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what is the difference between terminal phase ,terminal half life and
elimination phase , biological half life.
shobha
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> what is the difference between terminal phase ,terminal half life and
> elimination phase , biological half life.
By convention the slowest half life describing drug time course is
described as being terminal and is usually thought of as being
associated with elimination. However, there are situations e.g. when
absorption is slow compared with elimination, when the terminal
half-life is actually a description of the absorption process.
Biological half-life is almost always an inappropriate term. Most
commonly it has been used to describe the time course of
disappearance of drug effect. But half-life is a parameter that is
only appropriate for describing an exponential (e.g. first-order)
process. The time course of drug effect is typically not exponential
so there is no such thing as a half-life to describe it. The only
time drug effect disappearance is approximately exponential is when
concentrations are much less than the EC50 for th drug. In this case
the effect is essentially linearly related to drug concentration and
the time course of effect will parallel that of concentration. The
drug effect will then seem to have a half-life which will be the same
as the drug concentration half-life. I prefer never to use the term
"biological half life". IMHO it is almost always a marker for those
who do not understand what they are talking about when it comes to
describing PKPD events.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.at.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
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[A few replies - db]
Date: Mon, 6 Sep 1999 03:22:10 -0700 (MST)
X-Sender: ml11439.aaa.pop.goodnet.com
To: PharmPK.at.boomer.org
From: ml11439.-a-.goodnet.com (Michael J. Leibold)
Subject: Re: PharmPK terminal and biological t 1/2
Hello Shobha,
These are some short definitions:
1) Terminal Phase
This refers to the last elimination phase of a drug which shows
multicompartment pharmacokinetics. For example, for a drug with two
compartment kinetics, this would refer to the second elimination phase(beta).
The first phase is the distribution phase.
In the case of a one compartment model, there is only one phase
and a distribution phase is not modeled. The one compartment model
usually is simplification of a drug with two compartment kinetics, and
thus the one phase studied usually represents the terminal, elimination
phase of a drug with multicompartment kinetics.
2) Terminal T1/2
This refers to the effective half-life of the elimination phase.
For example, for the two compartment model, the beta phase constant
(beta=elimination constant) would be used to calculate the half-life
of the elimination phase:
T1/2= .693/beta
3) Elimination phase
This refers to the portion of the plasma concentration curve which
represents elimination. That is, in the two compartment case, this would
refer to the beta phase. In the alpha phase, the drug is undergoing
distribution mainly, with some elimination. In the elimination phase
the drug has already distributed, and the plasma concentration is
decreasing as the drug is cleared from the body.
In short, this is the second "dip" or slope in the plasma concentration
curve
4) Biological Half-life
This refers to the half-life as defined in pharmacokinetics. That is,
the half-life that results from distribution and/or elimination processes
of a drug in a biological organism. In short, the time is takes for the
plasma concentration to decrease by 1/2. In the linear first order systems that
occur in pharmacokinetics, this is a constant.
The T1/2 is a theoretical constant since it is a function of elimination
constants, which are considered mathematical constants of the differential
equations describing the one compartment, or multicompartment models. In
reality, the T1/2 is fould to vary with physiological variables such as
creatinine clearance and cardiac output. Hoever, The Ke and T1/2 are
considered constants in pharmacokinetic equations.
One compartment:
Ke = [Ln C1- Ln C2]/[time]
T1/2 = .693/Ke
ln(2) = 0.693 (i.e. C2 = 1/2 C1)
Two compartment:
beta = [Ln C1 - Ln C2]/[time] during beta phase
alpha = [Ln C1- Ln C2]/[time] during alpha phase**
**(if alpha>>>beta this method OK, otherwise must use residuals for alpha)
Elimination half-life:
T1/2beta= .693/beta
Distribution half-life:
T1/2alpha= .693/alpha
5) Textbooks
The pharmacokinetic textbooks contain the above definitions with
more illustrations [e.g. Gibaldi& Perrier Pharmcokinetics].
I hope this was helpful!!
Mike Leibold, PharmD, RPh
ML11439.-a-.goodnet.com
---
From: Nils Ove Hoem
To: PharmPK, Multiple recipients of PharmPK -
Sent by
Subject: Re: PharmPK Re: terminal and biological t 1/2
Date: Mon, 6 Sep 1999 07:13:53 +0200
X-Priority: 3
At least outside the "PKPD community" the word "halflife" seems to have
become equivalent with " speed of elimination"!, which is of course wrong.
