From: "Bonate, Peter" - pbonate@ilexonc.com
Subject:[NMusers] Scaling of pharmacokinetics in peds
Date: 12/17/2003 12:27 PM

Hello everyone.  I know we have have this conversation in the past.
I am modeling some pharmacokinetic data in kids.  I think it was
pretty much agreed in those earlier discussions that weight should
be built into the structural model a priori.  Everyone also pretty
much also agreed that weight should go on CL and Q with fixed power 
0.7 and weight on volume terms with fixed power 1.0.

So here is my question.  Clearance for the drug I am modeling is 
dose-dependent.  I wanted to get some opinions on what I am doing.  
Without any immediate knowledge I am assuming that Km does not change 
with weight, but Vmax does.  So what do you think, should the power 
term on Vmax be estimated or treated as fixed at 0.7?  I am treating 
it as estimable.  If it is anywhere near 0.7, I will make it fixed 
to 0.7.

Any thoughts?  Does this seem reasonable.

Thanks,

Pete

Peter L. Bonate, PhD, FCP
Director, Pharmacokinetics
ILEX Oncology, Inc
4545 Horizon Hill Blvd
San Antonio, TX  78229
phone: 210-949-8662
fax: 210-949-8219
email: pbonate@ilexonc.com

_______________________________________________________

From: Paul Hutson - prhutson@pharmacy.wisc.edu
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/17/2003 1:40 PM

Peter:
Seems reasonable, but it seems to me that the variability (or consistency) 
of the power term would be somewhat apparent if you were to plot (ln Vmax) vs (ln wt).
Good luck.
Paul
_______________________________________________________

From: Nick Holford - n.holford@auckland.ac.nz
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/17/2003 3:22 PM

Peter,

I don't know who is the advocate for an allometric exponent of 0.7 
for clearance. I do not wish to be counted among the "everyone 
[who] pretty much agreed" to a value of .7

Here (again) are some references for theory and experiment in
support of a value of 0.75.

Peters R.
The ecological implications of body size.
Cambridge: Cambridge University Press; 1983.

West GB, Brown JH, Enquist BJ.
A general model for the origin of allometric scaling laws in biology.
Science 1997;276:122-26.

West GB, Brown JH, Enquist BJ.
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
Science 1999;284(5420):1677-9.

Anderson BJ, van Lingen RA, Hansen TG, Lin YC, Holford NHG.
Acetaminophen developmental pharmacokinetics in premature neonates and infants: a pooled population analysis.
Anesthesiology 2002;96(6):1336-45.

This is a useful page explaining some background to allometric ideas:
http://www.anaesthetist.com/physiol/basics/scaling/Kleiber.htm

At any given conc then CL is

               Vmax
CL =        ---------- 
             Km + Conc

It can be allometrically scaled as follows:

               VmaxStd
CLStd*Fsize = (---------)*Fize
               Km + Conc

where Fsize=(WT/WTstd)**0.75

No allometric scaling would be expected a priori on Km. So I think it
might be reasonable to restate this expression as:

               VmaxStd*Fsize
CLStd*Fsize =  -------------
                 Km + Conc
i.e. apply the allometric scaling directly to Vmax alone.

Note, factors other than size (such as age) may be associated with between
subject differences in Km. It is important to recognize that size scaling
is not the only factor that explains between and within species differences.
These other factors may sometimes obscure the view of what the emperor is wearing 

Bonate PL, Howard D.
Prospective allometric scaling: does the emperor have clothes?
J Clin Pharmacol 2000;40(6):665-70; discussion 671-6.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: Nick Holford - n.holford@auckland.ac.nz
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/19/2003 3:00 AM

Paul,

Fine in theory but in practice I expect it would require a wide range of
weights plus doses and intensive sampling to expect to be able to
distinguish any departure from the theoretical expectation of 0.75
for the allometric exponent. 

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: Paul Hutson - prhutson@pharmacy.wisc.edu
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/19/2003 10:25 AM

Another beautiful theory brutalized by a vicious gang of facts.
_______________________________________________________

From: Jenny Yuehling Chien - CHIEN_JENNY_YUEHLING@lilly.com
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/19/2003 10:27 AM

Nick and Pete,

another good reference to support 0.75 for clearance:
Hu and Hayton, Allometric scaling of xenobiotic clearance:
uncertainty vs universality. AAPS PharmSci 2001; 3(4) article 29.

The treatment of Km will depend on the source of nonlinearity. 
If source of nonlinearity is metabolism-based, tons of literature
exist on ontogeny of drug metabolizing enzymes to support no scaling on
Km, I would agree the effect of weight would only be on Vmax.   If
source of nonlinearity is due to other biological factors, you will
need to know the impact of age-related physiological changes on the
empirical "Km,"  in that case, I imagine simple scaling on Km would
not make any sense either.

Jenny Chien, PhD
research scientist
Global PK/PD & TS
Lilly Research Laboratories
Lilly Corporate Center
Indianapolis, IN 46285 
_______________________________________________________

From: Nick Holford - n.holford@auckland.ac.nz
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/20/2003 7:36 PM

Jenny,

Thanks for the additional reference which I had not seen before.
This is an excellent source for experimental confirmation of allometric
scaling, in particular an exponent of 0.75 for metabolic clearance.
I was surprised, as were the authors, that an exponent closer to
0.67 was observed for renal clearance. This would be a good area for
future allometric/physiological research to try to understand why
this might be and why measures of renal functon (e.g. GFR) seem to
scale with an exponent of 0.75.

You bring up a good point about age and Km. I agree with you that
any such relationship can only be considered empirical and does
not have any theoretical backing like allometric scaling can provide.
I mentioned age and Km as an example because it is one of the results
from a very early population analysis of the pharmacokinetics of
phenytoin by Ted Grasela et al. I am not sure of the reference. I
think it was in JPB but cannot locate it via PubMed.

I think of Km as an enzyme molecule property and would not expect
this to change by simply increasing the number of molecules as
body mass increases. Estimates of Km in vivo are more complex
and hard to estimate. I expect they could be 'contaminated' by
size if blood flow is an important determinant of clearance.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
_______________________________________________________

From: Jenny Yuehling Chien - CHIEN_JENNY_YUEHLING@lilly.com
Subject: Re: [NMusers] Scaling of pharmacokinetics in peds
Date: 12/23/2003 3:57 PM

Nick,

There are 2 papers on phenytoin, Ted can probably verify that:

- steady-state pharmacokinetics of phenytoin from routinelycollected patient data.
Clinical Pharmacokinetics. 8(4):355-64, 1983.

- phenytoin pharmacokinetics: inappropriate data analysis.
American Journal of Hospital Pharmacy. 39(1):41-3, 1982

You must be thinking of the first paper with an age effect on Km.

jenny 

Jenny Chien, PhD
research scientist
Global PK/PD & TS
Lilly Research Laboratories
Lilly Corporate Center
Indianapolis, IN 46285 
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