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This is a fairly simple question, but the concept of volume and clearance being independent has
always confused me.
Can the value of total plasma clearance of two different drugs be compared to one another?
My initial reaction is yes of course, but then I thought of the following example:
Drug A has a half life of 1 hour, Drug B has a half life of 100 hours.
If Drug A has a Vd of 2 L and Drug B has a Vd of 200 L, total clearance values from NCA could be the
same/similar despite the drastic difference in half life.
I think the issue here is that the terms clearance and half-life are often used almost
interchangability in the literature to refer to how "rapid" a drug is cleared from the plasma. For
instance the drug with a one hour half life may be referred to as being cleared much more rapidly
than the agent with a 100 hour half-life, but in this case, the term "cleared" does not refer to
clearance really, it's referring to half life. I believe this is the source of my confusion but
would like a confirmation from someone else.
Thanks!
Parag
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Dear Parag,
You are absolutely right and your point is very illustrative, as the saying goes "All Half-Lives Are
Wrong, Some Are Useful". I think half-life is the most commonly used PK parameter and yet it is also
the most misleading PK parameter, especially when the drug undergoes multi-compartmental kinetics. I
have seen half life of the drug quoted as 100 hours yet it was the half life of less than 1 of the
administered dose. For drugs with multi-compartmental kinetics we need to use the "Effective
Half-Life". Can we have some more discussion on Effective Half Life.
Regards.
Aziz Karim
[Aziz, can you define this 'effective half-life' of which you speak? I thought that 'saying' was
referring to models ;-) -db]
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Dear Aziz,
Some references for effective half-life:
1. Boxenbaum H. J Clin Pharm 1995;35:763-766.
2. Sahin S. Pharm Res 2008;25(12);2869-2877.
3. Grover A. J Pharmacokinet Pharmacodyn 2011:38:369-383.
Regards,
Raju
Nagaraju.Poola.-a-.sunovion.com
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The effective half-life was a concept developed by Kwan and colleagues at Merck many years ago and
then made more explicit in the papers by the late Harold Boxenbaum.
I copy below a PharmPK discussion from November 1, 2010. The Sahin and Benet 2008 paper provides
what I believe is the only use for a half-life measure, prediction of accumulation upon multiple
dosing.
The various uses, nonuses of half-life are referenced in Sahin and Benet. I had a long
correspondence with Harold before publishing that paper, after which he did agree with us.
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
Email: leslie.benet.-at-.ucsf.edu
>Subject: PharmPK Re: Enterohepatic reabsorption half-life
>
> PharmPK - Discussions about Pharmacokinetics Pharmacodynamics and related topics
> >
> The following message was posted to: PharmPK
> >
> Hi Lisa,
> >
> The "effective half-life" is estimated from the observed extent of accumulation in plasma (and
> known dosing interval) after repeated dosing as described by Boxenbaum et al. The "effective
> half-life" is simply that half-life consistent with the observed accumulation. Therefore, for a
> drug undergoing EHC, the extent of accumulation in plasma after different dosing regimens may be
> predicted from the effective half-life.
> >
> However, there has been a lot of discussion around assessment of accumulation on PharmPK and the
> use of "effective half-life" has been criticized. The relationship between drug accumulation and
> dosing interval is comprehensively reviewed in [Sahin and Benet, Pharm Res 25:2869 (2008)].
> >
> Regards,
> >
> Charlie
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Dear Parag,
In addition to the answer of Aziz: the topic of clearance and half-life has
been discussed several times in PharmPK over the last years; please check
the archive at http://www.pharmpk.com/.
> This is a fairly simple question, but the concept of volume and clearance
> being independent has always confused me.
In short: clearance is a measure of drug elimination capacity, and is
independent of volume of distribution. Half-life is the net result of
clearance and volume.
Clearance is (among others) used to calculate the dose needed to maintain a
target drug concentration, based on the following equation at steady state,
i.e. administration rate = elimination
F * Dose / tau = CL * Css
where F is bioavailability, tau is the dosing interval, CL is clearance and
Css is the concentration at steady state (note that there is no volume of
distribution or half-life in this equation!).
Half-life is (among others) used to calculate the dosing interval to
maintain the drug concentration within the therapeutic window; e.g. if the
dosing interval is equal to the half-life, the ratio of maximum and minimum
concentration will be 2 (or smaller in the case of slow absorption), since
it takes one half-life to reduce the concentration from the maximum to the
minimum.
