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Dear colleague,
I am developing a two compartment model with both linear and nonlinear clearance for a monoclonal
antibody. The study was conducted in monkeys at multiple dosing levels (non-linearity was observed).
For the current model, I have 6 parameters (CL, V1, V2, Q, Vmax and Km). The model failed to run
even if I assume all the observations from one individual (No between subject variability). I am
thinking to fix some parameters but not confident which one could be fixed as they all connect to
each other closely. I saw other people fix the Linear CL (obtained from the high dose). Appreciated
any suggestions from you.
Dating
[Have you started with a one compartment model. Does that 'work'? Be careful about the magnitude of
the Vm and Km values. They need to be in range for the concentration or amount used internally, i.e.
described in the differential equations - db]
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First off start at the beginning. Have you run a NCA to get initial estimates? Then as suggested
start with a simple 1CM with linear elim. It will fit horribly so then add the nonlinearity. Try to
isolate the problem. And what exactly do you mean by did not run? What software platform?
Dr. Wolowich
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Dear Dating:
What software are you using? I have 2 comments and suggestions.
1. I would suggest you use a nonparametric (NP) modeling approach such as Pmetrics, in which
you do NOT have to specify the shape of the population parameter distributions, and do not have to
summarize them as mean, SD, etc., although of course you get these as well. You might look at
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric
Population Methods: Their Comparative Performance in Analyzing a Clinical Data Set and Two Monte
Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
Further, NP models permit easy detection of unexpected subpopulations. You might see
Neely M, van Guilder M, Yamada W, Schumitzky A, and Jelliffe R: Accurate Detection of Outliers and
Subpopulations with Pmetrics, a Nonparametric and Parametric Pharmacometric Modeling and Simulation
Package for R. Therap. Drug Monit. 34: 467-476, 2012.
In addition, using NP models lets you evaluate and maximize the precision with which a dosage
regimen is best able to hit a desired therapeutic target goal. The entire issue of therapeutic
precision can never even be perceived using parametric models such as NONMEM, for example. You might
see
Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
I do not think you should have to fix parameter values from literature data. And you can
write the differential equations to have both linear and nonlinear relationships as you wish.
Michael Neely’s Pmetrics software for NP modeling is freely available and downloadable from
www.lapk.org.
2. I do not understand why you wish to use clearance as a parameter. When you take care of
patients, clearance gives you no direct clinical information about the rate of movement of the drug
from one compartment to another. Its dimensions are vol/time, and the actual information you are
clinically interested in is the rate of elimination, which is provided by the rate constant. Volume
helps the clinician to evaluate the patient in terms of his fluid balance and needs, and Kel
provides the direct information you need about the movement of the drug from one compartment to
another, and about elimination. Clearance does not do this, It obscures and hides the information
behind the volume, as clearance is actually NOT synonymous with elimination, but really is V times
K, as everyone knows if you think about it, and both are comingled. It is interesting to me that
even experienced pharmacometricians who actually know this still behave as though clearance is the
same as elimination in their everyday speech and thoughts. I bet this is why you are using clearance
now.
This is a trap, and results in PK models which are of suboptimal use clinically. If you say that
these models are used only for research, why does one do this if not to have some useful information
for social use? Science should not be conducted in a social vacuum. Please think about this issue,
and please consider that NO research is done in a social vacuum. You might look at
Jelliffe R: Challenges in Individualizing Drug Dosage for Intensive Care Unit Patients: Is Augmented
Renal Clearance What We Really Want to Know? Some Suggested Management Approaches and Clinical
Software Tools. Clinical Pharmacokinetics. 2016; 55 (8): 897-905. DOI 10.1007/s40262-016-0369-4
Very best regards and good luck!
Roger Jelliffe
Roger Jelliffe MD, Professor of Medicine Emeritus, Founder and Director Emeritus, Laboratory of
Applied Pharmacokinetics and Bioinformatics, USC School of Medicine,
Consultant in Infectious Diseases, Children’s Hospital of Los Angeles
We have a book coming out in November. “Individualized Drug Therapy – Basic Techniques, Relevant
Software, and Clinical Applications”, edited by Roger Jelliffe, MD and Michael Neely, MD, is in
press by Elsevier, and is planned to be available November 2016.
