- On 27 Sep 2001 at 22:34:54, Nick Holford (n.holford.at.auckland.ac.nz) sent the message

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The following message was posted to: PharmPK

"Hans Proost (by way of David Bourne)" wrote:

> You proposed to use the following equations:

> > V(blood)*C(blood)'=Q*C(liver)-Q*C(blood)-k12*C(blood)+k21*C(tissue)

> > V(tissue)*C(tissue)'=k12*C(blood)-k21*C(tissue).

> These equations are wrong, as can be seen from the dimensions:

> k12 and k21 cannot be rate contants with dimension 1/time.

> Written in this form, k12 and k21 are intercompartmental

> clearances.

> In classical compartmental modeling, differential equations are

> written in terms of amounts, and in that case rate constants are

> used.

I agree with your concern that the symbols used for the equations are

misleading but the equations appear to be correct otherwise. 'k12'

does indeed have dimensions of volume/time and would be more

appropriately written as a clearance e.g. 'CL12'. However, there is

no need to insist on using rate constants.

IMHO rate constants are obsolete artefacts and modern understanding

of pharmacokinetics is based on clearance (David -- are you reading

this?

[Yes - I'll try to answer within your message even though it is

probably confusing - quicker than waiting for the original to be sent

out ;-) - db]

Your teaching web site http://www.boomer.org/c/p1/ would be wonderful

[thank you :-) - db]

if you used clearance instead of rate constants e.g.

http://www.boomer.org/c/p1/Ch04/Ch0403.html Equation IV-1 implies

rate of elimination is dC/dt

[I'm trying to get the students started with the basics of first

order kinetics - seemed a reasonable way to start - db]

when I think it is more sensible to think of elimination rate as

dA/dt because this immediately leads to prediction of the maintenance

dose rate from the steady state elimination rate).

[I don't get to multiple doses for many chapters later - BTW how do

you calculate Cpmin and Cpmax using clearance? - db]

When solving differential equations it makes no difference from a

strictly mathematical perspective whether you use rate constants or

clearances (provided the dimensions are correct).

[You are right about the differential equations. Actually I have no

problem using rate constants with dC/dt or dA/dt, especially for

empirically based compartmental models. I use dA/dt and C with PBPK

using blood flow == clearance does that count? - db]

The important reason to parameterise in terms of clearance and

volume comes when applying pharmacokinetics in a population context.

Covariates usually influence clearance and volume independently.

Clearance and volume are reasonable population constants whose group

values can then be sensibly adjusted in light of covariate

information such as weight, renal function, other drugs, etc.

[You can do the same thing with rate constants if you have an

'appropriate' model

Changes in clearance can be readily applied to other models e.g.

with a different number of compartments, but this won't work with rate

constants.

[I don't understand this - db]

--

Nick Holford, Divn Pharmacology & Clinical Pharmacology

University of Auckland, 85 Park Rd, 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

[I'm sure you know a lot of the early PK work (preceding my

involvement ;-) was done with physical pharmacy people familiar with

chemical kinetics. Thus the use of dC/dt = -k*Cp. Even today it seems

easier to get students to basic dosage regimen development and

graphical parameter estimation using compartmental models. You are

right you can do some of this with clearance approaches, especially

maintenance infusions and steady state concentrations. But how do you

calculate how long it takes to get to therapeutic levels? I know you

can reparameterize using CL = V*k or k = CL/V. I still think the

choice is a matter of what type of model you are using.

For compartmental models - empirically defined you can easily use kel

and V to calculate dosing regimens, parameters from data, effect of

renal functions, effect of protein binding, non-linear elimination

etc...

The non-compartmental, 'model independent', moment analysis method

have the advantage of being easy to automate and give a number of

useful parameters. However, the 'finer' detail available with more

'complete' modeling can be lost.

For even more detail, physiologically based pk models are available

including blood flow and clearance terms. These models require more

data and extensive modeling.

Many experienced pharmacokinetic analyst is able to work with any of

these model types. For beginners needing some detail the

compartmental approach is attractive.

I've revisited a text or two today and thought of some simulations

for my graduate student to try since I found you message in my inbox.

I do need to revisit clearance...maybe I can add some non

compartmental material earlier in class. Actually I find I'm teaching

two new courses in our new PharmD program combining the first course

material referenced above with computer modeling and equation

derivation (http://www.boomer.org/c/p2/ - still just pdf from my

powerpoint presentations). I may need to include more clearance

emphasis is this material. Our clinical pk course is taught as an

elective by another faculty member. - db] - On 1 Oct 2001 at 10:31:56, "Hans Proost" (J.H.Proost.at.farm.rug.nl) sent the message

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The following message was posted to: PharmPK

Dear Dr. Holford,

Thank you with your reply on my comments. My concern was

related both to the use of the symbol k12 (suggesting the meaning

of a rate constant) and the use of the word microconstant, also

suggesting a rate constant.

I apologize to Dr. Nagaraja that my statement was as imprecise as

his equations.

In addition you wrote:

> IMHO rate constants are obsolete artefacts and modern

> understanding of pharmacokinetics is based on clearance

I fully agree, as I do with your excellent explanation about the

difference. I am happy with your ongoing efforts to clarify the

difference between PK and mathematics.

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.aaa.farm.rug.nl

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