1. What is Length Constant (λ)?

Definition: The length constant (λ) represents the distance at which the depolarization of a neuron's membrane decays to 1/e (about 37%) of its original value along the axon.

Purpose: It's a crucial parameter in neurophysiology that describes how far electrical signals can propagate passively along neuronal processes.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \lambda \) — Length constant (meters, m)
• \( R_m \) — Membrane resistance (Ohms·m²)
• \( R_i \) — Intracellular resistance (Ohms·m)

Explanation: The length constant is determined by the square root of the ratio between membrane resistance and intracellular resistance.

3. Importance of Length Constant

Details: A larger λ means signals can travel farther before decaying, which is important for neuronal signal transmission efficiency.

4. Using the Calculator

Tips: Enter the membrane resistance (R_m) in Ohms·m² and intracellular resistance (R_i) in Ohms·m. Both values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for R_m and R_i?
A: In neurons, R_m typically ranges 0.1-10 Ohms·m², while R_i is about 0.1-1 Ohms·m, but varies by cell type.

Q2: How does axon diameter affect λ?
A: Larger diameter increases λ because it effectively decreases R_i (more cross-sectional area for current flow).

Q3: What units should I use?
A: Use consistent units - Ohms·m² for R_m and Ohms·m for R_i to get λ in meters.

Q4: Can this be used for dendrites?
A: Yes, the same principles apply to any neuronal process where passive conduction occurs.

Q5: What affects membrane resistance?
A: R_m depends on the number and type of ion channels - more channels means lower resistance.