Dendritic Length Constant
Evaluate the passive cylindrical cable length constant sqrt(d·Rm/(4·Ri)) with explicit micrometre/ohm-centimetre conversion; branching and active conductances are excluded.
Description
A passive cylindrical cable has a length constant relating membrane leakage to axial conduction.
A passive cylindrical cable has a length constant relating membrane leakage to axial conduction. Diameter and specific resistances determine the spatial scale.
The tool returns lengthConstantMicrometers (length constant micrometers). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Dendritic Length Constant
Use Dendritic Length Constant when you already have diameterMicrometers, specificMembraneResistanceOhmCm2, axialResistivityOhmCm and want lengthConstantMicrometers. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Dendritic Length Constant and understand its results
- Enter diameterMicrometers, specificMembraneResistanceOhmCm2, axialResistivityOhmCm using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read lengthConstantMicrometers. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| diameterMicrometers | Diameter micrometers | number | Required |
| specificMembraneResistanceOhmCm2 | Specific membrane resistance ohm cm2 | number | Required |
| axialResistivityOhmCm | Axial resistivity ohm cm | number | Required |
Require positive parameters. Convert micrometres to cm using 10⁻⁴, evaluate the cylindrical formula, then multiply by 10000 to return micrometres.
lambdaCm = sqrt(diameterCm×membraneResistanceOhmCm²/(4×axialResistivityOhmCm)) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"diameterMicrometers": 4,
"specificMembraneResistanceOhmCm2": 10000,
"axialResistivityOhmCm": 100
},
"output": {
"lengthConstantMicrometers": 1000
}
}Limitations and assumptions
The homogeneous passive cylinder excludes branching, active conductances and boundary effects.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Synaptic Conductance: Convert a leak-subtracted voltage-clamp current trace into conductance at a fixed nonzero driving force; pA/mV yields nS. Impedance Amplitude: Fit sine/cosine components with a DC intercept to simultaneous voltage/current samples at a supplied injection frequency and derive complex impedance magnitude/phase; no FFT leakage assumption is needed.
Methodological background: Dendrites and cable equations.1
References
-
Dendrites and cable equations — Gerstner et al.; Neuronal Dynamics
Similar or alternative tools
- Synaptic Conductance
Convert a leak-subtracted voltage-clamp current trace into conductance at a fixed nonzero driving force; pA/mV yields nS.
- Impedance Amplitude
Fit sine/cosine components with a DC intercept to simultaneous voltage/current samples at a supplied injection frequency and derive complex impedance magnitude/phase; no FFT leakage assumption is needed.