> Can the value of total plasma clearance of two different drugs be compared
> to one another?
I would say: yes, but it is questionable whether this comparison is
meaningful. As long as you do not take into account half-life, there is no
problem.
In your example: the maintenance dose of drug A and drug B, expressed in
mg/day would be the same. However, drug A needs to be given many times a
day, probably by infusion of by a controlled-release formulation, whereas
drug B can be given once-a-day. In addition, for drug B a loading dose might
be required if a rapid effect is to be achieved (the large volume needs to
be filled), but not for drug A. However, maintenance dose will be the same.
> I think the issue here is that the terms clearance and half-life are often
> used almost interchangability in the literature to refer to how "rapid" a
> drug is cleared from the plasma. For instance the drug with a one hour
> half life may be referred to as being cleared much more rapidly than the
> agent with a 100 hour half-life, but in this case, the term "cleared" does
> not refer to clearance really, it's referring to half life. I believe
> this is the source of my confusion but would like a confirmation from
> someone else.
Yes, this makes sense. Your virtual drug B has a high clearance, but it is
slowly cleared from the body!
best regards,
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.at.rug.nl
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Les,
The half-life is a concept for beginners in PK (which is when I learned it from you). But it has
very limited usefulness as a parameter.
I encourage readers to review my previous remarks on this topic (see
http://www.pharmpk.com/PK10/PK2010109.html and copied below).
If you want to call an apple an orange then go ahead. But the terms effective half-live, context
sensitive half-life, operational half-life and other uses of the term half-life do not refer to a
parameter but to a fuzzy, "feel good" term.
The description of the time course of drug concentration and effect requires more than one
parameter. The fundamental scientific principle is that you cannot describe the time course of a
multi-parameter system with one parameter.
Nick
On 21 Feb 2010 at 11:00:53, Nick Holford (n.holford.-at-.auckland.ac.nz) sent the message
Markus,
Thanks for your further comments and for pointing out the paper by Boxenbaum & Battle which uses a
term originally proposed by Kwan & Duggan (1977) at a time when pharmacokinetics was defined as
describing the time course of both drug concentrations and drug effect (Benet 2008). However, at
least since 1980 (see Benet 2008) the importance of distinguishing the time course of drug
concentrations and drug effects has been central to modern clinical pharmacology.
I think that the use of the term 'effective' half-life to describe the time course of concentration
is a misnomer which should therefore be avoided. As illustrated earlier in this thread, the use of
the term "effective" without qualification can be easily confused with a half-life trying to
describe the time course of effect. The use of this term today to describe a pharmacokinetic
property reflects some ignorance about the meaning of the word "effect" in clinical pharmacology.
Sahin & Benet have more recently proposed an "operational half-life" and Eger & Shafer have
described a "context sensitive decrement time" which along with the Kwan & Duggan/Boxenbaum & Battle
"effective half-life" are similar in trying to describe a time course which depends on multiple
processes with just one parameter. This is necessarily an approximation because it is impossible to
define a multiple parameter system accurately with just one parameter. Boxenbaum & Battle
acknowledged this as a weakness of the "effective half-life".
If I want to understand the time course of drug concentrations and drug effects then I use model
based simulation e.g. to find out when the concentrations reach 90% of the predicted steady state or
drug effects have fallen to 50% of the value when drug input stopped. Simulation is as accurate as
the original model parameters and can be used to demonstrate graphically what is predicted to happen
both for PK and PD. This is especially valuable in communicating with those who are not familiar
with quantitative models. Simulation has been accepted for over a decade (Bonate 2000) as an
important tool for understanding clinical pharmacology in drug development in order to make the best
predictions for future clinical trials and clinical use of drugs.
Nick
1. Boxenbaum H, Battle M. Effective half-life in clinical pharmacology. J Clin Pharmacol. 1995
Aug;35(8):763-6.
2. Kwan KC, Duggan DE. Pharmacokinetics of Sulindac. Acta Rhumatol Belg. 1977
Jul-Dec;1(3-4):168-78.
3. Benet, LZ. http://www.cognigencorp.com/nonmem/current/2008-November/1225.html 2008
3. Sahin S, Benet LZ. The operational multiple dosing half-life: a key to defining drug
accumulation in patients and to designing extended release dosage forms. Pharm Res. 2008
Dec;25(12):2869-77.
