# PharmPK Discussion - Definition of MRT

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• On 19 Oct 2011 at 15:32:45, "Birgersson, Johan [CONSE]" (JBirgers.aaa.its.jnj.com) sent the message
`Dear all,I've read that  MRT denotes the time it takes to eliminate the dose by 63.2%(Biopharmaceutics and Clinical Pharmacokinetics. Milo Gibalbi. 4th edition. Lea & Febiger.1991). However I can't find out where this percentage comes from. Does anyone know?Kind regards,Johan Birgersson`
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• On 19 Oct 2011 at 16:39:24, "Jack G. Shi" (JShi.at.incyte.com) sent the message
`The following message was posted to: PharmPKDear Johan,MRT can be defined as the geometric mean of the times needed to eliminate drug molecules(ie, residence time).  At MRT, 1/e = 36.8% of molecules are still remaining and therefore63.2% of dose is eliminated.  Hope this helps.Jack`
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• On 19 Oct 2011 at 16:48:32, Andrew Volosov (avolosov.at.gmail.com) sent the message
`Johan,This is true only for first-order elimination after IV bolus.The ratio between AUC(0 to MRT) and AUC(MRT to inf) equals e - 1, or 1.718. =46rom here itis easy to calculate that AUC(0 to MRT) represents 63.2% of the total AUC. To see thedetailed math you can use this reference:Volosov A, Bialer M. Biopharm Drug Dispos. 1999 Jan; 20(1):3-9.Hope this helps.Andrew VolosovShire HGT`
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• On 20 Oct 2011 at 08:38:13, Stefan Soback (stefan.soback.-a-.gmail.com) sent the message
`Andrew,I think you wanted to say that this percentage (63.2%) is correct onlyif the PK of the drug can be best characterized by a one-compartmentmodel after IV bolus administration. One may add to this that itpractically never occurs as most drugs are best characterized bymulti-compartment models after IV bolus administration.Stefan Soback`
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• On 20 Oct 2011 at 10:24:49, Wojciech Jawien (mfjawien.aaa.cyf-kr.edu.pl) sent the message
`The following message was posted to: PharmPKDear Johan,1-exp(-1)=0.6312...The statement you cite is correct for one compartment model with i.v.administration.It is by no means the general definition of MRT.In general MRT is defined as expectance of time the drug molecule spendin the body before it is eliminated:MRT = AUMC / AUC.If C(t)=Co*exp(-k*t), then AUC=Co/k; AUMC=Co/k^2; therefore MRT=1/k. Ifyou substitute t=1/k you will obtain C(MRT)=Co*exp(-1).At t-=MRT the part of drug dose remaining in circulation is exp(-1), so1-exp(-1) is the percentage eliminated.Best regards,Wojciech JawienJagiellonian UniversityKrakow, Poland`
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• On 20 Oct 2011 at 16:24:23, "J.H.Proost" (j.h.proost.at.rug.nl) sent the message
`The following message was posted to: PharmPKDear Johan,MRT can be defined as the arithmetic (not the geometric mean assuggested by Jack Shi) of the residence times of each drug molecule inthe body, i.e. the time between administration and elimination.For any PK model where the drug elimination is proportional to theplasma concentration, it follows that the hazard of a molecule to beeliminated is proportional to the plasma concentration. Therefore MRTcan be obtained by summing the product of hazard and time (AUMC), andnormalize this to the cumulative hazard (AUC). This implies thatMRT = AUMC / AUCwhere AUMC is the area under the C*t versus time profile integral(0-inf) { C*t }(C*t is the product of concentration and time)For a one-comparment model the concentration - time profile at IV bolusis C = C0 * exp(-k*t), soMRT = integral(0-inf) { C*t } / integral(0-inf) { C }= integral(0-inf) { C0 * t * exp(-k*t) } / integral(0-inf) { C0 *exp(-k*t) }= ( C0 / k^2 ) / (C0 / k) = 1 / kAt time t = MRT it follows: C / C0 = exp(-k*MRT) = exp(-1) = 0.367879.Therefore a fraction 1 - 0.367879  = 0.632... = 63.2% of the dose hasbeen eliminated.Jack Shi wrote:> At MRT, 1/e = 36.8% of molecules are still remainingOK, but where does this come from?Andrew Volosov wrote:> The ratio between AUC(0 to MRT) and AUC(MRT to inf) equals e - 1, or1.718. From> here it is easy to calculate that AUC(0 to MRT) represents 63.2% ofthe total AUC.For me this is not so easy.I understand that all this is described inyour cited paper, but I think my explanation is easier.best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics, Toxicology and TargetingUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlands`
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• On 21 Oct 2011 at 08:49:35, Stefan Soback (stefan.soback.-a-.gmail.com) sent the message
`I think we are getting a little bit carried away in this discussion. The63.2% is a curiosity that occurs when the (specific) drug exhibitsone-compartment model disposition after IV bolus administration. It isnot a definition of the MRT. I think the reason for this confusionresults from our general less than perfect understanding of thedifferences between one-compartment and multi-compartment model PK,which, unfortunately, has to be taken into account also in thenon-compartmental PK analysis.One has to keep in mind that MRT = 1/K (and I suggest that we use thecapital K for clarity) only when the compound can be best characterizedby one-compartment model PK. In such case we can also utilize therelationship t1/2 = ln2 * MRT as long as you remember the limitation. Isee a similarity here in the use of the term Vss/F. This, too, can bedetermined only for compounds that exhibit one-compartment model PKafter IV bolus administration (i.e. you have to know that a priori whendealing with non-IV administration PK). Still Vss/F is, incorrectly,determined in quite a few papers for compounds that clearly do not meetthis criterion.Stefan Soback`
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• On 21 Oct 2011 at 09:32:29, "Jack G. Shi" (JShi.aaa.incyte.com) sent the message
`MRT is defined as the arithmetic average (my mistake) of residence time,and in the context of mono-exponential decline, MRT simply is the timeneeded for drug concentration to decrease by 1 (natural) logarithmicunit, whereas half-life may be thought as the median residence time.Jack`
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• On 21 Oct 2011 at 16:13:04, Andrew Volosov (avolosov.at.gmail.com) sent the message
`I certainly agree with Stefan that 63.2% has a lot to do with math, and little to do withactual PK. Could be a good question to test students though.Andrew`
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