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The following message was posted to: PharmPK
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]
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The following message was posted to: PharmPK
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]
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The following message was posted to: PharmPK
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
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The following message was posted to: PharmPK
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
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The following message was posted to: PharmPK
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
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The following message was posted to: PharmPK
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]
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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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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)