Two-Compartment Model

Evaluate a supplied biexponential disposition curve and exact finite/infinite AUC; parameters are not fitted and no dose or clinical recommendation is generated.

Description

Evaluate a supplied biexponential concentration curve and its analytical finite and infinite AUC.

A biexponential disposition curve combines a faster and a slower decay phase. Such curves can describe concentration after distribution and elimination in a two-compartment setting, but their amplitudes and decay rates are macroparameters rather than direct compartment-transfer rates.^[1]

This tool receives the curve parameters rather than fitting concentrations or solving a dose regimen. Amplitudes share a concentration unit, rates use 1/hour, and times use hours. Concentrations retain the amplitude unit; area under the curve, or AUC, has that concentration unit multiplied by hours.

When to use Two-Compartment Model

Use it to reproduce a specified disposition curve or compare its observed-window AUC with the extrapolated area under unchanged parameters.

How to use Two-Compartment Model and understand its results

Enter nonnegative amplitudeA and amplitudeB, with positive alphaPerHour strictly greater than positive betaPerHour.
Enter a nonempty list of nonnegative timesHours and nonnegative aucEndHours. Requested times may be unsorted or repeated.
Run the tool and read concentrations in input order, aucZeroToEnd over the chosen window, and aucZeroToInfinity for the full modeled tail.

C(t) = A × exp(−αt) + B × exp(−βt)

The initial modeled concentration is A + B.

AUC(0,T) = A(1 − exp(−αT))/α + B(1 − exp(−βT))/β; AUC(0,∞) = A/α + B/β

The finite area uses expm1 for numerical stability near zero. It is analytical integration, not a trapezoidal sum of the requested observations.

json

{
  "input": {
    "amplitudeA": 8,
    "amplitudeB": 2,
    "alphaPerHour": 1,
    "betaPerHour": 0.1,
    "timesHours": [
      0,
      1
    ],
    "aucEndHours": 1
  },
  "output": {
    "concentrations": [
      10,
      4.752710365443457
    ],
    "aucZeroToEnd": 6.96021610990927,
    "aucZeroToInfinity": 28
  }
}

At end time zero, finite AUC is zero. Either amplitude may be zero, and both zero produce a zero curve. Equal or reversed rates are rejected even if an amplitude is zero. Observation times need not end at aucEndHours.

Limitations and assumptions

No parameters, compartment volumes, clearance, doses, or dosing recommendations are inferred. The supplied curve cannot verify that two compartments describe the data adequately.

Infinite AUC assumes both exponential terms continue indefinitely. There is no absorption term, repeated-dose accumulation, variable kinetics, or parameter uncertainty.

Alternative or Complementary methods

Use a physiological tissue model when blood flow and partitioning are the intended inputs. Clearance scaling addresses another part of pharmacokinetic interpretation and does not substitute for fitting this curve.

References

Modeling: An Introduction, Drinking Water and Health, Volume 8 — National Research Council

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