Dear NM_Users,
we have all been good students and listened to Nick when he told us again
and again the rock-solid truths of allometry:
Volume: *(WT/70)
CL: *(WT/70)**0.75
any rate constant related to distribution or elimination:
*(WT/70)**(-0.25)
Here my questions:
a) how do we allometrically scale a first-order rate constant of
absorption after oral dosing?
b) how do we allometrically scale a first-order rate constant of
absorption from a subcutaneous injection site?
Thank you for your thoughts,
Joachim
__________________________________________
Joachim GREVEL, Ph.D.
MERCK SERONO International S.A.
Exploratory Medicine
1202 Geneva
Tel: +41.22.414.4751
Fax: +41.22.414.3059
Email: joachim.grevel
-----------------------------------------
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--=_alternative 0047F7DEC12574C9_=--
Scaling for pediatric study planning
Dear NM_Users,
we have all been good students and listened to Nick when he told us again
and again the rock-solid truths of allometry:
Volume: *(WT/70)
CL: *(WT/70)**0.75
any rate constant related to distribution or elimination:
*(WT/70)**(-0.25)
Here my questions:
a) how do we allometrically scale a first-order rate constant of
absorption after oral dosing?
b) how do we allometrically scale a first-order rate constant of
absorption from a subcutaneous injection site?
Thank you for your thoughts,
Joachim
__________________________________________
Joachim GREVEL, Ph.D.
MERCK SERONO International S.A.
Exploratory Medicine
1202 Geneva
Tel: +41.22.414.4751
Fax: +41.22.414.3059
Email: [EMAIL PROTECTED]
-----------------------------------------
This message and any attachment are confidential, may be privileged
or otherwise protected from disclosure and are intended only for
use by the addressee(s) named herein. If you are not the intended
recipient, you must not copy this message or attachment or disclose
the contents to any other person. If you have received this
transmission in error, please notify the sender immediately and
delete the message and any attachment from your system. Merck
Serono does not accept liability for any omissions or errors in
this message which may arise as a result of E-Mail-transmission or
for damages resulting from any unauthorized changes of the content
of this message and any attachment thereto. If verification is
required, please request a hard-copy version. Merck Serono does not
guarantee that this message is free of viruses and does not accept
liability for any damages caused by any virus transmitted
therewith.
Just to add:
c) how do we allometrically scale a VM rate constant of the Michaelis-Menten elimination model:
C1=A(1)/V1
DADT(1)= ... -A(1)*VM/(KM+C1)
d) do we need to allometrically scale a KM constant of the Michaelis-Menten elimination model ?
any experience with these quantities (for example, if they were estimated, what were the estimates, with the precision)?
My suggestion would be NOT to scale a), b) and d), and scale VM as the rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to support those suggestions.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[EMAIL PROTECTED] wrote:
> Dear NM_Users,
>
> we have all been good students and listened to Nick when he told us again and again the rock-solid truths of allometry:
>
> Volume: *(WT/70)
>
> CL: *(WT/70)**0.75
>
> any rate constant related to distribution or elimination: *(WT/70)**(-0.25)
>
> Here my questions:
>
> a) how do we allometrically scale a first-order rate constant of absorption after oral dosing?
>
> b) how do we allometrically scale a first-order rate constant of absorption from a subcutaneous injection site?
>
> Thank you for your thoughts,
>
> Joachim
>
> __________________________________________
> Joachim GREVEL, Ph.D.
> MERCK SERONO International S.A.
> Exploratory Medicine
> 1202 Geneva
> Tel: +41.22.414.4751
> Fax: +41.22.414.3059
> Email: [EMAIL PROTECTED]
>
> ------------------------------------------------------------------------
>
> This message and any attachment are confidential, may be privileged or otherwise protected from disclosure and are intended only for use by the addressee(s) named herein. If you are not the intended recipient, you must not copy this message or attachment or disclose the contents to any other person. If you have received this transmission in error, please notify the sender immediately and delete the message and any attachment from your system.
Leonid / Joachim,
I think we're pushing the envelope on empiricism here. Two facts of
reality prevail here:
1) we seldom collect enough data during the absorption phase to assess
any meaningful age/developmental dependencies across the age continuum.
