duration of this current, and the position on the cable in which the current is injected. In this Demonstration, these parameters can be varied and their effect on the spatiotemporal evolution of the voltage distribution viewed.