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Dear Colleagues,
Since we are on the topic of non-compartmental
analysis (NCA) I would like to bring an old issue up,
which was previously, discuss but we did not really
close the loop on it. Often Vz values obtained via
NCA are much higher than Vss for compounds exhibiting
bi-exponential decay (fit a 2-compartmental model).
Is this true for all the compounds showing bi-phasic
decay? In other words, is this reflective of a
two-compartment system: a larger volume (Vz) is needed
to accommodate the amount of drug in the body to
generate initial plasma concentrations but after
equilibrium is achieved and some of the drug is
excreted smaller volume is needed to generate
equilibrium concentrations (Vss) or there is more to
it. Any explanations?
How accurately can we say that the terminal phase
represents distribution rather than elimination and
what does the initial phase represents? If I do not
make any mistakes while ago someone (Hi Allen)
suggested if Vz/Vss > 2 the terminal phase is
distribution. Why?
Rostam
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Dear Rostam,
You wrote:
> Often Vz values obtained via
> NCA are much higher than Vss for compounds exhibiting
> bi-exponential decay (fit a 2-compartmental model).
> Is this true for all the compounds showing bi-phasic
> decay? In other words, is this reflective of a
> two-compartment system:
Yes, this is true for all multi-compartment systems with elimination solely
from the central compartment (the usual assumption, in many cases tacitly).
> a larger volume (Vz) is needed
> to accommodate the amount of drug in the body to
> generate initial plasma concentrations but after
> equilibrium is achieved and some of the drug is
> excreted smaller volume is needed to generate
> equilibrium concentrations (Vss) or there is more to
> it. Any explanations?
You may say it so, but this explanation is rather vague in my opinion.
First, both terms should be defined:
Vz is the apparent volume of distribution during the terminal phase, i.e.
the total amount in the body divided by the plasma concentration (=central
compartment concentration) during the terminal phase.
Vss is the apparent volume of distribution during steady state, i.e. the
total amount in the body divided by the plasma concentration during steady
state. Please note that both definitions are independent of any
compartmental or NCA approach.
During steady state there is equilibrium of the concentrations in all
compartments, and there is no net transport between compartments (if
elimination is solely from the central compartment). During the terminal
phase, however, there is no equilibrium due to the elimination process in
the central compartment. The concentration in the central compartment is
lower than the concentration that would correspond to the equilibrium
concentration. This concentration gradient is the driving force for the
transport of drug from the peripheral compartments to the central
compartment. As a result, the ratio of the total amount in the body and the
plasma concentration (=Vz) is higher than during equilibrium (=Vss).
During the terminal phase, the ratio of concentrations in the peripheral and
central compartments remains the same (some may call this situation a
pseudo-equilibrium), and thus Vz is a constant. To be more accurate, the
ratio of the amount in the body and the plasma concentration becomes
asymptotically equal to Vz. Finally, note that Vss is independent of
clearance, but Vz is dependent on clearance; a decrease of clearance results
in a decrease of Vz (i..e more closely to Vss).
> How accurately can we say that the terminal phase
> represents distribution rather than elimination and
> what does the initial phase represents? If I do not
> make any mistakes while ago someone (Hi Allen)
> suggested if Vz/Vss > 2 the terminal phase is
> distribution. Why?
IMHO, the phrase 'terminal phase represents distribution rather than
elimination' makes not much sense. The entire plasma concentration profile
is determined by the volumes of both compartments, clearance and
intercompartmental clearance. In extreme situations one may say that the
terminal half-life is mainly determined by the distribution process, and
less by the elimination process (e.g. gentamicin). This would imply that a
change in clearance hardly affects the terminal half-life (by the way, this
is probably the only reason why this question is relevant). This could be
checked easily by a simple calculation, and provides a reliable statement.
In contrast, any indirect reference, e.g. the value of Vz/Vss, seems rather
artificial, and I am not sure whether firm conclusions can be drawn from
this ratio. At least, the value of 2 seems highly arbitrary.