This is a book by clinicians for clinicians. If you wish to prescribe therapeutic drugs to each of
your patients with skill, optimal precision, and consideration for each patient’s individual needs,
and to minimize the poor treatment outcomes from blunt, overly simplistic last century
one-size-fits-all dosing for the fictitious average patient, then this book is for you.
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Dear Zhang,
Yes, I think that fixing the Linear CL is a good approach in your situation.
This can be done also by considering Literature values of the average Linear CL of mAb in Monkey.
Article below my help finding this lit. value.
Dong JQ1, Quantitative prediction of human pharmacokinetics for monoclonal antibodies: retrospective
analysis of monkey as a single species for first-in-human prediction.
Clin Pharmacokinet. 2011 Feb;50(2):131-42.
BR
Marc Laisney - DMPK basel
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Hi, I can surmise the software is Phoenix's NLME engine as Daping also posted to the product forum
where the question has also been answered with some suggested code corrections.
https://support.certara.com/forums/topic/901-model-with-micro-parameterization/?p=3857
Best regards,
Simon.
Simon DAVIS
Senior Scientific Consultant
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Hello, Roger.
I've indeed enjoyed using Pmetrics.
I have to take issue with your item #2, though. Clearance is not K * V except as a convenience of
being able to model or draw the slope of an exponential and extrapolate its intercept (K and D/V,
respectively). Clearance is the rate of drug removal (by additive processes) relative to the drug
concentration, and intrinsic clearance is that same rate of drug removal relative to the
concentration of unbound drug. The fact that the units of clearance are Volume/Time is just
unfortunate, as are the units of R in the ideal gas law (or the units on the "72" in the denominator
of the Cockcroft-Gault equation, for that matter). Defining Clearance as anything other than
Rate/Conc makes my head explode when trying to explain to students why clearance changes in
saturable elimination.
Be well.
Paul Hutson, PharmD, BCOP
Professor
UWisc School of Pharmacy
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Dear all,
Thanks for you your great comments.
To Dr. Wolowich’s comments,
I ran the NCA and found the dose-dependent pharmacokinetics. Two-compartment model was commonly used
to describe the disposition of the mAb. So I added michaelis menten kinetics parallel with linear
elimination in the central compartment to characterize the nonlinearity (potentially due to the
mAb-target binding and internalization).
To Dr. Jelliffe’s comments,
I am using Phoenix NLME from Pharsight. I only have 100 observations from 24 subjects at multiple
dose levels. In the model, there are 6 parameters (CL, V1, V2, Q, Vmax and Km). Because of
overparameterization and limited data, the normal population pk model failed to converge. I used
naïve pooled method in Phoenix, which assumes all observations from one single individual and
ignores the inter-individual variations in ETA values (All ETAs are forced to zero), but respects
inter-individual differences in dosing and covariate values. So I guess parametric or nonparametric
is not the issue here.
I agree with your point that clearance didn’t give direct clinical information about the drug’s
disposition as it hides the information behind volume (CL=K*V), and clearance is different from
elimination. However, with one dataset, the results would be the same whether it is parameterized by
rate constant (Kel, K12, K21) or clearance (CL, Q). And the secondary parameter could always be
calculated.
For the model I am trying to develop, I used both micro constant (Kel, K12, K21) parameterization
and clearance parameterization (CL, Q). The results are the same. If I want to fix some parameter
due to convergence failure and small dataset, I am not confident if I could fix Kel or CL. If CL is
fixed, Kel could be changed depending the change of V (CL=Kel*V).
To Dr. Laisney’s comments,
I saw people fixed linear CL from higher dose group (assuming linear CL doesn’t change crossing
dose). As Roger’s comments above, CL is not the same concept with elimination. If we fix CL, the Kel
may change or not depending on the change of volume (Kel*V). In this case, is it more appropriate to
fix Kel?
