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I'm having trouble wrapping my head around this question from an online pharmacology quiz. The question is "The larger the volume of distribution, the smaller the AUC of a given drug." The answer is given as "False."
As I look at the equation AUC = D/KV, it would seem that if V is larger, then AUC would be smaller. Can anyone explain how the question is false instead of true?
Thanks,
Ruby
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Is it autoinduction?
Regards,
Anila
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Ruby
> I'm having trouble wrapping my head around this question from an online pharmacology quiz. The question is "The larger the volume of distribution, the smaller the AUC of a given drug." The answer is given as "False."
>
> As I look at the equation AUC = D/KV, it would seem that if V is larger, then AUC would be smaller.
>
> Can anyone explain how the question is false instead of true?
This is a classic misunderstanding by using maths and not biology to understand reality. The AUC is determined by dose and Clearance (CL).
AUC = Dose/CL
Dose is real. Clearance is abstract but nevertheless directly linked to the ability to eliminate a drug which is real. Volume (V) is also abstract but directly related to how much drug is in the body and therefore real.
On the other hand the so called 'rate constant' (K) is a mathematical abstraction determined by the ratio of Clearance/Volume. i.e.
K=CL/V
This biological relationship determining K can be re-arranged mathematically to come up with
CL=K * V
But this does not make biological sense because K is determined by CL not the other way around. Unfortunately in some textbooks it may be written that
AUC=Dose/(K * V)
but this is maths not biology and is quite misleading because it implies that a change in K will mean a change in AUC.
Despite it's name, K is not constant. If either Clearance or Volume changes then K will change. It is possible to have a change in V which will change K but because CL does not change the AUC will not change.
Perhaps you should contact the author of the source of your equation 'AUC=D/KV' and ask them to re-write the equation in a more sensible form. Feel free to use this email to support this view.
Best wishes,
Nick
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Hi Ruby,
The actual formula is AUC = Dose / CL. Now, since CL = k * Vd, you can replace the CL and get the formula you refer to. However, you have to remember that if CL is constant, when Vd changes so does the k. In other words, in your formula, an increase/decrease in Vd results in a corresponding decrease/increase in k so the CL, and thereby AUC is unchanged.
Toufigh
Toufigh Gordi, PhD
President, PK/PD and Clinical Pharmacology Services
Rosa & Co. LLC (www.rosaandco.com)
E-mail: tgordi.at.rosaandco.com
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Ruby,
The important thing to remember is that V and CL are independent of each other, and AUC = D/CL; therefore, AUC depends on CL, not on V. In a (very) simplified case of a perfectly mono-exponential decline after IV dosing, K = CL/V, which means that K depends both on CL and V. Rearranging this equation to CL = KV gives the impression that CL depends on V, hence the confusion. The increase in V will not increase CL - rather, it will decrease K.
Andrew
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Dear Ruby,
The AUC is equal to Dose/Clearance and not Dose/KV. The reason I say this
is, is because even though clearance and volume are related to each other by
the equation K = CL/V, clearance is not dependent on volume. So even if the
volume changes, the clearance will not change and hence the AUC will remain
the same. Change in volume will only change K, not CL.
Hope this helps.
Sagar
--
Sagar Agarwal
Graduate Student - Ph.D. Candidate
3-140 WDH, 308 Harvard Street SE
Minneapolis, MN 55455
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Hi Ruby,
Remember that K is also dependent on V. So if V goes up, K will decrease proportionately and AUC stays the same!
Ronette
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I do not agree with that the k is dependent on the CL. And V can affect the k.
For the compartment model of iv. Bolus, the TBCL=kV (k is the elimination rate constant, and the V is the apparent volume of distribution).
We can understand the K and V is the parameter for physiological condition of body.
1, K is the parameter that can express the physiological condition of central compartment, such as the hepatic clearance, renal clearance et al. So we can say the k is the physiological parameter of elimination.
2, And the V is another physiological parameter (if I can say). It is co-related with the body weight et al. We can say the V is the physiology parameter of distribution.
And we assume that the V and k is independent to each other.
In this equation the TBCL is the dependent parameter and the k and V are the independent parameter. That means, the change of TBCL depend on (or can say "because of") the change of k or V, or both of them. In the equation the AUC=X0/(kV), we can know that the AUC only depends on the k and V., AUC do not has the direct relationship with the CL.
So we can say the K and v is the primary parameter of PK, otherwise the CL and AUC is the secondary parameter of PK.
This question has two sides.
1, if we assume that the k does not change (the physiological condition of elimination does not change), V increase, the AUC should decrease.
If we assume that the V does not change, the k increase, the AUC should decrease also.
2, If the k and V change at same time. The changing of AUC will depend on the (kV)
xiaoming
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It is unfortunate that misunderstanding continues for the relations that involve clearance, volume of distribution, AUC, elimination rate constant and elimination half-life.
See Nick Holford's concise summary (25 January 2011) that has the correct interpretation in response to earlier correspondence (see attached). The elimination rate constant always depends on both clearance and volume.
Again to summarise, clearance and V are both primary pharmacokinetic parameters that depend on the chemical properties of the drug and the composition of the body in which the drug circulates. The elimination rate constant, k, is not a primary pharmacokinetic function and is derived from k = Cl/V. Clearly, from this relationship, k depends on both Cl and V. We measure log(C) vs time to estimate k and also measure AUC from plasma drug concentration vs time profiles, but that does not make k a primary pharmacokinetic function. The observed plasma drug profiles result from the specific values of Cl and V for a specific drug. It is an excessively common mistake to call k a primary pharmacokinetic function and it would be good for the scientific and clinical community if this mistake could be at least minimised, preferably eliminated. (The half-life for elimination of this mistake is slow. Perhaps we have reached a steady-state situation.)
