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A number of compounds are eliminated by organ-independent mechanisms. For
instance, cisatracurium, a bisisoquinolinium neuromuscular blocker, which
undergoes temperature and pH dependent Hofmann elimination;
2-amino-6-methoxypurine arabinoside, a deoxyguanosine analog, which is
eliminated via adenosine deaminase; and antibodies which undergo typical
protein catabolism.
I have been looking at pharmacokinetic parameter relationships and have
consistently identified a positive statistically significant relationship
between the volume of distribution and clearance. Of course, protein
binding could explain the apparent relationship (i.e., Vss = Vb +
Vt(fub/fut) and CL = Clint x fub (for a low E compound)). Also, there was
no identified relationship between t1/2 and CL and t1/2 and Vss. For these
compounds, within an individual, the elimination rate constant is
essentially "fixed" and is independent of organ function. Classical
application of PK relationships do not appear to be appropriate here. The
elimination rate constant appears to be the independent parameter and CL
and Vss appear related. This would make the interpretation of CL an issue.
I have worked with many organ-dependent elimated drugs which are, as
expected, explained clearly by the "classic" PK parameter relationships. I
know the idea of CL and Vss being related is not the common view, but then
again, these are not the common organ-dependent eliminated compounds.
Again, protein binding could possibly explain the relationships seen, but I
do not believe that this would explain the relationships for these drugs,
either because of the type of elimination, low protein binding, or the type
of compound.
Any thoughts on organ-independent elimination with respect to PK parameter
relationships would be appreciated.
Dave Kisor
Ohio Northern University
College of Pharmacy
Ada, Ohio, USA
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"Kisor, David (by way of David_Bourne)" wrote:
> A number of compounds are eliminated by organ-independent mechanisms.
....
> I have been looking at pharmacokinetic parameter relationships and have
> consistently identified a positive statistically significant relationship
> between the volume of distribution and clearance.
....
> The elimination rate constant appears to be the independent parameter and CL
> and Vss appear related. This would make the interpretation of CL an issue.
>
This is in interesting issue. But I think the classical independence of CL and
V still holds. I like to think of CL being a parameter reflecting function and
V reflecting structure. As such they can be thought of as being conceptually
distinct and independently varying entities. But it is common to find they are
correlated when a group of individuals are examined and this correlation can
often be understood in terms of other covariates such as body size. Bigger
people have bigger structure (water, fat) and bigger function (liver, kidneys)
but the relationship between size and V and size and CL is not usually the same
so half-life changes with body size.
In the case of drugs which are metabolized in the blood itself (which covers
some if not most of the cases David refers to) then the blood provides both the
structure (volume) and function (clearance). An increase in blood mass can be
expected to produce exactly proportional increases in volume and clearance if
all other things remain equal and I think this is what underlies the
observations David has made. However, the independence of volume and clearance
could be revealed e.g. suppose the CL is due to enzymatic activity in red cells
then a change in haematocrit would change the ratio of volume to clearance and
one would expect to see a change in half-life.
So I have to disagree with David's assertion that the elimination rate constant
is an independent parameter. It just appears to be the case because the same
organ (blood and other extracellular "tissues") is responsible for both
structure (V) and function (CL).
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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Just to add a few more reasons that CL and V may correlate:
Variability in plasma protein binding usually affects CL and V in similar
directions (note
the common models for low extraction, high V drug (CL=fu*CLint and V=fu*Vtissue)
Variability in bioavailability affects CL/F and V/F similarly
Variability in pulmonary first-pass affects CL and V similarly
Differences between nominal and actual dose given affects CL and V the same
Best regards,
Mats
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Thanks for the comments.
I am still struggling with this. Cisatracurium may be the best example to
talk about. This bisisoquinolinium neuromuscular blocker degrades in blood
and tissue based on temperature and pH (Hofmann elimination). Of course
these parameters are kept in "tight" physiologic control. The in vitro
degradation rate constant, at pH 7.4 and 37 C, is very similar to that
found in vivo in many different populations. In fact, the interpatient
variability in t=BD across 5 different studies (including 79 patient) as
represented by the C.V. was ~ 11.5%! When comparing this to t=BD estimates
for other drugs, this is an extremely low C.V. When looking at patients
with end-stage liver disease and patients with renal failure, the t=BD was
very similar to that in patients with normal renal and hepatic function,
and the C.V. was 17%, again very low.
So, here we have the case that the elimination rate constant (and t=BD) (with
degradation in vitro and degredation, with minimal organ elimination in
vivo) appears to be depenedent on pH and temperature and independent of
clearance and volume, which, by the way were significantly different in
liver failure patients, for example, versus patient with normal hepatic
function.
