# PharmPK Discussion - Accumulation ratio calculations

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• On 30 Oct 1996 at 23:05:44, "Faruq" (f.noormohamed.aaa.s1.cxwms.ac.uk) sent the message
`I would appreciate if any members of PharmPK can advise me on what shouldbe a very simple question on how to calculate accumulation ratio (AR).Drugs were administered either once (QD) daily or twice daily (BID) for 8consecutive days.  AUC0-dosing interval and AUC 0-infinity are availablefor both days 1 and 8 on QD and BID.Is AR:1.	AUC0-dosing interval day8/AUC0-dosing interval day12.	AUC0-infinity day8/AUC0-infinity day13.	AUC0-dosing interval day8/AUC0-infinity day1All three ways have been suggested but there must be one correct way ofcalculating ARmany thanks in advanceFaruq H NoormohamedDepartment of TherapeuticsChelsea andWestminster Hospital369 Fulham RoadLONDONSW10 9NHTel +44 (0)181 746 8141Fax +44 (0)181 746 8887email f.noormohamed.-at-.cxwms.ac.uk`
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• On 31 Oct 1996 at 12:28:07, Nick Holford (n.holford.-a-.auckland.ac.nz) sent the message
`>> Is AR:> 1.	AUC0-dosing interval day8/AUC0-dosing interval day1This fits closest to my own definition of AR which is the ratio ofthe conc at SS (or after N doses) to the conc after the first dose atthe same time after the dose e.g. the ratio of the trough conc at SS tothe conc immediately before the second dose. Using the AUC gives somekind of time averaged conc on day 8 divided by the conc averaged over the sameperiod after the first dose.> 2.	AUC0-infinity day8/AUC0-infinity day1No. Doesnt fit my definition of AR.> 3.	AUC0-dosing interval day8/AUC0-infinity day1No. This ratio should be <= 1 (approaches 1 as steady state is reached).The AR should always be > 1.--Nick Holford, Dept Pharmacology & Clinical PharmacologyUniversity of Auckland, Private Bag 92019, Auckland, New Zealandemail:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html`
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• On 31 Oct 1996 at 12:28:28, "Vladimir Piotrovskij" (VPIOTROV.at.JANBELC1.SSW.JNJ.COM) sent the message
`     Faruq:     There is no unique definition of the accumulation ratio (AR), so there     is no *correct* way of its calculating. In Gibaldi & Perrier (2nd     edition) you will find 3 versions of AR:     1. AR = C_ss_min/C_1_min,     where the subscript min corresponds to the plasma concentration     immediately before the dose intake. If the dose is administered in the     post-absorbtive, post-distributive phase this definition of AR will     result in a well-known equation:                AR = 1/(1 - exp(-lambda_z*tau))                 (1)     2. AR = C_ss_max/C_1_max,     where the subscript max indicates that the peak concentration is used     in calculating AR. If the drug kinetics can be described by the     one-compartment model you will get again Equation (1).     3. AR = C_ss_av/C_1_av,     where average concentrations at steady state and during the first dose     are used. The latter definition is the most common since it results in     a simple non-compartmental formula, and is, therefore, the most     appropriate:                AR = AUC_ss_tau/AUC_1_tau     Thus, in you three formulas:     1.      AUC0-dosing interval day8/AUC0-dosing interval day1     2.      AUC0-infinity day8/AUC0-infinity day1     3.      AUC0-dosing interval day8/AUC0-infinity day1     the first one is consistent with the latter definition. However, to     get an unbiased estimate, steady state should be achieved at day 8,     otherwise you will under-estimate AR.     By the way, if you have steady state at day 8, your third formula will     give unity if the kinetics of your drug is linear and time-invariant.     If there is auto-induction the ratio will be lower than one. In the     case of auto-inhibition it will be higher than one. So, this ratio is     of importance, too.     Best regards,     Vladimir     --------     Vladimir Piotrovskij, Ph.D.           Fax: +32-14-603768     Janssen Research Foundation           Email: vpiotrov.-at-.janbe.jnj.com     Clinical Pharmacokinetics     B-2340 Beerse     Belgiumfrom: "Vladimir Piotrovskij" `
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• On 31 Oct 1996 at 12:29:32, Ivan Alexandrov Nestorov (IVAN.at.fs1.pa.man.ac.uk) sent the message
`Faruq:By a definition, the AR (or often referred to as "fraction of thesteady state, achieved in the K-th period of the dosing schedule" iscalculated as the ratio between the AUC in the K-th period and theAUC in a period at steady state.As AUC in a period at steady state is equal to the AUC to infinityafter the first dosing, obviously the correct way is number 3.Kind regards,Ivan Nestorov, PhD>> I would appreciate if any members of PharmPK can advise me on what should> be a very simple question on how to calculate accumulation ratio (AR).>> Drugs were administered either once (QD) daily or twice daily (BID) for 8> consecutive days.  AUC0-dosing interval and AUC 0-infinity are available> for both days 1 and 8 on QD and BID.>> Is AR:> 1.  AUC0-dosing interval day8/AUC0-dosing interval day1> 2.  AUC0-infinity day8/AUC0-infinity day1> 3.  AUC0-dosing interval day8/AUC0-infinity day1> All three ways have been suggested but there must be one correct way of> calculating AR>> many thanks in advance>> Faruq H Noormohamed>+ + + + + + + + + + + + + + + + + + + + + ++                                         ++      Dr. Ivan Nestorov                  ++      Department of Pharmacy             ++      University of Manchester           ++      Oxford Rd.                         ++      Manchester, M13 9PL                ++      UK                                 ++      Tel: +44-161-275-6886              ++      Fax: +44-161-273-8196              ++      E-Mail: IVAN.aaa.fs1.pa.man.ac.uk      ++                                         ++ + + + + + + + + + + + + + + + + + + + + +`
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