PharmPK Discussion - Half-life calculations

PharmPK Discussion List Archive Index page
• On 5 Dec 2005 at 08:31:40, "Prof. Stefan Soback" (stefans.-a-.moag.gov.il) sent the message

I'm sorry, but it appears that I failed to understand this point. Can
I get some clarification to these sentences?
"The elimination rate constant is clearance divided by volume of
distribution. If clearance and volume of distribution are normally
distributed, the elimination rate constant is not normally distributed."
And then
"In particular in the case of wide distributions, the differences
between the (harmonic) mean of half-life and the half-life estimated
from mean clearance and mean volume of distribution can be
considerable. And what is the best answer?"
As far as I can understand Vss/CL = MRT and MRT =1/K. In other words
CL/Vss = K. The use of K derived from the ratio of Vss and CL for
half-life calculation (ln2/K) can be applied only to one-compartment
model.
In other words, what is meant by "half-life estimated from mean
clearance and mean volume of distribution"?
Best regards
Stefan

[The MRT = 1/K refers to a one compartment model only(?). It's not
equal to beta (two compartment) is it? A problem (I think) with the
non compartmental approach is that you loose some of the model detail
- db]

Back to the Top

• On 5 Dec 2005 at 11:40:00, "Davies, Brian" (brian.davies.at.roche.com) sent the message

The following message was posted to: PharmPK

See comments below which I have added to clarify some of the points for
Prof Soback

-----Original Message-----
From: david.-a-.boomer.org [mailto:david.aaa.boomer.org] On Behalf Of Prof.
Stefan Soback

I'm sorry, but it appears that I failed to understand this point. Can
I get some clarification to these sentences?
"The elimination rate constant is clearance divided by volume of
distribution. If clearance and volume of distribution are normally
distributed, the elimination rate constant is not normally distributed."
And then "In particular in the case of wide distributions, the
differences
between the (harmonic) mean of half-life and the half-life estimated
from mean clearance and mean volume of distribution can be
considerable. And what is the best answer?"

>>The volume of distribution referred to above is Vz, the apparent
volume of distribution and not Vss<<

As far as I can understand Vss/CL = MRT and MRT =1/K. In other words
CL/Vss = K. The use of K derived from the ratio of Vss and CL for
half-life calculation (ln2/K) can be applied only to one-compartment
model.

>>This is true that K is the elimination rate constant for a 1
compartment model. In the case of the 2 compartment model or higher,
CL/Vss = kss, the steady-state rate constant.
kss = 0.693/t1/2ss = 0.693 x MRT. T1/2ss or effective half-life is a
very useful concept in pharmacokinetics<<

In other words, what is meant by "half-life estimated from mean
clearance and mean volume of distribution"?
Best regards
Stefan

Back to the Top

• On 6 Dec 2005 at 08:46:30, "Hans Proost" (j.h.proost.at.rug.nl) sent the message

The following message was posted to: PharmPK

Dear Stefan,

An explanation of my earlier message:

> "The elimination rate constant is clearance divided by volume of
> distribution. If clearance and volume of distribution are normally
> distributed, the elimination rate constant is not normally
distributed."

This refers to the distribution of clearance and volume of
distribution over
the individuals of a population, often assumed to be a normal
distribution
(although a log-normal distribution is likely to be more close to the
real
situation, as was the subject of the original thread). For each
individidual
the elimination rate constant k = CL/V. As a result, the individual
values
for k have also some statistical distribution. However, this is not a
normal
distribution.

> "In particular in the case of wide distributions, the differences
> between the (harmonic) mean of half-life and the half-life estimated
> from mean clearance and mean volume of distribution can be
> considerable. And what is the best answer?"

