Calculator
Formula Used
The calculator uses a passive cable approximation for membrane voltage spread.
Voltage at distance: Vm(d) = Vrest + Iinj × Rin × e-d/λ × F(t)
Transient factor: F(t) = 1 - e-t/τ
Distance to target: d = -λ × ln((Vtarget - Vrest) / (Iinj × Rin × F(t)))
Derived length constant: λ = √(diameter × Rm / (4 × Ri))
In the unit system used here, nA multiplied by MΩ gives mV.
How to Use This Calculator
- Enter injection current and choose its unit.
- Enter resting membrane voltage in mV.
- Enter input or transfer resistance in MΩ.
- Choose direct lambda or derive lambda from cable properties.
- Enter distance from the injection point.
- Add target and threshold voltages for distance checks.
- Enable transient response when pulse duration matters.
- Press calculate and review the result above the form.
Example Data Table
| Current nA | Rin MΩ | Lambda mm | Distance mm | Vrest mV | Estimated Vm mV |
|---|---|---|---|---|---|
| 0.2 | 50 | 1.0 | 0.5 | -70 | -63.93 |
| 0.1 | 80 | 0.8 | 1.0 | -70 | -67.71 |
| -0.15 | 60 | 1.2 | 0.4 | -70 | -76.45 |
Physics Background
Current injection changes the membrane voltage near an electrode. In a passive cable model, the strongest change appears at the injection point. The signal then falls with distance. This fall is controlled by the length constant. A larger length constant means voltage spreads farther. A smaller value means faster decay. The tool uses this idea for neurons, fibers, and simple conductive models. Record assumptions beside exported values. This helps reviewers separate measured data from estimated cable properties and simple teaching defaults. Update results when pulse settings change.
Why Distance Matters
Distance changes how much voltage reaches a target point. A synapse, sensor, or recording site may be far from the injected current. The local membrane voltage can look strong. The distant voltage may be weak. This calculator helps compare those points. It also estimates where a selected voltage will occur.
Advanced Inputs
You may enter the length constant directly. You may also derive it from cable diameter, membrane resistivity, and axial resistivity. Direct entry is useful when data already gives lambda. Derived entry is useful for planning and teaching. The resistance field sets the transfer response at the injection point. Current sign is kept. Positive current depolarizes above rest. Negative current hyperpolarizes below rest.
Time Option
Steady state assumes the current lasted long enough. Real membranes charge over time. The optional transient factor uses a simple exponential charging term. It compares the pulse time with the membrane time constant. Long pulses approach the steady value. Short pulses produce a smaller voltage response.
Interpreting Results
The main result is Vm at the selected distance. The report also shows voltage change, attenuation, normalized distance, and distance to target voltage. A threshold distance is included for quick excitability checks. Values are estimates. They assume a passive, linear, uniform cable. Active ion channels, branching, electrode losses, and boundary effects can change real measurements.
Practical Use
Use consistent units. Check that resistance and current match expected biology or physics. Try several distances. Export the table for notes or reports. Compare direct lambda with derived lambda when cable properties are known. Small changes in lambda can strongly affect distant voltage. That sensitivity makes this model useful for planning experiments and understanding spatial voltage decay.
FAQs
What does Vm mean?
Vm means membrane voltage. It is the electrical potential across a membrane, usually measured in millivolts.
What is injection current?
Injection current is current applied at one point. It changes membrane voltage near the injection site and spreads along the cable.
Why does voltage fall with distance?
Passive membranes leak current. Axial resistance also limits spread. These effects make voltage decay away from the injection point.
What is the length constant?
The length constant describes spatial decay. At one length constant, the voltage change falls to about 36.8 percent.
Can I use negative current?
Yes. Negative current is supported. It produces a negative voltage change and can model hyperpolarizing responses.
What resistance should I enter?
Use input resistance or effective transfer resistance at the injection point. The value should match your model or experiment.
When should I enable the transient option?
Enable it when the current pulse is short. It estimates incomplete membrane charging before steady state is reached.
Are the results exact for real neurons?
No. The model is passive and simplified. Active channels, branches, electrode effects, and boundaries can change measured voltage.