# PharmPK Discussion - AUC, fm and MRT

PharmPK Discussion List Archive Index page
• On 15 Oct 2002 at 14:25:54, "SK. Abdul Mohammed Jafar Sadik Basha" (h2002032.at.bits-pilani.ac.in) sent the message
`Dear all,i would be glad to know the answers of the following questions1) What is the difference between AUCall and AUC0-infinity in noncompartmental analysis by WinNonlin?2) How to calculate the fraction of dose converted into metabolite bynon-compartmental analysis in case of iv bolus ( oral also)?3) How to find out MRT incase of iv infusion for a definite period oftime?Thanks in advance.		*************************************		*SK.ABDUL MOHAMMED JAFAR SADIK BASHA*		*2002H108032			    *			*Room No.: 230, Bhagirath Bhavan    *		*BITS, Pilani                       *		*Rajasthan                          *		*************************************`
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• On 15 Oct 2002 at 14:39:10, "Davies, Brian {CLIN~Nutley}" (BRIAN.DAVIES.-at-.ROCHE.COM) sent the message
`> 1) What is the difference between AUCall and AUC0-infinity in non> compartmental analysis by WinNonlin?AUCinf is the total AUC i.e. AUClast plus AUClast to inf (Clast/lambdaz)AUCall is AUClast plus the area of the triangle assuming that the nexttime point after Clast is zero.> 2) How to calculate the fraction of dose converted into metabolite by> non-compartmental analysis in case of iv bolus ( oral also)?Fm = AUC'x/AUC', where AUC'x is the total area under the curve ofmetabolite in plasma after IV drug and AUC' is the total area under thecurve of metabolite after an equimolar IV dose of metabolite.> 3) How to find out MRT incase of iv infusion for a definite period of> time?MRTinfusion = MRT + (Infusion time/2)Brian E. DaviesClinical Director, PDMPHoffmann-La Roche, Nutley, NJ* brian.davies.aaa.roche.com* (973) 235-2053`
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• On 15 Oct 2002 at 14:46:46, Art Straughn (astraughn.aaa.utmem.edu) sent the message
`Abdul,To make the correct calculation of MRT from in infusion of finite timeplease see:  Straughn, AB. "Model-independent steady-state volume ofdistribution",  J Pharm Sci  1982  May: 715):597-8. Note an originalpaperon this subject has an integration error in the proof and gives thewronganswer.Art Straughn, Pharm.D.Professor and DirectorDrug Research LaboratoryUniversity of Tennessee874 Union AveSuite 5PMemphis, TN  38163E-mail: ASTRAUGHN.aaa.UTMEM.EDU`
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• On 15 Oct 2002 at 22:40:46, "Aziz Karim" (aakari.at.msn.com) sent the message
`I have attached a graph (both as .pdf and .jpg format) which clearlydescribes differences between AUC (all) and AUC (inf). Hope this helps.Aziz Karim[As attachments aren't possible on the PharmPK list I have put the jpegimage on the PharmPK website athttp://www.boomer.org/pkin/pk/AUCinf.jpg - db]`
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• On 17 Oct 2002 at 08:42:23, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message
`Dear colleaguesIn answer to the following question:>> 3) How to find out MRT incase of iv infusion for a definite period of>> time?Brian Davies wrote:> MRTinfusion = MRT + (Infusion time/2)This is correct. However, it may be confusing. In non-compartmentalanalysis, MRT is calculated asMRT = AUMC/AUCThis value of MRT includes the term (Infusion time/2), and thus equalstheMRTinfusion in your equation.On the other hand, in compartmental analysis, MRT is usually calculatedasMRT = Vss / CLThis value of MRT refers to a bolus dose administration.So, if MRT is calculated from AUMC/AUC, addition of (Infusion time/2)shouldbe omitted. The actual MRT is obtained by subtraction of (Infusiontime/2)from MRTinfusion.By the way, I do not know which MRT is provided by WinNonlin. Anyhow, itshould be made clear which value is reported. I would suggest to sticktothe 'real' MRT, i.e. after a bolus dose administration. IMHO, the valueofMRTinfusion does not make much sense.Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The NetherlandsEmail: j.h.proost.-a-.farm.rug.nl[I'm not sure what real MRT means...MRT probably should always beprovided with a subscript... MRT(IV-Bolus), MRT(IV-Infusion), orMRT(Oral) etc.Thus, MRT(xxx) is 'always' = AUMC/AUCand the calculations:MRT(IV-infusion) - MRT(IV-bolus) = MIT (mean infusion time ;-) =Duration/2 <- no new informationMRT(Oral) - MRT(IV-bolus) = MAT (mean absorption time) <- might beusefulcan/may be performed...do I have the right? - db]`