4. Eger EI, 2nd, Shafer SL. Tutorial: context-sensitive decrement times for inhaled anesthetics.
Anesth Analg. 2005 Sep;101(3):688-96, table of contents.
5. Bonate PL. Clinical trial simulation in drug development. Pharm Res. 2000 Mar;17(3):252-6.
-- Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
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Dear Parag:
You are quite right. V and Cl are not independent. Cl = V x k, and K = Cl/v. Either way works
equally well. This will probably bring down a host of screams upon my head, as many people Have the
opinion that clearance is somehow more "biological". However, it is true. One can describe behavior
equally well as V and K (which I prefer) or as V and Cl (which many others prefer). Either is
equally good for most purposes. The rate constant for the drug with T1/2 of 1hr is 0.693. The one
for the other is 0.00693. Very different rates of elimination regardless of equal clearances.
Very best regards,
Roger Jelliffe
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Dear Roger,
As you expected, you get a reaction from oue of those who think that clearance and volume are
independent.
>One can describe behavior equally well as V and K (which I prefer) or as V and Cl (which many
>others prefer). Either is equally good for most purposes.
>
Indeed, I agree. But this is not what the discussion was about. The discussion was about the
fundamentals of pharmacokinetics. I will not repeat my arguments why I think that clearance and
volume are fundamentally independent. In that discussions I posted several times a (theoretical)
case, and I repost it here:
"What happens with the pharmacokinetic variables in a patient after connection to an extracorporeal
circulation?"
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 (an additional loading dose may be required to fill the increased volume).
The increased 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 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?
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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Dear Hans:
If clearance and volume are independent, why is volume part of the expression for clearance? It
simply doesn't make any sense. To say they are independent is simply a contradiction in terms. It is
about as fundamental as you can get. In your example the overall volume is increased, the rate
constants for elimination decrease, and the volume cleared by each organ stays the same. Again,
clearance and volume are not independent, but are very closely related.
Best,
Roger
Roger W. Jelliffe, M.D., F.C.P., F.A.A.P.S.
Professor of Medicine,
Founder and Co-Director, Laboratory of Applied Pharmacokinetics
www.lapk.org
USC Keck School of Medicine
2250 Alcazar St, Room 134-B
Los Angeles CA 90033
email = jelliffe.-a-.usc.edu
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Roger
At the risk of being blunt, your argument makes no sense.
Assuming organ-based clearance (as opposed to less common elimination in plasma), clearance has a
true biologic meaning -- it is the product of the extraction ratio of the eliminating organ and
blood flow to that organ. Distribution volume is a bit less "physiologic" -- it relates some
quantity of drug in the body (e.g., at steady state) to a concentration at some reference site.
No one disagrees with your claim that there is a mathematical relationship between the two. But,
consider this analogy:
a car travels a distance equal to speed x time. but the independent parts of the system are speed
and time, not distance -- one does not "instruct" a car to travel a distance.
One regulates speed, which accumulates distance over time. Similarly, k is a function of CL and V
Consider this experiment -- a drug is eliminated only via the kidneys. A surgeon clamps the renal
artery. Clearance goes to zero. In turn, k also goes to zero. But, volume (which is part of k)
did not change.
This argument has gone on for years and Proost and Holford have provided eloquent arguments
consistent with mine. I am always surprised when the discussion resurfaces.
Dennis
Dennis Fisher MD
P < (The "P Less Than" Company)
www.PLessThan.com
[Your car analogy is curious. Of the three terms, speed, distance and time, distance is the only
constant. One gets in a car to travel a distance. Speed and time depend on all sorts of variables.
BTW, one day (maybe in NV now) we may be able to instruct a car to travel a distance.
"But, volume (which is part of k)" So is volume a secondary parameter of k or is it independent? ;-)
- db]
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I would like to try contributing to the discussion with the following two points:
A) Cl represents the total volume of fluid cleared from the drug per unit of time. The total amount
of drug cleared from the fluid is equal to the product of CL and concentration. To confirm this we
can work out the units for instance: (ml/min).(mg/ml) = mg/min.
Since concentration (that as seen above affects CL) depends on the ratio dose/Vd (at least after
intravenous dosing), it would appear that Vd affects CL.