Sincerely,
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
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Rostam - There are some classical papers on this (dating back at least to
the early 1960's). As I recall, they show that in a 2 compartment model Vz
increases linearly with clearance. I am not sure what the slope is, but it
is probably a function of all the other parameters in the 2 compartment
model. I wish I could produce an exact reference for you, if only for
historical interest, but my files don't go back that far. References
notwithstanding, a simple set of simulations - taking about 5 minutes -
could demonstrate this relationship empirically; a little more work could
define the slope. IMHO all of it would be a waste of time. Getting back to
your question about distribution versus elimination in the terminal
phase...I would never make a conclusion one way or the other on this just on
the basis of an NCA analysis. Given the above relationship, this ratio
would only indirectly inform you about clearance which you would already
have obtained from NCA as Dose/AUC. Depending on the data you have and what
you know about the drug, a model based approach may not always be able to
answer this question either. However, it will always allow you to test the
sensitivity of your assumptions and point out where new data can be obtained
to resolve the issue.
Regards,
Jeff
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Dear Colleagues,
My thoughts on this are that you need to have a very good estimation of the
terminal elimination phase to get an accurate estimation of both Vz and
Vss. They should be the same if you really have reached the terminal
elimination phase. This can mean sampling for a surprising amount of time
and having a good bioanalytical method with a low LOQ if you use single
dose experiments to estimate volumes. The alternative is a multiple dose
experiment to steady-state, which avoids the problems with estimating the
terminal phase and the need for a low LOQ, but introduces the added
complication of dose to dose variability in absorption, unless i.v.
administration is used.
I hope this acceptable [sorry but attachment aren't allowed on this
list - db] but I have attached a spreadsheet which I have used
within the company to demonstrate the necessity to extrapolate, especially
for AUMC. There is a tendancy to use the non-extrapolated AUC(0-t) and
AUMC(0-t) to calculate MRT and Vss (e.g. AUMClast and MRTlast in
WinNonlin). This should be avoided unless you sample for a long time as the
estimate of Vss will be lower than Vz.
To answer the last point, the terminal phase (if you are really seeing it)
should represent the combination of elimination and distribution from the
tissues. Either can be rate limiting - just think of getting DDT out of
fatty tissues, or bisphosphonates from bone. The initial phase (or phases)
mostly represent distribution to the tissues - but of course there is an
influence of elimination even here.
Best regards, Phil.
(See attached file: MRT and Vss.xls)
[Not attached - I have placed it online at
http://www.boomer.org/pkin/xcel/MRT_vss.xls, is this OK Phil? - db]
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Jeff et al,
You might like to add the following to your reference collection.
Joga and used a simple example to illustrate that conclusions based
on changes in Vz should be considered artefacts of model
misspecification. Vz should be discarded from all PK analyses in
favour of Vss.
Nick
Gobburu JVS, Holford NHG. Vz, the terminal phase volume: Time for its
terminal phase?. Journal of Biopharmaceutical Statistics
2001;11(4):373-375.
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford.aaa.auckland.ac.nz
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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Phil Lowe stated:
> My thoughts on this are that you need to have a very good estimation of the
> terminal elimination phase to get an accurate estimation of both Vz and
> Vss.
I agree.
>They (i.e. Vz and Vss ) should be the same if you really have reached the
> terminal elimination phase.
I disagree. If you are dealing with a two compartment model where
elimination takes place from the central compartment, Vextrap > Vz > Vss.
For those who wish to understand the reason why, it might help to consult
the following reference, in particular pages 100 - 101, equations 35 - 37.
Collier, P.S. (1983). Some considerations on the estimation of steady state
apparent volume of distribution and the relationships between volume terms.
J. Pharmacokinetics and Biopharmaceutics, 11, 93-105.
> There is a tendancy to use the non-extrapolated AUC(0-t) and
> AUMC(0-t) to calculate MRT and Vss (e.g. AUMClast and MRTlast in
> WinNonlin). This should be avoided unless you sample for a long time as the
> estimate of Vss will be lower than Vz.