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• On 17 Oct 2002 at 09:48:22, "Wolna, Peter" (Wolna.-at-.IKP.DE) sent the message
`Dear Aziz,a graph using the original scale might be a better demonstrationof the phenomenon, since AUC calculation is based on non-transformeddata.In addition, you cannot display points with concentration zero inlog-scale.RegardsPeterPeter WolnaInst. f. Klin. PharmakologieD-67269 Gruenstadt`
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• On 17 Oct 2002 at 13:45:26, "Dr. Ibrahim Wasfi" (iawasfi.-a-.emirates.net.ae) sent the message
`Dear Aziz:Congratulations. Perfect graph.Dr. Ibrahim WasfiForensic Science LaboratoryP O BOX 253, Abu DhabiUnited Arab Emirates`
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• On 17 Oct 2002 at 17:37:57, Paul Collier (p.collier.-at-.qub.ac.uk) sent the message
`Aziz,The graph that you have supplied is misleading. Because you havelabelledthe y-axis as being a log scale this is not the graph that representstheAUC that is required. You cannot plot zero on a log scale and thereforethisdoes not give the correct visual representation of the relevant areas.PaulDr Paul S. CollierSchool of PharmacyQueen's University, Belfast97 Lisburn RoadBelfast BT9 7BLN. Ireland, UK`
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• On 17 Oct 2002 at 15:02:14, "Davies, Brian {CLIN~Nutley}" (BRIAN.DAVIES.at.ROCHE.COM) sent the message
`HansThe MRT given by WinNonlin is always the 'real' MRT because the programautomatically adjusts for the infusion time.regardsBrianBrian E. DaviesClinical Director, PDMPHoffmann-La Roche, Nutley, NJ* brian.davies.-a-.roche.com* (973) 235-2053`
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• On 18 Oct 2002 at 10:54:51, Nick Holford (n.holford.aaa.auckland.ac.nz) sent the message
`>> MRTinfusion = MRT + (Infusion time/2)>> This is correct. However, it may be confusing. In non-compartmental> analysis, MRT is calculated as>> MRT = AUMC/AUC>I think this is the most widespread actual use of MRT.> By the way, I do not know which MRT is provided by WinNonlin. Anyhow,> it> should be made clear which value is reported. I would suggest to stick> to> the 'real' MRT, i.e. after a bolus dose administration. IMHO, the value> of> MRTinfusion does not make much sense.I like to use the term Mean Disposition Time (MDT) to refer to Vss/CLbecause it refers to the residence time attributable to disposition(distribution and elimination) and excludes the input process which hasa Mean Input Time (MIT) (aka Mean Absorption Time MAT). They are simplyrelated like this:MRT  = MIT + MDTThe MDT is the same as MRT for a bolus input because MIT=0.NickNick Holford, Divn Pharmacology & Clinical PharmacologyUniversity of Auckland, 85 Park Rd, Private Bag 92019, Auckland, NewZealandemail:n.holford.at.auckland.ac.nzhttp://www.health.auckland.ac.nz/pharmacology/staff/nholford/`
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• On 18 Oct 2002 at 08:07:24, "Aziz Karim" (aakari.-at-.msn.com) sent the message
`Dear Paul:You are absolutely right that you can not show zero value in the logscale.The graph was for illustrative purpose only. The problem with using thelinear scale would be that the terminal phase elimination phase wouldnot beobvious because of the exponential decay. I should omit the zero valuefromthe graph and just say value below lqc.Again thanks for your comments.Aziz`
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• On 21 Oct 2002 at 11:01:47, Rostam Namdari (chista90.aaa.yahoo.com) sent the message
`Dear Hans,You rather have an interesting opinion regardingMRTinfusion.  Would you please provide a little moreinsight as to why do you think MRTinfusion does notmake much sense?  What about slow release formulation?Should do not be still meaningful/ useful if theplasma concentration-time curve decline in amono-exponential manner?Rostam`
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• On 23 Oct 2002 at 10:52:16, "J.H.Proost" (J.H.Proost.aaa.farm.rug.nl) sent the message
