Pharmacokinetic Modeling

One- and two-compartment pharmacokinetic models calculate the concentration of a drug in the body as a function of time for a given dosing scheme. There are two options for administering the drug: injection into compartment 1 (e.g., inject into the blood stream with a needle) or absorption into compartment 1 from compartment 2 (e.g., drug in stomach absorbed into blood stream). Select the mass of the dose, number of doses and intervals between doses with sliders. The objective is to select a dosing scheme so that as much of the drug as possible has a concentration between the effective dose and the toxic dose (the therapeutic window). The drug can be eliminated from compartment 1 (set rate constant with a slider) or transferred to compartment 2 (slider ). Similarly, in compartment 2 the drug can be eliminated (slider ) or transferred back to compartment 1 (slider ). Change the reaction order of the drug elimination kinetics with buttons. The areas under the curves correspond to the total exposure to the drug.


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The drug is well-mixed in either compartment. The drug is either administered as a rapid dose (i.e., bolus injection) or it absorbs into compartment 1. The constants and represent the rate transfer coefficients from compartment 1 to compartment 2 and vice versa, assuming a first-order transfer between them. Each compartment has its own elimination rate and . The absorption coefficient determines the rate at which the drug absorbs into compartment 1, and it assumes first-order absorption in the amount of the dose. The concentrations and time are intentionally left unit-less, but the system is dimensionally consistent. The drug elimination reaction order is .
When the dose absorbs into compartment 1, then the amount changes with time:
If there is no absorption and the dose is directly injected, then the dose amount is distributed within compartment 1 at the injection time. The first dose is at time zero, and the same mass is then injected for each subsequent dose.
Compartment 1:
where is the drug concentration in compartment 1, is the drug concentration in compartment 2 and is the volume of compartments 1 and 2.
Initial condition for compartment 1:
when absorption occurs
when absorption does not occur.
Compartment 2:
with initial condition .
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