The fisrt-order assumption is always bad even in adults but we live with
it because we seldom have absorption as a primary phase of interest.
2) a physiologic approach, in addition to a more fundamental
approximation of reality also has more options with respect to
functional expressions that can accomodate developmental factors such as
changes in pH dependency, the surface area of the GI tract, or the site
and expression of presystemic P450 enzymes all of which factor into the
size surrogacy issue.
Hence, I'm not sure that I would consider the allometric
characterization of absorption in the same manner as one would treat CL
or V considerations as it is indeed a hybrid process. I will defer to
Nick's wisdom on this but if I am pressed for a guess, I would not scale
but pursue more physiologic expressions. In actuality, this is a place
where "bottom-up" approaches would seem to have a decided advantage.
Jeff
Jeffrey S. Barrett, Ph.D., FCP
Research Associate Professor, Pediatrics
Director, Pediatric Pharmacology Research Unit,
Laboratory for Applied PK/PD
Clinical Pharmacology & Therapeutics
Abramson Research Center, Rm 916H
The Children's Hospital of Philadelphia
3615 Civic Center Blvd.
Philadelphia, PA 19104
KMAS (Kinetic Modeling & Simulation)
Institute for Translational Medicine
University of Pennsylvania
email: [EMAIL PROTECTED]
Ph: (267) 426-5479
>>> Leonid Gibiansky <[EMAIL PROTECTED]> 9/19/2008 11:20 AM
>>>
Just to add:
c) how do we allometrically scale a VM rate constant of the
Michaelis-Menten elimination model:
C1=A(1)/V1
DADT(1)= ... -A(1)*VM/(KM+C1)
d) do we need to allometrically scale a KM constant of the
Michaelis-Menten elimination model ?
any experience with these quantities (for example, if they were
estimated, what were the estimates, with the precision)?
My suggestion would be NOT to scale a), b) and d), and scale VM as the
rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
support those suggestions.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[EMAIL PROTECTED] wrote:
>
> Dear NM_Users,
>
> we have all been good students and listened to Nick when he told us
> again and again the rock-solid truths of allometry:
>
> Volume: *(WT/70)
>
> CL: *(WT/70)**0.75
>
> any rate constant related to distribution or elimination:
*(WT/70)**(-0.25)
>
> Here my questions:
> a) how do we allometrically scale a first-order rate constant of
> absorption after oral dosing?
>
> b) how do we allometrically scale a first-order rate constant of
> absorption from a subcutaneous injection site?
>
> Thank you for your thoughts,
>
> Joachim
>
> __________________________________________
> Joachim GREVEL, Ph.D.
> MERCK SERONO International S.A.
> Exploratory Medicine
> 1202 Geneva
> Tel: +41.22.414.4751
> Fax: +41.22.414.3059
> Email: [EMAIL PROTECTED]
>
>
------------------------------------------------------------------------
>
> This message and any attachment are confidential, may be privileged
or
> otherwise protected from disclosure and are intended only for use by
the
> addressee(s) named herein. If you are not the intended recipient, you
> must not copy this message or attachment or disclose the contents to
any
> other person. If you have received this transmission in error, please
> notify the sender immediately and delete the message and any
attachment
> from your system.
Here's my philosophy:
c) VM scales to wt**0.75 as it is a measure of enzyme concentration and
liver volume relative to body size goes wt**0.75 (Johnson TN et al. 2005) -
any age-related differences to this are due to developmental factors.
d) KM - don't scale it, it is a measure of enzyme affinity and shouldn't
change with size, differences are due to polymorphisms.
BW,
Joe
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Leonid Gibiansky
Sent: den 19 september 2008 17:21
To: [EMAIL PROTECTED]
Cc: [email protected]
Subject: Re: [NMusers] Scaling for pediatric study planning
Just to add:
c) how do we allometrically scale a VM rate constant of the
Michaelis-Menten elimination model:
C1=A(1)/V1
DADT(1)= ... -A(1)*VM/(KM+C1)
d) do we need to allometrically scale a KM constant of the
Michaelis-Menten elimination model ?
any experience with these quantities (for example, if they were
estimated, what were the estimates, with the precision)?