Finally, if Cl goes down, often from reduced liver function, or competition for metabolising enzymes, or from reduced renal clearance then k will decrease if V remains constant. If Cl goes down and V decreases to roughly the same proportion, then k, hence half-life, will not change significantly. Other scenarios are easy to imagine.
Des Williams
--
Des Williams, PhD, BPharm, FRACI, CChem Program Director, Pharmaceutical Sciences Sansom Institute for Health Research, and School of Pharmacy and Medical Sciences | CEA19
University of South Australia North Terrace Adelaide
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Thanks Des for the clearly explanation.
I had processed a set of date for a friend. The result was interesting.
He would like to study the bioavailability of old pharmaceutical form (Oral Suspension) and new form (Granules). He did the experiment according to the guidance of SFDA for the studying of bioavailability.
The data of old form can be simulated by using one compartment model. The data of the new form is interesting. Data of some animals is fitted with one compartment model, and data of others can be fitted with the two compartment model. Cmax, ka and half-life decrease but not so much; K decrease and V increase. Because of the k and V, the AUC and the CL did not have the significantly change. If we just see the CL and AUC, the new form of the drug is not different from the old form. However, the K and V changed.
I thought that some of the excipients of the new form maybe affects the clearance of drug. And some of the excipient can help the drug distribute extensively, that can explain why some of the animal has the distribution phase (two compartment model). Consider the the drug can be extensively metabolized by CYP, I suggested him to investigate the inhibition between the excipient and the drug by using in-vitro method.
For this case, I think that the k and V are more "sensitive" than the CL and AUC when the drug property or body physiological condition changed. CL and AUC are depending on the k and V.
Xiaoming
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Dear All
It's certainly very unfortunate to perpetuate this misunderstanding and persist in arguing whether the egg or the chicken comes first. Mainly for the elucidation of the new generations, I strongly advice reading the original theoretical foundations of PK modeling. It's false to say that k is derived from k=CL/V. This expression only applies to a single compartment disposition. It's false to say that "the elimination rate constant always depends on both clearance and volume". Truthfully, every first order process has a rate proportional to its driving force, with a proportionality constant denoted as rate constant, regardless of the volume or clearance concepts (e.g. radioactive decay). In terms of mass transfer, e.g. drug elimination, for a first order process, the rate is proportional to the amount driving the process, regardless of the APPARENT volume we choose to assess it. If we decide to conceptualize that driving force in terms of concentration, which given biological heterogeneity require
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First of all I think the original question was poorly worded and, therefore, any answer can be accepted. In order to make things clear, let's consider only Vss.
We are obviously talking strictly about IV administration, as Vss cannot be determined from extravascular administration data (and neither can Vss/F, contrary to a number of papers claiming that). After IV administration vast majority of drugs are best described by multicompartment models (as Luis accurately pointed out).
As we know, K = CL/Vss is correct only for one compartment model (Vss = CL * 1/K) and the equation for any compartment model, which we obviously have to use here, is Vss = CL * MRT. Maybe it is now easier to understand that the MRT is not a constant determining the Vss or the CL.
It is also easy to see that if AUC changes, i.e. CL decreases or increases for instance because of enzyme inhibition or induction, the MRT will change, not the Vss.
Regards,
Stefan
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Dear Luis,
You seem to have missed the long discussion 'A question of clearance' on
this forum from December 2009 to February 2010 between the supporters of the
'rate constant approach' and the 'clearance approach'. I suggest to read
that discussion carefully. You will read that all arguments in favor of the
rate constant approach were shown to be weak or incorrect, and that no
convincing arguments were given contradicting the clearance approach. There
can be no doubt that the 'frivolous contest' was won by the clearance
approach.
In addition, you may read the recent excellent contributions of Nick
Holford and Des Williams, who very clearly explained why k is dependent on
V, and why CL is independent of V.
You wrote:
> Mainly for the elucidation of the new generations, I strongly advice
> reading the original theoretical foundations of PK modeling. It's false to
> say that k is derived from k=CL/V.
The original theoretical foundations were very useful and very important,
but not fully correct. The original PK started in the 1930s, and the
clearance concept entered PK in the 1970s. This has led to a much better
understanding of PK, in particular with respect to clinical
pharmacokinetics. Keeping on original concepts does not seem to be fruitful.
> This expression only applies to a single compartment disposition.
Yes and no. It also applies to multicompartment models if written as k10 =
CL/V1. Moreover, the problem is here in k (the 'toy' of the rate constant
supporters) and V, not in CL.
> In terms of mass transfer, e.g. drug elimination, for a first order
> process, the rate is proportional to the amount driving the process,
> regardless of the APPARENT volume we choose to assess it.
The driving force is not amount of drug, but concentration. To say it
simple: How does your liver and kidneys know how much drug is present in
your body? They only 'feel' the blood concentration.
> If we decide to conceptualize that driving force in terms of
> concentration, which given biological heterogeneity requires the
> assumption of an APPARENT volume, then for a first order process, the
> proportionality constant between rate and concentration is defined as
> clearance.
Here we agree. This is indeed the basis of the clearance concept.
> It's the fraction of that APPARENT volume that gets cleared of drug per
> unit time.
No, cleareance is not the fraction of the apparent volume that gets cleared;
The rate constant is the fraction of the apparent volume that gets cleared
(and therefore it is dependent of that apparent volume).
> I hope that the capitalizations above extol the fact that the blood
> concentrations we work with daily, are really a surrogate measure of the
> underlying amount of drug driving the elimination process.
Yes, but again, the driving force is not amount of drug, but concentration.
See above. Blood concentration is not a 'surrogate measure'.
