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Dear Colleagues
How to explain the drug inteaction where Cl increases and Vd decrease because
Cl = KVd
Thanks a
Dr zafar
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Dear Dr Zafar,
The relationship CL=K x Vd is a mathematical expression not a biological one.
The biology is k = CL/Vd
This mean you can have an increase in CL and a decrease in Vd with a resultant
increase in k.
Nick
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Dear Dr Zafar,
I strongly recommend that you read the article by Dr Leslie Z. Benet, J
Pharmacokinet pharmacodyn (2010)37:529-539.
Regards
Fady M. Ibrahim, Ph.D.
Postdoctoral Fellow| Faculty of Pharmaceutical Sciences
The University of British Columbia | Vancouver
2146 East Mall | Vancouver, BC Canada V6T 1Z3
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Dr. Zafar
Fady's comment to your question to read my review article will provide potential answers.
I believe you were asking for the potential mechanism since the math of the relationship
discussed by Nick would not explain the finding, e.g., changes due to protein binding.
To provide a useful answer and explanation, we need to know if the drug is dosed iv or
orally and whether it is a BDDCS class 1 or 2 drug (metabolism is the major route of
elimination) or a BDDCS class 3 or 4 drug (urinary or biliary excretion of unchanged drug
is the major route of elimination). The V change will be due to a transporter
interaction, but I can't give you a potential explanation (uptake or efflux) or the reason
for the clearance change until I know the route of elimination and the route of
administration.
Les.
Leslie Z. Benet, Ph.D.
Professor
Department of Bioengineering & Therapeutic Sciences
Schools of Pharmacy & Medicine
University of California San Francisco
533 Parnassus Avenue, Room U-68
San Francisco, CA 94143-0912
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Dear All:
Nick is exactly right. Processes can be described totally
interchangeably in terms of Cl = KV or K = Cl/V. However, I think the
biology simply what it is. There is nothing in either expression that is
given by God to say that one is biology and the other not. All that is in
the eye of the beholder. We are the beholders who tell each other about
what we think we see, and some of these descriptions are called biology by
some. For a good introduction to the subject, one might read the first
several chapters of that oldie but very goodie, "The Grammar of Science", by
Karl Pearson, about 1911. It is also a most interesting book in other
respects, as he redescribes Newton's laws of motion most illuminatingly, the
theory of the ether is not yet quite dead, and relativity is just beginning.
A most interesting time in the history of our culture.
Best to all,
Roger W. Jelliffe, M.D., F.C.P.
Professor of Medicine,
Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
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Dear Leslie,
Thanks for help. These are orally administered drugs.
Dr Zafar
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Dear Roger,
Good to hear that the 'CL or k' question is still in your interest. In my mails of
February 1 and 25, 2011, I explained my view extensively. In the mail of February 1, I
cited a question from an earlier message. In my view, this questions illustrate nicely
that clearance and elimination rate constant are not interchangeable in a biological sense
(mathematically they are interchangeable, via k = CL/V, of course). =46rom my message to
Yaning Wang, 22-12-2009 (slightly modified):
What happens with the pharmacokinetic variables in a patient after connection to an
extracorporeal circulation?
In the 'rate constant approach', k would not be affected, and the increase in V will lead
to an increase in clearance. Does this imply that the renal and/or hepatic function of the
patient is increased?
In the clearance approach, one would assume that renal and/or hepatic function of the
patient are not (essentially) altered, so clearance remains the same. As a result, dosing
rate at steady state should not be modified. The increased volume results in a decrease of
k, and an increase of half-life.
I would really appreciate your view on this question.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
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I personally think that the Benet & Galeazzi equation Vss = CL*MRT is one of the
greatest in PK. People tend to forget the rules involved. I assume that Vss is
actually the only relevant volume term worth dealing with. In that case the
equation k = CL/Vss in correct only if the drug PK is best characterized by
one-compartment model (depending what you mean by k).
