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The following message was posted to: PharmPK
If one runs a two-compartment model and calculate all the rates (K01,
K12, K21, and K10), K10 being the rate of elimination from plasma. The
elimination curve is biphasic and therefore an alpha and beta phases are
also calculated. What is K01 in this case? Is it a composite of alpha
and beta? Can it be written as total body elimination rate (K10)
comprising of alpha and beta? What is meant when alpha is close to K01
or close to beta rates? Can it be defined as most elimination occurring
by alpha elimination rate when the rate of the alpha is close to K01 and
vice versa?
Thanks.
[See http://www.boomer.org/c/p4/c19/c1903.html (Note: kel = k10) or http://www.boomer.org/c/p4/c19/c1902.html
- db]
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The following message was posted to: PharmPK
Dear Shakil,
You wrote:
> If one runs a two-compartment model and calculate all the rates
>(K01, K12, K21, and K10), K10 being the rate of elimination from
> plasma. The elimination curve is biphasic and therefore an alpha
> and beta phases are also calculated. What is K01 in this case?
Probably, K01 refers to the absorption rate constant. It is
independent of the other rate constants.
> What is meant when alpha is close to K01 or close to beta rates?
In the case of a two-compartment model with drug input that can be
modelled by a first-order absorption rate constant, the model can be
written as the sum of three exponentials: K01, alpha, and beta. By
convention, alpha > beta.
There are two problems:
a) There is no unique solution for assigning the numerical values of
the exponentials, as found by the data analysis, to K01, alpha, and
beta. There are always two equally valid solutions; in the
one-compartment model this is usually referred to as the 'flip-flop'
situation.
b) The data analysis may result in a solution where K01 is close to
alpha, or close to beta. In my experience this situation is not
uncommon, although it is unlikely that the true value of K01 is close
to alpha or beta. Several years ago I raised this question in the
PharmPK group, but this did not result in a clear solution. Anyhow,
such a result should be regarded as suspicious.
best regards,
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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The following message was posted to: PharmPK
Dear Shakil,
K10 is an overall elimination rate constant which can be expressed in
a relationship to alpha and beta as follows: K10 = alpha*beta/K21. The
half-life of K10 is known as the half-life of elimination. which
represents the collective effects of metabolism and excretion and
equals 0.693/K10. The half-life of beta is the biological half-life
(or disposition half-life) and represents the combined effects of
distribution and elimination and equals to 0.693/beta. The half-life
of alpha describes various processes (i.e., dilution, distribution and
elimination from the central compartment) that occur immediately after
injection; it is not biological and does not describe elimination.
Khalid Alkharfy
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The following message was posted to: PharmPK
Dear Shakil,
Looking at the components of alpha and beta
If K01decline.
When K01>k21 and K12>k21 then you will see biphasic decline.
else when K01>k21 and K12k21, a biphasic decline
else k21>k10, a monophasic decline. (liang 1998 JPP)
The magnitude of error you make by calling the terminal slope as beta
depends upon the relative difference in the
magnitude of rate constants see Byron 1976 JPS for further information.
Varun Goel
PhD Candidate, Pharmacometrics
Experimental and Clinical Pharmacology
University of Minnesota
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The following message was posted to: PharmPK
Dear Khalid,
You wrote:
> K10 is an overall elimination rate constant which can be expressed
>in a relationship to alpha and beta as follows: K10 =
>alpha*beta/K21.
The calculation is correct, but it seems confusing to denote K10 as an
'overall elimination rate constant'. Why 'overall'? K10 is simply
'the' elimination rate constant from the central compartment.
> The half-life of K10 is known as the half-life of elimination.
This does not make sense to me, and it is quite confusing. There was
an extensive discussion in the group on 'elimination half-life' and
related terms, but I don't remember than anybody used 'half-life of
elimination' for ln(2)/K10. Do we really need a half-life associated
to K10? I don't think so.
>The half-life of beta is the
>biological half-life (or disposition half-life) and represents the
>combined effects of distribution and elimination and equals to
>0.693/beta.