My suggestion would be NOT to scale a), b) and d), and scale VM as the
rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
support those suggestions.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[EMAIL PROTECTED] wrote:
>
> Dear NM_Users,
>
> we have all been good students and listened to Nick when he told us
> again and again the rock-solid truths of allometry:
>
> Volume: *(WT/70)
>
> CL: *(WT/70)**0.75
>
> any rate constant related to distribution or elimination:
*(WT/70)**(-0.25)
>
> Here my questions:
> a) how do we allometrically scale a first-order rate constant of
> absorption after oral dosing?
>
> b) how do we allometrically scale a first-order rate constant of
> absorption from a subcutaneous injection site?
>
> Thank you for your thoughts,
>
> Joachim
>
> __________________________________________
> Joachim GREVEL, Ph.D.
> MERCK SERONO International S.A.
> Exploratory Medicine
> 1202 Geneva
> Tel: +41.22.414.4751
> Fax: +41.22.414.3059
> Email: [EMAIL PROTECTED]
>
> ------------------------------------------------------------------------
>
> This message and any attachment are confidential, may be privileged or
> otherwise protected from disclosure and are intended only for use by the
> addressee(s) named herein. If you are not the intended recipient, you
> must not copy this message or attachment or disclose the contents to any
> other person. If you have received this transmission in error, please
> notify the sender immediately and delete the message and any attachment
> from your system.
Title: Paul R
Dear Leonid:
Regarding d): I would not expect to need to scale the KM at all unless
the affinity of the substrate (drug) is known to be different between
species. Size alone would not be expected to affect the KM of
elimination. It could clearly affect the KM of a passive or active gut
absorption process due to the surface area of the intestine.
my $0.02
Paul
Leonid Gibiansky wrote:
Just
to add:
c) how do we allometrically scale a VM rate constant of the
Michaelis-Menten elimination model:
C1=A(1)/V1
DADT(1)= ... -A(1)*VM/(KM+C1)
d) do we need to allometrically scale a KM constant of the
Michaelis-Menten elimination model ?
any experience with these quantities (for example, if they were
estimated, what were the estimates, with the precision)?
My suggestion would be NOT to scale a), b) and d), and scale VM as the
rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
support those suggestions.
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
[EMAIL PROTECTED] wrote:
Dear NM_Users,
we have all been good students and listened to Nick when he told us
again and again the rock-solid truths of allometry:
Volume: *(WT/70)
CL: *(WT/70)**0.75
any rate constant related to distribution or elimination:
*(WT/70)**(-0.25)
Here my questions:
a) how do we allometrically scale a first-order rate constant of
absorption after oral dosing?
b) how do we allometrically scale a first-order rate constant of
absorption from a subcutaneous injection site?
Thank you for your thoughts,
Joachim
__________________________________________
Joachim GREVEL, Ph.D.
MERCK SERONO International S.A.
Exploratory Medicine
1202 Geneva
Tel: +41.22.414.4751
Fax: +41.22.414.3059
Email: [EMAIL PROTECTED]
------------------------------------------------------------------------
This message and any attachment are confidential, may be privileged or
otherwise protected from disclosure and are intended only for use by
the addressee(s) named herein. If you are not the intended recipient,
you must not copy this message or attachment or disclose the contents
to any other person. If you have received this transmission in error,
please notify the sender immediately and delete the message and any
attachment from your system.
I can't agree more with Jeff's comments that we should "pursue more
physiologic expressions" and this is a "place where "bottom-up" approaches"
are advantageous.
The allometric scaling may be useful for children older than 2 years but for
younger subjects surely the developmental factors should be considered as
explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006) Prediction
of the clearance of eleven drugs and associated variability in neonates,
infants and children. Clin Pharmacokinet 45:931-956.
Regards
Masoud
Quoted reply history
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:owner-
> [EMAIL PROTECTED] On Behalf Of Jeffrey Barrett
> Sent: 19 September 2008 16:54
> To: [EMAIL PROTECTED]; [EMAIL PROTECTED]
> Cc: [email protected]
> Subject: Re: [NMusers] Scaling for pediatric study planning
>
> Leonid / Joachim,
>
> I think we're pushing the envelope on empiricism here. Two facts of
> reality prevail here:
>
> 1) we seldom collect enough data during the absorption phase to assess
> any meaningful age/developmental dependencies across the age continuum.