B) After IV dosing, if clearance occurs rapidly due to some rapid and efficient eliminating process
and there is no plasma protein binding, this will affect distribution as blood concentrations will
be low and there will be not enough concentrations gradient (in case of passive diffusion) or time
(in case of transporter mediated distribution) for the drug to distribute into a large volume of
distribution.
Conclusions from A: Vd affects CL and from B CL affects Vd therefore, it appears to me that CL and
Vd are NOT independent.
Therefore, going back to the original question: can you compare total clearance values for different
drugs? My answer would be NO as it depends on what are the Volumes of distribution.
Regards
STEFANO PERSIANI, Ph.D.
Director
Translational Sciences and Pharmacokinetics Department
ROTTAPHARM | MADAUS
R&D Division
Rottapharm Spa
Via Valosa di Sopra, 9
20900 Monza - ITALY
stefano.persiani.aaa.rottapharm.com
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Dear Roger,
Thank you for your reply. Here a reply.
> If clearance and volume are independent, why is volume part of the expression for clearance?
>
This is a common mistake in the concept of clearance. Volume is not part of the expression for
clearance. Clearance is defined as the rate of drug elimination (amount/time) divided by the drug
concentration (amount/volume), or in other words, clearance is the proportionality constant relating
the rate of drug elimination to drug concentration.. So, the volume is there only because of the
concentration, not a volume in the sense of the volume of distribution.
> It simply doesn't make any sense.
>
What does not make any sense?
> To say they are independent is simply a contradiction in terms.
>
I don't see any contradiction in terms.
> It is about as fundamental as you can get.
>
I have explained many time how fundamental clearance is. See the above definition: the fundament is
that the concentration is the driving force for drug elimination.
> In your example the overall volume is increased, the rate constants for elimination decrease, and
> the volume cleared by each organ stays the same.
>
I'm very happy to see that we agree about the consequences of expanding the volume of distribution.
But why does the elimination rate constant decrease? If it would be a 'fundamental' primary
parameter, I don't understand why it changes. Please explain.
The explanation: clearance remains the same, since there is no change in the eliminating capacity of
the body. As a result (sic!), the elimination rate constant decreases.
> Again, clearance and volume are not independent, but are very closely related.
>
Again, this example shows that clearance and volume are, in principle, completely independent.
However, there are many situations that they are related: e.g. both will increase with body size
(weight), but by a different mechanism and at a different relationship: volume increases broadly
proportional to mass (of course, depending on the nature of that mass increase), and clearance
increases because of the increase of liver size and function and renal size and function, broadly
proportional to mass^0.75.
Let's 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. As in Parag's example:
If Drug A has a Vd of 2 L and Drug B has a Vd of 200 L, the upper limit for the elimination rate
constant for drug A is 0.5 min^-1, and for drug B 0.005 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 in the volume of distribution. Is the elimination rate constant
dependent on clearance, or is the clearance dependent on the elimination rate constant?
Finally the example of renal excretion. Glomerular filtration rate (GFR) is considered as the most
relevant measure of renal function. The most common approximation of GFR is the creatinine clearance
(your contributions in this area are highly appreciated!). 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 from the very beginning! The renal clearance of creatinine is
'fundamentally' determined as the rate of creatinine elimination divided by the creatinine serum
concentration (similar to the above definition). Even in non-steady-state conditions, the creatinine
clearance can be estimated by application of this fundamental equation, as you did in your 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 also clarify that your 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.
best regards,
Hans
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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Stefano,
I am sorry, I might be missing something, but what you wrote does not make
sense to me.
To me, your point "A" actually proves that Vd and CL are independent. Just
look at the units that you have worked out in your reply. You correctly
defined CL as having units of volume (of fluid)/time. And of note here is
that this volume does not refer to the physical volume that the drug is
dissolved into, but the volume that gets cleared over time. So even though
Vd has units of volume it is not the same volume referred to when we talk
about clearance. Maybe that is the source of confusion? Also, when you are
looking into mg/min, you are looking into a rate - in this case the rate of
elimination - which is not clearance, according to what you correctly
defined yourself. This rate of elimination, I agree, is dependent on Vd,
since dX/dt = - CL/Vd * X, in the simplest of the cases. But CL is not.
As for your point "B", even if the drug is cleared extremely fast, I cannot
see that changing the physical volume that is available to dissolve the
drug. It changes the amount of drug available to be dissolved in such
volume, not the volume itself. And again, the example you gave, to me,
refers to a rate - the rate of transfer from one compartment to another.
