- On 11 Feb 2003 at 11:16:14, "Dalton-Brown, Emma" (Emma.Dalton-Brown.-at-.covance.com) sent the message

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Dear All,

I need to calculate VRT(0-tz) and VRT(0-infinity), VRT being Variance in

Residence Time. I have the software of WinNonlin, SAS and Excel

available

to me. I think I can calculate VRT(0-tz) in WinNonlin using C.t versus

t (C

= concentration and t = time) however this is not suitable for

VRT(0-infinity).

Any help would be greatly appreciated.

Many thanks

Emma

[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] - On 12 Feb 2003 at 13:14:25, "Durisova Maria" (exfamadu.aaa.savba.sk) sent the message

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Dear 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) has

no

meaning.

The same is true for MRT(0-tz) and AUC(t-tz).

If you use several different times tz, you would obtain several

different

VRT(0-tz),

MRT(0-tz) and AUC(t-tz). The general use of tz=12 h or tz=24 h has no

reason, because the appropriate value of the last sampling point

strongly

depends on the

particular drug under study. Despite this, "the magic times" tz=12 h or

tz=24 h are

frequently used in practice. The reason is very simple: it is

convenient to

start

sampling e.g. at 8 a.m. and to stop it at 8 p.m., or even better at 8

a.m.

on the next day.

Only the quantities VRT(0-infinity), MRT(0-infinity) and AUC(t-infinity)

have

reasonable meaning. For example, using AUC(t-infinity) you can

determine

such

an important parameter characterizing the drug behavior in the body as

is

the drug

clearance.

> [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 moment

of the

drug

concentration profile and the zero moment of the drug concentration

profile

(AUC(t-infinity)).

Regards,

Maria Durisova, PhD, DSc,

Head of Department of Pharmacokinetics

and Scientific Secretary

Institute of Experimental Pharmacology

Slovak Academy of Sciences

841 04 Bratislava 4

Slovak Republic

Phone/Fax: +421 2 54775928

http://www.uef.sav.sk/durisova.htm

[Maria is right I had left off the rest of the formula for VRT. It is

VRT = Area under second moment curve divided by the AUC (the zero

moment curve) - db] - On 14 Feb 2003 at 17:08:04, "Hans Proost" (j.h.proost.-a-.farm.rug.nl) sent the message

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Dear Emma Dalton-Brown,

As was raised by others, only VRT(0-infinity) should be used; VRT(0-tz)

does

not make sense, since this values depends on the time point of the last

sample. In addition, one might question whether VRT makes sense anyway:

1) What does it mean? It is a measure of the variability of the

residence

times of individual molecules in the body, similar as the MRT is the

mean of

these residence times. MRT is a clear and easily understandable

parameter.

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 I

doubt

why one would calculate VRT.

2) The precision of estimates of VRT is questionable in cases where the

concentration at the last sampling point is not zero (i.e. below LOQ,

which

should be sufficiently low). Please note that the extrapolated area

increases progressively from AUC (zero moment, i.e. integral of C), MRT

(obtained from first moment, i.e. integral of C.t), to VRT (obtained

from

second moment, i.e. integral of C.t^2). Therefore the errors in VRT may

be

quite large.

Best regards,

Hans Proost

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.aaa.farm.rug.nl - On 14 Feb 2003 at 15:05:37, Angusmdmclean.-at-.aol.com sent the message

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2/14/22003:

Hans:

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?

Angus McLean PhD

BioPharm Global Inc.

Suite 100

8125 Langport Terrace,

Gaithersburg,

MD 20877

Tel 301-869-1009

Fax 301-869-5737 - On 17 Feb 2003 at 15:23:53, "Hans Proost" (j.h.proost.aaa.farm.rug.nl) sent the message

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Dear 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 process

by a

particular parameter, one should at least know how its values can be

interpreted. E.g., I would not know whether a low value is preferable

over a

large value, or the other way around. And if it does not matter, what

are we

using VRT for?