This is the kind of data that led to my thought of t=BD (and of course the
elimination rate constant) being independent of clearance and volume.
I have thought about the protein binding issue, unforunately, when the
blood is collected from patients, it is acidified to prevent further in
vitro degradation. This acidification confounds protein binding=
measurements.
I would really like to "have my cake and eat it too" in that I would like
to believe that the CL and V relationship is just something "seen". But if
I continue thinking about the definition of clearance (the volume of
biologic fluid from which drug is removed per unit time), I can't help
think that, for instance in the liver failure patient with the larger
volume, that cisatracurium degrades based on temperature and pH and
therefore, with the larger volume, a larger volume of biologic fluid has
drug removed from it per unit time. This relates CL and V!
More thoughts are greatly appreciated. Thanks for listening.
David
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Not only is there a positive correlation between Cl and V among drugs, there
is a positive correlation within a particular drug. What I mean by that is
that there is an artificial correlation induced by modeling. For most, if
not all, nonlinear models that are fit using least-squares, the partial
derivatives are are not independent. Thus the parameter estimates within a
fit will be correlated. It doesn't matter if Cl and V are truly
independent, the process of fitting them will make them correlated. This
applies to both individual and population data. This is why it is important
to review the correlation matrix in the output of an analysis.
PETER L. BONATE, PhD.
Clinical Pharmacokinetics
Quintiles
POB 9708 (L4-M2828)
Kansas City, MO 64134
phone: 816-767-6084
fax: 816-767-3602
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"Kisor, David" wrote:
> I am still struggling with this. Cisatracurium may be the best example to
> talk about. This bisisoquinolinium neuromuscular blocker degrades in blood
> and tissue based on temperature and pH (Hofmann elimination).
>
> I have thought about the protein binding issue, unforunately, when the
> blood is collected from patients, it is acidified to prevent further in
> vitro degradation. This acidification confounds protein binding measurements.
>
Just because you didn't measure plasma protein binding does not invalidate this as one of the causes of the correlation of CL and V.
> I continue thinking about the definition of clearance (the volume of
> biologic fluid from which drug is removed per unit time),
You cite a definition that is technically correct but biologically misleading. It happens to have dimensions of volume/time but that does not mean that there is mechanistic relationship between CL and V. A better definition of clearance is the factor that relates elimination rate to concentration.
Several biologically plausible explanations have been offered to you to explain why CL and V might be correlated. You have suggested no mechanistic reasons to explain why the elimination rate constant is an independent "constant".
I think it should be recognized that this discussion is a matter of perspective. The mathematical persective sees the elimination rate "constant" as an independent parameter and defines CL as the product of V and this "constant". The biological perspective see CL and V as independent on mechanistic grounds and is happy to accept the elimination rate "constant" as a dependent parameter.
Finally, to come back to the application of PK in clinical pharmacology. Suppose that therapeutic benefit of a drug is best achieved by a constant steady state conc. Then the parameter of interest would be CL. Factors (such as body size) which predicted differences in CL would be useful to know in order to individualize dose rate to achieve the target concentration. It makes no difference that the half-life among individuals has lower variability than CL. The important thing is to understand why CL varies not why half-life does not!
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
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Dear colleagues,
Nick Holford replied to David Kisor:
> This is in interesting issue. But I think the classical independence of CL and
> V still holds. I like to think of CL being a parameter reflecting function and
> V reflecting structure. As such they can be thought of as being conceptually
> distinct and independently varying entities.
This statement is true for organ-independent mechanisms of
elimination taking place in plasma, eg. the hydrolysis of
suxamethonium and mivacurium by plasma cholinesterase.
However, it is NOT true for drugs which are broken down by 'true'
organ-independent elimination, as is the case for atracurium and
cisatracurium (one of the isomers in the mixture 'atracurium'): this
molecules breaks down spontaneously at a pH-and temperature-dependent
rate by a chemical process called 'Hofmann elimination'.
This process takes place according to 'normal' chemical reaction
kinetics with a fixed rate constant (if pH is constant).
Therefore, in this process k and V should be regarded as the
independent parameters, and CL as the dependent parameter.
The only argument I can raise against this reasoning is that the rate
constant may be different in different tissues as a result of
differences in pH, temperature and possibly other factors. However,
even in that case there is no argument for considering clearance as
the independent parameter, since it is still dependent on the volume.
