Simple PBPK Model

Solve a single perfusion-limited tissue with constant arterial input and tissue-concentration-based clearance; a reduced PBPK component, not a complete physiology or human dose prediction.

Description

Evaluate the analytical concentration response of one perfusion-limited tissue to a constant arterial input.

Physiologically based pharmacokinetic models connect chemical disposition with quantities such as tissue volume, blood flow, and partitioning. Model scope, equations, and parameter assumptions are needed to interpret a concentration prediction.^[1]

This tool represents one well-mixed, perfusion-limited tissue supplied by a constant arterial concentration. A tissue-to-blood partition ratio determines venous outflow concentration, and a linear tissue clearance removes material in proportion to tissue concentration.

It reports the concentration at each requested time, a steady-state tissue concentration, and an equilibration rate in 1/hour. Volumes are liters, flow and clearance are L/hour, times are hours, and both concentrations must use a compatible mass-per-volume unit.

When to use Simple PBPK Model

Use it to explore a single-compartment step response or verify an analytical concentration trajectory under fixed arterial input and constant tissue parameters.

How to use Simple PBPK Model and interpret its calculation

Enter nonnegative arterialConcentration and initialTissueConcentration, positive tissueVolumeLiters, tissueBloodPartition, and tissueFlowLitersPerHour, and nonnegative tissueClearanceLitersPerHour.
Enter a nonempty timesHours list of nonnegative times measured from the initial condition. Unsorted and repeated times are allowed.
Run the model and read tissueConcentrations in the same order as your times. Compare them with steadyStateTissueConcentration and equilibrationRatePerHour.

V × dCt/dt = Q × Ca − (Q/K + CLt) × Ct; λ = (Q/K + CLt)/V; Css = Q × Ca/(Q/K + CLt)

Ca is the constant arterial concentration; Ct is tissue concentration; K is tissue-to-blood partition; CLt multiplies Ct, not blood concentration.

Ct(t) = Css + (Ct(0) − Css) × exp(−λ × t)

The implementation evaluates this analytical expression independently for each requested time. No numerical time stepping is used.

json

{
  "input": {
    "arterialConcentration": 10,
    "tissueVolumeLiters": 2,
    "tissueBloodPartition": 3,
    "tissueFlowLitersPerHour": 1,
    "tissueClearanceLitersPerHour": 0.5,
    "initialTissueConcentration": 0,
    "timesHours": [
      0,
      1,
      2
    ]
  },
  "output": {
    "tissueConcentrations": [
      0,
      4.089112437594675,
      6.784821497915061
    ],
    "steadyStateTissueConcentration": 12,
    "equilibrationRatePerHour": 0.4166666666666667
  }
}

Model boundary	Behavior
Time zero	Returns the initial tissue concentration.
Zero tissue clearance	Steady state equals partition ratio times arterial concentration.
Initial concentration equals steady state	Every output concentration stays at steady state.
Zero arterial concentration	A positive initial tissue concentration decays toward zero.

Limitations and assumptions

Arterial concentration is held constant; no dose-to-blood conversion, changing input schedule, inter-organ circulation, systemic mass balance, or whole-body model is included.

Partitioning, flow, volume, and clearance are constant, and clearance uses a tissue-concentration basis. Saturation, permeability limitation, active transport, nonlinear binding, and uncertainty are omitted. The result is a scenario calculation rather than a validated prediction for a person.

Alternative or Complementary methods

A hepatic IVIVE estimate can inform a separate disposition analysis, but hepatic blood clearance and this tissue-based clearance are different quantities; verify definitions and units before connecting models. Aggregate absorbed dose also requires a separate model to establish an arterial concentration.

References

Physiologically Based Pharmacokinetic Analyses — Format and Content: Guidance for Industry — U.S. Food and Drug Administration

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