As pointed out by Nick Holford, the concept of half life is just another way
of stating 1.order behaviour. I have quite frequently, when reviewing
monographies and drug information, come across the use of the concept even
in non-linear situations. You then often find the statement (half life is X
h at plasma concentration Z and half life is Y at plasma concentration P).
Now, these days when more sensitive analytical procedures become widespread
(eg. LC-MS and CE-MS) people start to report "deep compartments". In line
with reasoning that the "true" elimination is represented by the last
(terminal) part of the time-concentration profile, the first order constant
for this phare is then reported as the "elimination " constant for the
overall process. In theoretical terms, would there not always be another
even deeper compartment for any drug? and how important are such "deep
compartments" if/when they represent only a tiny fraction of the total AUC?
Maybe we need a clearer definition of the "terminal phase" concept ?
Nils Ove Hoem
---
Date: Mon, 6 Sep 1999 08:53:00 +0100
From: cawello.at.schwarzpharma.com
Sender: cawello.-a-.schwarzpharma.com
Reply-To:
Organization: Schwarz Pharma Group
To: PharmPK.aaa.boomer.org,
shobha24.-a-.yahoo.com (Multiple recipients of PharmPK - Sent by)
Subject: re: PharmPK terminal and biological t 1/2
Importance: Normal
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The term 'terminal half life' is used for the slowest process of
concentration decrease. If you use a semilogarithmic view of your data the
last period of linearity will be named 'terminal half life'. In contrast to
'elimination half life' characterizes the transport process of elimination.
Sometimes both half lives are the same, elimination is the shortest process
of transports. But in our would of high specific drugs and analytical
methods to detect very low concentrations the terminal half life
characterizes the elimination from the target receptor (for example ACE
inhibitors with a high affinity to ACE, e.g. moexipril or quinapril).
The elimination phase is the interval of all your concentrations-time-data
dominant effected by the elimination process. The terminal phase is the
corresponding interval of concentrations data collected for the calculation
of the terminal half life (the last linear period of your semilogarithimic
data view).
Apart from the terminal half-life there is another half-life which deserves
attention, namely the dominant half-life. In a multi-phasic decline of
plasma concentrations, the dominant half-life is the half-life of that phase
contributing most to the area under the curve.
Owing to the above definitions, the dominant half-life will always be
smaller than or equal to the terminal half-life. Very often both quantities
are the same, but there are cases (e.g. the aminoglycoside antibiotic
gentamycin) in which the dominant half-life (2-3 h) is much shorter than the
terminal half-life (>50 h).
All the half lives we used now are biological half lives. The term
'biological half life' is a general term for half lives effected by the
biological system. I think we will not use this term, we go in details
because we can?
For more details please have a look at chapter 4 of my new textbook
'Parameters for Compartment-free Pharmacokinetics' (Shaker 1999, ISBN
3-8265-4767-5, ISSN 0945-0890).
****************
Willi Cawello, PhD, Schwarz Pharma AG
Alfred-Nobel-Str, D40770 Monheim am Rhein, Germany
***************
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[Two more replies - db]
From: "Thomas Senderovitz"
To:
Subject: Sv: PharmPK Re: terminal and biological t 1/2
Date: Mon, 6 Sep 1999 21:31:26 +0200
X-Priority: 3
To continue the halflife debate, I just want to add that for any drug
with multicompartmental kinetics, the concept of only one halflife is
meaningless. It is a question of how much is eliminated duringeach
phase. Thus, there is a halflife associated with each exponential
term , so to say. It is therefore not always true that the terminal
phase halflife is the "real" halflife associated with the elimination
of the drug.
I also agree with Niels Ove that newer assays will perhaps reveal
so called "deeper" compartments. It's important to remember, though,
that these may not necessarily have any physiological meaning, since
we are "only" describing the data mathematically - and each
exponential term can not necessarily be explained by yet another
compartment.
Thomas Senderovitz
---
Reply-To:
From: "Steven Shafer"
To:
Subject: RE: PharmPK Re: terminal and biological t 1/2
Date: Mon, 6 Sep 1999 11:28:17 -0700
X-Priority: 3 (Normal)
Importance: Normal
Colleagues:
Additional comments on half-lives:
1) Terminal half-life:
As pointed out, the terminal phase is the final log-linear portion of
the concentration vs time curve for multicompartmental pharmacokinetics.