Again, very confusing. Half-life of beta is usually called
'elimination half-life' or 'terminal half-life'. Why 'biological'?
(everything in pharmacokinetics is biological). And why 'disposition
half-life'?
> The half-life of alpha describes various processes
>(i.e., dilution, distribution and elimination from the central
>compartment) that occur immediately after injection; it is not
>biological and does not describe elimination.
A strange sentence. Why is the half-life of alpha not 'biological'?
And in the first part you state that it describes processes including
elimination, and in the latter part you say that it does not describe
elimination.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.at.rug.nl
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The following message was posted to: PharmPK
Dear Hans
K10 is a collective rate constant of metabolism and excretion (i.e.,
elimination) from the central compartment containing major organs of
elimination (liver and kidney) which are assumed to represent the
overall
elimination unless proven otherwise. Given this, the half-life of K10
is in
essence the true elimination half-life which can be significantly
different
from beta half-life due to the fact that beta is a hybrid constant
represents the combined effect of distribution-within and between
compartments-and elimination (i.e., slow disposition). Therefore, for an
obvious biological reason, we use beta half-life to calculate how long
it
would it for a drug to be completely eliminated from the body. After
an IV
bolus, the rate of distribution between two compartments of a given
drug is
generally assumed to be proportional to the difference in concentration
between the two compartments. Thus, alpha is a composite of many
processes
including rapidness of the IV push and drug dilution in the central
compartment (both are physical processes) rapid distribution to the
peripheral compartment and elimination by organs centrally (i.e., rapid
disposition). Against this, half-life of alpha is not entirely
biological
and it can not be used to specifically calculate elimination during
distributive phase.
Kind regards,
Khalid Alkharfy
Dept. of Clinical Pharmacy
College of Pharmacy, KSU
Riyadh, Saudi Arabia
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The following message was posted to: PharmPK
Dear Khalid,
Thank you for your reply.
> Given this, the half-life of K10 is in essence the true elimination
> half-life
I don't agree. There is nothing like a 'true elimination half-life', at
least not in a multicompartment model, and that's what we are talking
about.
Yes, IF the model would consist of a central compartment only, the
'half-life of K10' is indeed the half-life that would be observed. But
the
model has at least one peripheral compartment, and as a result, the
'half-life of K10' is NOT the half-life that would be observed, as a
result
of distribution.
> Therefore, for an obvious biological reason, we use beta half-life to
> calculate how long it would it for a drug to be completely
eliminated
> from the body.
Two comments:
1) The reason for using half-life is to know how long it would take to
decrease the concentration to half of its value. That's what half-life
is.
Who is interested in the half-life of a process that cannot be observed?
2) 'Completely eliminated from the body' is a meaningless phrase.
According
to the exponential decline, this would take infinite time. Using a
value of
5 half-lives or 7 half-lives or whatever may be useful in practice,
but is
totally arbitrary.
> Thus, alpha is a composite of many processes
> including rapidness of the IV push and drug dilution in the central
> compartment (both are physical processes) rapid distribution to the
> peripheral compartment and elimination by organs centrally (i.e.,
rapid
> disposition). Against this, half-life of alpha is not entirely
biological
I agree that the processes of drug dilution and distribution may be
regarded
as 'physical processes', in the sense that they are related to the
physicochemical properties of the drug. However, these processes are
governed by the properties of the body, e.g. anatomy and physiology of
the
vascular system, cardiac output, permeability of capillaries, et
cetera. So
I do not agree that the 'half-life of alpha' is not entirely
biological. Is
there anything in the body that is not biological?
> and it can not be used to specifically calculate elimination during
> distributive phase.
I don't understand your point here.
best regards,
Hans Proost
Johannes H. Proost
Dept. of Pharmacokinetics and Drug Delivery
University Centre for Pharmacy
Antonius Deusinglaan 1
9713 AV Groningen, The Netherlands
Email: j.h.proost.aaa.rug.nl
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