> Consequently, AUC is just the integral of the concentrations profile over
> time. Again, only under specific modeling assumptions, and data
> availability, it may be estimated as D/CL, or Co/k, or D/kV, or
> Co.t1/2/ln2, and on, and on.
The only assumption for AUC = F*Dose/CL is that linear kinetics apply (as in
the whole discussion), irrespective of the model. It is CL=kV that is true
only for a one-compartment model.
> I will not participate in the frivolous contest for which parameters are
> primary and which are secondary.
You actually participated in the contest with your statement "It's false to
say that k is derived from k=CL/V". You have voted in favor of the 'rate
constant approach'!
> That's so beyond the point that I just regret it being indoctrinated in
> the minds of those starting to learn the field.
Why would we regret to learn the basics of PK correctly?
> All parameters (and models) are in fact secondary to reality.
Of course, you are right here. But in this view, k is a tertiary parameter.
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 Xiaoming,
You are making some wrong inferences, probably as a result of the incorrect
'rate constant approach' (see other messages in this thread).
> However, the K and V changed.
It is not likely that V, and as a result k, will change by using a different
formulation. How can an excipient change the volume of distribution?
> I thought that some of the excipients of the new form maybe affects the
> clearance of drug.
But you explained that CL was unaltered.
> And some of the excipient can help the drug distribute extensively, that
> can explain why some of the animal has the distribution phase (two
> compartment model).
Seems unlikely. What could be the mechanism? See above.
> For this case, I think that the k and V are more "sensitive" than the CL
> and AUC when the drug property or body physiological condition changed.
Indeed, a change in V does not change CL and AUC; so CL and AUC are indeed
insensitive to changes in V. But you should not generalize this statement.
For example, CL is 'sensitive' to changes in CYP activity, whereas V is not
affected.
> CL and AUC are depending on the k and V.
Again, CL and AUC are independent of V. See earlier messages of Nick Holford
and Des Williams.
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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The following message was posted to: PharmPK
Dear Hans, Xiaoming and All,
I won't give up assuming that we are all genuinely convinced of our rightfulness and this is above all a scientific forum for the spreading knowledge. But as much as I respect everybody's opinion, whoever engages on a clan feud between "supporters of this" and "supporters of that", or a "contest was won" state of mind, or "that's your 'toy' " and therefore you're wrong, may only get my commiseration. There's no place in science for this line of argumentation. Science is not about being 'fruitful' and retiring what is not. The Jan10 thread was not the only one, nor apparently will be the last, on this topic. But if I recall correctly, it ended with a clear cut and scientific argumentation by Roger Jelliffe, as he always does, showing that ranking parameters by level of importance is nonsense. Believes and preferences are not facts. I just intervened this time because the recent contributions to this tread were again very misleading. To say that CL=K.V and CL=k10.V1, therefore CL is one and the s
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Dear Hans:
I think you yourself should read that discussion more carefully. You
are simply wrong when you say that " all arguments in favor of the rate
constant approach were shown to be weak or incorrect, and that no convincing
arguments were given contradicting the clearance approach. There can be no
doubt that the 'frivolous contest' was won by the clearance". Where is your
science? Where is your good sense? The plain fact is that kel and clearance
are simply interconvertible. You have many words but few make sense.
I enclose once again our contribution (with references) to the subject.
Please pay more attention this time. I would greatly appreciate knowing just
what is "weak or incorrect" about our discussion. You seem to be stuck
somewhere.
Sincerely,
Roger Jelliffe
Dear All: from 1/26/10 in PharmPK:
Let us return once again to the question of kel and clearance. I
would like to respond to several recent comments.
It is disappointing to hear some of the discussants trying to "get away from
theoretical arguments and deal with real data". Really now, if we don't have
theory, what do we have, after all? Isn't that what we, as scientists, are
really trying to develop - a firm theory that helps us explain, predict, and
control drug behavior? What about other theories, such as those of quantum
mechanics and Einstein? Once we can construct them, we have a firm
foundation and rationale for our actions. We have had so many words about
this issue that some theory might, after all, be helpful. It was Kurt Lewin,
I think, who said, "there is nothing as practical as a good theory".
Why shouldn't we base our discussion on theoretical arguments?
If we don't do this, what basis do we have for what we actually do, and what
is our scientific rationale for our actions? Let's look at the data, and
the theory, that will help us evaluate the utility of K and Cl. In my view,
K and Cl are both equally useful. The beauty is in the eye of the beholder.
No one is more "biologically relevant" than the other, unless someone thinks
so. Then that is a belief, not a fact.
No one is more "orthogonal" than the other. That depends upon the particular
model parameter values. The correlation between Cl and V simply depends on
the model parameter values one is dealing with. By itself, Cl is no more
orthogonal than K with respect to V.
The result presented, Corr(CL&V)=0 gets one's attention. Is this real or an
accident? Answer - an accident of the values for V, CL and K that were used.
In an earlier discussion, the model used was
ln(y)= ln(1/V) - Kt + noise
Alan says it is straightforward to calculate analytically the formula for
the asymptotic covariance matrix between CL and V. The off-diagonal term,
Corr(CL&V), is exactly
Corr(CL&V)= -((1/4)*V-CL)*V
The stated parameter values were V=1, K=0.25, which implies CL=V*K=0.25 and
Corr(CL=0.25&V=1)=0
But what if K=0.35? Fixing V=1, Alan shows a short table for CL
vs.Corr(CL&V)
CL Corr(CL&V)
0.0500 -0.2000
0.1500 -0.1000
0.2500 0
0.3500 0.1000
0.4500 0.2000
0.5500 0.3000
0.6500 0.4000
0.7500 0.5000
0.8500 0.6000
0.9500 0.7000
So the correlation between Cl and V simply depends on the model parameter
values one is dealing with. By itself, Cl is no more orthogonal than K with
respect to V.