Stefan Soback
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Dear All,
Not to dwell on the theory extensively explained in previous threads, the case
Hans asks advice about is indeed very revealing. We have surgical patients on
cardiac pulmonary bypass (CPB) almost daily, from whom we extract both blood and
filtrate samples, both during and after CPB. Since the circuit has to be primed
usually with a crystalloid solution (of variable composition) it's most
plausible to assume some degree of hemodilution. Assuming that elimination and
distribution are independent processes (with rare exceptions), and assuming a
constancy of renal and hepatic functions (not always the case too), it's most
plausible to assume that drug distribution is the most impacted process by
extracorporeal circulation. One way to tell is to model the rate of elimination
separately from the rate of distribution. We may theoretically have all four
combinations (high rate, high vol.; high rate, low vol. ...) (notice that there
should be no such thing as a 'rate constant approach' since elimination kinetics
is different from first order kinetics). An increase in volume (recall, apparent
volume!) does lead to an increased clearance, but obviously does not "imply that
the renal and/or hepatic function of the patient is increased". It's absolutely
obvious in this case, since we were the ones promoting the hemodilution, that it
implies a change in volume. And that's precisely the caveat of a clearance
parameterization. It can go up or down by both reasons of elimination or
distribution. Actually, it may even remain unaltered if changes in both
processes theoretically compensate each other, and clinical repercussions may
not be captured by a clearance parameter.
So, there's nothing wrong in parameterizing the disposition (i.e. elimination +
distribution) with a clearance term as long as we keep in mind its correct
interpretation. When Hans says, "one would assume that renal and/or hepatic
function of the patient are not (essentially) altered, so clearance remains the
same" the word 'clearance' is wrongfully used for rate of elimination. The
volume that is cleared per time depends both on that volume and on the clearing
rate (by simple dimensional analysis). And assessing renal and/or hepatic
functions for their role in elimination is a separate issue from how the drug
distributes throughout the body (or even out of it). There's no way an increase
in volume can "result in a decrease of k" since by the very definition of a rate
constant there's no scaling or volume term involved in the mass balance. In
practical terms, some drugs require indeed dosing adjustments with CPB while
others don't, depending on which component of the clearance, i.e. elimination or
distribution, is most affected.
I regret that this confusion keeps surfing from time to time. But, no matter how
we prune the rose bush some beautiful blooms will always grow the wrong way.
Cheers,
Luis
-
Luis Pereira, PhD
Director Quantitative Clinical Pharmacology and Pharmacokinetics Laboratory
Anesthesiology and Perioperative Pain Medicine Department, Children's Hospital
Boston
Instructor Anesthesia, Harvard Medical School
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Dear Hans, Luis, and all:
Hans, it is good to hear now that you realize that rate constants
and clearances are interchangeable. But just how do you decide that one is
"mathematical" and the other is somehow more "biological"? As I said to
Nick, it is most useful to ask what is science and what is biology, and
how do we learn about them? How do we describe and interpret what we
perceive? All we really have is perceptions. In The Grammar of Science"
about 1911, Karl Pearson discusses these questions very well and
thoughtfully and with, I believe, great depth. It seems to me that to call
one mathematical and the other more biological, when we all know they are
totally interchangeable in our descriptions of what we see, is something I
for one simply do not understand.
Luis, a first order process is something that is described using a
first order differential equation. What is this? It is an equation that uses
the first derivative. That is a first order process. It has rate constants,
clearances, etc. Second order uses the 2nd derivative, etc.
About your sentence "assuming that elimination and distribution are
independent processes", I do not understand what you mean. Distribution
implies moving from one compartment to another. Further, how is drug
distribution affected by hemodilution? The volume of the apparent vascular
compartment is increased. OK. Then what? I do not understand your point.
How can clearance go up or down by reason of elimination or distribution? I
do not understand. If a volume is increased, OK. That says nothing about
elimination. Yes, it is part of the definition of clearance. The other is
the rate constant. What do we really want to describe? What do we really
mean here? These are things I do not understand from what you have said.
Very best regards,
Roger W. Jelliffe, M.D., F.C.P.
Professor of Medicine,
Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
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Dear Colleagues
Let's see if I can give Zafar some help in interpreting his drug interaction findings.
Zafar's mentioning of the k, V, CL relationship for the one-compartment model led to
further PharmPK discussions that in my opinion don't provide useful information in
addressing real data.
=46rom my perspective PK parameters are only useful if they will allow one to understand and
rationalize data, as Zafar was asking in his drug interaction questions.