The terminal half-life is the half-life associated with this terminal
phase. However, as assays become more sensitive, we often see residual
drug washing out of deep tissues at very low concentrations, resulting in
longer and longer terminal phases. Since the rate at which drug washes out
of bone and cartilage is not terribly interesting, the terminal half-life
is often of limited clinical interest.
2) Elimination half-life
This is often used interchangeably with terminal half-life, as mentioned in
several of the responses so far. However, I think this is misleading.
Obviously,
in a first-order system the actual rate of elimination is proportional to
concentration. Thus, the fastest elimination is actually during the initial
phase (e.g., the "distribution" phase), and not during the terminal phase.
One could, I guess, calculate the AUC associated with each half-life (e.g.,
coefficient1/lambda1, coefficient2/lambda2, coefficient3/lambda3), and
then pick the largest of these and designate it the "elimination half-life"
since it is responsible for the bulk of the elimination. However, to me this
seems like a bizarre exercise. I think the reason that people get hung up
on the "elimination phase" is that they want to stick with one compartment
concepts when dealing with multicompartment drugs (e.g., "tell me where
elimination occurs.") Well, elimination is always occurring. A better
question is "tell me when 50% of the drug has been eliminated." This can
be easily done, but the calculation requires consideration of all coefficients
and exponents.
To quote from one of the comments offered by other readers of the list about
the elimination phase:
> This refers to the portion of the plasma concentration curve which
> represents elimination. That is, in the two compartment case, this would
> refer to the beta phase.
No, no, no! Elimination is ALWAYS occurring - not just during the "beta" phase,
(by which I assume the author means the terminal phase). In fact,
elimination is
slowest during the terminal phase. Clearly, the term "elimination phase" is
misleading, even among readers of this discussion group.
Personally, I don't use the term elimination phase or elimination half-life.
These terms are misleading, suggesting that some phases are associated with
distribution, and others are associated with elimination. It just isn't that
simple.
3) Biological half-life
As suggested by the discussions, there is no consistent definition for the
biological half-life. For this reason, the term should not be used, unless
it is specifically defined in the text.
In the field of anesthesia, we now discuss multicompartmental pharmacokinetics
(which applies to all intravenous anesthetic drugs) using the
"context-sensitive
half-time." This is the time for a 50% decrease in plasma
concentration, in which
the context is the duration of drug administration. The context-sensitive
half-time is calculated using simulations. The concept has been expanded to
the notion of "x% decrement times", where "x" is a percentage (e.g., 50%
decrement time, 75% decrement time, or whatever % is clinically appropriate.
Additionally, the decrement times can either be for the plasma or for the
site of drug effect.
More recently, the notion of "mean effect time has been added, which integrates
the PK simulations with the type of PD simulations Nick Holford was
referring to.
All of these terms have very specific definitions.
For more information, see:
Anesthesiology 1991 74:53-63.
Anesthesiology 1992 76:327-330
Anesthesiology 1992 76:334-341
Anesthesiology 1994 81:833-842.
Anesthesiology 1995 83:1095-1103
Similarly, for the muscle relaxants the "recovery phase half-life "
has been defined
as the time for the drug effect to decrease from 75% neuromuscular
blockade to 25%
blockade. For example, see Anesthesiology 1994 81:59-68.
-----
To conclude:
Multicompartment pharmacokinetics are not easily described with
"one-compartment"
concepts. The terminal half-life is a function of the assay
sensitivity and probably
has no clinical relevance for many drugs. The elimination half-life
is a misnomer,
as the drug is always being eliminated and thus designating a
particular half-life
as contributing the "major" portion of elimination is of little value
(if there are
5 exponents, does it really matter that one of them is associated
with 25% of the AUC,
and the others are 19% of the AUC?). Additionally, if the offset of
drug effect occurs
during the first half-life, then is the designation of a "dominant"
half-life of any
particular interest? What if one half life is associated with 45% of
the AUC, and the
other has 55% of the AUC? If one gives an infusion, then the
half-life that is "dominant"
may well change, depending on the duration of the infusion. Lastly, biological
half-life appears to have no precise definition, and should not be
used without the
author supplying a specific definition. All of this nonsense stems
from wanting to
apply one compartment shortcuts (e.g., 1 half life = 50%, 2
half-lives = 75%, etc)
to drugs described by multicompartment pharmacokinetics. Forget it.
It can't be done.
The only honest way to deal with multicompartment pharmacokinetics is to accept
that they are complex, not easily summarized with a single term, and
then define
specific metrics of clinical interest and solve them, either in
closed form or using
computer simulations. The "context-sensitive decrement times" and
"mean effect times"
have been specifically defined for anesthetic drugs, because these
metrics relate to
clinically important aspects of the pharmacokinetics of the drugs.
