PharmPK Discussion - Calculation of VRT

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• On 11 Feb 2003 at 11:16:14, "Dalton-Brown, Emma" (Emma.Dalton-Brown.-at-.covance.com) sent the message
`The following message was posted to: PharmPKDear All,I need to calculate VRT(0-tz) and VRT(0-infinity), VRT being Variance inResidence Time.  I have the software of WinNonlin, SAS and Excelavailableto me.  I think I can calculate VRT(0-tz) in WinNonlin using C.t versust (C= concentration and t = time) however this is not suitable forVRT(0-infinity).Any help would be greatly appreciated.Many thanksEmma[From my second edition Gibaldi and Perrier (p410) VRT is defined asarea under the second moment curve, seems to be the area under the C *t^2 versus time curve - db]`
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• On 12 Feb 2003 at 13:14:25, "Durisova Maria" (exfamadu.aaa.savba.sk) sent the message
`The following message was posted to: PharmPKDear Emma,> I need to calculate VRT(0-tz) and VRT(0-infinity), VRT being Variance> in> Residence Time.I guess tz is the last sampling time. If so, the quantity VRT(0-tz) hasnomeaning.The same is true for MRT(0-tz) and AUC(t-tz).If you use several different times tz, you would obtain severaldifferentVRT(0-tz),MRT(0-tz) and AUC(t-tz). The general use of tz=12 h or tz=24 h has noreason, because the  appropriate value of the last sampling pointstronglydepends on  theparticular drug under study. Despite this, "the magic times"  tz=12 h ortz=24 h arefrequently used in practice. The reason is very simple: it isconvenient tostartsampling e.g. at 8 a.m. and to stop it at 8 p.m., or even better at 8a.m.on the next day.Only the quantities VRT(0-infinity), MRT(0-infinity) and AUC(t-infinity)havereasonable  meaning. For example, using  AUC(t-infinity) you candeterminesuchan important parameter characterizing the drug behavior in the body asisthe drugclearance.> [From my second edition Gibaldi and Perrier (p410) VRT is defined as> area under the second moment curve, seems to be the area under the C *> t^2 versus time curve - db]VRT is defined as the ratio of two quantities, i.e. the second momentof thedrugconcentration profile and the zero moment of the drug concentrationprofile(AUC(t-infinity)).Regards,Maria Durisova, PhD, DSc,Head of Department of  Pharmacokineticsand Scientific SecretaryInstitute of Experimental PharmacologySlovak Academy of Sciences841 04 Bratislava 4Slovak RepublicPhone/Fax: +421 2 54775928http://www.uef.sav.sk/durisova.htm[Maria is right I had left off the rest of the formula for VRT. It isVRT = Area under second moment curve divided by the AUC (the zeromoment curve) - db]`
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• On 14 Feb 2003 at 17:08:04, "Hans Proost" (j.h.proost.-a-.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Emma Dalton-Brown,As was raised by others, only VRT(0-infinity) should be used; VRT(0-tz)doesnot make sense, since this values depends on the time point of the lastsample. In addition, one might question whether VRT makes sense anyway:1) What does it mean? It is a measure of the variability of theresidencetimes of individual molecules in the body, similar as the MRT is themean ofthese residence times. MRT is a clear and easily understandableparameter.But is it really interesting to know the variability of residence times?What would one conclude from its value? This is not an easy task, so Idoubtwhy one would calculate VRT.2) The precision of estimates of VRT is questionable in cases where theconcentration at the last sampling point is not zero (i.e. below LOQ,whichshould be sufficiently low). Please note that the extrapolated areaincreases progressively from AUC (zero moment, i.e. integral of C), MRT(obtained from first moment, i.e. integral of C.t), to VRT (obtainedfromsecond moment, i.e. integral of C.t^2). Therefore the errors in VRT maybequite large.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.aaa.farm.rug.nl`
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• On 14 Feb 2003 at 15:05:37, Angusmdmclean.-at-.aol.com sent the message
`The following message was posted to: PharmPK2/14/22003:Hans:how about for the pharmacokinetics of an extended release formulation:if MRTis a useful shape metric for the plasma concentration time profilecould VRTprovide some insight as to the variability in profile shape?Angus McLean PhDBioPharm Global Inc.Suite 1008125 Langport Terrace,Gaithersburg,MD 20877Tel 301-869-1009Fax 301-869-5737`
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• On 17 Feb 2003 at 15:23:53, "Hans Proost" (j.h.proost.aaa.farm.rug.nl) sent the message