Thus, I look at PK with CL as a measure of the body's ability to eliminate drug. If CL
changes then this indicates that some mechanism of drug elimination has been altered.
That is, the activity of the organs of elimination has changed.
V is a measure of the space in the body in which a drug may distribute. If V changes then
the drug concentration in the blood flowing to the organs of elimination has changed.
Since the organs of elimination can only eliminate drug in the blood flowing to them, the
rate of elimination of drug from the body will change when V changes even though the
ability of the organs of elimination to eliminate drug has not changed (i.e., CL is
constant). A good example is the increasing half-life of diazepam with age, which results
from increasing V with age although CL is unchanged. =46rom the perspective of trying to
understand the mechanism of changes in drug kinetics, I prefer to think of CL and Vss as
the independent variables, with k, but more properly MRT as noted by Stefan Soback to
account for all potential models, as the dependent variable.
The relationships above hold for unbound drug, since if one measures total drug it may
appear that V and CL change due to a protein binding interaction. But following an iv
dose, if the changes are due to a protein binding interaction then CL and Vss will change
in parallel and MRT will be unchanged.
Now let's get to Zafar's interaction questions. For some of his interactions he observed
CL and V changing in the same direction (his May 6 inquiry), but then he repeated his
question on May 23 as to how one could explain an interaction yielding increasing V and
decreasing CL. I responded on May 23, that I needed to know if the victim drugs were
being dosed oral or iv and what were the BDDCS classes, i.e., whether the victim drug was
primarily eliminated by metabolism (BDDCS classes 1 & 2) or primarily as excretion of
unchanged drug in the urine and bile (Classes 3 &4). Zafar responded that the drugs were
dosed orally, but didn't tell me about the elimination pathways. So for this answer I'm
going to initially assume the victim drug is primarily eliminated by metabolism.
First, it is critical to realize that when drugs are administered orally you are
determining CL/F and V/F. One of the clues to understanding interactions is looking also
at how MRT changes.
When your interactions show CL/F and V/F going in the same direction, it may be that F is
changing and CL and V are not changing. This can happen when your interaction is
affecting gut and liver first pass metabolism, e.g., the grapefruit juice inhibition of
CYP3A4 in the gut. If MRT does not change when CL/F and V/F change in the same direction
this is diagnostic of the interaction being a first pass metabolism or a protein binding
phenomena, when measuring total drug.
For the interaction with increasing V/F and decreasing CL/F. Here, I believe one
potential explanation is that you are blocking an efflux transporter for a drug that is
primarily metabolized in the intestine. The decreased cycling of drug between the gut
lumen and the enterocyte increases F and the decrease in CL/F primarily results from the F
increase. Of course the F increase would also theoretically cause V/F to increase, but if
the victim drug is a good substrate for an efflux transporter such as P-gp the overall
increase in V due to blocking the transporter in the rest of the body will overwhelm the F
increase and overall V/F will increase. It is important to recognize that my thinking is
always in terms of Vss, not Varea which can change when CL changes and is not an
independent parameter, as I addressed in a number of very early publications. Since it is
harder to calculate Vss/F following oral dosing than Varea/F, this is frequently not done
and I suspect it is part of the PharmPK community's problem in addressing the CL, V, k
relationship.
Now, having given that explanation the interactions Zafar is observing are probably more
easily explained for BDDCS class 3 and 4 drugs in terms of transporter interactions.
In fact, I have published a paper in 2009 in which Table I summarizes 39 transporter-based
interactions and their effect on volume, clearance and half-life. Five of those 39
interactions are exactly what Zafar was asking about; an increase in V and a decrease in
CL. Twenty of the 39 interactions show CL and V changing in the same direction. Ten of
the 39 interactions show CL changing and V being unchanged (Grover and Benet, AAPS J,
11:250-261, 2009). I did note that on May 6, Mukul did reference the ritonavir effect on
digoxin, showing increased V and decreased CL, as well as suggesting that my 2009 paper be
reviewed, but I thought it might be useful to the community to go into more detail.
Les
Leslie Z. Benet, Ph.D.