The context-sensitive
50% plasma decrement times (a.k.a., context-sensitive half-times) have now been
calculated for virtually all of the intravenous hypnotics, anxiolytics, and
analgesics used in anesthesia. Similarly, the "recovery phase
half-life" has been
defined for virtually all muscle relaxants. Clinical
anesthesiologists use these
terms when discussing anesthetic drugs and select their drugs and
design their infusion
regimens based on the reported decrement times for the anesthetic drugs.
So, if you want to report multicompartment pharmacokinetics, report
the unit disposition
function (e.g., ALL of the coefficients and exponents of the impulse
response function),
which tell the complete story (assuming first order PK). Then put
your intellectual
effort into defining metrics of clinical interest and solving these
for your clinical
audience.
Best regards,
Steven Shafer, M.D.
---
Steven L. Shafer, M.D.
Associate Professor of Anesthesia
Phone: 650 852-3419
FAX: 650 852-3414
Pager: 650 723-8222 #13477
E-mail: Steven.Shafer.-a-.Stanford.Edu
WWW: http://pkpd.icon.palo-alto.med.va.gov
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[Two more replies - db]
Date: Tue, 07 Sep 1999 21:39:41 +1200
From: Nick Holford
X-Accept-Language: en
To: PharmPK.-at-.boomer.org
Subject: Re: PharmPK Re: terminal and biological t 1/2
> From: "Steven Shafer"
> To:
> Subject: RE: PharmPK Re: terminal and biological t 1/2
> Date: Mon, 6 Sep 1999 11:28:17 -0700
> The only honest way to deal with multicompartment pharmacokinetics
>is to accept
> that they are complex, not easily summarized with a single term, and
> then define specific metrics of clinical interest and solve them, either in
> closed form or using computer simulations. The "context-sensitive
>decrement times" and
> "mean effect times" have been specifically defined for anesthetic drugs
I agree with the above but would state it even more strongly.
Multiparameter models involving multicompartment PK models plus
non-linear conc-effect models CANNOT be summarized by a single term.
Its not a question of "not easily summarized". It is impossible to
use one parameter to describe the full properties of a
multi-parameter system.
IMHO the "context sensitive half-life" is just as ill thought out as
the "biological half-life" idea. When applied to the time course of
drug effect it is quite pointless to use the idea of a "half-life"
for a situation that is not exponential and which therefore cannot be
described by a half-life. The "context sensitive half-life" is a
descriptive statistic and is not a true parameter. Using the term
"half-life" perpetuates confusion because of the well established
meaning of half-life as a parameter of an exponential process.
Half-lives describing exponential processes have strong predictive
properties for extrapolation and interpolation.
I dont think any extra value is added by using the "context sensitive
half-life" fiction. If the context sensitive half-life is 1 hour then
what further predictions can we make? We certainly cannot expect that
the effect after 2 hours will be 50% of that seen at 1 hour. So what
is the point of abusing the term "half-life" when no useful
prediction can be made beyond the self-defining time for the effect
to become half of the starting effect.
The other terms that Steve mentions "context-sensitive decrement
times" and "mean effect times" are much more honest because they dont
try to over-load the words with inappropriate meaning.
> So, if you want to report multicompartment pharmacokinetics, report
> the unit disposition function (e.g., ALL of the coefficients and
>exponents of the impulse
> response function),which tell the complete story (assuming first
>order PK). Then put
> your intellectual effort into defining metrics of clinical interest
>and solving these
> for your clinical audience.
Agreed. But don't use the term "half-lives" for these metrics!
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-at-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.html
---
X-Authentication-Warning: aidan.ncl.ac.uk: n7950211 owned process doing -bs
Date: Tue, 7 Sep 1999 18:05:12 +0100 (GMT)
From: "J.G. Wright"
Reply-To: "J.G. Wright"
To: PharmPK.aaa.boomer.org
Subject: Re: PharmPK Re: terminal and biological t 1/2
Dear PharmPK,
I have read with interest the debate about various uses of the term
half-life, particularly the last post by Thomas Senderovitz and Steven
Schafer. Whilst I am
inclined to agree with many of their comments, I do think the notion of
terminal half-life has its uses. For example, reporting a complex set of
coefficients to someone without pharmacokinetic expertise would be
confusing. In many practical circumstances (for example after bolus
doses), the terminal half-life can be representative of what is going on.