I would suggest that even sampling "for a long time" is insufficient if you
do not extrapolate to time infinity. This tendency that Phil refers to may
be the result of reading the paper by Yamaoka et al (1978) but Riegelman et
al (1980, references given below) pointed out on page 524 that failure to
extrapolate to infinity results in values that are meaningless.
Vss = AUMCƒ/AUCƒ Therefore determining Vss involves the estimation of two
area terms. At any given time, the percentage area remaining to be
extrapolated (i.e. to time infinity) will differ between AUMC and AUC and
the ratio (Vss) will increase to a maximum at time infinity.
Riegelman, S., Collier, P.S. (1980). The application of statistical moment
theory to the evaluation of in vivo dissolution time and absorption time.
J. Pharmacokinetics and Biopharmaceutics, 8, 509-534.
Yamaoka, K., Nakagawa, T. & Uno, T. (1978). Statistical moments in
pharmacokinetics. J. Pharmacokinetics and Biopharmaceutics, 6, 547-558.
Dr Paul S. Collier
School of Pharmacy
Queen's University, Belfast
97 Lisburn Road
Belfast BT9 7BL
N. Ireland, UK
Email: p.collier.-at-.qub.ac.uk
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Re: Vz versus Vss
Gentlemen,
Whilst it has been fascinating to read the various contributions on this
topic, I feel that I must clarify my original request for information.
Please bear in mind throughout that I am talking in terns of NCA. The
problem I have arises from what some may call pedantry. Using NCA it is not
possible to state that the terminal phase of a profile represents
elimination, therefore I use the term "terminal phase/half-life" rather than
elimination phase/half-life". Unfortunately, I have found that many people
(perhaps not fellow kineticists) automatically describe the terminal phase
as the elimination phase, irrespective of what it actually represents. It
then becomes necessary to explain the use of my terminology and what the
terminal phase may represent if it is not elimination. Obviously, the
explanation could be that the terminal phase represents distribution.
However, what if the next question is? what evidence have you that the
terminal phase represents distribution rather than elimination? Without
performing a compartmental analysis, how do I respond? It is all very well
to say that inspection of the profile reveals an initial substantial rapid
decline, followed by a slower smaller decline and that this would indicate
that the initial AUC was greater than the second AUC and therefore the
initial phase represented elimination. People tend not to believe such
"woolly" explanations, they prefer numbers. My original question was posed
to find out if anybody had a "rule of thumb" which related Vz to Vss in such
a way as to distinguish between the two situations, ie where the terminal
phase represented elimination and where it represented distribution. The
ratio of 2 was chosen completely arbitrarily and was not intended to be a
meaningful value. So far, the answer to my original question appears to
have been, "why bother?", "you shouldn't use Vz anyway", "set up a simple
simulation".
This may all seem rather a waste of time to the more theoretically
orientated kineticists but if we cannot communicate clearly to
non-kineticists, how can we expect people to understand us or the reports we
write?
Yours in the interests of simple and effective communication.
Alan
HUNTINGDON LIFE.SCIENCES LIMITED
http://www.huntingdon.com
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Thanks for your encouraging comments re simple explanation of
pharmacokinetics.
It needs to be said loud clear and often.
Thanks again.
John Ray
John Ray M.Sc.
Clinical Pharmacology & Toxicology
St. Vincent's Hospital
Darlinghurst 2010
Sydney, Australia
jray.at.stvincents.com.au
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Unfortunately, sometimes there is a difference between a simple explanation
and the correct one :(
Andrew Volosov, PhD
Senior Scientist
UCB Research Inc.
840 Memorial Drive
Cambridge, MA 02139
andrew.volosov.-a-.ucb-group.com
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Dear Colleagues,
It has been one of the most interesting discussions
among the group for a long time and I would like to
thank all of the contributors particularly Johannes,
Jeff, Paul and Phil (for sharing his informative demo
file).