That does not change volume, right? The only case where I can see something
like that happening - with the type of drug that you used in your example -
is if you do not design your study well enough to a characterize the PK
properties of the compound (e.g., not enough timepoints). So what seems to
be the case of clearance affecting Vd is nothing but an artifact of the
design of the study. I am still convinced Vd and CL are independent.
regards,
Edgar L. Schuck, Ph.D.
Sr. Principal Scientist
DMPK Andover
Biopharmaceutical Assessments Core Function Unit
Eisai
Edgar_Schuck.-a-.eisai.com
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Dear Stefano,
Thank you for your comments.
> A) Cl represents the total volume of fluid cleared from the drug per unit of time. The total
> amount of drug cleared from the fluid is equal to the product of CL and concentration. To confirm
> this we can work out the units for instance: (ml/min).(mg/ml) = mg/min.
>
OK (although the correct units do not necessary imply that the statement is true).
> Since concentration (that as seen above affects CL) depends on the ratio dose/Vd (at least after
> intravenous dosing), it would appear that Vd affects CL.
>
It might appear, but it is not true. Indeed, the concentration is dependent on Vd. And the
concentration some time after administration is also dependent on CL. But this does not prove that
Vd affects CL. Both Vd and CL determine the concentration - time profile, but are independent of
concentration (at least in the case of linear PK, which is usually the case, or assumed). Of course,
to estimate Vd and CL, one needs concentration measurements, and Vd and CL are calculated from these
concentration measurement. But this does not imply that Vd and CL are dependent of concentration in
a mechanistic sense. If a dose is administered iv, Vd and CL determine the concentration - time
profile, not the other way around.
> B) After IV dosing, if clearance occurs rapidly due to some rapid and efficient eliminating
> process and there is no plasma protein binding, this will affect distribution as blood
> concentrations will be low and there will be not enough concentrations gradient (in case of
> passive diffusion) or time (in case of transporter mediated distribution) for the drug to
> distribute into a large volume of distribution.
>
You are fully correct that clearance may affect distribution, but this can be described only in
multi-compartment models. If these processes are assumed to be fast enough to ignore for the
concentration - time profile (as concluded from a straight line in a ln(C) - t plot), a
one-compartment model can be used, and the concentration is assumed to be homogenous in that
compartment; so in this case clearance does not affect distribution.
If these processes are not fast enough to ignore (as concluded from a curved line in a ln(C) - t
plot), a two- (or more-) compartment model should be used. However, even if the concentration is
declining very fast due to high clearance and low central volume, there will be some transport to
the peripheral compartment. (there is nothing as 'no time for distribution'). Again, the volume of
the central compartment V1 and the steady-state volume of distribution Vss are independent of
clearance. However, the 'volume of distribution during the terminal phase', often denoted Vbeta, is
dependent of clearance; Vbeta is a secondary parameter, just as elimination rate constant and
half-life (half-lives in the case of multicompartment kinetics).
Please note that the discussion on dependency of CL and Vd refers primarily to the one-compartment
case, and may be extended to multi-compartment models provided Vd refers to Vss or V1, but not to
Vbeta.
> Conclusions from A: Vd affects CL and from B CL affects Vd therefore, it appears to me that CL and
> Vd are NOT independent.
>
As can be concluded from my reply, both statements are not correct, except for the relationship
between CL and Vbeta: Vbeta is dependent on CL, but CL is independent of Vbeta (Vbeta is a secondary
parameter).
> Therefore, going back to the original question: can you compare total clearance values for
> different drugs? My answer would be NO as it depends on what are the Volumes of distribution.
>
My answer is still YES, with the return question: 'why 'comparing clearances?'
best regards,
Hans
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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Thanks Hans for your elegant explanation, of course, with which I agree.
But since I am one of the oldest participants in PHARMPK along with Roger and Aziz, I thought it
might be useful from a historical perspective to explain why PKers started out with rate constants
rather than clearance.