The truest represenatation of the data is the data itself, we convert this
data into parmaeters using assumptions to render it easily interpretable.
I suspect there are differences in the nature of the data available in
different contexts and indications. It is my understanding that in
anaesthesiolgy it is possible to have extremely dense data and reliable
endpoints (also sampled densly). In my experience of oncology, we rarely
have enough samples or different schedules to accurately characterize such
complicated phenomena, or endpoints sensitive enough to reflect their
significance.
I believe the "correct" summary of the data is dependent on its purpose
and for whom it is intended. Sometimes applying "one-compartmental"
concepts to data which is, invariably, generated by a more complex process
is both useful and generally informative.
James Wright
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[A few replies - db]
Reply-To:
From: "Steven Shafer"
To:
Subject: RE: PharmPK Re: terminal and biological t 1/2
Date: Tue, 7 Sep 1999 22:52:21 -0700
X-Priority: 3 (Normal)
Importance: Normal
Dear Colleagues:
1. Nick raises a good point - and one that I should have caught.
The actual term is "Context-Sensitive Half-Time" quite specifically
to get away from the term "Half-Life" and the various connotations
of that term (e.g., 2 half-lives yields a 75% decrease, 3 half-
lives yields an 88% decrease, etc). The original manuscript by
Hughes called it a half-life, which was changed to "half-time"
in the review process for exactly the reasons Nick sites. Of course,
this raises concern with being confused with the mid point of a
football game...
As to the uses of the "context-sensitive half-time," I refer the
reader to the original manuscript (Anesthesiology 1992 76:334-341)
and the accompanying editorial (Anesthesiology 1992 76:327-330) which
addresses the questions Nick raised. The concept has proved very
useful in anesthesia, and may find uses in other clinical arenas
as well. As Nick suggests, the more general concepts of decrement
times and mean effect times are more powerful and probably more
widely applicable.
2. Dr. Wright notes "the "correct" summary of the data is dependent
on its purpose and for whom it is intended." This is true, of course.
However, I would pose the question whether you really want your
"interpretable" parameter to depend on having a sufficiently
insensitive assay that it just happens to capture the time course
of interest. When a more sensitive assay becomes available, do you
still want to emphasize the half-life of drug leeching out of bone
at vanishingly small concentrations?
My guess is you will instead want to design a specific metric, one
appropriate for "its purpose and for whom it is intended." This is
the safer approach, rather then depending on serendipity to render
the terminal slope meaningful in with multicompartmental
pharmacokinetics.
Best regards,
Steve Shafer
---
From: RH06442.-at-.rh.dk
X-Lotus-FromDomain: INTRANOTES
To: PharmPK.aaa.boomer.org
Date: Wed, 8 Sep 1999 09:39:46 +0200
Subject: Re: PharmPK Re: terminal and biological t 1/2
One last halflife comment:
Okay, let's focus on the purpose of the parameters we report from PK studies.
If you want to report the actual, scientific correct parameters, and perhaps
event ry to understand what's going on in the system, I think that both Nick's,
Steve's and my own viewpoint is true. Do NOT try to use one single parameter,
such as "terminal halflife". It is simply not informative, and might indeed be
misleading. On the other hand, I can understand James' viewpoint. I
still think,
though, it's important to explain to that "someone without pharmacokinetic
expertise" that it is meaningless to give him ONE single halflife. Furthermore,
this is complicated by the fact that you HAVE to think of the PD as well -
halflife itself is not informative without the PD! So - complex PK/PD
relationships should not be oversimplified just because the pharmacokineticist
can't explain himself. Rather, it's important to ask your non-expert collegue:
What exactly is it that you want to know about this drug? And why do you want
only ONE parameter (the terminal halflife)?
Regards,
Thomas Senderovitz, M.D.
Dpt. Of Clinical Pharmacology Q7642
Rigshospitalet
University of Copenhagen
Tagensvej 20
DK-2200 Copenhagen N
Denmark
Phone: +45 35 45 69 44
Fax: +45 35 45 27 45
E-mail: senderovitz.-a-.rh.dk
---
X-Sender: jelliffe.aaa.hsc.usc.edu
Date: Wed, 08 Sep 1999 16:57:59 -0700
To: PharmPK.aaa.boomer.org
From: Roger Jelliffe
Subject: Re: PharmPK Re: terminal and biological t 1/2
Dear All:
In all this discussion about half-times in multicompartment models, how
about the concept of clearance? What happens to it when we get into large
multicompartment models?