Getting back to our discussion, I still have some
difficulty grasping the concept that under certain
conditions (e.g., Vz > Vss if we even should be
considering Vz) Terminal Phase represents Distribution
as reemphasized by Allen. Johannes mentioned this
does not much sense and Jeff stated that he would
never make a conclusion one-way or other on this just
on the basis of NCA. I have to agree with Jeff that
this would be a hard sell based on NCA. If the
Terminal Phase really represents Distribution, by
using compartmental modeling should not we see Kdist <
Ke? Can we apply some kind of analog concept to
flip-flop situation here?
Also it has been frequently mentioned (Hi Brian) that
if initial AUC > second AUC then initial phase
represents elimination and terminal half-life reflects
distribution rather than elimination. Would someone
provide some explanation, physiological (ADME) and/or
equations, to describe this? How do you calculate
these AUCs? Just by using simple trapezoid rule and
selecting partial areas or using equations A/alpha and
B/beta, then in latter case is not it true that what
we are refereeing to, as beta is really alpha and visa
versa? Any comments? Jeff did you experience any of
these (elimination/distribution flip flop) with
monoclonal antibodies? Would you please share your
experience with the group?
Rostam
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Dear Andrew:
Good for you! We need to be very careful about this. Population
modeling, and therapeutic drug monitoring and dosage individualization for
unstable patients are good examples. Many current methods of population
modeling and TDM have very significant deficiencies, and the explanations
for them, and the strategies for doing better, are not simple. We have some
things on our web site (www.lapk.org) which relate to this, under new
advances in population modeling, and under teaching topics, for example,
and under software. We try to do it right, and it is often not so simple.
Very best regards,
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine,
Division of Geriatric Medicine,
Laboratory of Applied Pharmacokinetics,
USC Keck School of Medicine
2250 Alcazar St, Los Angeles CA 90033, USA
email= jelliffe.-a-.usc.edu
Our web site= http://www.lapk.org
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Dear Dr McBurney,
You are right to point again to your original question. However, I
take the liberty not to answer your question directly, but to ask you
more about your question.
Why are you interested in the question whether the initial phase
represents distribution or elimination, and similar for the terminal
phase? As I stated earlier, both the initial phase and the terminal
phase are determined by both distribution and elimination. Only in
extreme situations one of the process is dominant. For that reason, I
prefer the terms 'initial' phase and 'terminal' phase over
distribution and elimination phase, since the latter suggest
something that does not exist. Initial and terminal have a real
meaning, both in compartmental analysis and NCA. So we agree about
terminology.
But why bother about distribution and elimination phase? Perhaps
there may be important aspects, but I am not aware of any. If anybody
could give some light on this topic, I would be happy.
Besides, knowing why this topic is interesting, is necessary to
derive some relevant measure. As mentioned by Nick Holford, the ratio
Vz/Vss is not suited to this purpose. But there may be others?
However, at least one should know exactly what such a measure is
supposed to represent.
So I am afraid that we are still in the stage "why bother?".
Simple and effective communications is possible only if we know
exactly what we are saying, and why.
Sincerely,
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.at.farm.rug.nl
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[Two relies - db]
From:
Date: Fri, 30 Aug 2002 13:36:17 +0200
To: david.-a-.boomer.org
Subject: RE: PharmPK Re: Vz versus Vss
Dear,
I just want to add some interesing observations we had in one of
recent studies.
After oral intake the experimental compound X follows a biphasic
distribution with sequential half-lives of 2 and 10 hours. The
initial half-life is the most important (characterizes most of the
AUC) and that's why the drug is given three times a day to maintain
adequate steady-state levels (demonstrates that the terminal
half-life is often not that important, but that's another discussion).