Half-life of each individual is calculated from each individual's k by
ln(2)/k. Again, the distribution of half-life in the population will
not be
a normal distribution. Because of the calculation from the reciprocal
of k,
it has been suggested to calculate the harmonic mean of half-life as a
measure of 'central tendency'. The harmonic mean is 1 / (1/x1 + 1/x2
+ 1/x3
+ ...). This results in a 'mean half-life' that is the same as
calculated
from ln(2) / 'mean k'. If k is normally distributed, this is a
reasonable
approach.
My point was that if k is not normally distributed (and indeed, it is
not)
that this is not a reasonable approach. One can also calculate a mean
CL and
mean V, and calculate a mean k ( = mean CL / mean V) and mean half-
life ( ln(2) / mean k)
from these mean values. This results in a different value
for mean k and mean half-life. And what is the best answer? Without any
knowledge or assumption about the statistical distribution there is
nothing
to say about that. So one needs to make some reasonable assumption
statistical distribution. In my opinion, the log-normal distribution
is the
best choice, unless there are obvious reasons for something else
(e.g. in
case of apparent bimodal distributions). Of course one can always
calculate
and report a mean ('a mean is a mean'), but does not make much sense
if this
'mean' is not a good descriptor of 'central tendency', i.e. the
centre of
the distribution. What else is the meaning of a 'mean'?

> As far as I can understand Vss/CL = MRT and MRT =1/K. In other words
> CL/Vss = K. The use of K derived from the ratio of Vss and CL for
> half-life calculation (ln2/K) can be applied only to one-compartment
> model.

Yes, this refers to the one-compartment model only. But if the volume of
distribution during the terminal phase V (also denoted V_beta, or Vz) is
used, this still works since the terminal rate constant lambda_z
(also k_z)
= CL / V. And the terminal half-life is (ln2) / lambda_z, so it still
works
for multi-compartment models. Actually this is a noncompartmental
approach
(only the expression MRT = 1/k does not hold; at least, this k does
not have
a particular meaning).

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

tel. 31-50 363 3292
fax 31-50 363 3247

Email: j.h.proost.-a-.rug.nl

Back to the Top

• On 6 Dec 2005 at 10:53:17, "Prof. Stefan Soback" (stefans.-a-.moag.gov.il) sent the message

Thank you for your answer, but I still have some problems with your
clarification.

>>The volume of distribution referred to above is Vz, the apparent
volume of distribution and not Vss<<

As long as we have a one-compartment model, it doesn't matter which
volume term we use. They are all the same. Not so in multi-
compartment models. Still I consider the Vss the "true" volume term,
but this is obviously not the right place to discuss that.

>>This is true that K is the elimination rate constant for a 1
compartment model. In the case of the 2 compartment model or higher,
CL/Vss = kss, the steady-state rate constant kss = 0.693/t1/2ss =
0.693 x MRT. T1/2ss or effective half-life is a very useful concept
in pharmacokinetics<<

The Benet & Galeazzi equation Vss = CL x MRT is about volume of
distribution at steady state and is valid in any compartment model.
I'm not familiar with the kss, so I'm unable to comment on that.
However, I seem to have a problem with your equations. The latter
part (0.693 x MRT) is the half-life in one-compartment model. The kss
= 0.693/ t1/2ss is obviously O.K., but it doesn't say anything to me.
However, 0.693/t1/2ss = 0.693 x MRT I don't understand. When you have
an unequivocal MRT, why would you want to translate that to an
artificial t1/2?

The concept of "effective half-life", whatever it means, as in
Gibaldi & Perrier (1982) is familiar to me, but I don't know why it
is very useful in pharmacokinetics.
Best regards
Stefan

Back to the Top

• On 7 Dec 2005 at 11:52:21, "Prof. Stefan Soback" (stefans.at.moag.gov.il) sent the message

Dear Hans,
As you said:
"But if the volume of distribution during the terminal phase V (also
denoted V_beta, or Vz) is used, this still works since the terminal
rate constant lambda_z (also k_z)
= CL / V. And the terminal half-life is (ln2) / lambda_z, so it
still works for multi-compartment models. Actually this is a
noncompartmental approach (only the expression MRT = 1/k does not
hold; at least, this k does not have a particular meaning)."
This is clear. When V is determined as the product of CL and 1/beta
(or lambda_z) the equation works (and k is the terminal slope), but
then V is a function of elimination. I was thinking of independently
determined CL and V (= Vss). I'm sorry for the poorly formulated
question.
Thanks again,
Stefan

Back to the Top

Want to post a follow-up message on this topic? If this link does not work with your browser send a follow-up message to PharmPK@boomer.org with "Half-life calculations" as the subject

Copyright 1995-2010 David W. A. Bourne (david@boomer.org)