Professor
Department of Bioengineering & Therapeutic Sciences
Schools of Pharmacy & Medicine
University of California San Francisco
533 Parnassus Avenue, Room U-68
San Francisco, CA 94143-0912
[Something I found today that I thought interesting and on topic - db
Benet, L. Z. (2012). Benet L Z and Galeazzi R L: Noncompartmental Determination of the Steady-State Volume of Distribution, J Pharm Sci 68, 1071-1074, 1979=97the Backstory. The AAPS Journal, 14(2), 164-167. doi:10.1208/s12248-012-9326-9]
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Les, there were some things I could not follow in your explanation:
> If MRT does not change when CL/F and V/F change in the same direction
> this is diagnostic of the interaction being a first pass metabolism or a
> protein binding
> phenomena, when measuring total drug.
To the best of my understanding MRT after extra-vascular administration is
always greater than MRT after IV administration. So, I can't understand how
the above could happen. Secondly, The ratio of Vss/F and CL/F is identical
to the ratio of Vss and CL (which is the MRT after IV administration). In
other words, if you don't know the MRT after IV administration, there is
very little one can say about volume changes.
> It is important to recognize that my thinking is always in terms of Vss,
> not Varea which can change when CL changes and is not an independent
> parameter, as I addressed in a number of very early publications. Since it
> is harder to calculate Vss/F following oral dosing than Varea/F, this is
> frequently not done and I suspect it is part of the PharmPK community's
> problem in addressing the CL, V, k relationship.
I totally agree with you. Varea is a volume term that I would not use
unless the IV data are bad, i.e. does not allow calculation of the Vss.
Varea/F would be correct only if the terminal slope does not change (CL/F
is not much help here, because we do not know if it changed unless we know
what value of F is). I don't see any value in using it.
I still don't know how the Vss/F can be calculated unless you know the MRT
after IV administration. If one has the IV data of that particular drug,
the situation becomes workable.
Best regards,
Stefan
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Thanks Les,
You are absolutely correct. The computer programs use PK equations, but the
program users do not always seem to be sufficiently aware or appreciate what
their limitations (initial assumptions) were.
I hope everybody read carefully what you indicated as the "reasonable estimate",
because one should appreciate that it is an estimate when we live in the
multi-compartment world. On top of that I would be happy if people went back to
the Ronfeld & Benet (J. Pharm Sci, 1977) paper on ka estimations. Personally I
think ka is one of the most loosely used terms in PK.
Stefan
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Thanks Stefan.
AUMC/AUC is always greater after oral than iv administration. MRT is a
characteristic of a drug, just as CL and Vss. MRT is by definition Vss/CL.
Unfortunately some of the computer programs call AUMC/AUC as MRT. When you give
a drug orally AUMC/AUC = MRT + MAT.
Under most conditions you can get a reasonable estimate of MAT as 1/ka for
immediate release dosage forms. If you look at some of our CPT papers, I
believe for atorvastatin and glyburide recently, we fit the oral data to get an
estimate of ka, so as to be able to calculate MRT and then do a sensitivity
analysis to estimate how big an error we could have. At least for those two
drugs, we showed that the potential error would be small and thus were able to
compare the MRT under the conditions of control versus DDI.
Les
Leslie Z. Benet, Ph.D.
Professor
Department of Bioengineering & Therapeutic Sciences
Schools of Pharmacy & Medicine
University of California San Francisco
533 Parnassus Avenue, Room U-68
San Francisco, CA 94143-0912
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Dear Friends and All,
Having discussed several months ago the mathematics, we came now to discuss the
biology behind the concept of clearance. I'm sure we all agree that if drug
absorption takes place, still more careful we must be with interpreting
clearance estimates. In this day and age of pull-down menus and built-in
libraries, I totally agree that the glamour of colorful outputs often neglects
the underlying assumptions with which equations are derived. It's just our
responsibility to acknowledge their applicability and inherent meaning.
Since the original query was about CL, Vd and k, I'll focus on the intravenous
case for the sake of simplicity. I think that absorption kinetics,
bioavailability, rate limiting steps, non-homogeneity, and so on, are goodies
for another opportunity. So let me summarize first what I think we all agree
upon about clearance:
1- All algebraic relationships between CL and other PK parameters are valid.
They do not imply any causality or hierarchy. Labeling them as math, biology or
pretty scribblings is irrelevant. One among others may be more advantageous for
regression and parameter estimation, depending on the methodology. This is a
legitimate and even recommendable practice.