When PK publications with human data first were published the only assays we had were colorimetric
and then UV (Trinder reaction, Bratton-Marshall, even prior to Roger's digoxin measurements, also in
urine). Drug concentrations in the urine could be measured, because you could concentrate the urine
by evaporation, but there was not sufficient sensitivity to measure any plasma, serum, blood
concentrations. Therefore, it was not possible to calculate drug clearance, renal or total, and all
of the initial theoretical papers were based on rate constants (half-lives), reflecting the
parameter we could measure. We just didn't have the choice initially to determine anything but rate
constants and half-life until the introduction of clearance constants in the early 1970's when we
then did have the analytical sensitivity to measure plasma concentrations. But by then we had an
enormous literature based on rate constants from the giants in the field prior to the mid-1970's
(Wagner, Levy, Riegelman, Jelliffe, Garrett, Krueger-Thiemer, Dost, Teorell, Widmark, Tandberg,
Dominguez). Those pharmacokineticists were not wrong, they just didn't have the analytical tools
necessary to determine clearance and their teachings affected our heritage.
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
Email: leslie.benet.at.ucsf.edu
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Stefano's input is the argument frequently given to counter Hans' explanation. Let's go back to the
classical 1975 diazepam studies of Klotz and Wilkinson published in Journal of Clinical
Investigation, as discussed in my early PK chapters in G&G. As you age, the terminal half-life of
diazepam (which accounts for greater than 90% of the area under the curve) increases. In fact, on
average if you take your age in years and convert it to hours, that will be the diazepam terminal
half-life in you. It was originally hypothesized that metabolic function (diazepam is completely
metabolized in the body) may decrease with age, as is seen with renal function. But clearance is a
measure of the body's ability to eliminate drug, and metabolic clearance of diazepam (which is
almost completely hepatic) does not decrease with age. But if clearance doesn't change with age,
and half-life increases, what must have changed? Volume of distribution, which for diazepam
increases with age. If the volume of distribution increases, less diazepam is present in the blood
to be cleared by the liver. Thus the body's ability to metabolize diazepam did not decrease with
age, but the amount metabolized with time did, because less drug was available to be metabolized due
to the increased volume of distribution. Therefore diazepam remains in the body longer as you age.
I am not bothered by Roger's advocacy of half-life, although I agree with Hans and Nick, because
pharmacokinetics is only a tool. What do you want to know about the drug? Determine the parameter
that defines the characteristic of drug disposition that you wish to know.
I also believe that the receptor sensitivity for diazepam does not necessarily increase with age,
although for the same plasma concentration elderly subjects will see a much greater PD effect than
young individuals. I suspect based on animal studies that when you age, one of the sources of
increased volume of distribution is the brain and that for the same plasma concentration, more drug
is present in the brain of elderly individuals, and thus the increased PD effect could be explained
by PK. Again, what is the question you are trying to answer? That defines the parameter to be
evaluated.
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
Email: leslie.benet.aaa.ucsf.edu
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Dear Les:
Thanks for the historical perspective. There is also the fact that many PK equations were
similar to those of radioactive decay, which is where I began. Thanks also for mentioning
Kruger-Thiiemer, Dost, and Teorell. But who are Widmark, Tandberg, and Dominguez? Can you tell me
more about them?
All the best,
Roger
[This Widmark? http://www.enotes.com/pharmacokinetics-alcohol-reference/pharmacokinetics-alcohol
Tandberg? Ref 1 in http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2811643/pdf/12248_2009_Article_9160.pdf (itself an interesting paper by A. Rescigno)
Domingues? Ref in http://deepblue.lib.umich.edu/bitstream/handle/2027.42/24565/0000847.pdf - db]
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Since Les has added an historical perspective, I would like to add something Doug Riggs sent me when
I was in graduate school:
"In the commonly-used two compartment model there are four independent {underlined} parameters: the
volume of distribution of the central compartment, the volume of distribution of the peripheral
compartment, the solute conductance between the two compartments, and the solute conductance
(=clearance) out of the system from the central compartment. All other "parameters", including rate
constants are dependent upon these four."
While PK has been refined over the years (this was 1983), the concept of independence of clearance
and volume was recognized even then. I think the problem lies in that the net efflux of a solute or
analyte is in terms of dX/dt, which (obviously) changes with time. Re-parameterization to clearance,
an established concept from renal physiology (we are talking very old here), allowed a time
independent (assuming linearity) parameter easier to deal with numerically and conceptually. It,
however, used units also used in volume parameters, hence the confusion.
The above quote was hand written. It and the accompanying letter are interesting. Contact me if you
would like copies.
Christopher J. Kemper, Ph.D.
