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Dear all,
Many papers on pharmacokinetics of ACE inhibitors describe
"effective half-lives".For example:
benazepril (Am-J-Vet-Res.1995,56:1620-8 &
Biopharm-Drug-Dispos.1989,10:365-76)
cilazapril (Eur-J-Drug-Metab-Pharmacokinet.1990,15:63-7)
lisinopril (Biopharm-Drug-Dispos.1989,10:397-409 &
Eur-J-Clin-Pharmacol.1988,34: 61-5)
enalapril (Biopharm-Drug-Dispos.1984,5: 273-80).
Does anyone know what the "effective half-life" means?
Does it reflect drug elimination?
Masaki Hiraoka
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From: Kazimierz H. Kozlowski, Pharm. D.
Laboratory of Pharmacokinetics
The Children's Memorial Health Institute
04-736 Warsaw, Poland
e-mail: khkoz.-at-.czd.waw.pl
Dear Dr Hiraoka,
Effective half-life is discussed in the article: Boxenbaum H. et al.:
Effective half-life
in clinical pharmacology. J. Clin. Pharmacol. 35(8), 736-6, 1995.
This pharmacokinetic phenomenon is reflect underestimation of terminal
half-life after single dose.
Mechanism is distributional or protein binding.
Sincerely
Kazimierz H. Kozlowski
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[A few replies - db]
=46rom: Thomas.Senderovitz.at.ferring.com
To: PharmPK.at.boomer.org
Subject: RE: PharmPK Effective half-life
Date: Tue, 23 Nov 1999 08:48:32 +0100
Dear Masaki Hiraoka,
The so-called "effective half-life" is not a very good term to use.=20
It is used for two-compartment models to describe one half-life for=20
the drug. This is not very precise, since such drugs have actually=20
two half-lives - one for each exponential phase, and to put them into=20
one will actually not describe the elimination accurately. I prefere=20
to use both of them instead (t=BD-lambda 1 and t=BD tambda 2) - and be=20
careful not to draw the conclusion that the lambda2-halflife=20
(previously called the beta half-life) is the elimination half-life,=20
as elimination may occur during the lambda-1 phase as well.
Regards
Thomas Senderovitz, MD
Associate Head of Clinical Pharmacology
Product Development, Clinical Research
Address:
=46erring Pharmaceuticals A/S
=46erring International Center
Borups All=E9 177
DK-2400 Copenhagen NV
Denmark
Phone:
Direct: +45 38 15 04 58
Switchboard: +45 38 15 03 00
Mobile: +45 24 25 52 24
=46ax: +45 38 15 04 58
E-mail address: Thomas.senderovitz.at.ferring.com
---
Date: Tue, 23 Nov 1999 02:47:02 -0700 (MST)
X-Sender: ml11439.-at-.pop.goodnet.com
To: PharmPK.-at-.boomer.org
=46rom: ml11439.-at-.goodnet.com (Michael J. Leibold)
Subject: Re: PharmPK Effective half-life
Hello Masaki,
In my experience the "effective half-life" refers to the "apparent
half-life" of a drug given the realities of multicompartment kinetics.
That is, gentamicin and vancomycin are dosed based on their effective
half-lives, which are derived from one-compartment kinetic analysis of
serum levels. However, these are "effective half-lives" since their
pharmacokinetics are actually multicompartment.
The half-life measured for gentamicin does not actually represent
the terminal elimination phase since the beta phase is followed by a
much longer washout phase reflecting the slow release of gentamicin
from renal tissue. Nevertheless, the T1/2beta measured for gentamicin
can be used to effectively dose the drug, since the T1/2gamma only
results in slow accumulation over a longer period of time.
Generally, the "effective half-life" represents the half-life of
the terminal elimination phase, except in the case of drugs which
accumulate in the tissues (like gentamicin). In the later case, the
"effective half-life" represents the half life of the principal
elimination phase, distinct from the deep tissue accumulation phase.
The half-life of the deep tissue accumulation phase reflects a much
slower deep tissue binding process not concerned with elimination of
the drug from the body.
So, the "effective half-life" is the half-life which is used in
the following equations to determine one compartment pharmacokinetic
constants:
One compartment pharmacokinetic model:
Cp2=3D (Cp1)e-Ket
ln Cp2- ln Cp1=3D -ket
1) Ke=3D [ln Cp1- ln Cp2]/[time]
If the ratio of Cp1/Cp2 equals two, then ln Cp1/Cp2=3D 0.693, and the
[time] in the denominator of equation becomes the half-life, since it
represents the time it takes for the Cp1 to decrease to 1/2 of Cp1.