2- "PK parameters are only useful if they will allow one to understand and
rationalize data" (sic. Leslie Benet).
3- Clearance is a measure of the ability of the body to irreversibly clear
itself of a drug (i.e. foreign substance). It's not the only one, but it's
certainly very useful (as I said before it has been around since the dawn of
PK). It corresponds to the rate of elimination normalized by the typical
concentration (at the time that rate is assessed, if it's not constant).
Physiologically, it's the fraction of drug (adimensional) extracted from an
incoming blood flow multiplied by that flow.
4- Total or systemic or plasma clearance is the unweighted sum of all parallel
clearances.
Many cases exist for which the biology of elimination is fully captured by the
clearance concept. E.g. impaired glomerular permeability, intratubular
obstruction and reduced renal blood flow justify the decrease of aminoglycosides
renal CL, even though Vd may increase due to the accumulation of interstitial
fluid. In the case of burn patients with systemic inflammatory response syndrome
causing depletion of plasma albumin and generalized edema, the Vd of many drugs
is increased. But for instance vancomycin CL increases due to an increased
glumerolar filtration, renal secretion and induced hypermetabolism, unrelated to
the Vd. Examples like these are the most common leading to the intuition that CL
and Vd are independent. Whether this is always the case it's something else.
Coming to the point of contention, Zafar's original query was about CL increase
and Vd decrease following oral administration, which I'd say is a less frequent
situation. I think Les and Stefan rightfully discuss most of the factors
involved. E.g., plasma protein binding reduces Vd and induced metabolism or
secretion increases elimination with a potential CL increase. With drug/food
interactions and extravascular administrations, the number of processes involved
may quickly become overwhelming. One more reason to model them individually as
much as possible and be aware of their individual leverages. I acknowledge the
advantage of mean time parameters but I won't go as far as saying it's always
the right thing to do. Again we must go back to the assumptions. Even with no
absorption, e.g. constant rate iv infusion, mean arrival time=T/2 for T=infusion
time. Also when we're interested in identifying details the mean is the most
unforgiving statistical parameter there is.
A more common assertion, also made in this thread, is that changes in Vd with CL
said to be constant, lead to the intuitive conclusion that elimination must
change because of the volume. This is where I recommend caution. About reducing
elimination kinetics to a 'rate constant approach" I meant that if the former
has a zero order or even mixed order nature there is just no rate constant.
Pardon for the correction Roger, but I know you know that 2nd order kinetics
does not imply a 2nd derivative but rather a 1st derivative of the square of the
driving force. But the bigger point is that equating CL with k leaves out a lot
to account for. Science is certainly about free thinking but any theory must
withstand all challenges before it can hold that title (I too recommend the
discussion between Pearson, Neyman and Fisher about probability versus
likelihood).
Not to use my words I quote, "Another explanation for the relationship between
CL and Vss is that because cisatracurium degrades via Hofmann elimination
throughout the body, as Vss increases, so does CL and hence the half-life
remains unchanged" (Anesth. Analg. 1996, 83:1065-71). Most notably, every time
we need to move away from the single compartment assumption, the way we model
distribution becomes key. Thinking Vss (=V1+V2) usually helps a lot. Considering
distribution clearance does too. But it's akin to summarizing elimination with
a k. The situation of extracorporeal circulation is in fact very revealing. An
interesting experiment was done in sheep as we cannot do in humans
(Anesthesiology 2004; 101:666-74). The authors conclude "renal excretion fails
to increase in proportion to the volume of infused fluid". Basically, for drugs
with a large Vd the lowering of plasma concentrations by hemodilution is
compensated by the back diffusion of the drug into plasma from the large tissue
reservoirs. On the other hand, hemodilution may also lead to the reduction of
circulating albumin and a1-acid glycoprotein affecting binding. In neonates the
effective circulating volume can be nearly doubled!
I'll finish accepting Roger's point that when I wrote "Assuming that elimination
and distribution are independent processes (with rare exceptions)" they may not
be that rare, and retracting the hint that Hans was 'wrong' when I should have
said 'biased', although I'm sure he disputes both. That's my act of contrition
for the day. Peace to all.