Roger Jelliffe
Roger W. Jelliffe, M.D. Professor of Medicine, USC
USC Laboratory of Applied Pharmacokinetics
2250 Alcazar St, Los Angeles CA 90033, USA
Phone (323)442-1300, fax (323)442-1302, email= jelliffe.at.hsc.usc.edu
Our web site= http://www.usc.edu/hsc/lab_apk
********************
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[Two replies - db]
From:
X-Lotus-FromDomain: SB_PHARM_RD
To: PharmPK.-at-.boomer.org
Date: Thu, 9 Sep 1999 10:22:04 -0400
Subject: Re: PharmPK Re: terminal and biological t 1/2
Dear All
I couldn't resist tossing in my 2p
Steve Shafer wrote:
/However, I would pose the question whether you really want your
/"interpretable" parameter to depend on having a sufficiently
/insensitive assay that it just happens to capture the time course
/of interest. When a more sensitive assay becomes available, do you
/still want to emphasize the half-life of drug leeching out of bone
/at vanishingly small concentrations?
I guess that I have always felt that the pharmacodynamics of a compound was
of greater clinical interest than the drug concentrations themselves -
except as those concentrations relate to (and are predictive of) a
biological effect. So if estimating drug leeching out of bone at
"vanishingly small concentrations" is necessary to be able to accurately
predict a clinical effect, then this is what we must do. Of course, then
this leads directly into questions about how one deals with non-measurable
concentrations and a host of other related issues.
/My guess is you will instead want to design a specific metric, one
/appropriate for "its purpose and for whom it is intended." This is
/the safer approach, rather then depending on serendipity to render
/the terminal slope meaningful in with multicompartmental
/pharmacokinetics.
The concept of developing interpretable parameters specific to an intended
use is an excellent one. I think that defining terminology becomes
especially important when a new modeling approach is being developed
because it helps the modeler determine if the model has any utility, and it
lets one know if the parameter estimates are reasonable. I say this, of
course, despite the fact that I have been convicted of parameterising using
micro-constants for the PK part of PK/PD models ;-) Nonetheless,
appropriate parameterisation does allow the effects of several drugs to be
compared more readily and focuses the reader on the real purpose of the
analysis and the metrics - which is to provide guidance for a safe and
effective dose regimen in the intended patient population.
Therefore, its always best to try to summarise the results of any analysis
in clinically relevant terms. It is particularly important that these
terms have a definition that is consistent across the therapeutic area. It
seems from the various responses that have been posted on this subject,
that the term "biological half-life" is not a universally understood term
and so is best not used. Instead, I would try to find out what sort of
terminology is used clinically, if possible, and then deal with data in
those preferred terms. For this reason, I usually refer to modeling
results in terms of things like "coverage", MEC (Minimally effective
concentrations) or "estimated safe limit of exposure". Terminology of
this type seems to relate the PK and the PD into things that a physician
can actually use and encourages more conversation between the modeler and
the clinician.
As a last follow up note, I feel compelled to point out that there isn't
any such thing as a 'humble opinion' either. Its an oxymoron.
Diane
---
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Date: Thu, 9 Sep 1999 17:40:20 +0100 (GMT)
From: "J.G. Wright"
Reply-To: "J.G. Wright"
To: PharmPK.-at-.boomer.org
Subject: Re: PharmPK Re: terminal and biological t 1/2
Dear People interested in half-lives,
Be warned this is quite a long email.
I used to think the great thing about half-life is that its easy to
explain. I certainly agree with
the
comments of Dr Schafer that the terminal half-life is not always a useful
summary of the data, but on the other hand it often is. Although whether it is
meaningful in terms of certain endpoints is another
question entirely, I would not necessarily be certain that drug
leaking out of
deep compartments isn't exerting any pharmacological effects. I have
never encountered the situation described by Dr Schafer, but if I did I
would not necessarily reach for additional exponential terms. We usually
run into the infamous BQL problem first.
I would also
remember that assay variability is not the only source of error, and cite
the famous quote by Box that "all models are wrong, but some are useful".
No matter how many exponential terms we use, we will not necessarily
capture what is going on. With such a long terminal phase, are we
confident
about the linearity of the system (ie that we should be using exponentials
to summarize this phase in the first place) or that we can estimate such
parameters
accurately? How do we believe the nature of the error behaves
in this region compared to higher concentrations? Its all
approximate in the end. Although, I would be inclined to think it is more
scientifically correct to model the process in detail, to say these are
scientifically correct, actual parameters would take a braver man than I.
