Back to the Top
The following message was posted to: PharmPK
Dear All,
As you fully know F (absolute bioavailabity) calculations depend of the
use
of different/same doses and participation of the same/different
volunteers:
1. Different subjects and doses:
F= [AUCpo/AUCiv]*[Doseiv/(weight*Cliv)/Dosepo/(weight*Clpo)]
(Spanish reference: Florez Ed. Farmacologia Humana, 1997)
2. The same subjects and different doses:
F= (AUCpo/AUCiv)*(Doseiv/Dosepo)
(Br J Clin Pharmacol 1999; 47: 483-91)
3. The same subjects and doses:
F= (AUCpo/AUCiv)
(Drug Res 1986; 36: 1278-83)
However, a scenario with different subjects and the same doses is
not
gathered by the equations mentioned above. Could you kindly confirm
me if
the next equation would be accceptable for this case?
F= [AUCpo/AUCiv]*[(weight*Clpo)/(weight*Cliv)]
Thanks in advance
Cándido Hernández-López, M.D.,Ph.D.
Clinical Pharmacology Section
Laboratorios VITA
Sant Joan Despí, Barcelona (SPAIN)
www.grupovita.com
[When did using different subjects become acceptable? - db]
Back to the Top
The following message was posted to: PharmPK
Dear Candido,
Let me suggest that we go back to the common basis for all these
equations.
First of all, there is a direct proportionality between the rate of
change
in the amount of drug present in the body (dA/dt) and the drug
concentration
C(t). The proportionality constant is the drug clearance CL.
dA/dt = CL*C(t)
Integrating both sides gives
Amount = integral (CL*C(t))
If, in addition, CL is constant (more specifically: CL is independent of
time and
concentration, i.e. PK is linear), then you can take the CL term out of
the
previous equation and you get the following equation applicable to
linear kinetics, and linear kinetics ONLY:
Amount = CL*integral(C(t)) = CL*AUC
You may wish to rewrite it for po administration
F.Dosepo = CLpo*AUCpo
and for iv administration as well
Doseiv = CLiv*AUCiv
Re-arranging the latter 2 equations yields
F = (AUCpo/AUCiv)*(CLpo/CLiv)*(Doseiv/Dosepo)
The dose ratio obviously cancels out when using the same doses iv and
po.
However, the rationale for cancelling out the CL ratio is that you
assume CL
to be the same iv and po. In other words, this is a
reasonable/acceptable
assumption if
(and only if) you dose the same subject iv and po.
My understanding of using the terms weight*CL is an extra assumption
that CL
is constant on a per kg basis. Nothing to deal with different subjects
of
different
body weight.
I hope this answers your questions.
Kind regards,
Henri
Henri Merdjan
Consultant for the Life Science Industries
PK and PK/PD specialist
NewFreelance sarl
Paris, France
+33 (0)6 23 97 67 34
hmerdjan.at.wanadoo.fr
Back to the Top
Hi Candido
> However, a scenario with different subjects and the same doses
is > > not
> gathered by the equations mentioned above. Could you kindly confirm
me if
> the next equation would be accceptable for this case?
> F= [AUCpo/AUCiv]*[(weight*Clpo)/(weight*Cliv)]
The above equation is not acceptable because, you can not calculate
Clpo independently of F in subjects in absence of IV information .
For example if you calculate:
Clpo= Dpo/AUCpo
And
Cliv=Div/AUCiv
The equation (the one you mentioned) always yields value 1.
In the case that CL changes for subjects, and you can assume that
Volume of distribution does not change (or remains constant)
You can use terminal slope lamda
Lamda=Cl/Vd
F= [AUCpo/AUCiv]*[lamdapo*Vd/(lamdaiv*Vd)]
Vd cancels, and
F=(AUCpo/AUCiv)*(lamdapo/lamdaiv)
This can be acceptable if variability of Ln(AUC*lamda) is least than
variability of Ln(AUC), obtained from ANOVA test
Back to the Top
The following message was posted to: PharmPK
Dear Dr. Casabo,
Your remark with respect to the first equation is correct. On the other
hand, the equation by itself is fully correct. The problem is indeed
that you cannot calculate or estimate CLpo, so the equations is not
applicable.
> For example if you calculate: Clpo= Dpo/AUCpo
Yes, but one should never calculate CLpo in this way. This is probably
done quite often, but it is definitely incorrect. The correct equation
is:
CLpo / Fpo = Dpo / AUCpo
You also proposed the following equation:
> F=(AUCpo/AUCiv)*(lamdapo/lamdaiv)
Since variability in clearance is usually larger than that in volume of
distribution, this approach may be suited, provided that lambdapo and
lambdaiv can be estimated accurately. In many cases the lambda values
are obtained from the last, say, 4 data points. Such estimates are not
accurate, and the 'lambda correction' may introduce large errors, not
unlikely larger than the error introduced by a true difference in
clearance between the two administrations.
I am not aware that this equation is used in practice. Any further
comments?
Best regards,
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
tel. 31-50 363 3292
fax 31-50 363 3247
Email: j.h.proost.-a-.farm.rug.nl
Back to the Top
The following message was posted to: PharmPK
Dear David, Henri, Vicente, and Johannes,
Many thanks for your useful explanations and clarifications.
The scenario described: Different subjects with the same doses tested
is a
common situation in initial clinical drug development. The use of
equations
to suggest an hypothetical F value seems also reasonable at this point.
Your focus in clear limitations (or nonsense) of F equations use when
different subjects are implicated makes me to think that no-solution is
possible in this common context and only the design of clinical trial
using
same subjects, and preferably same doses, can solve the question of F.
However, even in this case I find additional questions: At time to
select
an intravenous dose regimen to compare, Would be the same approach to
decide a bolus dosing or a short-term or long-term constant-rate
infusion?
(Please, I remark that usually in an initial clinical drug development
phase the dose regimen is still to be determined)
Having the answer to this question I believe we could have an idea of
the
best procedure to know the F value of a compound.
Thanks in advance
Cándido Hernández-López, M.D.,Ph.D.
Clinical Pharmacology Section
Laboratorios VITA
Sant Joan Despí, Barcelona (SPAIN)
www.grupovita.com
Back to the Top
The following message was posted to: PharmPK
Dear All,
For those who are interested in the fundamental theory behing
the equation called in this discussion "the F equation" I would
recomend our study: Dedík, L., Durisová , M.: CXT-MAIN:
a software package for determination of the analytical form
of the pharmacokinetic system weighting function,
Comput. Meth. Programs Biomed., 51, 1996, 183-192.
The full text of this study is available online via Science Direct.
On the basis of the equations presented in the Appendix of the given
study,
the correct
formulae can be derived for "the F equation" in the event of:
1) equal single drug doses given intravenously and orally;
2) nonequal single drug doses given intravenously and orally;
3) an intravenous drug dose given in an infusion (at a constant and/or
time
varying rate)
and a single oral drug dose.
Regards,
Maria Durisova PhD, DrSc (Math/Phys)
Head of Department of Pharmacokinetics
Institute of Experimental Pharmacology
Slovak Academy of Sciences
84104 Bratislava
Slovakia
PharmPK Discussion List Archive Index page
Copyright 1995-2010 David W. A. Bourne (david@boomer.org)