All mAb probably have similar volume of distribution and even linear clearance (The different might
be less than 5 fold). How do we verify the estimations of Vmax, Km and other parameters, if we fix
the linear clearance either from the higher dose group or from literature values?
To Simmon’s comments,
Phoenix’s NLME was employed in my analysis. I used both micro constant parameterization and
clearance parameterization, because I am not sure if should fix CL and Kel.
Daping
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Dear Daping:
Yes, of course the results are the same with either V and Cl or V and K parameterization. That is
not the issue. The issue simply is what information is most useful clinically. It seems you have
many parameters for not many observations. It may well be that it will be difficult to make such a
complex model from such sparse data, and I understand that is the problem you are trying to deal
with. Is such a model identifiable? Even if it might be, which I doubt that you will get results
that will make you happy with an average of about 4 observations per subject. In addition, though, I
really would suggest that you examine the nonparametric approach and look at
Bustad A, Terziivanov D, Leary R, Port R, Schumitzky A, and Jelliffe R: Parametric and Nonparametric
Population Methods: Their Comparative Performance in Analysing a Clinical Data Set and Two Monte
Carlo Simulation Studies. Clin. Pharmacokinet., 45: 365-383, 2006.
Parametric vs NP is still an issue always, Please consider this carefully. You get greater
likelihoods with NP modeling approaches simply because the shape of the parameter distributions in
the pop model are not specified there. Because there are no constraints put on the shape of the
distribution, there is no constraint on the maximum likelihood estimate due to that, and you get
better likelihood estimates. An example is shown in the paper above.
The other important issue here between P and NP, always, is the ability with NP models to design
dosage regimens that are maximally precise in hitting a desired target. Para metric approaches can
never detect ti issue, as they use only single valued parameter estimates which are designed only to
summarize, not to fully describe the parameter distributions. Please also look at
Jelliffe R, Bayard D, Milman M, Van Guilder M, and Schumitzky A: Achieving Target Goals most
Precisely using Nonparametric Compartmental Models and "Multiple Model" Design of Dosage Regimens.
Therap. Drug Monit. 22: 346-353, 2000.
I repeat. Parametric models will simply never detect this most important clinical issue of
evaluating dosage precision. Using parametric PK models, it is simply not possible to develop dosage
regimens that are maximally precise. Please consider the clinical utility of P and NP models most
carefully. And all models are made with some sort of final use in a setting that has social utility
– the clinical arena – what are able to do for patients.
How many dosage levels for each patient were there in your data set? It seems to me that it may well
be most difficult to get a model you seek with the data you have. But NP always seems more useful
than P because of the facts put forth above.
As to Dr. Proost’s comments, the fact that many people have used parametric procedures for a long
time is not an argument here any more than it is for sails over steam power in ships. We can also
forget wheeled vehicles, as there certainly were millions of years before people invented wheels.
Dr. Proost is entirely correct. I fail completely to understand his point, so I must of course fail
to understand basic principles of PK. I do, however, think I understand a bIt of math, of which PK
is a subset.
I also fail completely to understand why he says that knowing the half time of creatinine is not
relevant. Did God give us kidneys to make urine, or to excrete substances from the body? I would
suggest that making urine is a means toward the end of excreting things from the body. I simply do
not understand why, to Dr. Proost, and I quote, “Nobody ever talks about the elimination rate
constant of creatinine, because it is not relevant.” Oh, my!
All the best to everyone,
Roger Jelliffe
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Hi, Paul:
It is always so good to hear from you. The formula IS that Cl = V times K. It is unfortunate
that these units are what they are, but there it is. Clearance gives no direct information of the
rate of movement of drug from one compartment to another. V and K are comingled and the individual
contribution of each is obscured and hidden.
I also agree totally that one can look at clearance and think of it as the rate of excretion
of a drug per unit of drug in the serum or plasma. You are quite correct. That is another useful way
to think of it. I agree absolutely.