In addition, it is clear, as described by David Bayard, that "a fundamental
property of the maximum likelihood estimator is the result that the maximum
likelihood estimate of a function of the parameters can be computed by
taking the function of the maximum likelihood estimates of the parameters.
This property is known as the principle of invariance" [1]. Because of this,
the MLE estimation of = (K, V) gives exactly the same result as the MLE
estimation of g() = (Cl, V). If you estimate it in clearance form (Cl,V) and
then convert it to elimination form (K,V), you get the same estimate as if
you had originally estimated it in elimination form. And vice versa.
The examples of losing a kidney or losing 2 legs are interesting
examples. I am not sure what they settle. If you lose 2 legs you lose
volume. Renal perfusion probably stays the same, though. Lose a kidney and
you lose renal elimination - that is intuitive. For a drug eliminated from
the body only by glomerular filtration, for example, then ke is roughly
equivalent to creatinine clearance, as a relatively crude but easily
obtained estimate of GFR. Oral ganciclovir and the aminoglycoside
antibiotics are good examples of this.
In addition, there has been recent discussion about K and T1/2. In our
MM-USCPACK software, we often model ke as the product of knr + ke-slope
times CLCr. Therefore, if you lose a kidney and your CLCr halves (at least
until the other kidney hypertrophies to compensate), then ke will also
halve. By the way, there has been more recent discussion of the
misperception of ke as the percentage of drug eliminated over a period of
time. The precise way to view ke is the instantaneous rate of drug
elimination, i.e. when the slice of time is infinitely small.
Further, from another perspective, if the kidneys are responsible for
getting rid of the drug, then removing one will halve that function, and
will halve the fractional elimination of the drug. Alternatively, since we
have already agreed that CL and k are algebraically related by V, and the
argument has been made that if CL halves, then for a constant V, or for
constant renal perfusion, ke must halve as well.
It was also said that "no one makes any dose adjustments based
on volume of distribution changes". This actually contradicts much clinical
experience with acutely ill and unstable patents who have significant
changes in several parameters, including volume of distribution of the
central compartment, during their therapy. Most fitting methods do not
permit parameter values to change during data analysis. However, Marcus
Haug and Peter Slugg at the Cleveland Clinic in the 1980's fitted individual
clusters of TDM data, and found, for example, significant changes in
gentamicin volume of distribution. They would say that a patient had "VD
collapse", and that this decreasing gentamicin volume of distribution meant
that the patient would get well.
And they were right. This was about the time that it was becoming known that
ICU patients had larger volumes of distribution than general medical
patients. At about the same time we became aware that each patient would
often increase his/her aminoglycoside central compartment VD upon becoming
sicker, and later on decrease it as they recovered, perhaps due to changes
in capillary permeability. Clearly while they were sicker they needed larger
doses to achieve effective serum concentrations, and lower doses later. So
we, and quite a few others, I think, have quite often made dose adjustments
based on volume of distribution. We have even developed an interacting
multiple model (IMM) sequential Bayesian procedure to deal specifically with
this problem [2]. This method tracks the behavior of gentamicin and
vancomycin in post cardiac surgical patients better that any other method
[3]. The method comes from the aerospace community where it is widely used
to track and hit hostile targets trying to take evasive action.
"The half time following multiple dosing is only calculated when
dosing has ended and the kinetics are in the terminal phase". Clearly not
so. Clinically, using target oriented, model based TDM, one computes all
relevant parameter distributions during therapy, and uses that patient's
Bayesian posterior model to develop the next, adjusted, dosage regimen.
About digoxin. We use the equations described by Reuning and his
colleagues back in 1973 [4]. They clearly showed that the inotropic effect
of digoxin correlates not with the serum concentrations, but with
concentrations in the peripheral, nonserum, compartment. We have used his
model to develop a clinical model for the use of digoxin. It has worked very
well for us. You can see relationships between dose, serum concentration,
and clinical effect that you cannot see otherwise. And you can select target
therapeutic goals in either the central, but better in the peripheral
compartment, (especially in acute situations) and develop dosage regimens to
achieve them, not for a steady state, but NOW. You can control patients
clinically in acute situations when the simple raw data of serum
concentrations are not at all helpful. Good models and good software are the
thing. Further, using this model, it is clear that quinidine does not reduce
the clearance of digoxin - it simply reduces the uptake in the peripheral
compartment, raising the serum concentrations, and resulting in a smaller
apparent volume of distribution in the central compartment. If you add up
the total amount in digoxin in the central and peripheral compartments when
a patient is on quinidine in the steady state, and then off quinidine a week
later, there is surprisingly little difference in the total amount of
digoxin in the patient.
We have a number of materials in our web site www.lapk.org that
bear on these subjects. If you like, go there and click around. You can go
to Teaching Topics and to New Advances and download and print a bunch of
stuff.
Best regards to you all,
Roger Jelliffe
References
1. Goodwin and Payne: Dynamic System Identification - Experiment
Design and Data Analysis, Academic Press, NY, 1977,p.50].
2. Bayard D, and Jelliffe R: A Bayesian Approach to Tracking
Patients having Changing Pharmacokinetic Parameters. J. Pharmacokin.
Pharmacodyn. 31 (1): 75-107, 2004.
3. Macdonald I, Staatz C, Jelliffe R, and Thomson A: Evaluation and
Comparison of Simple Multiple Model, Richer Data Multiple Model, and
Sequential Interacting Multiple Model (IMM) Bayesian Analyses of Gentamicin
and Vancomycin Data Collected From Patients Undergoing Cardiothoracic
Surgery. Ther. Drug Monit. 30:67-74, 2008.
