Description
Research Bateman exponential-difference factor with the equal-rate limit.
Pharmacokinetic research describes concentration over time using measurement units and an explicit model. Concentration-time area, its time-weighted moment, inverse-time rate constants, clearance, and volume are related but distinct quantities. A conversion or local model term does not estimate every parameter or validate a complete study.
Research Bateman exponential-difference factor with the equal-rate limit.
When to use this tool
Use PK Absorption Elimination Rate Gap when you need this concentration-time conversion, sampling check, local integral panel, or explicitly supplied kinetic-model term.
How to use the tool and how it works
- Enter absorptionRate, eliminationRate, time. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read rateGap, timeFactor, peakTime. Use the output convention below.
For positive absorptionRate and eliminationRate and nonnegative time return rateGap=absorptionRate-eliminationRate and timeFactor=(exp(-eliminationRate*time)-exp(-absorptionRate*time))/rateGap. Use the equal-rate limit time*exp(-eliminationRate*time), stable expm1 branches, and log1p near equal rates. Return peakTime=ln(absorptionRate/eliminationRate)/rateGap, or 1/eliminationRate when rates are equal.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| absorptionRate | Absorption Rate | Required. Finite number; strictly above 0. |
| eliminationRate | Elimination Rate | Required. Finite number; strictly above 0. |
| time | Time | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| rateGap | Rate Gap | Required. Finite number. |
| timeFactor | Unscaled concentration-model factor, with time units. | Required. Finite number. |
| peakTime | Time of the ideal absorption/elimination term peak in the common time unit. | Required. Finite number. |
{
"input": {
"absorptionRate": 2,
"eliminationRate": 1,
"time": 1
},
"output": {
"rateGap": 1,
"timeFactor": 0.23254415793482963,
"peakTime": 0.6931471805599453
}
}Limitations and assumptions
- Rates use inverse the supplied time unit. TimeFactor is an unscaled model term with time units, not concentration; dose, bioavailability, volume, lag times, and clinical regimen selection are outside scope.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete study analysis when a local panel, transformation, or model factor is insufficient. Check sampling times, censoring, assay support, unit conventions, and the validity of the assumed kinetic regime.
References
Similar or alternative tools
- PK Infusion Research Approach Factor
Supplied first-order research approach to a plateau, without infusion-setting advice.
- PK Log Linear Terminal Slope Two Points
Two-point research log slope; no terminal-phase selection or dosing inference.