Pharma Navigators, LLC
chris_kemper.aaa.pharmanavigatorsllc.com
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Thanks Roger.
From the Wagner 1981 "History of Pharmacokinetics" paper in Pharmacol. Ther. Vol, 12, pp. 537-562
that I believe David has added below your response (deepblue.lib.umich)
And how could I have neglected to include Segre and Resignio; that became obvious when you mentioned
radioactive decay.
Les
Swedish investigators, Widmark and Tandberg, in 1924 published equations appropriate
to what are now called: (a) the one-compartment open model with bolus intravenous
injection and multiple doses administered at uniform time intervals, and (b) the
one-compartment open model with constant rate intravenous infusion (Widmark and
Tandberg, 1924).
During the period 1939 to 1950, Dominquez in the United States made significant
contributions with articles on the pharmacokinetics of creatinine, mannitol, xylose and
galactose (Dominguez, 1934; Dominguez and Pomerene, 1934; Dominguez et al., 1935;
Dominguez and Pomerene, 1944, 1945a,b; Dominguez et al., 1947a and 1947b; Dominguez,
1950). He introduced the concept of the volume of distribution and defined it as
the hypothetical volume of body fluid dissolving the substance at the same concentration
as that in plasma (Dominguez, 1934).
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
Email: leslie.benet.at.ucsf.edu
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Oh, Hans, I think I will stop now. We just don't seem to be getting anywhere. I am sorry about that.
Very best regards,
Roger
--
Thanks very much, Les.
All the best,
Roger
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Dear Roger, Les, Christopher, Dennis and others,
Thank you all for your contributions. It is useful to hear also from history. I apologize for saying
that these giants were wrong. Of course, they were doing fantastic work in a novel area. What I
meant is that their concepts, although very useful both theoretically and in clinical practice, have
evolved in the 70ies, thanks to Rowland and others, to the concepts of clearance leading to a better
understanding of pharmacokinetics, especically in altered clinical conditions.
best regards,
Hans
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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Hi Johannes
Although I tend to agree with your arguments and your perspective on the concept, I think there is
one (additional) exception that may be worth mentioning and that is where the volume of distribution
of a given drug may indeed affect organ blood flow and therefore clearance.
Consider Drug A, a vasodilator which is cleared unchanged renally. And where vasodilatation, hence
renal perfusion and hence renal clearance are a function of concentration of Drug A in the systemic
circulation. A lower volume of distribution, will increase systemic concentrations and hence renal
blood flow and renal clearance, and vice versa.
A real life example may be caffeine (a vasodilator affecting renal blood flow), particularly when
used in pre-term neonates and where renal clearance is the predominant elimination route (as opposed
to older children and adults where metabolism dominates). The large day to day variation in fluid
balance in such a population, coupled with a shift in water from ECF to ICF as the child develops,
perhaps partly explains why there is significant IOV in caffeine clearance (rendering TDM pointless)
that our group and others have determined.
Hussain
Hussain Mulla
Department of Pharmacy
Glenfield Hospital
University Hospitals of Leicester
UK
Refs
Charles, B.G et al. Caffeine citrate treatment for extremely premature infants with apnea:
population pharmacokinetics, absolute bioavailability, and implications for therapeutic drug
monitoring. Therapeutic Drug Monitoring 30, 709-16 (2008).
Patel P, et al Dried blood spots and sparse sampling: a practical approach to estimating
pharmacokinetic parameters of caffeine in preterm infants. Br J Clin Pharmacol 2013;75(3):805-13
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Hi Roger,
In addition to the information provided by Les (and David), it should be noted that Widmark's work
is the basis for much of the "understanding" of alcohol's pharmacokinetics in wide use by the
forensic toxicology community including the often dubious calculations used to estimate blood
alcohol concentrations at key times. {It's much simpler to assume and describe zero-order alcohol
elimination than to embark on a description of nonlinear (Michaelis-Menten) kinetics for jurists!}
A good review of Widmark's life and scientific work - including mention of the Widmark-Tandberg
paper - is to be found in the paper by Andrkasson, R. and Jones, A.W. {"Erik M.P. Widmark (1889-
1945): Swedish pioneer in forensic alcohol toxicology", Forensic Science International, 72 (1):1-14,
1995}.