4. Reuning R, Sams R, and Notari R: Role of Pharmacokinetic s in
Drug Dosage Adjustment. I. Pharmacologic Effect Kinetics and Apparent Volume
of Distribution of Digoxin. J. Clin. Pharmacol. 13:127-141, 1973.
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> Luis wrote:
>
> "if the consideration of the bioavailability factor in the interpretation
> of V/F and CL/F. Again, the extent of absorption does not affect the
> elimination kinetics. Once drug molecules reach the systemic circulation
> they bear no recollection about whether they came from a suspension, a
> tablet or a syringe, and the body will not process ones differently from
> others."
Dear Luis,
I may have missed the point, but was this remark for me? I personally think
that Vss is the only volume term of interest. The original PK quiz question
(title of the thread) was about the connection between the apparent volume
of distribution and the AUC. What I wanted to say in my previous message was
that there is no such thing as calculating Vss/F unless we *a priori* assume
one compartment model (of that drug after IV administration). Otherwise
Vss/F cannot be calculated because its value is not dependent only on F but
also on MAT. Therefore, I considered the original quiz question (AUC vs.
volume of distribution) certainly inappropriate for extravascular
administration data.
Vss = CL * MRT. In other words the ratio of Vss and CL is MRT. Clearly we
can determine CL/F and it is often a useful tool for PK data analysis. If we
could also determine Vss/F, the ratio of Vss/F and CL/F would be identical
to the ratio of Vss and CL, i.e. the MRT after intravenous administration.
To the best of my understanding we cannot determine the MRT after
intravenous administration from extravascular administration data. Hence,
Vss/F can be determined only if IV data is available (and who needs Vss/F in
such case?).
Roger, convincingly, pointed out the clinical relevance of changes in the
central compartment volume. In the case of gentamicin, I presume that was
based on IV data. As indicated CL = Vc * k10 and any change in Vc would also
change the k10 (at least if CL is unaffected). After extravascular
administration CL/F = Vc/F * k10, but only if the k10 here is identical to
the k10 obtained after IV administration. Obviously we need IV data here
too. So every time I see a volume term based on extravascular administration
data, I wonder how they were calculated mathematically (in the case of Vbeta
you only have to have a strong faith that the terminal slope is identical to
the IV administration data). We actually wrote a short communication on this
in the J. Vet. Pharmacol. Therap. (presently available as an online
pre-publication).
Best regards,
Stefan
Stefan Soback, DVM, PhD
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The following message was posted to: PharmPK
Dear Roger,
Thank you for your comments. You wrote in reply to my message to Luis Pereira:
> You are simply wrong when you say that " all arguments in favor of the rate constant approach were shown to be weak or incorrect, and that no convincing arguments were given contradicting the clearance approach.
I have not seen the arguments in favor of the rate constant approach that were not refuted by me or others, and I have not seen any convincing argument refuting the clearance approach.
> Where is your science?
My science is in my arguments.
> Where is your good sense?
My good sense is in discussing ALL arguments mentioned by others, instead of ignoring them. Indeed, in this particular case I did not mention all my arguments in my message, since that would have taken many pages. Therefore I simply referred to the discussion.
> The plain fact is that kel and clearance are simply interconvertible.
No, this is not a plain fact. For me, and I have explained this in numerous messages in this group, this statement is simply false, and this is certainly not trivial. Please see my message today to Luis Pereira.
> I enclose once again our contribution (with references) to the subject. Please pay more attention this time. I would greatly appreciate knowing just what is "weak or incorrect" about our discussion. You seem to be stuck somewhere.
Please note I replied to your message of from 1/26/10 in PharmPK on 1/28/10, which you seem to have missed. I will repeat my message, so you can see that I carefully read your contribution:
--
The following message was posted to: PharmPK
Dear Roger,
Thank you for your thoughful comments. I fully agree with your plea for theory and theoretical arguments. But I have still a few comments.
> In my view, K and Cl are both equally useful. The beauty is in the
> eye of the beholder. No one is more "biologically relevant" than
> the other, unless someone thinks so. Then that is a belief, not a
> fact.
Over the last two months I have given several arguments why clearance is more "biologically relevant" than elimination rate constant. This is not a belief, and it is not a fact. It follows from sound theory. All arguments in favor of K by Peter Mullen and Yaning Wang were refuted by Nick Holford or by me. Do you have an argument why K is 'as biologically relevant' as clearance?
> No one is more "orthogonal" than the other.
I agree. Please note that I stated this explicitly in my message of December 9 to David. Your numerical example is a nice illustration of my theoretical view in that message.
ADDED COMMENT: Please note that orthogonality is a mathematical property. We are not dealing with mathematics (although we use mathematics), but with pharmacokinetics. The mechanistic basis of pharmacokinetics is physiology, not mathematics.
> If you lose 2 legs you lose volume. Renal perfusion probably
> stays the same, though.
OK, but the question was also: what changes, CL, K, CL and K, or none? I would like to hear your opinion.
ADDED COMMENT: I repeated this question in my message today to Luis Pereira.
Your examples on TDM of antiobiotics and digoxin are important 'golden classics', and are highly appreciated. I have one comment to:
> Further, using this model, it is clear that quinidine does not
> reduce the clearance of digoxin - it simply reduces the uptake in
> the peripheral compartment, raising the serum concentrations, and
> resulting in a smaller apparent volume of distribution in the
> central compartment.
