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Hi,
I have been using PK/PD models to investigate antimalarial drug resistance. We recently published a
paper describing how we can extend the PK component of our model from a one- to a two-compartment
model. The mathematics for the 2-compartment model was published in the appendix of our recent paper
http://www.ploscompbiol.org/article/info%3Adoi%2F10.1371%2Fjournal.pcbi.1003151
We are now working on extending this work further to model drugs using a three-compartment PK model.
Using laplace transformations and the finger print method to back-transform the equations into the
time domain, we think we have successfully derived the necessary equations. However, it would be
very helpful to know if anyone has done this previously so we can check our equations. Despite a
number of internet searches we have been unable to find anyone who describes the mathematics behind
a three-compartment PK model.
So, my question is does anyone know of any papers or reliable online sources that do provide the
equations necessary to model a three-compartment PK model?
Thank you,
Katherine
Katherine Kay
Parasitology
Liverpool School of Tropical Medicine
Pembroke Place
Liverpool L3 5QA
United Kingdom
E-mail: kwinter.aaa.liverpool.ac.uk
[You might look at http://www.boomer.org/c/p3/c07/c0707.html to check your Laplace derivation - db]
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Hi Katherine,
You can find the necessary equations for three compartment on page no. 92 of book Pharmacokinetics,
2nd Edition by Milo Gibaldi and Donald Perrier.
Satish Sharan
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Dear Katherine,
Have you looked in the monolix library?
http://www.lixoft.eu/wp-content/resources/docs/PKPDlibrary.pdf
Joe
--
Joseph F Standing
MRC Fellow, UCL Institute of Child Health
Antimicrobial Pharmacist, Great Ormond Street Hospital
Honorary Lecturer, UCL School of Pharmacy
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Katherine,
I have found that John Wagner's book Pharmacokinetics for the Pharmaceutical Scientist is an
excellent resource for compartmental equations. While it isn't bedside reading, it has excellent
technical and mathematical information. You can look on pages 57 through 62 for information and
equations on various 3-compartment models.
Kind regards,
Nathan
--
Nathan S. Teuscher, PhD
Founder and President, PK/PD Associates
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Hi Katherine,
You can also look at:
Upton RN. Calculating the hybrid (macro) rate constants of a
three-compartment mamillary pharmacokinetic model from known micro-rate
constants. J Pharmacol Toxicol Methods. 2004 Jan-Feb;49(1):65-8.
Regards, Richard
Richard Upton
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Katherine,
Sorry for not responding before- I was out of the office with training courses a lot the last few
weeks of the year, but building these type of models is very easy with the Graphical model builder
of Phoenix WinNonlin (a couple of Library models include 3 compartments and these are explored
further in the examples guide C:\Program Files (x86)\Pharsight\Phoenix\docs)
The code of these models is always explicitly stated so you can really understand what is happening.
Best regards,
Simon.
--
Simon.Davis.aaa.certara.com
Senior Scientific Consultant
Pharsight- A Certara™ Company
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