I think the real question here is not PK or math, but rather what is the most useful way to
present the information for clinical use. The patient has one issue of V and fluid balance. The
other issue re is the behavior of the drug and its rate of movement from one compartment to another.
I submit that it is more useful clinically, for the practical aspects of patient care, to see the
behavior of the drug presented as its rate of movement out of the body or from one compartment to
another in units of time (K) and the issue of the patient's fluid balance presented separately in
terms of V. Clearance simply obscures this information, and one must divide it by V to get the
important K.
All the best,
Roger
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Dear Roger,
Thank you for your reply. I don't think your comparison with sails and
steam power holds for nonparametric vs parametric, but I fully agree
that the number of users is not a convincing argument pro or con.
I know that you understand a bit of math, but I don't agree with your
vision that PK is a subset of mathematics. In my view, PK is a subset of
biology, using mathematics to describe processes quantitatively. In the
biological view, clearance is the measure of the capacity of the body to
remove drugs, and the elimination rate constant k = CL/V. Mathematically
this is exactly the same as CL=k*V, but in the biological view there is
a big difference in both equations (the same difference as between our
views ...).
You quoted me in “Nobody ever talks about the elimination rate constant
of creatinine, because it is not relevant.” followed by 'Oh my!'. Now I
don't understand what you mean, and I still don't know why one should
know the elimination rate constant of creatinine. But I fully understand
why we need creatinine clearance, as we need clearance as the primary
parameter of drug elimination,
best regards,
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University of Groningen, the Netherlands
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Dear All,
The discussion on CL vs. K approaches in PK analysis seems endless and evergreen and each
protagonist has his/her own arguments. I am not going to support neither. My clinical experience
with CL/V and K/V parameterizations, when using USC*PACK and MM-USCPACK versions, revealed their
interchangeability from statistical point of view. But not from clinical view point.
I do agree that in physics and chemistry, as mathematically oriented, rate constants are intuitively
understandable as is CL for physicians. Saying that, I have to agree with protagonists of K approach
that CL estimation is somewhat “commingled” since its estimation in clinical settings demands proper
design and volume measurements of a given biological fluid (e.g., urine, bile, saliva, etc.) in
order to assess renal, biliary or salivary clearances [Gibaldi, M. and D. Perrier (1975)
Pharmacokinetics. Marcel Dekker, Inc., pp. 6-17 and pp. 301-305; Terziivanov, D. et al. (1986)
Pharmacokinetics and quantitative characterization of cefotiam excretion after intravenous
administration to patients after cholecystectomy. Eur J Clin Pharmacol. 30:439-444]. That might
introduce additional errors in timing and sampling of these biological fluids. My humble experience
points out that quantitative characterization of drug excretion ways is more understandable for
medical students and physicians when it is performed in CL terms.
Frankly speaking, I do not see any ‘schism’ ;-) between the two approaches. Each has its own weight
when applied properly and does good job when applied appropriately.
Greetings,
Dimiter
Dimiter Terziivanov, MD,PhD,DSc, Professor
Head, Dept. of Pharmacology and Clinical Pharmacology
SOFIA UNIVERSITY ST. KLIMENT OHRIDSKI
FACULTY OF MEDICINE
LECTURER, FAC CHEM&PHARMACY
UNIV HOSP LOZENETZ
1 Koziak str.
1407 Sofia, BULGARIA
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Dear Dimiter,
Thank you for your 'balanced view' in this discussion. Unfortunately, in my humble opinion, such a
balanced view does not hold.
Please note that the question 'CL or k' does NOT refer to the question which parameter can be
understood most easily, nor which parameter can be estimated most easily or precisely, nor which
parameter is most useful in clinical practice, and so on.
The question is: Is k dependent on CL, or CL dependent on k? There is no 'balanced view' here, since
one has to choose, as can be concluded from the following examples (that I posted several times in
the past):
1) What happens with the pharmacokinetic variables in a patient in the case of displacement of
tissue binding? This results in an decrease of the volume of distribution, as we all will agree. But
what happens with clearance and elimination rate constant, and how should be the maintenance dose be
adjusted?
