# 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 questions
1) What is the difference between AUCall and AUC0-infinity in non
compartmental analysis by WinNonlin?

2) How to calculate the fraction of dose converted into metabolite by
non-compartmental analysis in case of iv bolus ( oral also)?

3) How to find out MRT incase of iv infusion for a definite period of
time?

*************************************
*2002H108032 *
*Room No.: 230, Bhagirath Bhavan *
*BITS, Pilani *
*Rajasthan *
*************************************

Back to the Top

• 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 next
time 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 of
metabolite in plasma after IV drug and AUC' is the total area under the
curve 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. Davies
Clinical Director, PDMP
Hoffmann-La Roche, Nutley, NJ
* brian.davies.aaa.roche.com
* (973) 235-2053

Back to the Top

• 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 time
distribution", J Pharm Sci 1982 May: 715):597-8. Note an original
paper
on this subject has an integration error in the proof and gives the
wrong

Art Straughn, Pharm.D.
Professor and Director
Drug Research Laboratory
University of Tennessee
874 Union Ave
Suite 5P
Memphis, TN 38163
E-mail: ASTRAUGHN.aaa.UTMEM.EDU

Back to the Top

• 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 clearly
describes 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 jpeg
image on the PharmPK website at
http://www.boomer.org/pkin/pk/AUCinf.jpg - db]

Back to the Top

• On 17 Oct 2002 at 08:42:23, "Hans Proost" (j.h.proost.-at-.farm.rug.nl) sent the message

Dear colleagues

In 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-compartmental
analysis, MRT is calculated as

MRT = AUMC/AUC

This value of MRT includes the term (Infusion time/2), and thus equals
the
On the other hand, in compartmental analysis, MRT is usually calculated
as

MRT = Vss / CL

This value of MRT refers to a bolus dose administration.

So, if MRT is calculated from AUMC/AUC, addition of (Infusion time/2)
should
be omitted. The actual MRT is obtained by subtraction of (Infusion
time/2)
from MRTinfusion.
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.

Hans Proost

Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands

Email: j.h.proost.-a-.farm.rug.nl

[I'm not sure what real MRT means...MRT probably should always be
provided with a subscript... MRT(IV-Bolus), MRT(IV-Infusion), or
MRT(Oral) etc.

Thus, MRT(xxx) is 'always' = AUMC/AUC

and the calculations:

MRT(IV-infusion) - MRT(IV-bolus) = MIT (mean infusion time ;-) =
Duration/2 <- no new information

MRT(Oral) - MRT(IV-bolus) = MAT (mean absorption time) <- might be
useful

can/may be performed...do I have the right? - db]

Back to the Top

• 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 demonstration
of the phenomenon, since AUC calculation is based on non-transformed
data.
In addition, you cannot display points with concentration zero in
log-scale.

Regards
Peter

Peter Wolna
Inst. f. Klin. Pharmakologie

Back to the Top

• 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 Wasfi
Forensic Science Laboratory
P O BOX 253, Abu Dhabi
United Arab Emirates

Back to the Top

• 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 have
labelled
the y-axis as being a log scale this is not the graph that represents
the
AUC that is required. You cannot plot zero on a log scale and therefore
this
does not give the correct visual representation of the relevant areas.

Paul

Dr Paul S. Collier
School of Pharmacy
Queen's University, Belfast
Belfast BT9 7BL
N. Ireland, UK

Back to the Top

• On 17 Oct 2002 at 15:02:14, "Davies, Brian {CLIN~Nutley}" (BRIAN.DAVIES.at.ROCHE.COM) sent the message

Hans

The MRT given by WinNonlin is always the 'real' MRT because the program
automatically adjusts for the infusion time.

regards

Brian

Brian E. Davies
Clinical Director, PDMP
Hoffmann-La Roche, Nutley, NJ
* brian.davies.-a-.roche.com
* (973) 235-2053

Back to the Top

• 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/CL
because it refers to the residence time attributable to disposition
(distribution and elimination) and excludes the input process which has
a Mean Input Time (MIT) (aka Mean Absorption Time MAT). They are simply
related like this:

MRT = MIT + MDT

The MDT is the same as MRT for a bolus input because MIT=0.