2) MRT and VRT are both determined by drug disposition and (in case of

an

extended release formulation) by drug release from the dosage form and

drug

absorption. By comparison to an intravenous dose or a rapidly absorbed

formulation, one can calculate an MIT (mean input time) and VIT

(variance of

the input time) by subtraction. For MIT this may work. But for VIT one

should be extremely careful, since subtraction of variances is a 'sin'

in

statistics. In particular in this case, since we know that the

precision of

VRT is generally bad (see my previous message).

So, I am still not convinced of any profit from VRT.

Best regards,

Hans Proost

Johannes H. Proost

Dept. of Pharmacokinetics and Drug Delivery

University Centre for Pharmacy

Antonius Deusinglaan 1

9713 AV Groningen, The Netherlands

tel. 31-50 363 3292

fax 31-50 363 3247

Email: j.h.proost.at.farm.rug.nl - On 17 Feb 2003 at 12:29:25, "Bert L. Lum" (bert.lum.at.coastside.net) sent the message

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Dear Emma,

In regards to your perceived need to calculate VRT, others have

discussed the merits (or lack of) of calculating VRT and I will not

belabor that issue. If you wish to calculate VRT you might look at the

Lagran program published in the paper: Rocci ML and Jusko WJ. Lagran

program for area and moments in pharmacokinetic analysis. Comput Progr

Biomed 15:203-217, 1983. I believe this program calculates VRT and is

coded in Fortran. I may still have it in an executable file somewhere

in the dark corners.

Bert Lum

blum.-at-.stanford.edu

[The program listing isn't included with the paper but should be

requested from the Authors...if available ;-) - db] - On 18 Feb 2003 at 11:30:08, "Durisova Maria" (exfamadu.-a-.savba.sk) sent the message

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The following message was posted to: PharmPK

As far as the calculation of VRT(0-infinity), thereafter VRT, on the

basis

of 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 formulas

MRT=b1-a1/a0 Eq.1

VRT=b1^2-2b2+2a2/a0-(a1/a0)^2, Eq.2

where a1, a0, b1, b2 are the model parameters (3,4).

The formula given by Eq.1 was presented in study (5) where its outcome

was

named the

sojourn time of a drug in the compartment. However, the right site of

Eq.1

gives

the general model-based formula for the determination of the mean time

parameter.

Analogously, the right site of Eq.2 gives the general model-based

formula

for the

determination of the variance of the respective mean time parameter.

The biological purport of the mean time parameter determined according

to

the general formula given at the right site of Eq.2 depends on a

particular

process under study. For example, this formula can be used to calculate

the

mean time

of bioavailability process (6), the mean absorption time (7), the mean

dissolution time (8),

or the mean time of metabolite formation (9), etc.

1. Dedik L, Durisova M. J Pharmacokin Biopharm 1994; 22: 293-307

2. Durisova M, Dedik L. J Pharmacokin Pharmacodyn 2002; 29: 427-444

3. Dedik L, Durisova M. Clin Res Regul Affairs 1996; 13: 199-210

4. Dedik L, Durisova M. Pharmazie 1997; 52: 404-405

5. G. Segre. J Pharmacokin. Biopharm, 1988; 16: 657-666.

6. Durisova M, Dedik L, Balan M. Bull Math Biol 1995; 57: 787-808

7. Dedik L, Durisova M. Methods Find Exp Clin Pharmacol 2001; 23:

213-217

8. Dedik L, Durisova M. Comput Methods Programs Biomed 2002; 69: 49-55

9. Dedik L, Durisova M. Methods Find Exp Clin Pharmacol 2002; 24:

481-486

Regards,

Maria Durisova, PhD, DSc,

Head of Department of Pharmacokinetics

and Scientific Secretary

Institute of Experimental Pharmacology

Slovak Academy of Sciences

841 04 Bratislava 4

Slovak Republic

Phone/Fax: +421 2 54775928

http://www.uef.sav.sk/durisova.htm

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