In the presence of a strong inhibitor of CYP3A4 the initial phase
completely disappeared and concentrations declined monophasically
with a half-life of 10 hours. Thus only the first phase of decay was
affected in the presence of the inhibitor and not the terminal phase !
Without this study many people would have said that the first phase
represents the distribution phase, the second phase the elimination
phase. I guess you have to do more studies to come to such
conclusions........
Best regards,
Kees
Kees Bol, PhD
Director Clinical Pharmacokinetics
Kinesis Holding
Lage Mosten 29
4822 NK Breda
The Netherlands
kees.bol.-a-.kinesis-pharma.com
www.kinesis-pharma.com
---
From: Paul Collier
Date: Fri, 30 Aug 2002 16:42:47 +0100
To: david.aaa.boomer.org
Subject: PharmPK Re: Vz versus Vss
Some further thoughts on Vz and Vss in relation to the ongoing discussion
about distribution versus elimination.
When plasma concentration data decline in a bi-exponential manner following
the administration of a bolus dose, a two compartment body model (2CBM) is
often used to describe the data. The initial rapid decline in concentration
is the result of BOTH distribution and elimination. The relative
contributions of each of these processed will differ from one drug to
another. In most cases this initial phase is dominated by distribution but
the aminoglycosides provide an example of a group of drugs where the
majority of a single dose is eliminated before distribution-equilibrium is
achieved.
During the terminal phase, the decrease in plasma concentration is due
entirely to elimination of drug as distribution is complete at this stage.
In the case of a conventional 2CBM where elimination is assumed to take
place from the central compartment only (Model 1), the terminal rate
constant (Lambda-z) will always be less than the elimination rate constant
(k10) because total clearance = k10 x V1 = Lambda-z x Vz and Vz > V1). In
that sense, the rate of elimination is controlled by the rate at which drug
returns to the plasma from tissues into which it has distributed; however, I
fail to see how one can describe the terminal phase as a distribution phase.
There are, of course two other possible 2CBMs - one where elimination takes
place from both compartments (Model 2) and the other where elimination
occurs from the peripheral compartment only (Model 3). Unless the peripheral
compartment corresponds to a specific physiological compartment that can be
sampled, it is not possible to know which 2CBM is the correct one as all
will fit the data equally well giving the same estimates for the initial and
terminal rate constants. In all 2CBMs once distribution-equilibrium has been
achieved and the terminal phase reached, the decline in drug concentration
in both compartments will be parallel.
If Model 3 is the correct model to describe the data, the decline in plasma
concentration will be parallel to the decline in concentration in the
peripheral compartment from which the drug is eliminated. This time it will
be the rate at which drug moves from the plasma to the peripheral
compartment that determines the rate at which drug is eliminated, (again the
terminal rate constant (Lambda-z) will always be less than the elimination
rate constant (k20) because total clearance = k20 x V2 = Lambda-z x Vz and
Vz > V2)
Although distribution is involved here (i.e. drug moving from the central to
the peripheral compartment), I would argue that what one is really observing
is elimination of drug from the body, albeit one is not observing directly
the compartment from which the drug is eliminated. Again I would not call
this terminal phase a distribution phase as the decline in plasma
concentration would not occur unless drug was being eliminated.
Estimates of V1 and Vz will be identical for all three possible 2CBMs but
the value for Vss will differ between models, being least for Model 1, and
greatest for Model 3, (see reference given below for details on how to
calculate Vss for each possible 2CBM). One should realise that the estimate
of Vss that is normally reported assumes that elimination takes place from
the central compartment only (i.e. Model 1) and, as such, is the minimum
value for this parameter - the 'true' value may be greater !
Reference: Collier, P.S. (1983). Some considerations on the estimation of
steady state apparent volume of distribution and the relationships between
volume terms. J. Pharmacokinetics and Biopharmaceutics, 11, 93-105
Dr Paul S. Collier
School of Pharmacy
Queen's University, Belfast
97 Lisburn Road
Belfast BT9 7BL
N. Ireland, UK
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