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 decreased volume results in a decrease of k, and an increase of
half-life.
In the 'rate constant approach', k would not be affected, and the decrease in V will lead to an
decrease in clearance. Does this imply that the renal and/or hepatic function of the patient is
decreased? The decrease in clearance would imply that the maintenance dose be decreased. I'm quite
sure that this will not be beneficial for the patient.
2) Consider the perfusion rate-limited drug elimination by the liver. For a drug with very high
affinity for the metabolizing enzymes (i.e., a drug with a high intrinsic clearance), the extraction
ratio may be close to 1. In this situation, the hepatic clearance is limited by liver blood flow
(because of differences between blood and plasma the real situation may be more complicated, but
this is not relevant for the current discussion). Assuming a relatively small contribution of renal
excretion, the upper limit of clearance is the liver blood flow, say 1 L/min. If Drug A has a Vd of
5 L and Drug B has a Vd of 500 L, the upper limit for the elimination rate constant for drug A is
0.2 min-1, and for drug B 0.002 min-1. How would you explain this large difference in elimination
rate constant? Both drugs are eliminated 'at the maximum capacity of the liver', and the only
difference is the volume of distribution. Is the elimination rate constant dependent on clearance,
or is the clearance dependent on the elimination rate constant?
3) Glomerular filtration rate (GFR) is considered as the most relevant measure of renal function.
The most common approximation of GFR is the creatinine clearance. This is a very useful concept,
both for nephrologists and for the adjustment of doses in patient with impaired renal function.
Fortunately, the clearance approach was used here from the very beginning! The renal clearance of
creatinine is 'fundamentally' determined as the rate of creatinine elimination divided by the
creatinine serum concentration, or, in other words, the volume of plasma cleared per unit of time.
Even in non-steady-state conditions, the creatinine clearance can be estimated by application of
this fundamental equation, as Roger Jelliffe did in his very elegant and useful paper (Math BioSc
1972; 14: 17-24). As far as I know, nobody in this field has ever considered the rate constant
approach, and I'm happy they didn't. Unfortunately, pharmacokineticists started the rate constant
approach from the concept of half-life, and it took about 40 years to convince the
pharmacokineticists that they were wrong.
These examples demonstrate that a view of 'equal priority' of clearance and elimination rate
constant does not hold. It is not a 'chicked-and-egg' question. There can be only one way of
dependence.
One more reply to your comment:
> I have to agree with protagonists of K approach that CL estimation is somewhat “commingled” since
> its estimation in clinical settings demands proper design and volume measurements of a given
> biological fluid (e.g., urine, bile, saliva, etc.) in order to assess renal, biliary or salivary
> clearances.
>
This is true for the estimation of renal clearance, biliary clearance etcetera, but not for total
clearance, and that is what we are discussing. Total clearance (or CL/F in the case of extravascular
dosing) can be estimated easily from Dose/AUC, and AUC can be estimated easily and precisely in most
cases. I cannot imagine a data set where k and V can be estimated precisely, and CL cannot be
estimated precisely. So, I don't agree with your argument of precision.
best regards,
Hans
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University of Groningen, the Netherlands
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Hi everybody,
The "One more reply..." part in Hans' reply is the part that always interests me. The discussion
seems to always relate to IV-administration, because there is no way, to the best of my knowledge,
to determine any volume term after non-IV administration unless we assume 1-compartment model. I
noticed that Dimiter talks about K while Hans indicated k. I can understand that K can be determined
in 1-compartment model also after non-IV administration, but I can't understand how you could
determine k (any k) after non-IV administration in a multi-compartment model. The logic to that is
the following:
K = CL/V
It would make no difference if this drug was administered non-IV, because replacing CL with CL/F and
V with V/F gives exactly the same K (at least mathematically). However, this would not be correct if
your drug is best characterized by multi-compartment disposition (like most drugs are). It can be
easily seen from equations like:
Vss = CL * 1/K (one compartment model) and it would not change if you gave the drug IV or non-IV
because 1/K = MRT. However,
Vss = CL * MRT (multi-compartment model) after non-IV administration becomes
Vss/F = CL/F * (MRTnon-IV - MAT)
after non-IV administration to be consistent with the original equation. Again the F is eliminated.