To look at the problem in a different way: Do you consider the
physical half-life of radionuclides as a parameter dependent on the
clearance and volume of distribution of the radionuclide?
The situation of atracurium and cisatracurium is not very diffent!
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.farm.rug.nl
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Dear colleagues,
In my previous comment I did not mention the following points:
1. The degradation of atracurium / cisatracurium by Hofmann
elimination (note: 'elimination' is here a chemical term referring to
the elimination of a part from the molecule) is not the only route of
elimination (note: 'elimination' is here the familiar PK term).
In addition, ester hydrolysis occurs, and some renal elimination.
2. Plasma protein binding and tissue binding make the situation even
more complicated. Is the rate constant of elimination of the bound
drug the same as for the unbound drug? I don't know.
Looking at this aspect, the concepts of 'structure' and 'function'
raised by Nick Holford are again in the picture!
Therefore, the semantic problem is considerable, since both k and CL
are for some part 'independent' parameters and for some part
'dependent' parameters.
So, discussing too long about the semantic problem does not seem
really fruitful. Nevertheless, the clearance of atracurium /
cisatracurium is something special!
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.farm.rug.nl
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Thanks for the thoughts. I am not dissmissing the protein binging issue.
I am simply stating why this piece of information is not available. I
pointed out the potential explanation of protein binding in my initial
inquiry. I suggested the pH and temperature dependence (chemical
degradation; Welch et al., CPT 1995; General Chemistry Textbooks) as the
mechanistic reasons to explain why the elimination rate constant is an
independent "constant".
Thanks
DK
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Hans Proost wrote:
> However, it is NOT true for drugs which are broken down by 'true'
> organ-independent elimination, as is the case for atracurium and
> cisatracurium (one of the isomers in the mixture 'atracurium'): this
> molecules breaks down spontaneously at a pH-and temperature-dependent
> rate by a chemical process called 'Hofmann elimination'.
> This process takes place according to 'normal' chemical reaction
> kinetics with a fixed rate constant (if pH is constant).
It seems you are trying to say that there is something different about 'normal' chemical reactions (e.g. Hofmann elimination) and enzymatically catalyzed reactions (classical clearance mechanisms) because of pH and temperature dependence. Enzyme mediated catalysis is pH and temperature dependent so I don't see that there is really any difference between cisatracurium and succinylcholine in this regard. I accept radioanuclide breakdown as spontaneous but breakdown is not 'spontaneous' if dependent on hydrogen ion concentration and temperature.
The key test for the independent existence of clearance is to infuse drug to the same steady state concentration under two different conditions of volume of distribution. If the infusion rate of drug increases when volume increases then clearance is not independent. Suppose extracellular fluid volume (ECF) is the main determinant of the apparent volume of distribution. Then if I increase it by infusing a few liters of saline then I should be able to change the volume of distribution. Does the rate of elimination of drug change? Does the Css change?
Consider the pH (i.e. hydrogen ion concentration) dependence of cisatracurium elimination. Because pH is under homeostatic control I would not expect pH to change with an increase in volume. From the point of view of a cisatracurium molecule in the ECF nothing has changed. At the same steady state concentration I would expect to have more cisatracurium in the body because the volume is bigger but does the rate of elimination increase? Do I need to infuse cisatracurium at a faster rate to maintain the same steady state concentration?
I suspect the answer is that the rate of elimination *does* increase and a faster infusion rate is required because the extra volume of ECF with hydrogen ion in it will be able to breakdown more cisatracurium. So in this case clearance would not be independent of a change in volume.
So what about succinylcholine elimination by cholinesterase? Given the same increase in volume of ECF it really depends on what happens to the amount of cholinesterase in the ECF. In the short term (say hours after a quick increase in volume by saline infusion) I expect the cholinesterase amount would not change and I would expect the rate of elimination of succinylcholine would not change and thus the steady state conc would be unchanged and clearance would thus be independent of volume. However, if plasma cholinesterase conc is under homeostatic regulation then eventually the amount of cholinesterase in the ECF would increase and the rate of elimination would increase and a faster infusion rate would be needed. I would then accept that clearance is not independent of volume.
Both of these examples represent the case I tried to point out earlier where structure and function are determined by the same physical entity and thus CL and V will necessarily be correlated. As I hope I have argued for the succinylcholine case, the ability to independently vary V and CL depends not on the mechanism of the chemical reaction but on how long you want to wait for the body to establish a new steady state.