2) Ke=3D 0.693/T1/2
3) T1/2=3D .693/Ke
4) T1/2=3D 0.693(Vd)/Cl
5) Cl=3D 0.693(Vd)/(T1/2)=3D KeVd
In effect, these equations can used to dose most drugs which exhibit
linear pharmacokinetics. In reality however, virtually all drugs obey
multicompartment pharmacokinetics. As a result, the T1/2 of a drug is
frequently referred to as the apparent half-life, or the effective half-life=
=2E
I have even read a paper on phenytoin phramacokinetics in which the author
assumed a one compartment linear pharmacokinetic model to determine the
apparent T1/2 for phenytoin. Although phenytoin obeys nonlinear kinetics,
the author was able to dose several patients using the apparent half-life
of phenytoin in each patient.
In short, the "effective half-life" refers to the assumption of one
compartment pharmacokinetics for drugs which actually obey more complicated
pharmacokinetic models. That is, the term "effective" half-life reflects
that it is a simplification of a more complex pharmacokinetic process.
Mike Leibold, PharmD, RPh
ML11439.aaa.goodnet.com
---
Date: Tue, 23 Nov 1999 08:05:49 -0500
=46rom: Sriram
X-Accept-Language: en
To: PharmPK.at.boomer.org
CC: Multiple recipients of PharmPK - Sent by
Subject: Re: PharmPK Effective half-life
Here is a reference for your question
Harold Boxenbaum and Michele Battle, J Clin Pharmacol 1995; 35: 763-766
---
=46rom: "Brian E. Davies"
To:
Subject: Re: PharmPK Effective half-life
Date: Tue, 23 Nov 1999 10:08:27 -0500
X-Priority: 3
My own definition of effective half-life would be derived from the MRT as
follows:
CL =3D Vss x kss
kss =3D 1/MRT
Effective half-life =3D 0.693 / kss
=3D 0.693 x MRT
see also the paper by Harold Boxenbaum which uses the accumulation factor in
the calculation of effective half-life.
The effective half-life is used for a multicompartment drug and is
particularly useful when the contribution of the first phase is considerably
greater than that of the terminal phase i.e. elimination is faster than
distribution. In this case the terminal rate constant will approximate k21
and will not reflect the elimination of the drug. A good example of a drug
of this type is gentamycin. Over 98% of an intravenous dose is eliminated
before distribution equilibrium with all tissues of the body has been
achieved. Using f1 and f2 to denote the fraction of elimination associated
with the 2 exponential terms of a 2-compartment model, for gentamycin f2 is
close to 0 and so it is the half-life of the first phase that primarily
determines the elimination and the time to reach plateau. The effective
half-life is a reflection of the relative contributions of the 2 phases and
is the ideal solution to the question: "what is the half-life" and can be
used for estimating time to plateau and dosing intervals for those drugs
that need to be dosed in multiples of the half-life.
Brian Davies
Advanced Biomedical Research, Inc.
brian.davies.at.abr-pharma.com
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Date: Thu, 25 Nov 1999 19:34:33 +0900
From:
To: PharmPK.at.boomer.org
Subject: Re: Effective half-life
Many thanks to Kazimierz, Thomas, Mike, Brian, Sriram, Gary,
Michael, David and all of you.
Following is my understanding:
"Effective half-life" is calculated from accumulation factor
of the drug with apparent multiple compartment model. So it
is better called as "accumulation half-life."
Accumulation factors are usually calculated from the ratios
of AUC(tau, at SS)/AUC(tau, single), Cave(SS)/Cave(single),
Cmin(SS)/Cmin(single) etc.
For a drug whose trough is in terminal elimination phase, the
trough values at SS may reflect accumulation factor from
Cmin(SS)/Cmin(single), and "effective half-life" may be close
to terminal elimination half-life. And in the case accumulation
occurs in first order, increase in AUC(tau) can be interpreted
"effective half-life" from AUC(tau, at SS)/AUC(tau, single).
This is useful when terminal half-life is not precisely
obtained or is not a dominant factor for accumulation.
But I think there may be several factors that cause increase
in AUC(tau), Cave or Cmin after repeated administration.
Some may not relate to elimination of drugs.
Thus, consideration on the factors affecting accumulation
factor is necessary for each specific case to use "effective
half-life".
How does my understanding sound?
Any comments are welcome.
Masaki Hiraoka
---
Date: Thu, 25 Nov 1999 09:31:06 -0500
From: "Oo, Charles {CLIN~Nutley}"
Subject: RE: PharmPK Re: Effective half-life and multiple dosing
To: "'PharmPK.aaa.boomer.org'"
Dear all,
Would like to expand on what is being discussed.
Effective or accumulative half-life is a practical concept in
assessing drug accumulation ratio, steady-state Cmax, Cmin and
fluctuation during multiple dosing of a multi-compartmental drug.
