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hello all,
here i wanted to ask how to calculate AUC in multiple dosing by
mathematical formula when we got predose concentration.
Rahul vats
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The following message was posted to: PharmPK
Sum of coefficients over exponents i.e. A/alpha + B/beta etc.
William Webster, PharmD, FCCP, BCPS
9525 Blind Pass Rd
Courageous 1001
St Pete Beach, FL 33706
[Alternately at steady state, numerical integration (trapezoidal rule,
etc) of Cp during an interval, zero to tau. See
http://www.boomer.org/c/p4/c15/c1504.html
- db]
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The following message was posted to: PharmPK
rahul vats wrote:
>
> here i wanted to ask how to calculate AUC in multiple dosing by
> mathematical formula when we got predose concentration.
>
> Rahul vats
Dear Rahul,
your question is not very precise and therefore too broad to be answered
in just one statement or even email.
Let me try to guess your intention:
*If* pharmacokinetics *is linear* you may use a superposition principle:
calculate AUC1 as if no predose was given and add AUC2 calculated for
that predose concentration as if no more doses were given.
How? - this is another question :) . Probably you neeed to know some
linear PK model parameters and use formulas like that reminded by Dr.
Webster.
*If* pharmacokinetics *is nonlinear* the problem is harder. On the other
hand calculating AUC for nonlinear PK is not very useful.
regards
Wojciech
--
Wojciech Jawien
Dept. of Pharmacokinetics
Jagiellonian Univ.
Krakow, Poland
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Apply trapezoidal rule but nowadays there are several computer
programs that can do it for you even if mathematically traditionally
one is not so good.
s.o.o
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Dear Rahul,
Using your data points, submit to a polyexponential model in an
iterative fitting algorithm. There is no assumption of compartments
and the exponents can be negative or positive. Dr. Wagner has pointed
out that you will need one more data point than the number of
exponents. So if you have a pre dose concentration, you will need at
least two samples post dose if you use a biexponential equation such
as C=A1*exp(a1)+A2*exp(a2).
Then as Dr. Jawien points out, use the principle of superpositioning
to calculate AUC.
Cordially,
William Webster, PharmD, FCCP, BCPS
9525 Blind Pass Rd
Courageous 1001
St Pete Beach, FL 33706
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The following message was posted to: PharmPK
Dear Rahul and William,
William Webster wrote:
> Using your data points, submit to a polyexponential model in an
iterative
> fitting algorithm. There is no assumption of compartments and the
> exponents can be negative or positive. Dr. Wagner has pointed out
that
> you will need one more data point than the number of exponents. So
if you
> have a pre dose concentration, you will need at least two samples
post
> dose if you use a biexponential equation such as
C=A1*exp(a1)+A2*exp(a2).
I would not recommend this procedure. If the number of data points is
relatively low, fitting may result in imprecise estimates of the
parameters,
and as a result, in an imprecise estimate of AUC.
Besides, your citation of Dr. Wagner (reference?) does not seem to be
correct; the minimum number of data points is the number of independent
parameters, so at least four in this case.
The problem does not arise using the trapezoidal method for estimating
AUC,
as suggested by David Bourne. The trapezoidal method is robust and
really
model-independent.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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The following message was posted to: PharmPK
Thank you Dr Proost, and I apologize for the misquote. Dr Wagner
showed it is the number of parameters + one and not number of
exponents. The reference to the best of my recollection was, Do you
need a pharmacokinetic model, and, if so, which one? J Pharmacokinet
Biopharm. in the 1970's - I haven't re-read it in years.
If one is integrating a discrete interval, then one of the trapezoidal
methods is the only practical choice.
Cordially,
William Webster, PharmD, FCCP, BCPS
9525 Blind Pass Rd
Courageous 1001
St Pete Beach, FL 33706
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Dear Rahul,
"PK Solutions" is an easy to use pharmacokinetics data analysis
program that calculates several common variations of the AUC as well
as some 74 additional PK parameters. A free listing of the equations
used for all PK calculations is available, as well as links to the
popular PK Solutions software, can be obtained at:
http://www.summitpk.com/equations/equations.htm
I think this will be useful to your .request.
Regards,
Dr. David S. Farrier
Summit Research Services
Home of PK Solutions - software for easy pharmacokinetics analysis
David S. Farrier, Ph.D.
Summit Research Services
68911 Open Field Dr. Email: DFarrier.aaa.SummitPK.com
Montrose, CO 81401 Web: http://www.SummitPK.com
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