The same thing could even apply to classical organ-dependent clearance. Suppose one kidney is removed (and assume this had a negligible effect on V) then renal clearance would be halved with no change in volume. But over time some degree of hypertrophy would take place in the remaining kidney and clearance would increase (to some degree) and the elimination rate constant (half-life) would seem not to have changed (much). This could be argued as empirical evidence for non-independence of CL and V!
IMHO the issue of whether CL and V are independent or not depends it part on your perspective and in part of how long you want to wait for the body to compensate for changes in either structure (ECF expansion) or function (kidney removal).
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
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Dear Colleagues,
Nick Holford wrote in reply to my remarks:
> It seems you are trying to say that there is something different about 'normal' chemical reactions (e.g. Hofmann elimination) and enzymatically catalyzed reactions (classical clearance mechanisms) because of pH and temperature dependence. Enzyme mediated catalysis is pH and temperature
dependent so I don't see that there is really any difference between cisatracurium and succinylcholine in this regard. I accept radioanuclide breakdown as spontaneous but breakdown is not 'spontaneous' if dependent on hydrogen ion concentration and temperature.
Indeed, it is a matter of taste how you define 'spontaneous'. In my
view, Hofmann elimination is, at least, 'more spontaneous' than
hydrolysis by plasma cholinesterase, since it does not require an
enzyme. So, there is some gradual difference from radioactive
decay, via Hofmann elimination, via plasma cholinesterase
breakdown (not dependent on blood flow!) to 'normal' organ
elimination.
I agree with your key test, and your comments are very clear. As I
stated in my second message, your concept of 'structure' and
'function' is very useful for a proper understanding. But I still feel
that atracurium / cisatracurium do not completely naturally fit into
this concept. With respect to the Hofmann elimination, the
independence of clearance and volume should not be regarded as
some form of religion. At least, we should take into account that
the situation is different here. This is particularly important when
using pharmacokinetics for dose predictions in altered situations,
as in your example with an increase volume. The same holds for
dose prediction in infants and children.
Thank you for your thoughful comments.
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.aaa.farm.rug.nl
>
> The key test for the independent existence of clearance is to infuse drug to the same steady state concentration under two different conditions of volume of distribution. If the infusion rate of drug increases when volume increases then clearance is not independent. Suppose extracellular fluid
volume (ECF) is the main determinant of the apparent volume of distribution. Then if I increase it by infusing a few liters of saline then I should be able to change the volume of distribution. Does the rate of elimination of drug change? Does the Css change?
>
> Consider the pH (i.e. hydrogen ion concentration) dependence of cisatracurium elimination. Because pH is under homeostatic control I would not expect pH to change with an increase in volume. From the point of view of a cisatracurium molecule in the ECF nothing has changed. At the same steady
state concentration I would expect to have more cisatracurium in the body because the volume is bigger but does the rate of elimination increase? Do I need to infuse cisatracurium at a faster rate to maintain the same steady state concentration?
> I suspect the answer is that the rate of elimination *does* increase and a faster infusion rate is required because the extra volume of ECF with hydrogen ion in it will be able to breakdown more cisatracurium. So in this case clearance would not be independent of a change in volume.
>
> So what about succinylcholine elimination by cholinesterase? Given the same increase in volume of ECF it really depends on what happens to the amount of cholinesterase in the ECF. In the short term (say hours after a quick increase in volume by saline infusion) I expect the cholinesterase
amount would not change and I would expect the rate of elimination of succinylcholine would not change and thus the steady state conc would be unchanged and clearance would thus be independent of volume. However, if plasma cholinesterase conc is under homeostatic regulation then eventually the
amount of cholinesterase in the ECF would increase and the rate of elimination would increase and a faster infusion rate would be needed. I would then accept that clearance is not independent of volume.
>
> Both of these examples represent the case I tried to point out earlier where structure and function are determined by the same physical entity and thus CL and V will necessarily be correlated. As I hope I have argued for the succinylcholine case, the ability to independently vary V and CL
depends not on the mechanism of the chemical reaction but on how long you want to wait for the body to establish a new steady state.
>
> The same thing could even apply to classical organ-dependent clearance. Suppose one kidney is removed (and assume this had a negligible effect on V) then renal clearance would be halved with no change in volume. But over time some degree of hypertrophy would take place in the remaining kidney
and clearance would increase (to some degree) and the elimination rate constant (half-life) would se
em not to have changed (much). This could be argued as empirical evidence for non-independence of C
L and V!
>
> IMHO the issue of whether CL and V are independent or not depends it part on your perspective and
in part of how long you want to wait for the body to compensate for changes in either structure (E
CF expansion) or function (kidney removal).
>
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)