> The fisrt-order assumption is always bad even in adults but we live
> with it because we seldom have absorption as a primary phase of
> interest.
>
> 2) a physiologic approach, in addition to a more fundamental
> approximation of reality also has more options with respect to
> functional expressions that can accomodate developmental factors such
> as changes in pH dependency, the surface area of the GI tract, or the
> site and expression of presystemic P450 enzymes all of which factor
> into the size surrogacy issue.
>
> Hence, I'm not sure that I would consider the allometric
> characterization of absorption in the same manner as one would treat CL
> or V considerations as it is indeed a hybrid process. I will defer to
> Nick's wisdom on this but if I am pressed for a guess, I would not
> scale but pursue more physiologic expressions. In actuality, this is a
> place where "bottom-up" approaches would seem to have a decided
> advantage.
>
> Jeff
>
>
>
> Jeffrey S. Barrett, Ph.D., FCP
> Research Associate Professor, Pediatrics Director, Pediatric
> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
> Children's Hospital of Philadelphia
> 3615 Civic Center Blvd.
> Philadelphia, PA 19104
>
> KMAS (Kinetic Modeling & Simulation)
> Institute for Translational Medicine
> University of Pennsylvania
> email: [EMAIL PROTECTED]
> Ph: (267) 426-5479
>
> >>> Leonid Gibiansky <[EMAIL PROTECTED]> 9/19/2008 11:20 AM
> >>>
> Just to add:
>
> c) how do we allometrically scale a VM rate constant of the Michaelis-
> Menten elimination model:
>
> C1=A(1)/V1
> DADT(1)= ... -A(1)*VM/(KM+C1)
>
> d) do we need to allometrically scale a KM constant of the Michaelis-
> Menten elimination model ?
>
> any experience with these quantities (for example, if they were
> estimated, what were the estimates, with the precision)?
>
>
> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>
> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
> support those suggestions.
>
> Leonid
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> [EMAIL PROTECTED] wrote:
> >
> > Dear NM_Users,
> >
> > we have all been good students and listened to Nick when he told us
> > again and again the rock-solid truths of allometry:
> >
> > Volume: *(WT/70)
> >
> > CL: *(WT/70)**0.75
> >
> > any rate constant related to distribution or elimination:
> *(WT/70)**(-0.25)
> >
> > Here my questions:
> > a) how do we allometrically scale a first-order rate constant of
> > absorption after oral dosing?
> >
> > b) how do we allometrically scale a first-order rate constant of
> > absorption from a subcutaneous injection site?
> >
> > Thank you for your thoughts,
> >
> > Joachim
> >
> > __________________________________________
> > Joachim GREVEL, Ph.D.
> > MERCK SERONO International S.A.
> > Exploratory Medicine
> > 1202 Geneva
> > Tel: +41.22.414.4751
> > Fax: +41.22.414.3059
> > Email: [EMAIL PROTECTED]
> >
> >
> -----------------------------------------------------------------------
> -
> >
> > This message and any attachment are confidential, may be privileged
> or
> > otherwise protected from disclosure and are intended only for use by
> the
> > addressee(s) named herein. If you are not the intended recipient, you
>
> > must not copy this message or attachment or disclose the contents to
> any
> > other person. If you have received this transmission in error, please
>
> > notify the sender immediately and delete the message and any
> attachment
> > from your system.
Hi Leonid
This is an interesting issue. Certainly for chemicals, I would consider
some sort of scaling for Vmax but not for Km (for reasons cited earlier) but
I have never seen any agreed on/standardized scaling factor for Vmax and
would be interested to hear of any reasonably well supported approaches.
For biologicals one would have to adjust Vmax on a case by case basis for
several reasons - but primarily that receptor density is not always
dependent on body size but is more often dependent on disease severity and
receptor/cell turnover rates. Consequently pediatric patients often have
higher values of Vmax than would be expected based only on their body size.
