Enter the membrane resistance and axial resistance into the calculator to determine the length constant of a neuron. The length constant is a measure of how far along an axon an electrical impulse can travel before it decays significantly.
Length Constant Formula
The following formula is used to calculate the length constant (λ):
λ = √(r<sub>m</sub> / r<sub>a</sub>)
Variables:
- λ (lambda) is the length constant (cm)
- rm is the membrane resistance (Ω·cm)
- ra is the axial resistance (Ω·cm-1)
To calculate the length constant, take the square root of the ratio of membrane resistance to axial resistance.
What is a Length Constant?
The length constant (λ) is a key parameter in neurophysiology that describes how far an electrical impulse can propagate along a neuron’s axon before it decays to 37% of its original amplitude. It is influenced by the properties of the axon’s membrane and its internal resistance. A larger length constant indicates that the impulse can travel further without significant decay, which is important for the efficient transmission of neural signals over long distances.
How to Calculate Length Constant?
The following steps outline how to calculate the Length Constant.
- First, determine the membrane resistance (rm) in Ω·cm.
- Next, determine the axial resistance (ra) in Ω·cm-1.
- Next, gather the formula from above λ = √(rm / ra).
- Finally, calculate the Length Constant (λ) in cm.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
membrane resistance (rm) = 1500 Ω·cm
axial resistance (ra) = 100 Ω·cm-1