Warmest regards,
Luis
-
Luis Pereira, PhD
Director Quantitative Clinical Pharmacology and Pharmacokinetics Laboratory
Anesthesiology and Perioperative Pain Medicine Department, Children's Hospital
Boston
Instructor Anesthesia, Harvard Medical School
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Les,
You wrote : " MRT is by definition Vss/CL. Unfortunately some of the computer
programs call AUMC/AUC as MRT. When you give a drug orally AUMC/AUC = MRT +
MAT. "
I suggest that this definition of MRT is a contributor to the problem you
discuss.
A more precise definition is that the Mean Disposition Time (MDT) is Vss/CL.
Then MRT = MDT + MIT where MIT is the Mean Input Time (See Watari& Benet 1989
for MIT andhttp://www.pharmpk.com/PK02/PK2002023.html for MRT=MDT+MIT)
Input is not necessarily just absorption (e.g. it could be IV infusion) but the
relation holds just as well for IV infusion as it does for input by absorption.
The three components are then clearly identifiable. MDT is determined by
disposition (distribution and elimination) while MIT is determined by input.
This also emphasizes that ADME is a poorly conceived and redundant acronym
because the fundamental processes of PK are input, distribution and elimination.
Absorption and metabolism are just sub-processes.
Nick
Watari N, Benet LZ. Determination of mean input time, mean residence time, and
steady-state volume of distribution with multiple drug inputs. 207-46 1989; 17:
593-9.
--
Nick Holford, Professor Clinical Pharmacology
First World Conference on Pharmacometrics, 5-7 September 2012
Seoul, Korea http://www.go-wcop.org
Dept Pharmacology& Clinical Pharmacology, Bldg 505 Room 202D
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
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Many thanks for that expose Luis.
May I add another anecdote from anaesthetics to illustrate your point about
different clearance from different compartments? Back in the 1970's Professor
Prys-Roberts of Bristol UK was working on the cardiovascular effects of the
volatile anaesthetic halothane in pigs. The animals had a good life for several
months after the experiment but eventually the time came for slaughter, but what
to do with the corpse? The meat could not go on the usual market so it was
decided to keep it for a departmental lunch to which I was invited. To
everyone's horror the only taste from the meat was halothane, one of the most
unpleasant culinary surprises I have ever had.
I guess it was a tribute to the lipophilicity of that molecule since the pigs
had ben given their last halothane many months before their end. That and the
extraordinary sensitivity of human taste buds
Andrew Sutton
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Dear Luis,
You are right and I apologize for my unclear expressions (disclaimer: I'm
writing these in the Canadian Rockies in the very early morning hours do to huge
jet lag). Fortunately Les clarified some of the expressions.
I also want to acknowledge that I very much appreciate the biology causing all
these effects on CL and Vss. When we claim that something happened to one or
both of these biological entities it is generally based on the math we apply to
the available biological data.
Regardless of all the biology (protein binding, transporters, metabolizing
enzymes etc.) the equation Vss = CL * MRT holds (with the limitations hotly
discussed at the time of its introduction). When the relationship between Vss
and CL is discussed, this is the equation until proven otherwise.
[Can I ask what happens to this equation when the DME (disposition) processes
are non-linear? - db]
I hope everybody noticed what Les wrote. MRT is the value after IV
administration and it does not change after extra-vascular administration.
Therefore, after non-IV administration the ratio AUMC/AUC (here for simplicity
MRTnon-IV) should be correctly expressed as MRT + MAT. How does this relate to
the original inquiry by Zafar?
If Zafar had administered his drug IV, a change in the ratio Vss/CL would be
observed in the value of the MRT and it would be very easy to show why it
happened. When the drug was administered orally, we only have Vss/F and CL/F due
to the lack of the value of F. Their ratio (i.e. Zafar's inquiry), however, is
still identical to Vss/CL because the F is the same. We do not know what the MRT
(after IV administration) is and, therefore, Vss/F = CL/F * (MRTnon-IV - MAT).
In other words, Vss/F is absorption rate dependent. From the biological point of
view it does not make any sense to me. Mathematically Vss/F can only be an
estimate and people, when using it, should indicate why they believe their
estimate is good enough. I would not use Vss/F, but if you do, do it very
carefully and remember, we live in a multi-compartment world.