For biologicals, I have scaled Vmax by covariates *associated* with receptor
density and that generally works well (and when estimated can be determined
with reasonable precision).
Diane
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Leonid Gibiansky
Sent: Friday, September 19, 2008 12:07 PM
To: Joseph Standing
Cc: [EMAIL PROTECTED]; [email protected]
Subject: Re: [NMusers] Scaling for pediatric study planning
Joe,
We could be talking about different VM definitions
I am thinking about the model
DADT(1)= -A(1)*VM/(KM+C1) - K10*A(1)
If we believe that the ratio of linear to nonlinear elimination should
not depend on WT (?), then k10 and VM should be scaled similarly ~
WT**(-0.25)
If we present the same equation as
DADT(1)= -C1*VM'/(KM+C1) - K10*A(1)
then
DADT(1)= -A(1)*(VM'/V1)/(KM+C1) - K10*A(1)
VM' is indeed should be scaled as WT**0.75 (thus leading to VM scaled as
WT**(-0.25).
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Joseph Standing wrote:
> Here's my philosophy:
>
> c) VM scales to wt**0.75 as it is a measure of enzyme concentration and
> liver volume relative to body size goes wt**0.75 (Johnson TN et al. 2005)
-
> any age-related differences to this are due to developmental factors.
> d) KM - don't scale it, it is a measure of enzyme affinity and shouldn't
> change with size, differences are due to polymorphisms.
> BW,
>
> Joe
>
>
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On
> Behalf Of Leonid Gibiansky
> Sent: den 19 september 2008 17:21
> To: [EMAIL PROTECTED]
> Cc: [email protected]
> Subject: Re: [NMusers] Scaling for pediatric study planning
>
> Just to add:
>
> c) how do we allometrically scale a VM rate constant of the
> Michaelis-Menten elimination model:
>
> C1=A(1)/V1
> DADT(1)= ... -A(1)*VM/(KM+C1)
>
> d) do we need to allometrically scale a KM constant of the
> Michaelis-Menten elimination model ?
>
> any experience with these quantities (for example, if they were
> estimated, what were the estimates, with the precision)?
>
>
> My suggestion would be NOT to scale a), b) and d), and scale VM as the
> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
> support those suggestions.
>
> Leonid
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> [EMAIL PROTECTED] wrote:
>> Dear NM_Users,
>>
>> we have all been good students and listened to Nick when he told us
>> again and again the rock-solid truths of allometry:
>>
>> Volume: *(WT/70)
>>
>> CL: *(WT/70)**0.75
>>
>> any rate constant related to distribution or elimination:
> *(WT/70)**(-0.25)
>> Here my questions:
>> a) how do we allometrically scale a first-order rate constant of
>> absorption after oral dosing?
>>
>> b) how do we allometrically scale a first-order rate constant of
>> absorption from a subcutaneous injection site?
>>
>> Thank you for your thoughts,
>>
>> Joachim
>>
>> __________________________________________
>> Joachim GREVEL, Ph.D.
>> MERCK SERONO International S.A.
>> Exploratory Medicine
>> 1202 Geneva
>> Tel: +41.22.414.4751
>> Fax: +41.22.414.3059
>> Email: [EMAIL PROTECTED]
>>
>> ------------------------------------------------------------------------
>>
>> This message and any attachment are confidential, may be privileged or
>> otherwise protected from disclosure and are intended only for use by the
>> addressee(s) named herein. If you are not the intended recipient, you
>> must not copy this message or attachment or disclose the contents to any
>> other person. If you have received this transmission in error, please
>> notify the sender immediately and delete the message and any attachment
>> from your system.
Hi Everyone,
Joachim, Thanks for starting this popular thread and for your clear statements of two allometric commandments as applied to pharmacokinetics. However, I feel I must emphasize that the first commandment is "allometry predictions ONLY explain the effects of size".
Many times discussions of allometric predictions conclude with something like 'allometry does not work' (e.g. see post in this thread from Masoud in relation to children under 2 years). These conclusions are based on ignoring the first commandment. Allometry ONLY explains the effect of size and not the multitude of other effects such as maturation in young children, body composition, renal function, species differences, pharmacogenetic differences, disease effects (e.g. receptor density as pointed out by Diane). Empirical tests of allometry are therefore very difficult because they need to account for all other important non-size related covariate that may be correlated with size e.g. age. See Savage et al. (2004) to appreciate the scale of this task and Anderson & Holford (2008) for the impracticality of common study designs in humans to obtain precise estimates of allometric coefficients.