However, MRTnon-IV - MAT is impossible to calculate without IV data (because 1/K is no longer equal
to MRT).
So, my question is this: Is the modeling done in a 1-compartment environment (after non-IV
administration)? If not, how is the V calculated and what does it represent?
Best,
Stefan
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Dear Hans,
Thank you so much for your in depth discussion of that issue. With my full respect to your arguments
I am a little bit confused by your argument #1:
>1) What happens with the pharmacokinetic variables in a patient in the case of displacement of
>tissue binding? This results in an decrease of the volume of distribution, as we all will agree.
>But what happens with clearance and elimination rate constant, and how should be the maintenance
>dose be adjusted?
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 decreased volume results in a decrease of k, and an increase of
half-life.<
If “clearance remains the same”(JHP) how, in mathematical terms, the decreased volume will result in
decreased K and increased half-life? That is challenging my primary school algebraic knowledge.
To your comment:
> This is true for the estimation of renal clearance, biliary clearance etcetera, but not for total
> clearance, and that is what we are discussing <.
>
Total CL, alike K, is a composite physiological parameter:
CL(tot) = CLh + CLr + CLb + …., just is K = k(h) + k(r) + k(b) +…. Both are dependent on
physiological (pathological) status of given clearance organ(s). Physiological and pathological
processes in living organisms are interrelated and interdependent. Pharmacometricians describe
mathematically these processes, but always under certain assumptions and with simplifications.
As a clinician I am interested in interrelationships between CL(tot) and K and not in what parameter
is dominating over the other.
Your comment:
> The question is: Is k dependent on CL, or CL dependent on k?<
>
presumes dominance. Let me give the following real life clinical situation. Suppose a drug whose
renal and hepatic clearances contribute for about 50% each of its CL(tot) and a patient with
slightly reduced renal function [renal insufficiency grade I (stage I)]. CL(tot), when measured, is
unaffected because of timely increased hepatic clearance (that compensatory involvement is
time-limited). When measuring renal excretion rate of the drug under discussion it is decreased in
dependency of reduced renal function. If I order dose adjustment based on CL(tot) measurement only I
may overload that patient. This kind of patients are my great concern.
With that reason in mind (and not only) I wrote “that CL(tot) estimation is somewhat “commingled”.
Responsible physician has to know clearance organs contributing for CL(tot) in order to be
therapeutically more efficient and less harmful. Otherwise all our PK knowledge (equations, models
and PK parameter estimations with more or less precision) is useless.
Finally, about my
>'balanced view' in this discussion< and your assertion that
>There is no 'balanced view' here<.
>
Medicine is science and art on balance. Hans, I am trained, unfortunately, to balance between 2
options – to be safe and therapeutically efficient or to be harmful. My way of thinking is to weigh
between the good and the bad. And I am sorry, indeed, if that is irritating to you.
With ALL my respect to you,
Yours,
Dimiter
Dimiter Terziivanov, MD,PhD,DSc, Professor
Head, Dept. of Pharmacology and Clinical Pharmacology
SOFIA UNIVERSITY ST. KLIMENT OHRIDSKI
FACULTY OF MEDICINE
LECTURER, FAC CHEM&PHARMACY
UNIV HOSP LOZENETZ
1 Koziak str.
1407 Sofia, BULGARIA
[Hopefully the quoting is correct. Some line feeds were missing from Dimiter's email - db]
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Hi all,
First of all, I thank all participants that are arguing about
clearance and ke because it is the occasion to think in depth about
the interpretation of these parameters.
I must say I am quite surprised by the question "Is k dependent on CL,
or CL dependent on k?" and its meaning.