In many handbooks it is stated that quinidine reduces both clearance (by competition of active secretion in the proximal tubules) and volume of distribution of digoxin (by displacement from tissue binding sites). I don't have primary references for this statement, which may be a wrong interpretation of data. But your reasoning does not seem to be correct: if the steady state serum concentration of digoxin raises after administration of quinidine, clearance is reduced, irrespective of any change in distribution.
best regards,
Hans Proost
--
So far the status at 28/1/10. For further discussion, please read my message today to Luis Pereira.
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
--
The following message was posted to: PharmPK
Dear Luis.
Thank you for your comments. You wrote in reply to me:
> But as much as I respect everybody's opinion, whoever engages on a clan feud between "supporters of this" and "supporters of that", or a "contest was won" state of mind, or "that's your 'toy' " and therefore you're wrong, may only get my commiseration. There's no place in science for this line of argumentation.
(Sorry, you started with the words 'the frivolous contest').
> But if I recall correctly, it ended with a clear cut and scientific argumentation by Roger Jelliffe, as he always does, showing that ranking parameters by level of importance is nonsense.
You have missed my reply to that message by Roger Jelliffe. And I have repeated this reply in my message today to Roger Jelliffe.
> To say that CL=K.V and CL=k10.V1, therefore CL is one and the same thing is flat out wrong.
I didn't say that. It's just the other way around. k = CL/V and also k10 = CL/V1. It is not a conclusion that CL is the same in both cases, it is the definition of k and k10 (k and k10 are dependent on one and the same CL).
> To say that liver and kidneys 'feel' blood concentrations is tremendously naive and misses the true understanding of what blood concentrations are all about.
Good to hear that I am tremendously naive. Please explain me the truth of what blood concentrations are all about. In my tremendously naive understanding the blood (or plasma) concentration of a drug is the concentration of that drug in blood (or plasma). That blood passes organs like liver and kidneys. The diffusion into the liver, metabolism in the liver, filtration in the kidneys and active secretion in the kidneys are all dependent on the blood (or plasma) concentration. Of course, the driving force is the unbound concentration, but in most cases the unbound concentration is proportional to the total concentration. So my tremendously naive understanding is that blood (or plasma) concentration is the driving force of drug elimination. Where am I wrong?
> To say that "rate constant is the fraction of the apparent volume" is even dimensionally incongruent.
The rate constant k is a fraction of the apparent volume cleared per unit of time. Nothing dimensionally incongruent here.
> So, the sheer number of molecules that enter a clearing organ is the driving force for a first order elimination, if that's the underlying kinetics, no matter which parameterization we choose.
To my opinion this is not true. Consider the situation of hepatic elimination with low extraction ratio (Eh).
Case A: blood concentration 10 mg/l, hepatic blood flow (Qh) 1 l/min
Case B: blood concentration 10 mg/l, hepatic blood flow (Qh) 0.5 l/min
In case A the number of molecules entering the clearing organ is two fold that in case B.
Now the question is: what is the elimination rate and what is the clearance in both cases?
Since the extraction ratio is low, hepatic clearance is not limited by hepatic blood flow, and so the clearance will be the same in both cases (the lower hepatic blood flow might result in a reduced metabolic clearance, e.g. due to limited oxygen supply, but that aspect is not considered here). As a result, the elimination rate (amount/time) and the elimination rate constant are the same in both cases. However, the number of molecules entering the clearing organ is different. So, that number cannot be the driving force.
> But it's still a free world, and anybody may decide to do differently at one's own peril.
I have indicated in earlier message that this question is not trivial in clinical situations, and that it would be strange or even dangerous if anybody may decide what to do. Two examples from earlier messages:
A) From my message to Yaning Wang, 22-12-2009:
What happens with the pharmacokinetic variables in a patient after connection to an extracorporeal circulation? In your view, 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? (the original posting mentioned here erroneously: decreased).
In the clearance approach, one would assume that renal and/or hepatic function of the patient are not altered, so clearance remains the same. The increased volume results in a decrease of k, and an increase of half-life.
What do you expect to happen?
B) From my message to Peter Mullen, 28-12-2009:
Let me add another example why this topic is not trivial, and why the clearance approach should be preferred.
Consider an interaction of drug A by drug B, which displaces drug A from tissue binding sites. Should the dose of drug A be adjusted in the case of coadministration of drug B?
The displacement from tissue binding sites causes a decrease of the volume of distribution of drug A.
The 'rate constant fetishists' might think that the elimination rate constant does not change (drug elimination is not affected, isn't it?). Would this imply that the dose need not to be changed? Or does a lower volume of distribution implies that the dose should be lowered? If it is known, either by reasoning or by measurement, that half-life is decreased, one might think that the dose should be increased. I really can't guess the answer in the rate constant approach, and I'm worried about the patient.
On the contrary, the 'clearance absolutists' have an easy job. Since clearance is not affected, the dosing rate (daily dose) should not be changed. Because of the decreased volume of distribution, half-life will be decreased, so a more frequent dosing (shorter dosing interval with proportionally lower dose) would be advisable. No puzzling here.
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
Back to the Top
> Hans Proost wrote:
> I didn't say that. It's just the other way around. k = CL/V and also k10 > CL/V1. It is not a conclusion that CL is the same in both cases, it is the
> definition of k and k10 (k and k10 are dependent on one and the same CL).
This was not intended for me, but I didn't quite understand the message
here. The equation K = CL/V is valid only for one-compartment model. The
equation k10 = CL/V1 can be used only for multi-compartment models. Although
CL is model independent, these equations would not exist simultaneously for
a single data set.
If you need to fit a (compartment) model for instance for dosing
predictions, you have to determine the rate constants. If you are only
interested in clearance, the non-compartmental approach works fine.
Best regards,
Stefan
Stefan Soback, DVM, PhD
Back to the Top
The following message was posted to: PharmPK
Dear Hans:
Please read the references. You really seem to have a blind spot.
