Cable theory - calculating cable length using graphs

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SUMMARY

The forum discussion focuses on calculating cable length (lambda), area specific conductance (Gm), and internal resistivity of a cell using a simulation program. The user injects a current of 1 µA and varies the electrode distance to obtain membrane voltage readings. Key equations include J = V Gm and λ = [Gm (ro+ri) πd]-1/2. The discussion emphasizes the exponential decay of voltage and suggests using semi-log paper for graphing to determine lambda effectively.

PREREQUISITES
  • Understanding of cable theory in neuroscience
  • Familiarity with electrical properties of biological cells
  • Knowledge of graphing techniques, specifically semi-logarithmic graphs
  • Basic proficiency in using simulation software for biological modeling
NEXT STEPS
  • Research the application of cable theory in neuroscience
  • Learn how to graph voltage decay on semi-log paper
  • Study the relationship between conductance (Gm) and resistance (Rm)
  • Explore simulation tools for modeling electrical properties in biological systems
USEFUL FOR

Neuroscientists, biomedical engineers, and students studying the electrical properties of cells will benefit from this discussion, particularly those involved in modeling and analyzing neuronal behavior.

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Homework Statement



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
Radius is 0.5mm

Homework Equations



J = V Gm

λ = [Gm (ro+ri) πd]-1/2

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.

please help!
 
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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.
 
Phrak said:
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.

Which of course it is based on.

To the OP, you might look http://en.wikipedia.org/wiki/Cable_theory" 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.
 
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