The half-life (or rate constant k) that affects drug accumulation is
the one that is just prior to a particular dosing interval tau. The
general equation is:
Accumulation ratio = (1)/(1-EXP(-k* Tau))
This effective or accumulative half-life is contingent upon the
dosing interval (tau) used. This is the half-life that will
determine accumulation with the respective dosing interval. This is
the half-life that is meaningful to multiple dose therapy and
steady-state simulation from single dose data.
The deeper compartmental half-life may be just an academic curiosity.
It has been said that with the advent of more sensitive bioanalytical
techniques, the terminal half-life of drugs get longer. The deep
compartment half-life may not mean anything if the dosing interval
(tau) used in therapy is shorter.
Also, I think we should stop using the word 'apparent' before
half-life because all half-lives are apparent.
Comments would be appreciated.
Charles Oo Pharm.D., Ph.D.
Hoffmann-La Roche Inc.
Clinical Pharmacology
Building 1/3C27
Nutley, NJ 07110-1199
Tel: 973-562-2575
Fax: 973-235-5635
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[A few replies - db]
From: "Hans Proost"
Organization: Pharmacy Dept Groningen University
To: PharmPK.-at-.boomer.org
Date: Fri, 26 Nov 1999 09:07:22 MET
Subject: Re: PharmPK Re: Effective half-life
X-Confirm-Reading-To: "Hans Proost"
X-pmrqc: 1
Priority: normal
With respect to 'effective half-life', Masaki Hiraoka wrote:
> This is useful when terminal half-life is not precisely
> obtained or is not a dominant factor for accumulation.
To my understanding, the longest (=terminal) half-life is always the
dominant factor for accumulation. Are there any circumstances
where the accumulation is not governed by the longest half-life.
Of course, if the terminal half-life is associated with a very small
intercept, it may not become apparent in the accumulation factor
observed from plasma concentration profile. But the accumulation
in the 'deepest' compartment is certainly governed by / associate
with this terminal half-life.
> But I think there may be several factors that cause increase
> in AUC(tau), Cave or Cmin after repeated administration.
> Some may not relate to elimination of drugs.
This is a rather cryptic phrase, and in my opinion not correct.
Accumulation, in terms of AUC(tau) and C_average is governed by
clearance only, and not by distribution.
Of course, the half-lives are related to clearance, and so it may be
said that the accumulation is related to the half-lives, but this is a
rather confusing and 'dangerous' way of reasoning.
Best regards,
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
---
Reply-To: "Stephen Duffull"
From: "Stephen Duffull"
To:
Subject: Re: PharmPK Re: Effective half-life
Date: Fri, 26 Nov 1999 09:01:29 -0000
Organization: University of Manchester
X-Priority: 3
Re discussion on half-life
If I remember correctly there was considerable discussion
about half-life on this discussion group around September
this year, when I believe much of the current topic and
related areas were battled out in the time honoured manner.
Is there a repository available for those who may have
missed this lively discussion?
[Yes there is...I have put the discussions on-line with annual
indexes on the page http://www.boomer.org/pkin/ - db]
Regards
Steve
=====================
Stephen Duffull
School of Pharmacy
University of Manchester
Manchester, M13 9PL, UK
Ph +44 161 275 2355
Fax +44 161 275 2396
---
X-Sender: klotx.-a-.mlucom6.urz.uni-halle.de
Date: Fri, 26 Nov 1999 11:41:31 +0100
To: PharmPK.at.boomer.org
From: "Prof. Michael Weiss"
Subject: Re: PharmPK Re: Effective half-life
In linear pharmacokinetics the only general valid concept (independent of
specific compartmental models or number of exponentials) is to deal with
accumulation and/or washout in terms of mean disposition residence time
(MDRT or MRTiv).
The accumulation ratio is RA = MDRT/T (T = dosage interval) and more than
90% of the plateau value (steady state) are reached in 3.7 MDRT (t90% < or
= 3.7 MDRT). After a single bolus dose more than 90% of the dose is
eliminated after 3.7 MDRT.
For more information, see: Weiss, M. The relevance of residence time theory
to pharmacokinetics. Eur. J. Clin. Pharmacol. 43: 571-579 (1992) and
references therein.
Michael Weiss
--------
Michael Weiss
Martin Luther Univ.
Dep of Pharmacology
Section of Pharmacokinetics
06097 Halle/Saale
Germany
Fax: 49-345-557 1657
Tel: 49-345-557 1835
michael.weiss.-a-.medizin.uni-halle.de
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PharmPK discussion group:
We recently presented some of our work regarding the dependence of
effective half-life values on the method used for estimation at the
recently concluded AAPS 1999 meeting at New Orleans (Abstract # 1047). I
have attached the abstract at the end of the present message for your
convenience.
