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Hello all:
I am having a hard time explaining two concepts to my PK students
(perhaps more, but they are at least politely smiling and nodding at
the others...)
1. How would you recommend describing the AUMC? The area under the
first moment curve is the way Benet's and other subsequent references
describe it, but it is not particularly satisfying on a visceral level.
2. For hepatic clearance of a high extraction drug given IV, the total
clearance can be approximated by Qh (hepatic blood flow). The
clearance of free drug is therefore Qh/fu. How do you explain why the
clearance of free drug goes down (Cave-free goes up) when the fraction
of unbound drug is made to increase with drug interactions or
hypoalbuminemia? Yes, a higher fraction of drug is unbound, but the
blood flow (substrate delivery) is limiting, so why can fu have so
inversely proportional an effect?
Insights on how to explain what I can derive will be most welcome.
Thank you in advance.
Stochastically yours.
Paul
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Paul,
> 1. How would you recommend describing the AUMC? The area under the
> first moment curve is the way Benet's and other subsequent references
> describe it, but it is not particularly satisfying on a visceral level.
Can't help with that one. The way I might describe it is that AUMC is
part of a formula for SHAM PK parameter estimation and good for getting
initial estimates of Vss (maybe) (but to be honest I don't teach that
stuff).
> 2. For hepatic clearance of a high extraction drug given IV, the total
> clearance can be approximated by Qh (hepatic blood flow). The
> clearance of free drug is therefore Qh/fu. How do you explain why the
> clearance of free drug goes down (Cave-free goes up) when the fraction
> of unbound drug is made to increase with drug interactions or
> hypoalbuminemia? Yes, a higher fraction of drug is unbound, but the
> blood flow (substrate delivery) is limiting, so why can fu have so
> inversely proportional an effect?
The key is "substrate delivery". Substrate delivery is increased by
increasing blood flow OR if blood flow is unchanged by increasing the
mass of drug per unit volume of blood e.g. by increasing plasma protein
binding or increasing partition into red cells. Increased delivery
means higher unbound organ clearance. When binding is decreased then
delivery decreases and unbound organ clearance goes down. Most
textbooks (and the original Wilkinson & Shand paper) write the model
for total organ clearance like this:
CLi*fu * Q
CLorg,total = --------------
CLi*fu + Q
but I prefer this:
CLi * Q
CLorg,total = --------------
CLi + Q/fu
Or for unbound organ clearance:
CLorg,unbound = CL,org,total/fu
CLi * Q/fu
CLorg,unbound = --------------
CLi + Q/fu
I think this helps to show that it is the ratio of Q/fu that really
counts for any given CLi and Q.
Holford NHG. Clinical Pharmacokinetics and Pharmacodynamics - The
Quantitative Basis for Therapeutics. Chapter 37 in "Clinical
Pharmacology - Basic Principles in Therapeutics". Edited by KL Melmon,
HF Morelli, B Hoffman, DW Nierenberg. Macmillan. (1992)
--
Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New
Zealand
email:n.holford.-a-.auckland.ac.nz
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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Dear Paul Hutson,
With respect to your questions:
1. Is there any reason to use a different term for AUMC? IMHO, it is not
even necessary to have any term for it, since by itself it is a
meaningless
value, at least, it does not seem to be understandable 'on a visceral
level'. The only thing what counts is that it is used to calculate MRT.
In a
very simplistic view, you might say that AUMC is a measure of the
'concentration - time' average of the profile, and AUC is a measure of
the
'concentration' average of the profile, and their ratio yield MRT, a
measure
of the 'time average' of the profile.
[This is essentially the approach I take ... i.e. it is a term required
to calculate MRT. I don't even give AUC much more status than as a
means of calculating F and other parameters - db]
2. You wrote:
> 2. For hepatic clearance of a high extraction drug given IV, the total
> clearance can be approximated by Qh (hepatic blood flow). The
> clearance of free drug is therefore Qh/fu. How do you explain why the
> clearance of free drug goes down (Cave-free goes up) when the fraction
> of unbound drug is made to increase with drug interactions or
> hypoalbuminemia? Yes, a higher fraction of drug is unbound, but the
> blood flow (substrate delivery) is limiting, so why can fu have so
> inversely proportional an effect?
The basis for a better understanding is the notion that clearance (or
plasma
clearance) is defined as the rate of drug elimination (in this case, by
the
liver) divided by the drug plasma concentration. Similarly, 'clearance
of
free drug' or 'unbound clearance' is defined as the rate of drug
elimination
divided by the unbound drug concentration, and 'blood clearance' is
defined
as the rate of drug elimination divided by the drug concentration in
blood.
In case of high extraction drugs, blood clearance is limited by blood
flow
as a result of limition in the supply of drug. Assuming a fixed
blood/plasma
concentration ratio, (plasma) clearance is limited as well (although the
value may be different from blood flow, depending on the blood/plasma
ratio!). Both blood clearance and plasma clearance are here independent
of
plasma protein binding, since this factor is not a limiting factor (if
it
was, the extraction would not be high).
Clearance of the unbound drug is much higher than plasma clearance. This
follows directly from the equations, but your question is: how can that
explained? The liver does not only remove the unbound drug, but also a
major
fraction of the bound drug: removal of the unbound drug results in a net
release of drug from the binding sites, thus maintaining the unbound
drug
concentration relatively high, and thus maintaining the driving force
for
hepatic uptake of unbound drug. For high extraction drug, this continues
until the total concentration of drug has decreased considerably
(again: if
not, extraction would not be high). So, the unbound concentration is
not a
limiting factor for the removal of drug.
Best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.farm.rug.nl
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> Hello all:
> I am having a hard time explaining two concepts to my PK students
> (perhaps more, but they are at least politely smiling and nodding at
> the others...)
>
> 1. How would you recommend describing the AUMC? The area under the
> first moment curve is the way Benet's and other subsequent references
> describe it, but it is not particularly satisfying on a visceral >
> level.
Hi Paul-
I have found that model-independent PK has always been a bit difficult
for pharmacy students to grasp, especially MRT and AUMC. It seems to
become just another set of letters in a sea of PK acronyms, especially
if you teach model-independent concepts near the end of a PK course or
module. I begin by discussing the origin of statstical moments and how
each of the moments (AUC, MRT, VRT) can be used (or misused) in
pharmacokinetics. I have not, unfortunately, be able to find a
satisfying review article that I could recommend, so I would suggest
sticking with the original literature. My greatest success (as measured
by the fewest blank stares) has been to describe AUMC visually with a
t*C vs. t graph and explain why the curve is shaped the way it is and
what might affect its shape. Since by the time I cover
model-independent PK, the students have already had multicompartmental
PK, I liken the use of AUMC to that of the microconstants K12 and K21.
These parameters, while important, are used to calculate more relevant
(from my perspective) PK values, like MRT for model-independent PK and
the macroconstants for multicompartmental PK. I hope this helps.
Lane
--
Lane J. Brunner, Ph.D.
College of Pharmacy
The University of Texas at Austin
University Station, A1920 (USPS)
2409 West University Street (courier)
Austin, TX 78712-0126
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Has anyone used the Chapter 13 "Noncomparmental Modeling: An Overview"
in Schoenwald's book "Pharmacokinetics in Drug Discovery and
Development" ?
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)