Peace,
Stefan
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[A repeat message but with the correct(?) sender in the from field. I'm not sure what happened but maybe I replied from the wrong message - db]
Dear Luis,
You are right and I apologize for my unclear expressions (disclaimer: I'm
writing these in the Canadian Rockies in the very early morning hours do to huge
jet lag). Fortunately Les clarified some of the expressions.
I also want to acknowledge that I very much appreciate the biology causing all
these effects on CL and Vss. When we claim that something happened to one or
both of these biological entities it is generally based on the math we apply to
the available biological data.
Regardless of all the biology (protein binding, transporters, metabolizing
enzymes etc.) the equation Vss = CL * MRT holds (with the limitations hotly
discussed at the time of its introduction). When the relationship between Vss
and CL is discussed, this is the equation until proven otherwise.
[Can I ask what happens to this equation when the DME (disposition) processes
are non-linear? - db]
I hope everybody noticed what Les wrote. MRT is the value after IV
administration and it does not change after extra-vascular administration.
Therefore, after non-IV administration the ratio AUMC/AUC (here for simplicity
MRTnon-IV) should be correctly expressed as MRT + MAT. How does this relate to
the original inquiry by Zafar?
If Zafar had administered his drug IV, a change in the ratio Vss/CL would be
observed in the value of the MRT and it would be very easy to show why it
happened. When the drug was administered orally, we only have Vss/F and CL/F due
to the lack of the value of F. Their ratio (i.e. Zafar's inquiry), however, is
still identical to Vss/CL because the F is the same. We do not know what the MRT
(after IV administration) is and, therefore, Vss/F = CL/F * (MRTnon-IV - MAT).
In other words, Vss/F is absorption rate dependent. =46rom the biological point of
view it does not make any sense to me. Mathematically Vss/F can only be an
estimate and people, when using it, should indicate why they believe their
estimate is good enough. I would not use Vss/F, but if you do, do it very
carefully and remember, we live in a multi-compartment world.
Peace,
Stefan
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Dear Stefan,
You wrote:
"I personally think that the Benet & Galeazzi equation Vss = CL*MRT is one of
the greatest in PK."
You do not provide argument for this greatness. I don't agree.
Why would one reduce the essential information in CL (e.g. determining dosing
rate at steady state) and Vss (e.g. determining loading dose) to a single value
without any meaningful value. I do not see any purpose of MRT than that given in
the excellent explanation of Leslie Benet; important, but not deserving the
epitheton 'greatest'.
Please note that the equation should be written MRT = Vss / CL, as stated by
Leslie, since the mean residence time MRT is dependent on CL and Vss, and not
the other way around (similar to k = CL / V). This is by no means trivial, as I
have indicated many times in the 'clearance versus rate constant battle'.
best regards,
Hans
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Dear Luis,
You wrote:
"1- All algebraic relationships between CL and other PK parameters are valid.
They do not imply any causality or hierarchy. Labeling them as math, biology or
pretty scribblings is irrelevant."
I don't agree. We should keep track of the right order of casuality, in order to
be able to draw the right conclusions, and the right decisions in drug dosing.
"Another explanation for the relationship between CL and Vss is that because
cisatracurium degrades via Hofmann elimination throughout the body, as Vss
increases, so does CL and hence the half-life remains unchanged"
The example of cisatracurium is an example where the relationship between CL, V
and k is different than for the majority of drugs. As you state correctly, this
drug is eliminated via Hofmann elimination throughout the body. This is a
chemical degradation, independent of the elimination capacity of the organs in
the body. In this case the body behaves like a homogenous system, and the
elimination rate constant is independent on organ function, body volume, and any
other physiological process. I totally agree that the clearance approach does
not work here, but that is because the drug elimination is not a 'regular'
clearance process.
Thank you for this interesting example.
best regards,
Hans
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Dear David,
In general these equations are valid also for non-linear kinetics. There is a
good review concerning their limitations in the Biopharmaceutics & Drug
Disposition Vol. 15, 627-641 (1994) by Cheng, Gillespie and Jusko "Mean
residence time concepts for non-linear pharmacokinetic systems".
