Pharmacokinetic Modelling

The one- and two-compartment pharmacokinetic models give the concentration profile of a drug in the body for a given dosing scheme. The area under these curves corresponds to the total exposure to the drug. The therapeutic window for a drug is the range between the effective dose and the toxic dose. The dosing scheme for a drug is designed to attain the target concentrations within the therapeutic window. The therapeutic window in this Demonstration is preset, but it is different for each drug. Drug elimination reactions can have varying reaction orders and associated rate constants depending on the system. Drugs are often absorbed in the first compartment when administered orally; the drug must first be absorbed in the stomach before entering the blood stream.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The main assumption here is that both compartments are well mixed. When the drug does not absorb, it is assumed to be administered in a rapid dose (i.e. bolus injection). 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 the first compartment, assuming absorption to be first order. The concentrations and time are intentionally left unitless but the whole system is dimensionally consistent. The drug elimination reaction order is .
Injected dose:
The first dose is at time zero, and the same mass is then injected for each subsequent dose.
Compartment one:
The initial condition for compartment one is that the drug concentration there is zero when absorption occurs, and it is the mass of the drug divided by the volume of compartment one when absorption does not occur.
Compartment two:
The initial condition for compartment two is that the concentration there is zero at time zero.

    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2015 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+