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Dear All,
I would like to know where I can find equations for calculating
concentration-time profiles for a 2-cpt open model with first order
absorption after multiple dosing. I know the PK parameters, dose
size and dosing interval.
Thank you very much.
Elinore Lau
Department of Psychology
Rutgers University
[My guess: After a single dose Cp = A*exp(-alpha*t) + B*exp(-beta*t)
+ C*exp(-ka*t)
where A + B + C = 0 and alpha > beta
If the doses and dosing intervals (T) are the same then Cp after n
doses at t since the last dose is
Cp(t,n) = A*[(1-exp(-n*alpha*T))/(1-exp(-alpha*T))]*exp(-alpha*t)
+ B*[(1-exp(-n*beta*T))/(1-exp(-beta*T))]*exp(-beta*t)
+ C*[(1-exp(-n*ka*T))/(1-exp(-ka*T))]*exp(-ka*t)
If the doses and intervals aren't the same then you could calculate
the Cp after each dose separately and add them together (with a
suitable time offset)
This all assumes first order disposition. Also, you probably have
other parameters ;-)
db]
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Thank you very much for your reply. The PK parameters are Vc, F, and
intercompartmental rate constants, and k10. We can calculate alpha
and beta from these values with first order disposition. I
would appreicate if you can give me reference that I can cite the
equations in my manuscript. The book of Gibaldi an Perrier (1982)
only listed the equations for 1-cpt model with first order
absorption.
Many thanks.
Elinore
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Dear Elinore:
The model you are describing is one that is included in WinNonlin's
library of Pharmacokinetic models. Our PK library includes 1-, 2-, and 3-
compartment models for the major administration routes (IV Bolus, IV
Infusion, and Extravascular (1st Order)). Models are provided in both
compiled form for speed and ASCII to allow for user-customization.
I'm not sure what platform you are currently using to model your data, I
will send to your personal email the ASCII code for the model of
interest. This code is written in WinNonlin's native modeling language,
but it should be fairly simple to port it over to whatever language you
are currently using.
If there is any way that I may be of further assistance, please feel free
to contact me directly (mlovern.-a-.pharsight.com). For more information
about WinNonlin and our other software packages, please see our website
(www.pharsight.com).
With Best Regards,
Mark Lovern
Pharsight Scientific Support
Mark Lovern
Consulting Scientist
Pharsight, Inc.
Phone: (919) 859-6868 ext. 4007
FAX: (919) 859-6871
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Elinore,
The equations for calculating plasma concentrations for a two
compartment linear mammillary model with first order input can
be found in several pharmacokinetic references:
1) Gilbadi, Milo and Perrier, Donald, Pharmacokinetics, Marcel Dekker,
New York 1975
2) Gilbaldi, Milo and Perrier, Donald, Pharmacokinetics 2nd Edition,
Marcell Dekker, New York 1982
3) Wagner, John G., Fundamental of Clinical Pharmacokinetics, Drug
Intelligence Publications, Hamilton 1975
Laplace Transformed Amount in Central compartment:
Asc= KaFXo(s+k21)/[(s+Ka)(S+a)(S+b)]
Concentration in central compartment:
C= KaFXo(k21-Ka)e-kat/[Vc(a-Ka)(b-Ka) +
KaFXo(k21-a)e-at/[Vc(ka-a)(b-a)] +
KaFXo(k21-b)e-bt/[Vc(ka-b)(a-b)]
Mike Leibold, PharmD, RPh
ML11439.-at-.goodet.com
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Dear Elinore:
There is a variety of software packages available to do such
calculations.
You might perhaps consider using one of them, such as our USC*PACK
collection. Yoou can get more info on our web site, which is given below.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.aaa.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
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