Whatever model you use, it is neither perfect, in that the parameters
truly describe the system, nor are the parameters estimated without error.
It is my
experience that people for example in drug development or the clinic
require the "bottom line", a concise answer, be it imperfect. Sometimes,
a half-life (terminal or otherwise) can fulfil this goal. Similarly,
we expect a clinician to give a diagnosis, not a list of symptoms.
Generally, people use the half-life to give an indication
of how long the drug spends in the body at meaningful concentrations ie
basically on what timescale the drug is eliminated. Hence the terminal
half-life of a sum of exponentials will not always be the key parameter of
interest, my point is that returning a complex model as the "correct"
answer also has its drawbacks. Graphs are useful, lists of
parameters usually are not. Pharmacokinetics is a component part of
medical science and we should try to return statistics that mean something
to the audience. This will not always be the terminal half-life by any
means, but such terms are not meaningless. A complex equation often will
be to a nonpharmacokineticist.
Having expressed these concerns, I wholeheartedly agree with the emphasis
on the PD and the definition of metrics which are useful rather than an
afterimage of the Gaussian paradigm. I can only wish I had an assay this
sensitive, no other source of error and the resources to sample
after the drug has reached what are presumably clinically irrelevant
concentrations.
James
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> From:
> To: PharmPK.aaa.boomer.org
> Date: Thu, 9 Sep 1999 10:22:04 -0400
> Subject: Re: PharmPK Re: terminal and biological t 1/2
> The concept of developing interpretable parameters specific to an intended
> use is an excellent one. I think that defining terminology becomes
> especially important when a new modeling approach is being developed
> because it helps the modeler determine if the model has any utility, and it
> lets one know if the parameter estimates are reasonable. I say this, of
> course, despite the fact that I have been convicted of parameterising using
> micro-constants for the PK part of PK/PD models ;-) Nonetheless,
> appropriate parameterisation does allow the effects of several drugs to be
> compared more readily and focuses the reader on the real purpose of the
> analysis and the metrics - which is to provide guidance for a safe and
> effective dose regimen in the intended patient population.
2c more on terminology. The "context sensitive half-*****" and other
metrics advocated by Steve Shafer are not parameters. Parameters are the
constants in PKPD models that let the model describe observations or
predict future behaviour. Metrics such as the "context sensitive" stuff
or "coverage" are not parameters because there is no way to
reparameterize the kinds of PKPD models used to generate these metrics
in terms of the metric itself.
We do need to pay attention to parameterization - some kind of
parameterization e.g. micro-constants, hinder the interpretation of
covariate influences in population PK models. Other kinds of
re-parameterizations of standard models offer advantages in terms of
estimation properties e.g. the re-parameterization of the sigmoid emax
model proposed by Gillespie and Bachman last year at ASCPT (Bill -- are
you there? When are you going to finish writing that up?).
We should also be creative in terms of using models and their parameters
to derive useful metrics as Steve and Diane have pointed out.
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, Private Bag 92019, Auckland, New Zealand
email:n.holford.-a-.auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm
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Dear All,
A comment from the dynamic system point of view:
Assuming applicability of the superposition principle, the
model given by Eq.1
H(s)=G. A(s)/B(s), 1
where
A(s)= a_0+a_1.s +a_2.s^2+.....+a_n.s^n,
B(s)= 1+b_1.s +b_2.s^2+.....+b_m.s^m,
a_0, a_1,..., a_m, b_1,..., b_m are the parameters, s is the
Laplace variable, G is the gain, and m represents the model
order (1)
can be used to model a dynamic system describing the fate of
a drug, or to model a dynamic system describing the effect of
a drug, e.g. after a single intravascular or extravascular
dose, during and after short or long time infusion, etc. (The
model given by Eq.1 is the Laplace transform of an m-order
linear differential equation, commonly used in bio-medical
modeling in the time domain. For example, the linear multiple
compartment models can be rewritten into this model
equation. For the single bolus dose of a drug, the gain
represents the reciprocal value of clearance.)
The model given by Eq.1 allows to determine the parameter MT
of a dynamic system describing the drug fate, or of a dynamic
system describing the drug effect, in a simple and uniform way
(2,3) according to Eq.2
MT=b_1 + a_1/a_0. 2
The variance VT of MT can be determined using Eq.3
VT=b_1^2 -2.b_2+2.a_2/a_0 -(a_1/a_0)^2. 3
For the dynamic system describing the drug fate, the
parameters MT and VT are very well known, i.e. they represent
the mean residence time and the variance of the mean
residence time, respectively. (For the first-order system,
the parameter MT represents the reciprocal value of the
elimination coefficient.)
