# Cable theory - calculating cable length using graphs

1. Dec 18, 2009

### af86

1. The problem statement, all variables and given/known data

Using a simulation program I must determine cable length (lambda), area specific conductance (Gm) and internal resistivity of a cell.

The program allows you to inject a current (in uA) and change the electrode distance from the centre of the cell.

The simulator then outputs a membrane voltage in mV.

Length is 60mm

2. Relevant equations

J = V Gm

λ = [Gm (ro+ri) πd]-1/2

3. The attempt at a solution

I have tabulated an injected current of 1uA against the distance, keeping current at 1uA and increasing distance by 2mm. I then plotted the membrane voltage against the distance.

Unsure how to find lambda and conductance from this point.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 18, 2009

### Phrak

Good grief. This is neuroscience. I'm sure you've generated a lot of head scratching from thos trying to understand what at first looks like a problem in electrical cables and voltaic cells.

3. Dec 19, 2009

### denverdoc

Which of course it is based on.

To the OP, you might look http://en.wikipedia.org/wiki/Cable_theory" [Broken]for some guidance. Is your model just outputting the steady state Em as a function of distance? If so, lambda can be obtained a few ways.

You could graph on semi-log paper or use the relation that the voltage decay is exponential--i.e.at one lambda,the delta V falls to 37% of the delta V at x=0. That delta V in the steady state is just i*Rm, or in terms of conductance, i/Gm is what you're calling Gm is the reciprocal of Rm. Once lambda is known,you should be able to work out the internal resistivity.

Last edited by a moderator: May 4, 2017