During our poster presentation at AAPS, the question most frequently
asked was,
1. Does effective half-life represent the half-life associated with
pharmacodynamic response (effect)?
Effective half-life does not relate to pharmacodynamics or effect. It is
a simplified half-life which when used in conjunction with the dosing
interval can predict the accumulation index of plasma/blood
concentrations at steady-state compared to the first dose.
Example: Let us consider a hypothetical compound, Drug X, which exhibits
multi exponential decline in plasma concentrations with a alpha, beta,
gamma and delta half-life (hours) of 1, 10, 75 and 150, respectively,
following oral administration. Let us also suppose that the drug is
administered once daily. The half-life which would help us in predicting
accumulation would obviously be the half-life associated with the major
phase (in terms of contribution to the total AUC). Similarly, the extent
of accumulation as reflected by the accumulation index (Rac) would shed
some light on identification of the major phase. If for the above
example, the Rac (ratio of the AUC in a dosing interval at steady state
to the first dosing interval) is approximately 4 to 5, then we know that
the major phase is the gamma phase or if the Rac is close to 9 then we
know the terminal phase is the major phase. Likewise, observed
accumulation (major phase concept) is used to calculate a hybrid
half-life, the effective half-life (Teff). The Teff concept might be
more readily understood when asked as a question, "No matter how many
half-lifes are associated with Drug X, if Drug X were to behave as one
with mono exponential characteristics what half-life would explain the
observed accumulation?"
To this end, the equation used for calculating accumulation index for
drugs with mono exponential characteristics is employed to estimate
Teff. The equation is Rac = (1)/[1-exp{-(0.693/Teff)tau}].
Researchers have used various methods such as, Cmax,ss/Cmax,1;
Cmin,ss/Cmin,1; AUCss/AUC0-tau; AUC0-inf/AUC0-tau and Css,ave/Cave,1
(same as AUCss/AUC0-tau). As was presented by us at AAPS, the Teff
values estimated from the ratio of trough concentrations at steady state
to trough concentration after the first dose (Cmin,ss/Cmin,1) might
result in overestimation of Teff. This is because the ratio of
Cmin,ss/Cmin,1 might reflect the terminal half-life and not Teff in
certain instances (high fluctuation between Cmax and Cmin - which is
dependent on dosing interval).
I hope this information helps.
Regards,
Gabriel Robbie, Ph.D.
Office of Clinical Pharmacology and Biopharmaceutics
CDER, FDA
ABSTRACT
Dependence of Effective Half-life on Estimation Method
G. J. Robbie and P. J. Marroum
Purpose: To evaluate the parameter dependence of accumulation index and
effective half-life and to identify an optimal pharmacokinetic parameter
for estimation of effective half-life.
Methods: Simulations of plasma concentrations were performed based on a
two-compartment open model with first order absorption. A fixed dosing
interval of 24 h, terminal half-life (T1/2,z) of 31.6 h and a terminal
area contribution of 30% to the total AUC were assumed. The Teff
estimated from three different ratios, Cmax,ss:Cmax,1,
AUC0-t,ss:AUC0-t,1, and Cmin,ss:Cmin,1 were compared. The effect of a
change in rate of absorption (Ka), absorption lag-time (Tlag), volume of
distribution (Vd) and elimination (K10) on Teff were evaluated.
Further, a sensitivity analysis was performed using Monte Carlo
simulations to assess the impact of variability (20-50%) in
pharmacokinetic parameter on Teff.
Results: The steady-state to single dose ratios of Cmax, AUC and Cmin
yielded Teff values of 8.2, 10.7 and 23.8 h, respectively. The Teff
estimated from the Cmin ratio was very different from Teff estimated
from the ratios of AUC and Cmax. Changes in Ka, Tlag and K10 had a
significant impact on Teff under certain conditions. A decrease in the
ratio of Ka:K10 (< 2) or an increase in Tlag resulted in a reduction in
the differences in Teff values estimated from the three ratios. The
results of the sensitivity analysis indicated that variability in
elimination would have a greater impact on Teff compared to variability
in absorption. The range of Teff values obtained based on AUC ratios for
high variability (50%) in K10 and Ka were 5.5 to 38.9 h and, 8.7 to 14.5
h, respectively.
Conclusions: Teff values are dependent on the parameter used for
estimation. At higher Ka:K10 ratios, the ratio of Cmin,ss:Cmin,1
overestimated Teff. Variability in elimination affects Teff to a larger
extent compared to absorption. The ratio of AUC0-t,ss:AUC0-t,1 is a more
reliable and robust method for estimation of Teff. However, the choice
of the estimation method used should also be based on clinical
considerations.
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