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Hi everyone,
I am investigating a drug delivery system in which there is a sigmoid
relationship between drug release and time, i.e. when drug is delivered
over a two hour period, there is a lag in drug release during the first
30mins, followed by a period of relatively rapid drug release which
continues until a plateau is reached at about 100 mins.
The resultant concentrations of drug in the plasma reflect the release
profile, i.e. there is a sigmoid relationship between drug concentration
and time, followed by a post-infusion decline in plasma drug
concentration. My question is: how do I build this particular drug input
function into a PK model. I have basic knowledge of model writing (in
WinNonlin), but I'm not sure about the approach I should take in this
case.
Any comments or suggestions will be gratefully received.
Wendy Ingram
Pharmaceutical and Biomedical Research Group
Dept of Pharmacy
Derriford Hospital
PLYMOUTH
PL6 8DH UK
Tel: 44 1752 763414
wingram.-at-.ingramw.freeserve.co.uk
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The following message was posted to: PharmPK
Wendy - I have attached a WinNonlin model from my bag-of-tricks that may
suit your situation. In it I have the release rate modeled as a gamma
function (You may recognize this as the variant of the Bateman function
where the input and output rate-constants are equal). If you integrate it,
you will see a cumulative absorption profile that is sigmoidal in shape.
This model is convenient because you can model the release profile with only
one parameter. If it does not work, you could try a lag-time and finally
there is a large number of more complicated functions of a similar form that
might get the release profile better. Just substitute it in on the line
where Input = Dose...
Good luck, Jeff
==
MODEL
COMMANDS
NFUNCTIONS 1
NDERIVATIVES 1
NPARAMETERS 3
PNAMES 'Cl', 'V', 'Rel'
NCON 1
END
TEMPORARY
T=X
DOSE=CON(1)
Input = DOSE*Rel*T*exp(-Rel*T)
END
START
Z(1) = 0
END
DIFFERENTIAL
DZ(1) = Input - (Cl/V)*z(1)
END
FUNCTION 1
F= Z(1)
END
EOM
==
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The following message was posted to: PharmPK
Wendy, the Weibull function is sometimes used to simulate various
controlled release profiles. With the proper parameters it will
probably reproduce your sigmoidal release relationship. I have
posted a spreadsheet that illustrates the Weibull function and allows
you to test various input parameters at:
ftp://labsoft.hsc.usc.edu/pub/Absorption/WeibullFunctionExport.xls
Have fun with this.
Mike
PS: GastroPlus(TM) from http://www.simulations-plus.com has an
implementation of the Weibull function built into its controlled
release section.
* Michael B. Bolger, Ph.D. Phone: (323) 442-1442
* USC School of Pharmacy FAX: (323) 442-1390
* Dept. of Pharm. Sci. Internet: bolger.-at-.usc.edu
* 1985 Zonal Ave. PSC 700
* Los Angeles, CA 90089-9121
* U.S.A.
* http://www-rcf.usc.edu/~bolger/
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The following message was posted to: PharmPK
Wendy
I think that the Weibull function would be appropriate in this instance. It
is a generalized function (full name is the Rosen, Ramler, Sperling, Bennet,
Weibull Distribution Function) used successfully for describing in vitro
dissolution data, which are usually Sigmoid in shape (see references by
Langenbucher). I used the Weibull function to fit Sigmoid data obtained
after deconvolution - ref. can be supplied on request. I could have in fact
used the Weibull as the oral input function. This has been discussed in
other publications but I can't remember the authors. Why not perform a lit.
search?
regards
Brian Davies
Advanced Biomedical Research, Inc.
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)