`Dear Rostam,Thank you for your response.> Would you please provide a little more> insight as to why do you think MRTinfusion does not> make much sense?I would say: the advocates of MRTinfusion should indicate what is theuse of this value.MRTinfusion is the average time that drug molecules reside in the bodyAND in the syringe (starting at time zero). To me, this makes no sensebecause the drug in the syringe is not in the patient. We have fullcontrol over the drug administration.I welcome the suggestion by Nick Holford about Mean Residence Time =AUMC/AUC and Mean Disposition Time = Vss/CL. Please note, however, thatin case of infusions, this definition of MRT cannot be translated tothe 'mean residence time in the body'. So, the confusion is not yetsolved completely.> What about slow release formulation?In this case the situation is different. In case we would know that therelease of drug obeys perfect zero-order over a defined time interval,the situation is almost similar to that of an infusion, but the drug isin the body (albeit not in the'pharmacokinetic system') and is out of control. In real life, slowrelease formulation are generally far from perfectzero-order over a defined time interval, so the concept of a Mean InputTime or Mean Absorption Time (as mentioned by Nick Holford) may beapplied.> Should do not be still meaningful/ useful if the> plasma concentration-time curve decline in a> mono-exponential manner?In case of a mono-exponential plasma concentration-time decline MRT andMRTinfusion may be useful, but also may be considered superfluous,since clearance and volume of distribution (two independentcharacteristics of the system) describe the system exactly. Half-lifeis useful for choosing anappropriate dosing interval, and indicates how fast steady state isreached. IMHO, that's enough, and we do not really need more parameters.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The NetherlandsEmail: j.h.proost.aaa.farm.rug.nl`
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• On 25 Oct 2002 at 15:02:08, "Prof. Dr. Michael Weiss" (michael.weiss.-a-.medizin.uni-halle.de) sent the message
`Some remarks to the recent discussion on the meaning and usefulness ofMRT:In view of a clear terminology I have proposed the names "meandisposition residence time" (MDRT) for disposition curves after a bolusiv dose and "mean body residence time" (MBRT) or "mean total residencetime" (MTRT)  after noninstantaneous input, i.e.MTRT = MDRT + MIT, where MIT= mean input timeMIT = T/2 for infusion time T (i.e., useful to calculate MDRT fromnumerically estimated MTRT).MIT = MDT + MAT (mean dissolution time + mean absorption time) afteroral administration.Since MDT (mean dissolution time) is an already established term inpharmacy and very useful for in vitro-in vivo correlation, the use MDTinstead of MDRT, as proposed by Nick, is open to question.Regarding the information given by MDRT on the disposition system, thefollowing holds for linear systems and only assumes that theelimination rate is proportional to C(t), but is independent of aspecific compartmental model.Besides the fundamental relationship MDRT= Vss/CL,   MDRT determinesthe degree of accumulation: Ass /FDm = MDRT/tau(Dm maintenance dose, tau dosing interval)More than 90% of a bolus dose is eliminated in t90% (washout) andfollowing infusion more than 90% of Css a reached in t90%, wheret90% = 3.7 MDRTNote that t63.2% =MDRT only holds for a one compartment model(monoexponential function) !Upper and lower bounds to the washout curves can be predicted when thevariance of RT is known after bolus injection or for log-concave curvesafter oral administration.e.g. ., time required for 63% of the total administered dose to beeliminated (Rostam's question):MDRT(1-CV^2)/2  < t63% <  MDRT  (where CV^2 = VDRT/MDRT^2)  (< means: <or =)The following inequality is general valid V0  < Vss < Vz. (< means: <or =)Weiss, M.: Generalizations in linear pharmacokinetics using propertiesof certain classes of residence time distributions. I. Log-convex drugdisposition curves. J. Pharmacokin. Biopharm. 14:635-657 (1986)Weiss, M.: Generalizations in linear pharmacokinetics using propertiesof certain classes of residence time distributions. II. Log-concavecurves following oral administration.J. Pharmacokin. Biopharm. 15:57-74(1987)Weiss, M.: Washout time versus mean residence time. Pharmazie43:126-127 (1988)Weiss, M.: The relevance of residence time theory to pharmacokinetics.Eur. J. Clin. Pharmacol. 43:571-579 (1992)The theory of residence time distributions also offers a method todefine measures of kinetics of drug distribution in the body (i.e.,which are not influenced by elimination as t1/2,alpha): Weiss, M, PangKS.: The dynamics of drug distribution. I. Role of the second and thirdcurve moment. J. Pharmacokinet. Biopharm. 20: 253-278 (1992)Best regards,Michael WeissMartin Luther Univ.Dep of PharmacologySection of PharmacokineticsD-06097 Halle/SaaleGermany`
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