# PharmPK Discussion - Calculation of AUC

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• On 24 May 2008 at 17:57:57, "rahul vats" (rahulvats1983.aaa.gmail.com) sent the message
`hello all,here i wanted to ask how to calculate AUC in multiple dosing bymathematical formula when we got predose concentration.Rahul vats`
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• On 24 May 2008 at 14:23:48, "Dr. W. Webster" (webster_w.aaa.popmail.firn.edu) sent the message
`The following message was posted to: PharmPKSum of coefficients over exponents i.e. A/alpha + B/beta etc.William Webster, PharmD, FCCP, BCPS9525 Blind Pass RdCourageous 1001St Pete Beach, FL 33706[Alternately at steady state, numerical integration (trapezoidal rule,etc) of Cp during an interval, zero to tau. Seehttp://www.boomer.org/c/p4/c15/c1504.html- db]`
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• On 24 May 2008 at 23:24:24, Wojciech Jawien (mfjawien.aaa.cyf-kr.edu.pl) sent the message
`The following message was posted to: PharmPKrahul vats wrote: > > here i wanted to ask how to calculate AUC in multiple dosing by > mathematical formula when we got predose concentration. > > Rahul vatsDear Rahul,your question is not very precise and therefore too broad to be answeredin 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 forthat predose concentration as if no more doses were given.How? - this is another question  :) . Probably you neeed to know somelinear PK model parameters and use formulas like that reminded by Dr.Webster.*If* pharmacokinetics *is nonlinear* the problem is harder. On the otherhand calculating AUC for nonlinear PK is not very useful.regardsWojciech--Wojciech JawienDept. of PharmacokineticsJagiellonian Univ.Krakow, Poland`
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• On 25 May 2008 at 10:43:57, ogwal sidney (sidneyogwal.aaa.hotmail.com) sent the message
`Apply trapezoidal rule but nowadays there are several computerprograms that can do it for you even if mathematically traditionallyone is not so good.s.o.o`
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• On 25 May 2008 at 16:15:53, "Dr. W. Webster" (webster_w.aaa.popmail.firn.edu) sent the message
`The following message was posted to: PharmPKDear Rahul,Using your data points, submit to a polyexponential model in aniterative fitting algorithm. There is no assumption of compartmentsand the exponents can be negative or positive. Dr. Wagner has pointedout that you will need one more data point than the number ofexponents. So if you have a pre dose concentration, you will need atleast two samples post dose if you use a biexponential equation suchas C=A1*exp(a1)+A2*exp(a2).Then as Dr. Jawien points out, use the principle of superpositioningto calculate AUC.Cordially,William Webster, PharmD, FCCP, BCPS9525 Blind Pass RdCourageous 1001St Pete Beach, FL 33706`
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• On 26 May 2008 at 09:20:01, "Hans Proost" (j.h.proost.aaa.rug.nl) sent the message
`The following message was posted to: PharmPKDear Rahul and William,William Webster wrote: > Using your data points, submit to a polyexponential model in aniterative > fitting algorithm. There is no assumption of compartments  and the > exponents can be negative or positive. Dr. Wagner has pointed  outthat > you will need one more data point than the number of  exponents. Soif you > have a pre dose concentration, you will need at  least two samplespost > dose if you use a biexponential equation such  asC=A1*exp(a1)+A2*exp(a2).I would not recommend this procedure. If the number of data points isrelatively low, fitting may result in imprecise estimates of theparameters,and as a result, in an imprecise estimate of AUC.Besides, your citation of Dr. Wagner (reference?) does not seem to becorrect; the minimum number of data points is the number of independentparameters, so at least four in this case.The problem does not arise using the trapezoidal method for estimatingAUC,as suggested by David Bourne. The trapezoidal method is robust andreallymodel-independent.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The NetherlandsEmail: j.h.proost.aaa.rug.nl`
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• On 26 May 2008 at 15:42:24, "Dr. W. Webster" (webster_w.at.popmail.firn.edu) sent the message
`The following message was posted to: PharmPKThank you Dr Proost, and I apologize for the misquote. Dr Wagnershowed it is the number of parameters + one and not number ofexponents. The reference to the best of my recollection was, Do youneed a pharmacokinetic model, and, if so, which one? J PharmacokinetBiopharm. in the 1970's  - I haven't re-read it in years.If one is integrating a discrete interval, then one of the trapezoidalmethods is the only practical choice.Cordially,William Webster, PharmD, FCCP, BCPS9525 Blind Pass RdCourageous 1001St Pete Beach, FL 33706`
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• On 26 May 2008 at 15:55:29, "David S. Farrrier" (DFarrier.aaa.SummitPK.com) sent the message
`Dear Rahul,"PK Solutions" is an easy to use pharmacokinetics data analysisprogram that calculates several common variations of the AUC as wellas some 74 additional PK parameters. A free listing of the equationsused for all PK calculations is available, as well as links to thepopular PK Solutions software, can be obtained at:          http://www.summitpk.com/equations/equations.htmI think this will be useful to your .request.Regards,Dr. David S. FarrierSummit Research ServicesHome of PK Solutions - software for easy pharmacokinetics analysisDavid S. Farrier, Ph.D.Summit Research Services68911 Open Field Dr.              Email:   DFarrier.aaa.SummitPK.comMontrose, CO 81401                 Web:  http://www.SummitPK.com`
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