For both, the dynamic system describing the drug fate and the
dynamic system describing the drug effect, the parameter MT
has the following meaning:
If a drug is administered at a constant rate over a period of
time, the system describing the drug fate, or the system
describing the drug effect, will reach 50% of the steady-state
level at time MT.
It follows then that, the parameter MT can be employed as
a mathematically elegant metrics (combining simplicity and
power) for uniform characterization of dynamic systems
describing fate or effect of drugs (and also e.g. for
investigations whether models of these systems indicate drug
washing out of deep tissues or not).
1. L.Dedik, M.Durisova, J. Pharmacokin. Biopharm., 22, 1994,
293-307.
2. G. Segre, Pharmacokin. Biopharm., 16, 1988, 657-666.
3. M.Durisova, L. Dedik, M. Balan, Bull. Math. Biol., 57,
1995, 787-808.
Best regards,
Maria Durisova
Institute of Experimental Pharmacology
Slovak Academy of Sciences
SK-842 16 Bratislava
Slovak Republic
Phone/Fax: 0042 7 5477 5928
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Dear All,
In my previous message I wrote:
>For the dynamic system describing the drug fate, the
>parameters MT and VT are very well known, i.e. they represent
>the mean residence time and the variance of the mean
>residence time, respectively. (For the first-order system,
>the parameter MT represents the reciprocal value of the
>elimination coefficient.)
>For both, the dynamic system describing the drug fate and the
>dynamic system describing the drug effect, the parameter MT
>has the following meaning:
>If a drug is administered at a constant rate over a period of
>time, the system describing the drug fate or the system
>describing the drug effect, will reach 50% of the steady-state
>level at time MT.
Leon Arons has warned me that the last sentence is not
correct. This sentence is a result of an erroneous copying of
some text parts.
The correct sentence is:
For both, the dynamic system describing the drug fate and the
dynamic system describing the drug effect, the parameter MT
represents the time ordinate of the center of gravity of the
area under the model weighting function from time zero to
infinity.
I apologize for this error.
Best regards,
Maria Durisova
Institute of Experimental Pharmacology
Slovak Academy of Sciences
SK-842 16 Bratislava
Slovak Republic
Phone/Fax: 0042 7 5477 5928
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The mean residence time = 1/ K (bar) K(bar)=sum of all rate constants -
elimination and transit.
However, MRT only applies to molecules ELIMINATED from the system and not
those that remain in the system. MRT (2nd statistical moment) is calculated
by the AUMC/AUC and this relationship is only valid for molecules eliminated
from the system. Additionally, since molecules only pass through the body
once, MRT=MTT (Mean Transit Time). MRT is related to MTT by a parameter,
"cycles." And in the case of total body elimination, cycles=1.
Veng-pedersen has given us many pharmacokinetic concepts. Since I deal in
radio-immuno diagnostics and radio-immuno therapeutics, I can actually see
where the molecules distribute and how they are eliminated (by external
scintigraphy). One concept that could be explored further is the probability
of distribution (PrD). If there is a specific target (binding epitope) in
the peripheral tissue, the PrD actually significantly increases over those
patients where there is not a specific epitope. It becomes even more
intriguing where the epitope is "soluble"
There seems to be a polarization over AUC or CL. if CL= DOSE/AUC then when I
have tried to use both of these parameters in an ANOVA statistical package,
it tells me to eliminate one. If one calculates AUC by the methods suggested
by Veng-Pedersen (Polyexponential equation-without bounding parameters to +
or -), then AUC become the most robust parameter with the least assumptions.
As to derivation, one can use many methods and a good look at the
assumptions can be gained from probability theorem.
Lastly, the term "biological:" half-life is well accepted in radiation
dosimetry and is included in many documents defining standards as well as
the term "effective" half-life and "physical" half-life. Dosimetry takes on
the same meanings as "pharmacokinetics" in nuclear medicine.
WW
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Dear All,
Well, I guess "half-life" is neither.
John Lukas
on behalf of:
Vermeer-Goldmann Institute, Hellas
Complex Systems/ Prognosis Center
140 Tritonos St
Paleo Faliro, 17562
Athens, Greece
tel: +(301) 9826200 UTC + 2 h
fax: +(301) 9825000
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