Best regards,
Peter
Peter W. Mullen, PhD, FCSFS
KEMIC BIORESEARCH
P.O. Box 878
Kentville
Nova Scotia, B4N 4H8
Canada
E-mail pmullen.-a-.kemic.com
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Dear Hussain,
Thank you for your contribution. You raise an interesting point of drugs influencing their own PK,
which may lead to situations not expected 'from theory'.
> Consider Drug A, a vasodilator which is cleared unchanged renally. And where vasodilatation, hence
> renal perfusion and hence renal clearance are a function of concentration of Drug A in the
> systemic circulation. A lower volume of distribution, will increase systemic concentrations and
> hence renal blood flow and renal clearance, and vice versa.
>
Please note that 'the theory' is still correct in your example of 'drug A': the increase of
clearance is not directly caused by the decrease in volume of distribution, but, as you described, a
result of the increase of concentration of the drug, which leads to vasodilatation, hence incrased
renal perfusion and hence an increased renal clearance.
Also note that in this example clearance increases as a result of a decrease of volume of
distribution. From the 'rate constant approach' point of view a quite remarkable finding!
best rgards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics, Toxicology and Targeting
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.-a-.rug.nl
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Hi Hans
In response to my example:
>> Consider Drug A, a vasodilator which is cleared unchanged renally. And where vasodilatation,
>> hence renal perfusion and hence
>> renal clearance are a function of concentration of Drug A in the systemic circulation. A lower
>> volume of distribution, will
>> increase systemic concentrations and hence renal blood flow and renal clearance, and vice versa.
You responded:
>Please note that 'the theory' is still correct in your example of 'drug A': the increase of
>clearance is not directly caused by the
> decrease in volume of distribution, but, as you described, a result of the increase of
> concentration of the drug, which leads to
> vasodilatation, hence incrased renal perfusion and hence an increased renal clearance.
> Also note that in this example clearance increases as a result of a decrease of volume of
> distribution. From the 'rate constant
> approach' point of view a quite remarkable finding!
O.k. but I think may be this is in the realms of semantics? From a practical clinical perspective,
for the example that I give, a change in Vd results (‘indirectly’) in a change in CL and hence I
need to alter the dosing rate.
Kr
Hussain
Hussain Mulla
Department of Pharmacy
Glenfield Hospital
University Hospitals of Leicester
UK
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Hussain,
I don't really understand your example where the drug has a vasodilating effect which increased
renal blood flow and increases renal clearance because you also propose a decrease in volume of
distribution.
If we separate these two possibilities and consider only the decrease in volume of distribution then
I'd like to comment on what you wrote:
> O.k. but I think may be this is in the realms of semantics? From a practical clinical perspective,
> for the example that I give, a
> change in Vd results (‘indirectly’) in a change in CL and hence I need to alter the dosing rate.
>
The fundamental theory of pharmacokinetics is that only unbound concentration and unbound clearance
determine elimination rate.
A reduction in volume of distribution (e.g. due to displacement from tissue binding sites unrelated
to clearance) will increase the unbound concentration of drug available to clearance processes but
does not change the unbound clearance. Therefore the rate of elimination will increase (transiently)
because of the increased unbound concentration. The unbound concentration will return to its
original steady state value after the drug displaced from tissue binding has been eliminated.
You should not increase the dosing rate in this case even though elimination rate is transiently
increased. In fact it may be appropriate to decrease the dosing rate in order to maintain the
desired target concentration.
Best wishes,
Nick
Nick Holford, Professor Clinical Pharmacology
Dept Pharmacology & Clinical Pharmacology, Bldg 503 Room 302A
University of Auckland,85 Park Rd,Private Bag 92019,Auckland,New Zealand
email: n.holford.at.auckland.ac.nz
http://holford.fmhs.auckland.ac.nz/
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Hi Nick
My thinking was, assuming a high extraction ratio drug, the increase in unbound concentration (due
to a reduction in Vd) could result in greater vasodilatation and hence enhanced renal blood flow and
therefore could increase renal clearance?
Hussain
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Seems to me you need to ask what the rate-limiting step in the process is before you jump to
conclusions.
Dr. Daniel S. Sitar
Editor in Chief, Journal of Clinical Pharmacology
Professor Emeritus
Dept of Internal Medicine (Clinical Pharmacology)
Dept of Pharmacology and Therapeutics
Web Address: www.umanitoba.ca/faculties/medicine/units/pharmacology
Email: sitar.-a-.cc.umanitoba.ca
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