- On 5 Dec 2003 at 09:01:32, chernandez.at.grupovita.com sent the message

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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] - On 6 Dec 2003 at 10:47:35, "Henri Merdjan" (hmerdjan.aaa.wanadoo.fr) sent the message

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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 - On 9 Dec 2003 at 11:24:37, "vgcasabo" (vicente.casabo.-at-.uv.es) sent the message

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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 - On 9 Dec 2003 at 17:22:30, "J.H.Proost" (J.H.Proost.-at-.farm.rug.nl) sent the message

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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 - On 10 Dec 2003 at 09:47:09, chernandez.-a-.grupovita.com sent the message

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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 - On 11 Dec 2003 at 13:26:53, "Durisova Maria" (exfamadu.-a-.savba.sk) sent the message

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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

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