Just read. It is all there. You haven't seen the facts that Kel and Cl are
interconvertible because I don't think you have read the relevant material.
Look at the references. Please. Your arguments are simply false because you
haven't incorporated the relevant references, which are there for you, and
everyone else, to see. Expand your horizons a bit. Please,
Hans, use a 2 compartment model of digoxin. Quinidine reduces the uptake of
digoxin on Na-K APTase and in most tissues except, perhaps, the CNS, which
is why the apparent central volume of distribution is reduced and the serum
concentrations increase. But the tissue amounts are less. It is interesting
that if you add up the total amount of drug in both compartments, on and off
quinidine, there is not a great deal of difference.
Sorry, Hans, but K and CL are in fact both equally useful and
interconvertible. Read the refs and you will see. I bet you haven't read
them, as they may not be in the usual PK culture, but there they are
nevertheless. If you prefer Cl for some reason, that is your choice. I don't
advocate anything except that they are equally useful and are
interconvertible, and are supported by good and well known work. Read the
refs please. They are good math, not arguments.
Sincerely,
Roger
Back to the Top
The following message was posted to: PharmPK
Dear Hans and All,
Naive reasoning is as old as human nature. We may all genuinely say that it just takes to step out the door and see the sun coming up on one side of the horizon in the morning, and going down on the other at the end of the day, to absolutely and conclusively say that the sun is going around the earth. It's such an obvious evidence. Not too long ago, whoever said the contrary would be imprisoned, tortured or even killed. But as much as there's no shame in any kind of naivete, every time we manage to leap ahead and reach understandings that essentially do not disprove our previous beliefs, but rather allow us to explain why we evolved beyond them, that's what scientific advancement is all about. Then it's just for each one to decide what to see.
Science is not in anyone's arguments, but rather in self-contained facts. Although I understand why Hans keeps going in circles, and by personal choice decides to be naive, as anyone is entitled to, I'll just try once more to point out where the fallacy is, as explained in so many textbook references in much more detail. What I cannot explain are statements like "It is not a conclusion that CL is the same ... k and k10 are dependent on one and the same CL".
When mass transfer occurs by passive diffusion, according to Fick's first law, the rate (mass per time) is proportional to the concentration gradient in a perfectly homogeneous, or well stirred, system. It's truly a probabilistic phenomenon which allows the derivation of this law from counting a finite number of molecules (with a binomial distribution) all the way to a macroscopic concentration (approximated by either a Gaussian function or an error function). Transferring this reasoning to a biological system one ought to remember that it's no longer about a beaker full of a solvent where a certain amount of drug is dissolved resulting in a concentration. The mere fact that organs and tissues and cells and all kinds of heterogeneous dwellings exist, must always remind us about where we started and what concentration now means. So, one possibility is to rationalize in terms of mass, or flux, (as with heat transfer or energy transfer), which eliminates the notion of volume. Then, according to the
Back to the Top
Dear Roger,
Thank you for your comments. You wrote:
> Please read the references. You really seem to have a blind spot. Just
> read. It is all there.
I don't have the book of Goodwin and Payne, but the title (Dynamic System
Identification - Experiment Design and Data Analysis) and year (1977) make
it unlikely that this book contains the modern pharmacokinetic concepts. In
refs. 2 and 3 there is nothing about the present discussion. Ref. 4 is an
interesting paper, but it is based on the rate constant approach, and the
word 'clearance' only appears twice as 'creatinine clearance'. Did you ever
realize why kidney function is expressed as creatinine clearance?
Physiologists know for long that renal function should be expressed as
clearance.
> Please, Hans, use a 2 compartment model of digoxin. Quinidine reduces the
> uptake of digoxin on Na-K APTase and in most tissues except, perhaps, the
> CNS, which is why the apparent central volume of distribution is reduced
> and the seum concentrations increase.
This is not the complete interpretation (see the contribution of Luis
Pereira about 'the sun is going around the earth'). If the volume of
distribution decreases, the serum concentration would rise indeed. However,
if clearance and dosing rate would remain the same, the increased serum
concentration would result in an increased rate of elimination, and the
serum concentration would decrease until the serum concentration is again at
the original average level; the average steady-state serum concentration
would not be altered.
However, it is observed that the serum concentration increases. This implies
that clearance decreases. This is not a result of the decrease of the volume
of distribution (probably your view), but a result of the reduced renal
excretion. This mechanism of interaction has been described in numerous
papers (e.g. Woodland C, Ito S, Koren G. A model for the prediction of
digoxin-drug interactions at the renal tubular cell level. Ther Drug Monit.
1998).
> But the tissue amounts are less. It is interesting that if you add up the
> total amount of drug in both compartments, on and off quinidine, there is
> not a great deal of difference.
Indeed, this is what is expected. The reduced uptake of digoxin results in a
decreased volume of distribution, AND in a decreased renal excretion (see
above). As a result of the decreased renal excretion, the steady-state serum
concentration increases, and from V=A/C it follows that A will not change
significantly.
Please note that the independence of V and CL is still true in the case
where V and CL change as a result of the same mechanistic cause, as is
probably the case here. The inhibition of Na-K APTase may result in a
decrease of V (as a result of reduced uptake of digoxin in various tissues)
and CL (as a result of reduced uptake and excretion by the tubular cells).
However, this does not imply that the decrease of V results in a decrease of
CL.
> Sorry, Hans, but K and CL are in fact both equally useful and
> interconvertible.
Of course they are both useful and interconvertible. That's not the
discussion. The point is that, physiologically and mechanistically, K is
dependent on CL, and not the other way around. That is not irrelevant, as
shown in my comment to the digoxin example.