I mean, either Cl = ke Vd for a fully linear pharmacokinetic, or Cl
and ke are not well defined (Cl changes with time and ke simply does
not exist) if any non-linearity exists in the PK.
If Cl = ke Vd, they are equivalent and both Cl depends on ke and ke
depends on Cl, it is just a subjective matter, but mathematically
"dependency" is a fully symmetric relationship, especially for a
such a functionnal relationship.
Of course, one can argue that « Cl is the physiological process and ke
is a measure of Cl » or any formulation that suggest a "causal" or
"directionnal" link. I guess this is what is suggested by the question
formulated.
But in that case, I would better say that both Cl and ke depends on
the underlying metabolic/physiologic processes at play, and that none
of them is relevant as a concrete description of what happens. And for
all specific cases interpretations, as the examples given below, it is
this underlying mechanism that matters. I mean clearance as a "volume
of plasma cleaned by unit of time" or as an imaged view of a "flux of
plasma/blood through a filtering membran" is just a mind-image and far
from what really happens in the body, right?
Of course, for _practical use_, both of them has advantages, and I
have no problem with the affirmation that clearance is clinically more
relevant (even if I personnaly prefer the ke approach): what matters
is that the clinician can use whatever he is comfortable with to cure
the patient in the best conditions.
(see also comments below for each of the three examples given; I also
join an answer to an old message you answered to one of mine about
this subject and I forgot to answer…)
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Dear Hans,
Thank you very much for your reply! Very much appreciated.
First to the CL vs. K controversy. Surprisingly nobody has taken up the fact that drugs are claimed
to undergo renal or metabolic clearance (or any combination thereof). Renal clearance is in fact the
only thing that we can truly determine after non-IV administration (= Ae/AUC) regardless of the
compartment model or route of administration. We can't even determine the CLm after IV
administration unless you know the CLr, as CLm is CLt - CLr. What about the K?
Obviously you did not need the K to determine CL, so it must be related to the V. In my humble
opinion the only correct volume term is the Vss. In a 1-compartment model Vss = CL * 1/K, but so is
the Vbeta. However, in any multi-compartment model Vss < Vbeta, because MRT < 1/beta. Again, this is
no news. What happens when we administer the drug non-IV? Vbeta/F = CL/F * 1/beta. This equation
will be correct only if the beta does not change after a non-IV administration. Well that is also a
possibility (sometimes), but how do you know when it is? If the absorption is in any way involved in
your determination of the beta (or lambda(z) or K), the Vbeta/F * F will not result in the Vbeta
determined after IV administration. In other words, the determination of Vbeta/F is dependent on
assumptions that you cannot control or verify. Anyway, as I indicated earlier, Vbeta has a limited
meaning as a volume term whichever way we look at it.
As I indicated in my previous post, Vss/F (for drugs exhibiting multi-compartment disposition) can
be determined only by determining the Vss after IV-administration and dividing it by F (obtained by
AUC comparison after IV- and non-IV administrations). Any other attempt to describe it is simply
incorrect, because we do not know the MAT unless we have IV data as well. Clearly Vss/F is
absorption rate dependent as Vss/F = CL/F * (MRTnon-IV - MAT). It would be even more striking in an
e.g. 2-compartment model (Vss = V1 * (1 + k12/k21)). V1 nor k12/k21 cannot be determined after a
non-IV administration so there cannot be a Vss/F.
So, if we can assume a 1-compartment model, I have no problem with the non-IV data and modeling. If
not, I don't understand what the V/F represents.
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Dear Stefan,
Thank you for your comments. A few comments from my side.
>
>>
> First to the CL vs. K controversy. Surprisingly nobody has taken up the fact that drugs are
> claimed to undergo renal or metabolic clearance (or any combination thereof).
You are correct, but for many purposes we do not need to know renal and
metabolic clearance; for example, to determine the dosing rate to reach
a specific steady-state plasma concentration, we need to know (total
(body)) clearance.
> Renal clearance is in fact the only thing that we can truly determine after non-IV administration
> (= Ae/AUC) regardless of the compartment model or route of administration. We can't even determine
> the CLm after IV administration unless you know the CLr, as CLm is CLt - CLr.