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.at.auckland.ac.nz
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

Back to the Top

• 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 log
scale.
The graph was for illustrative purpose only. The problem with using the
linear scale would be that the terminal phase elimination phase would
not be
obvious because of the exponential decay. I should omit the zero value
from
the graph and just say value below lqc.

Aziz

Back to the Top

• 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 regarding
MRTinfusion. Would you please provide a little more
insight as to why do you think MRTinfusion does not
make much sense? What about slow release formulation?
Should do not be still meaningful/ useful if the
plasma concentration-time curve decline in a
mono-exponential manner?

Rostam

Back to the Top

• On 23 Oct 2002 at 10:52:16, "J.H.Proost" (J.H.Proost.aaa.farm.rug.nl) sent the message

Dear Rostam,

> 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 the
use of this value.
MRTinfusion is the average time that drug molecules reside in the body
AND in the syringe (starting at time zero). To me, this makes no sense
because the drug in the syringe is not in the patient. We have full
I welcome the suggestion by Nick Holford about Mean Residence Time =
AUMC/AUC and Mean Disposition Time = Vss/CL. Please note, however, that
in case of infusions, this definition of MRT cannot be translated to
the 'mean residence time in the body'. So, the confusion is not yet
solved completely.

> What about slow release formulation?

In this case the situation is different. In case we would know that the
release of drug obeys perfect zero-order over a defined time interval,
the situation is almost similar to that of an infusion, but the drug is
in the body (albeit not in the
'pharmacokinetic system') and is out of control. In real life, slow
release formulation are generally far from perfect
zero-order over a defined time interval, so the concept of a Mean Input
Time or Mean Absorption Time (as mentioned by Nick Holford) may be
applied.

> 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 and
MRTinfusion may be useful, but also may be considered superfluous,
since clearance and volume of distribution (two independent
characteristics of the system) describe the system exactly. Half-life
is useful for choosing an
appropriate dosing interval, and indicates how fast steady state is
reached. IMHO, that's enough, and we do not really need more parameters.

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

Email: j.h.proost.aaa.farm.rug.nl

Back to the Top

• 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 of
MRT:

In view of a clear terminology I have proposed the names "mean
disposition residence time" (MDRT) for disposition curves after a bolus
iv dose and "mean body residence time" (MBRT) or "mean total residence
time" (MTRT) after noninstantaneous input, i.e.
MTRT = MDRT + MIT, where MIT= mean input time
MIT = T/2 for infusion time T (i.e., useful to calculate MDRT from
numerically estimated MTRT).
MIT = MDT + MAT (mean dissolution time + mean absorption time) after
Since MDT (mean dissolution time) is an already established term in
pharmacy and very useful for in vitro-in vivo correlation, the use MDT
instead of MDRT, as proposed by Nick, is open to question.

Regarding the information given by MDRT on the disposition system, the
following holds for linear systems and only assumes that the
elimination rate is proportional to C(t), but is independent of a
specific compartmental model.

Besides the fundamental relationship MDRT= Vss/CL, MDRT determines
the 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) and
following infusion more than 90% of Css a reached in t90%, where
t90% = 3.7 MDRT
Note 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 the
variance of RT is known after bolus injection or for log-concave curves
e.g. ., time required for 63% of the total administered dose to be
eliminated (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 properties
of certain classes of residence time distributions. I. Log-convex drug
disposition curves. J. Pharmacokin. Biopharm. 14:635-657 (1986)
Weiss, M.: Generalizations in linear pharmacokinetics using properties
of certain classes of residence time distributions. II. Log-concave
curves following oral administration.J. Pharmacokin. Biopharm. 15:57-74
(1987)
Weiss, M.: Washout time versus mean residence time. Pharmazie
43:126-127 (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 to
define measures of kinetics of drug distribution in the body (i.e.,
which are not influenced by elimination as t1/2,alpha): Weiss, M, Pang
KS.: The dynamics of drug distribution. I. Role of the second and third
curve moment. J. Pharmacokinet. Biopharm. 20: 253-278 (1992)

Best regards,

Michael Weiss

Martin Luther Univ.
Dep of Pharmacology
Section of Pharmacokinetics
D-06097 Halle/Saale
Germany

Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "AUC, fm and MRT" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)