> If you prefer Cl for some reason, that is your choice.
In my contributions to the current and previous discussions in this group
you may find the arguments for my preference for CL. Please read my two
question in the message to Luis Pereira, about extracorporeal circulation
and tissue binding. I would be happy to get your view.
> Read the refs please. They are good math, not arguments.
Here we agree. The refs are mathematics. I prefer pharmacokinetics, based on
physiological arguments. If you prefer math ignoring physiologicy, our
discussion stops.
best regards,
Hans Proost
Dear Luis,
Thank you for your extensive reply.
> I'll just try once more to point out where the fallacy is, as explained in
> so many textbook references in much more detail.
Indeed, many textbooks are still presenting the basics of pharmacokinetics
wrongly, or at least inconsistently. Please see 'Clinical Pharmacokinetics
(and Pharmacodynamics)' by Rowland and Tozer. This is state-of-the-art
pharmacokinetics (and pharmacodynamics).
> What I cannot explain are statements like "It is not a conclusion that CL
> is the same ... k and k10 are dependent on one and the same CL".
Clearance (total body clearance) is the primary parameter reflecting the
elimination capacity of the body. In a one-compartment model, the
elimination rate constant K equals CL/V; in multi-compartment models with
elimination from the central compartment, the elimination rate constant k10
equals CL/V1.
> When mass transfer occurs by passive diffusion, according to Fick's first
> law, the rate (mass per time) is proportional to the concentration
> gradient in a perfectly homogeneous, or well stirred, system.
This is a good starting point. Look at the word 'concentration'.
> Then, according to the same first order (passive diffusion) assumption,
> the rate is proportional to the driving force, i.e. the mass.
The driving force is concentration, as was the starting point of your
reasoning. You cannot changes the rules during the game. The driving force
does not change by mathematical transformations.
> So, if instead one decides to extend the homogeneity notion of a perfect
> solution, to the biological system at hand, then the rate is proportional
> to the concentration.
Yes, I fully agree. Concentration is the driving force.
> A key reminder here, should always be the true definition of concentration
> and the fact that in heterogeneous systems, we may only interpret it in
> light of an apparent (abstract, not biological) volume.
The definition of plasma and blood concentration is quite clear. Why can we
not interpret a concentration without an apparent, abstract volume?
> In regression terms, and depending on the irregularity of the parameter
> space on which an optimization algorithm may try to minimize an objective
> function, it does often help to try different parameterizations, since
> they will generate different parameter space landscapes.
This is irrelevant to this discussion.
> What is often the case too, is the forgetfulness about the meaning of a
> blood concentration and the price to pay for the conception of an apparent
> volume.
I don't understand how the meaning of a blood concentration can be a point
of discussion. And the 'conception of an apparent volume' is necessary to
relate amount in the body to (blood or plasma) concentration, or to relate
clearance to elimination rate constant, but not for the definition of
clearance.
> So, to say that "the blood (or plasma) concentration of a drug ... passes
> organs ... and metabolism and secretion ... are all dependent on the blood
> (or plasma) concentration", is as obvious as stating that the sun goes
> around the earth up in the sky. It's a correct phenomenological
> observation which depending on the purpose intended may very well suffice,
> as it suffices to follow the sun to count the days.
This statement was meant to clarify why it is rational to say that
concentration is the driving force for elimination, either by filtration,
metabolism, diffusion or active transport. I cannot imagine any other
reasonable view.
> It's just our choice and responsibility.
As you explained above in detail, there is firm theory that explains that
the rate of diffusion (as well as the rate of filtration and the rate of
metabolism) is proportional to concentration. This is not a matter of
choice.
> Unlike Hans said, the concept of clearance was not a late discovery, but
> it has been available all along since the 1930's (vide 'History of
> Pharmacokinetics' by JG Wagner).
Thank you for pointing to this.
> It's a valuable concept bearing in mind that it's a mixed parameter
> relating the rate and concentration, given that the latter refers to an
> abstract conception of volume, rather than a physical one.
This was perhaps the opinion in the 1930's, but in the 1970's this idea has
been refined by the physiological approach by Rowland and others. Once
again, clearance (total body clearance) is a measure of the elimination
capacity of the body. As stated above, we do not need an abstract conception
of volume to define a concentration.
> So, to say that "clearance is more "biologically relevant" than
> elimination rate constant" depends on how relevant one wants to be, and
> it's just a matter of opinion (don't tell me it's a club membership
> preference because I just won't argue with that).
I want to be very relevant, and for this reason I understand that the
elimination rate constant is dependent on clearance, and for that reason I
say that clearance is 'more biologically relevant' than elimination rate
constant.
> Hans' example of a low extraction drug is in fact self-explanatory. His
> mistake starts in saying that "the elimination rate (amount/time) and the
> elimination rate constant are the same".
Sorry for be unclear. I meant that the VALUES of the elimination rate
(amount/time) at a blood concentration of 10 mg/l are the same in case A and
case B, and that the VALUES of the elimination rate constant are the same in
case A and case B.
> Particularly with a low extraction ratio, one should always rationalize in
> terms of the intrinsic clearance which is independent of blood flow
> limitations.
Yes indeed. Did you even think about the reason why the term 'intrinsic
clearance' is used, and not 'intrinsic elimination rate'?
> Only doing it ALL one may say that we'll start perhaps understanding
> 'biological relevance'.
Yes, but I missed clearance in your list. Actually, you gave a long essay on
hepatic elimination, but I cannot find a single argument in favor of the
rate constant approach, and not a single argument contra the clearance
approach.
Unfortunately I did not find answers to my questions with respect to
extracorporeal circulation and tissue binding. I would be happy to get your
reply.
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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