This is correct, but see my previous comment.
>
> Obviously you did not need the K to determine CL, so it must be related to the V.
I don't understand what you want to say here. If you mean that CL is
related to V, I don't agree. CL and V are independent (albeit that both
may be correlated with body weight and with the degree of plasma protein
binding).
> What happens when we administer the drug non-IV? Vbeta/F = CL/F * 1/beta. This equation will be
> correct only if the beta does not change after a non-IV administration. Well that is also a
> possibility (sometimes), but how do you know when it is? If the absorption is in any way involved
> in your determination of the beta (or lambda(z) or K), the Vbeta/F * F will not result in the
> Vbeta determined after IV administration. In other words, the determination of Vbeta/F is
> dependent on assumptions that you cannot control or verify. Anyway, as I indicated earlier, Vbeta
> has a limited meaning as a volume term whichever way we look at it.
You are right, but this would apply only to cases where the elimination
is absorption rate-limited, i.e. the 'flip-flop kinetics'. In other
cases there is no reason why beta would change after a non-IV
administration.
> Clearly Vss/F is absorption rate dependent as Vss/F = CL/F * (MRTnon-IV - MAT).
What do you mean with 'dependent' here? If you mean that the calculated
value Vss/F depends on the calculated value of MAT, you are correct (of
course, it is in the equation). But if you mean that the 'true value' of
Vss/F depends on the 'true value' of MAT, I don't agree! In the latter
case, the difference '(MRTnon-iv - MAT)' is the MRT after intravenous
bolus dose, and its 'true value' is independent of MAT.
best regards,
Hans
Johannes H. Proost
Dept of Pharmacokinetics, Toxicology and Targeting
University of Groningen, the Netherlands
Back to the Top
Dear Hans,
Thanks you again for your response!
>I don't understand what you want to say here. If you mean that CL is related to V, I don't agree.
>CL and V are independent >>(albeit that both may be correlated with body weight and with the
>degree of plasma protein binding).
>
I totally agree. I just wanted to say that I can determine CLt and CLr without using (or knowing)
the K.
>You are right, but this would apply only to cases where the elimination is absorption rate-limited,
>
>i.e. the 'flip-flop kinetics'. In other cases there is no reason why beta would change after a
>non-IV
>administration.
>
First, many drugs actually show some degree of a "flip-flop" effect although you would seldom see a
situation in which the terminal slope and the absorption slopes actually "change places". Here we
get to the area in which I have fetishes. In my opinion half-life does not change after non-IV
administration (contrary to MRL). Therefore, its determination after non-IV administration is
dependent on assumptions (conditional). So, again in my opinion, there is always a level of
assumption involved there. I conclude from this that the V/F used in modeling is actually Vbeta/F
assuming that the terminal slope is identical to that after IV-administration. In any case, the
Vbeta describes the distribution at the terminal slope only, while I think the Vss is the volume we
should be interested in. Something that would be "logically" analogous to a constant rate infusion
(CRI) in an IV-administration situation. There too you would like to calculate the Vss using the
terminal slope (after termination of the CRI) for calculation of the MRT. It should not be used to
calculate the drug remaining in the body (Vbeta). What makes it different after non-IV
administration?
>What do you mean with 'dependent' here? If you mean that the calculated value Vss/F depends on
>the calculated value of MAT, you are correct (of course, it is in the equation). But if you mean
>that
>the 'true value' of Vss/F depends on the 'true value' of MAT, I don't agree! In the latter case,
>the
>difference '(MRTnon-iv - MAT)' is the MRT after intravenous bolus dose, and its 'true value' is
>independent of MAT.
>
Yes, probably a bad choice of words. The MRT after IV-administration is the ratio between Vss and CL
(as well as Vss/F and CL/F). However, MAT, as the only value that we don't have to calculate it
after non-IV administration, makes the calculation "dependent" on that.
Very best regards,
Stefan
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