Very best regards,
Stefan
[Stefan, I'll have to have a look at that reference. -db]
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Dear Hans,
Sure, the beauty is always in the eyes of the beholder. Because I find the Vss
the only "true" volume term, this equation reflects the interrelationship
between Vss, CL and MRT. I don't find MRT any more useless than t1/2. If people
just bothered to think about the meaning of MRT as much as they do about t1/2,
we would avoid a lot of complications. A spin-off of MRT is the MAT. In my mind
the most eloquent way of describing absorption. Again, just my opinions.
Very best,
Stefan
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Dear Luis,
Thank you for your comments on my example on hemodilution.
"An increase in volume (recall, apparent volume!) does lead to an increased
clearance, but obviously does not "imply that the renal and/or hepatic function
of the patient is increased".
In my opinion an increase in volume does not lead to an increased clearance,
since clearance is directly related to renal and/or hepatic function, and not
affected by the volume of distribution.
Let's make the example somewhat more specific, by assuming that the drug has
properties similar to creatinine (or inuline, or an other compound to assess
renal function), i.e. a drug that is not metabolized, not bound to plasma
proteins, not actively secreted into the urine, and not reabsorbed in the
tubules. For such compounds the (renal) clearance is a measure of the Glomerular
Filtration Rate (GFR). In your reasoning the clearance, and so the measured GFR,
would increase. So, the renal function of the patient is increased by
hemodilution. Do you agree? I would say that GFR and clearance remain
unaffected.
"And that's precisely the caveat of a clearance parameterization. It can go up
or down by both reasons of elimination or distribution."
Clearance is not affected by distribution, so this caveat can be ignored. It
would be better to say that clearance allows to separate elimination and
distribution.
"When Hans says, "one would assume that renal and/or hepatic function of the
patient are not (essentially) altered, so clearance remains the same" the word
'clearance' is wrongfully used for rate of elimination."
I don't think I misused the word 'clearance' for rate of elimination. With the
word 'clearance' I meant the pharmacokinetic parameter clearance, the parameter
characterizing the eliminating capacity (not: elimination rate) of all
eliminating organs. See also the above comment on GFR.
To clarify the terms elimination rate, elimination rate constant and clearance,
consider what happens after hemodilution: the volume of distribution increases,
so the drug concentration decreases immediately after hemodilution. Since the
elimination rate (amount/time) is the product of clearance and drug
concentration, and since clearance remains constant, the elimination rate
decreases. And the elimination rate constant k also decreases as can be derived
from its definition:
1) k = elimination rate / amount the body; elimination rate decreases, amount in
the body immediately after hemodilution is unchanged (and both are decreasing
with rate constant k if no further doses are administered);
2) k = CL / V; clearance remains the same, V increases.
(both definition look different, but they are essentially equal, as can be seen
by multiplying both numerator and denominator of eq. (2) by the plasma
concentration, yielding eq. (1)).
"There's no way an increase in volume can "result in a decrease of k" since by
the very definition of a rate constant there's no scaling or volume term
involved in the mass balance."
I don't understand this argument. As derived above, k will decrease, whatever
definition of k is used.
"In practical terms, some drugs require indeed dosing adjustments with CPB while
others don't, depending on which component of the clearance, i.e. elimination or
distribution, is most affected."
In my opinion, dosing adjustment with CPB is straightforward if the clearance
approach is used. In the case of hemodilution alone, an extra loading dose
should be administered to fill the extra volume of distribution. The
mainstenance dose should not be adjusted (except for the case that clearance is
affected by an effect on the eliminating capacity of liver and kidneys).
Best regards,
Hans
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Dear Roger,
You wrote:
"Hans, it is good to hear now that you realize that rate constants and
clearances are interchangeable."
I said: "clearance and elimination rate constant are not interchangeable in a
biological sense". The math is not under discussion.
"But just how do you decide that one is "mathematical" and the other is somehow
more "biological"?"
We should keep track of the right order of casuality, in order to be able to
draw the right conclusions, and the right decisions in drug dosing. The example
of hemodilution by extracorporeal circulation shows that it is necessary to
define this order of casuality: either CL depends on k, or k depends on CL,
since both assumption lead to a different conclusion about the changes in k and
CL. The 'biological' argumens in favor of the clearance approach have been
discussed in my numerous e-mails over the last years.
I am still very interested to hear your view on the example of hemodilution by
extracorporeal circulation.
best regards,
Hans
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