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A QUESTION FOR ANYONE WITH THE PATIENCE FOR A NEWCOMER TO PK/PD. IN A
STANDARD STUDY COMPARING BLOOD LEVELS OF A BRAND NAME AND GENERIC DRUG,
IS A POSSIBLE TO GET VALUES FOR AUC infinity THAT ARE LESS THAN THE
VALUES OBTAINED FOR AUCt?
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No, it is not possible to have values of AUC(0-inf) < AUC(0-t).
AUC(0-inf) = AUC(0-t*) + C*/ke where C* is the last measured
concentration at time (t*) and ke is the terminal elimination rate
constant. My guess is that ke was entered as a negative value. ke
is determined from the slope of the terminal linear portion of the
LN (Conc) vs time curve. The slope will always be negative since
concentrations are declining. It is sometimes an art in determining
which points to use in determining the terminal slope. The terminal
elimination rate constant term implies decreasing concentrations and
therefore the negative is not required (ke is always positve,
-(slope))
David
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The partial area under the curve (AUCt) is the area from t=0 to t=t.
AUCinfinity is the area from t=0 to t=infinity. Since there can be no
negative contributions to the AUC at any time after t (or before t, for
that matter) AUCinfinity is always greater than AUCt.
Of course, one might make the mistake of plotting the data on linear,
instead of semi-log, paper, and then extrapolating a fast (apparently
terminal) exponential through the horizontal axis and thus appear to
start accumulating negative contributions to AUCinfinity. It should be
clear however that the real blood concentration can never be a negative
number, so the AUC can only increase as the integration is carried out
toward infinity.
Regards,
Bob
--
Robert D. Phair, Ph.D. rphair.aaa.ix.netcom.com
BioInformatics Services http://www.webcom.com/rphair
Partnering and Outsourcing for Computational Biology
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It is possible and is also incorrect. Check your rules for determining half
life and extrapolation to infinity.
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Dear Bill:
You have raised a very interesting point. I too have come across occasions
when AUC(inf) values were lower than AUC(t). We need to clearly define the
AUC(t) values. Is this the AUC up to the last validated measurable plasma
concentration [C(last), I call the corresponding AUC, AUC(last)] or is it the
AUC up to the last point which is below the limit of quantitation [considered
zero in AUC calculation] which I call AUC(all).
It would be highly unusual to have AUC(last) larger than AUC(inf). However, it
is possible for AUC(all) to be larger than AUC(inf). This occurs when time
span is large between the last validated plasma concentration in the
disposition phase and the next sample with concentration below quantitation.
The above is difficult to explain in words. You will get a better appreciation
if you draw a figure. I would be happy to fax you one.
As a note, I don't particularly like to use AUC(inf) for drugs with short half
lives (T1/2 = < 12 hours). The reason for this is one single concentration
[C(last)] in the beta phase has a high influence on the AUC(inf) values since
AUC(inf) = AUC(last) + [C(last)/(0.693/T1/2)]. It is simply better to
determine AUC(last) with most sensitive assay and taking blood samples for a
time period exceeding 4*T1/2.
AUC(inf) is more appropriate for drugs with long T1/2 (>24 hours) provided
that the ratio of AUC(last)/AUC(inf) exceeds) 0.80.
I hope the above will stimulate discussion on AUC determinations since this
parameter is critical in bioavailability assessment.
Regards,
Aziz Karim
aakari.-at-.msn.com
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Bill,
While it is true that the actual AUC(inf) cannot be less than the actual
AUC(t), it is possible to calculate an AUC(t) value that is larger than the
calculated AUC(inf) value depending on the sampling scheme relative to the
half-life, as Dr. Karim discussed.
As a follow-up to his note on the potential inaccuracies of the calculation of
AUC(inf) for compounds with short half-lives, if variability of the low
concentrations is an issue, AUC(inf) could be extrapolated from a predicted
C(last) at the time of the last measurable concentration based on the half-life
(beta) regression. With this method, the data used to estimate half-life would
be weighted equally in the extrapolation to infinity. This method assumes that
there are adequate data to estimate the half-life relatively accurately.
Jo Cato
allen.cato.-at-.abbott.com
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AUCt cannot exceed AUCinfinity since AUCinf = AUCt + C(t)/?z.
However, it is possible to get AUCinfinity < AUC(0-24) or AUC(0-48),
AUCall, etc.
If your sampling points in the terminal phase are far apart and your last
sample is BQL (and your program treats BQL samples as zero), then ?z
may be larger than the slope connecting the last 2 points which are C(t)
and 0. This will cause AUCinf to be less than AUC0-24 because in the
calculation of AUCinf, zero is not used.
Brinda K Tammara
Otsuka America Pharm. Inc.
Rockville
MD-20850
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As indicated by several replies generated from the inquiry as to whether
one can get values of AUC(0-inf) which are less than AUC(0-t), the answer
is that in theory NO. However in practice you may come across data which
suggests that this is the case. Apart from the obvious error in
calculating AUCs. I assume you have used the correct formula for
calculating the area of trapezoids, or as David Nix pointed out you may
have used -ke rather than the absolute value of ke to calculate AUC(t-inf).
that is if you have devised you own routine for calculating the parameters.
Alternatively the problem may reside in the software package you are using
in that some software may calculate AUC(0-inf) either using the exponential
fitting parameters or alternatively use the expected concentration at time
't-last', derived from the terminal rate constant as opposed to observed
value whilst AUC(0-t) have been calculated using observed values. Bit
complicated but I hope it is clear.
Faruq H Noormohamed
Department of Therapeutics
Chelsea and Westminster Hospital
369 Fulham Road
LONDON
SW10 9NH
Tel +44 (0)181 746 8141
Fax +44 (0)181 746 8887
email f.noormohamed.at.cxwms.ac.uk
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Copyright 1995-2010 David W. A. Bourne (david@boomer.org)