# PharmPK Discussion - Equations to calculate drug concentrations

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• On 29 Jan 2000 at 15:44:51, "Elinore C Lau" (clau.-a-.email.rci.rutgers.edu) sent the message
`Dear All,I would like to know where I can find equations for calculatingconcentration-time profiles for a 2-cpt open model with first orderabsorption after multiple dosing.  I know the PK parameters, dosesize and dosing interval.Thank you very much.Elinore LauDepartment of PsychologyRutgers 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 > betaIf the doses and dosing intervals (T) are the same then Cp after ndoses at t since the last dose isCp(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 calculatethe Cp after each dose separately and add them together (with asuitable time offset)This all assumes first order disposition. Also, you probably haveother parameters ;-)db]`
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• On 31 Jan 2000 at 23:25:21, "Elinore C Lau" (clau.at.email.rci.rutgers.edu) sent the message
`Thank you very much for your reply.  The PK parameters are Vc, F, andintercompartmental rate constants, and k10.  We can calculate alphaand beta from these values with first order disposition.  Iwould appreicate if you can give me reference that I can cite theequations in my manuscript.  The book of Gibaldi an Perrier (1982)only listed the equations for 1-cpt model with first orderabsorption.Many thanks.Elinore`
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• On 1 Feb 2000 at 21:39:05, Mark Lovern (mlovern.-a-.pharsight.com) sent the message
`Dear Elinore:The model  you are describing is one that is included in WinNonlin'slibrary of Pharmacokinetic models. Our PK library includes 1-, 2-, and 3-compartment models for the major administration routes (IV Bolus, IVInfusion, and Extravascular (1st Order)). Models are provided in bothcompiled form for speed and ASCII to allow for user-customization.I'm not sure what platform you are currently using to model your data, Iwill send to your personal email the ASCII code for the model ofinterest. This code is written in WinNonlin's native modeling language,but it should be fairly simple to port it over to whatever language youare currently using.If there is any way that I may be of further assistance, please feel freeto contact me directly (mlovern.-a-.pharsight.com). For more informationabout WinNonlin and our other software packages, please see our website(www.pharsight.com).With Best Regards,Mark LovernPharsight Scientific SupportMark LovernConsulting ScientistPharsight, Inc.Phone: (919) 859-6868 ext. 4007FAX: (919) 859-6871`
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• On 1 Feb 2000 at 21:40:45, ml11439.at.goodnet.com (Michael J. Leibold) sent the message
`Elinore,     The equations for calculating plasma concentrations for a twocompartment linear mammillary model with first order input canbe found in several pharmacokinetic references:1) Gilbadi, Milo and Perrier, Donald, Pharmacokinetics, Marcel Dekker,    New York 19752) Gilbaldi, Milo and Perrier, Donald, Pharmacokinetics 2nd Edition,    Marcell Dekker, New York 19823) Wagner, John G., Fundamental of Clinical Pharmacokinetics, Drug    Intelligence Publications, Hamilton 1975Laplace 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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• On 16 Feb 2000 at 21:56:08, Roger Jelliffe (jelliffe.at.usc.edu) sent the message
`Dear Elinore:	There is a variety of software packages available to do suchcalculations.You might perhaps consider using one of them, such as our USC*PACKcollection. Yoou can get more info on our web site, which is given below.Very best regards,Roger JelliffeRoger W. Jelliffe, M.D. Professor of Medicine, USCUSC Laboratory of Applied Pharmacokinetics2250 Alcazar St, Los Angeles CA 90033, USAPhone (323)442-1300, fax (323)442-1302, email=  jelliffe.aaa.hsc.usc.eduOur web site=  http://www.usc.edu/hsc/lab_apk********************************************************************`
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