`The following message was posted to: PharmPKDear Dr. McLean,Thank you for your reply. You wrote:> how about for the pharmacokinetics of an extended release formulation:> if MRT is a useful shape metric for the plasma concentration time> profile> could VRT provide some insight as to the variability in profile shape?I see several limitations:1) How do we interpret VRT? If one wishes to characterize some processby aparticular parameter, one should at least know how its values can beinterpreted. E.g., I would not know whether a low value is preferableover alarge value, or the other way around. And if it does not matter, whatare weusing VRT for?2) MRT and VRT are both determined by drug disposition and (in case ofanextended release formulation) by drug release from the dosage form anddrugabsorption. By comparison to an intravenous dose or a rapidly absorbedformulation, one can calculate an MIT (mean input time) and VIT(variance ofthe input time) by subtraction. For MIT this may work. But for VIT oneshould be extremely careful, since subtraction of variances is a 'sin'instatistics. In particular in this case, since we know that theprecision ofVRT is generally bad (see my previous message).So, I am still not convinced of any profit from VRT.Best regards,Hans ProostJohannes H. ProostDept. of Pharmacokinetics and Drug DeliveryUniversity Centre for PharmacyAntonius Deusinglaan 19713 AV Groningen, The Netherlandstel. 31-50 363 3292fax  31-50 363 3247Email: j.h.proost.at.farm.rug.nl`
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• On 17 Feb 2003 at 12:29:25, "Bert L. Lum" (bert.lum.at.coastside.net) sent the message
`The following message was posted to: PharmPKDear Emma,In regards to your perceived need to calculate VRT, others havediscussed the merits (or lack of) of calculating VRT and I will notbelabor that issue. If you wish to calculate VRT you might look at theLagran program published in the paper: Rocci ML and Jusko WJ. Lagranprogram for area and moments in pharmacokinetic analysis. Comput ProgrBiomed 15:203-217, 1983. I believe this program calculates VRT and iscoded in Fortran. I may still have it in an executable file somewherein the dark corners.Bert Lumblum.-at-.stanford.edu[The program listing isn't included with the paper but should berequested from the Authors...if available ;-) - db]`
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• On 18 Feb 2003 at 11:30:08, "Durisova Maria" (exfamadu.-a-.savba.sk) sent the message
`The following message was posted to: PharmPKAs far as the calculation of VRT(0-infinity), thereafter VRT, on thebasisof measured data is concerned, I would like to add the following:One may want to use the model presented e.g. in our studies  (1,2)and to calculate  MRT and VRT  by using the simple  formulasMRT=b1-a1/a0                                                 Eq.1VRT=b1^2-2b2+2a2/a0-(a1/a0)^2,                  Eq.2where a1, a0, b1, b2 are the model parameters (3,4).The formula given by Eq.1 was presented in study (5) where its outcomewasnamed thesojourn time of a drug in the compartment. However,  the right site ofEq.1givesthe general model-based formula for the determination of the mean timeparameter.Analogously,  the right site of  Eq.2 gives the general model-basedformulafor thedetermination of the variance of the respective mean time parameter.The biological purport of the mean time parameter determined accordingtothe general formula given at the right site of Eq.2 depends on aparticularprocess under study. For example, this formula can be used to calculatethemean timeof bioavailability process (6), the mean absorption time (7), the meandissolution time (8),or the mean time of metabolite formation (9), etc.1. Dedik L,   Durisova M.  J Pharmacokin  Biopharm 1994;   22: 293-3072. Durisova M,  Dedik L.  J Pharmacokin Pharmacodyn 2002; 29: 427-4443. Dedik L, Durisova M. Clin Res Regul Affairs 1996; 13: 199-2104. Dedik L, Durisova M.  Pharmazie 1997; 52: 404-4055. G. Segre. J Pharmacokin. Biopharm, 1988; 16: 657-666.6. Durisova M,  Dedik L,   Balan M.  Bull Math Biol 1995;  57: 787-8087. Dedik L,   Durisova M.  Methods Find Exp Clin Pharmacol 2001; 23:213-2178. Dedik L,   Durisova M. Comput Methods Programs Biomed 2002; 69: 49-559. Dedik L,   Durisova M.  Methods Find Exp Clin Pharmacol 2002; 24:481-486Regards,Maria Durisova, PhD, DSc,Head of Department of  Pharmacokineticsand Scientific SecretaryInstitute of Experimental PharmacologySlovak Academy of Sciences841 04 Bratislava 4Slovak RepublicPhone/Fax: +421 2 54775928http://www.uef.sav.sk/durisova.htm`
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