- On 5 Dec 2005 at 08:31:40, "Prof. Stefan Soback" (stefans.-a-.moag.gov.il) sent the message

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

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

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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

about the

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

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

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Dear Hans,

Thank you for your detailed answer and your patience.

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

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