I've rewritten the next two commandments slightly to emphasise the relationship to the quarter power 'law' from which they are derived (See Savage et al. 2004 for references). Note that WTstd is a convenience for standardising human PK parameters to a 70 kg value and is not really a part of allometry itself.
Volume: Vstd*(WT/WTstd)** (4/4)
CL: CLstd*(WT/WTtd)**(3/4)
Joachim's statement about scaling of distribution and elimination rate constants does not really reflect a separate commandment because it is simply an algebraic consequence of applying the volume and clearance commandments.
Absorption rate constants used to describe the rate of oral drug absorption or absorption from a depot such as muscle are harder to relate to allometric scaling principles. Under the simplest of assumptions the absorption rate constant is just a diffusion coefficient reflecting the local membrane structure. Given that cell membrane structure is essentially the same for all sizes or organisms I would not expect it to scale with weight. Oral drug absorption is of course more complicated than just diffusion (cue for Walt W to appear). One of the major determinants of the rate of absorption of drugs such as BCS Type 1 (rapid dissolution, high permeability) is the rate of gastric emptying. This rate can be understood in terms of the flow of gastric contents into the duodenum which may well scale with size to the 3/4 power just like other flow like processes. The absorption process is then more like a zero-order process with a duration inversely proportional to the flow rate. Thus the duration might scale with a power 4/3.
My own preference is not to try to scale absorption rate processes using weight.
The Km of a mixed-order elimination process is of course a receptor affinity property and not expected to scale with size. If you empirically find a relationship with size then you should be looking elsewhere for the real cause because it is certainly not based on allometry.
I derive the allometric scaling of mixed order elimination from the clearance commandment. We know that CL at any given concentration for a mixed order process is:
CL=Vmax/(Km+C)
As C tends to zero we get the first-order CL:
CL=Vmax/Km
As explained above there is no expectation that Km will scale with size so in order to make first-order and mixed-order elimination consistent it is necessary that Vmax scales to the 3/4 power just like CL. Note that I prefer to parameterise Vmax as mass/time and not conc/time. The conc/time parameterisation is confounded with volume of distribution and thus the allometric power for that is -1/4. Leonid used the symbol VM' for the mass/time parameter and VM for the conc/time parameter but suggests the same conclusion.
Nick
Anderson BJ, Holford NH. Mechanism-based concepts of size and maturity in pharmacokinetics. Annu Rev Pharmacol Toxicol. 2008;48:303-32. Savage VM, Gillooly JF, Woodruff WH, West GB, Allen AP, Enquist BJ, et al. The predominance of quarter-power scaling in biology. Functional Ecology. 2004;18(2):257-82.
[EMAIL PROTECTED] wrote:
> Dear NM_Users,
>
> we have all been good students and listened to Nick when he told us again and again the rock-solid truths of allometry:
>
> Volume: *(WT/70)
>
> CL: *(WT/70)**0.75
>
> any rate constant related to distribution or elimination: *(WT/70)**(-0.25)
>
> Here my questions:
>
> a) how do we allometrically scale a first-order rate constant of absorption after oral dosing?
>
> b) how do we allometrically scale a first-order rate constant of absorption from a subcutaneous injection site?
>
> Thank you for your thoughts,
>
> Joachim
>
> __________________________________________
> Joachim GREVEL, Ph.D.
> MERCK SERONO International S.A.
> Exploratory Medicine
> 1202 Geneva
> Tel: +41.22.414.4751
> Fax: +41.22.414.3059
> Email: [EMAIL PROTECTED]
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
[EMAIL PROTECTED] tel:+64(9)923-6730 fax:+64(9)373-7090
http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford
Dear Nick
Many thanks for your comments. The two years of age is an estimated
post-natal age when most of the CYP enzymes, serum albumin level and also,
to some extent, the body composition reach those of adults and the
incorporation of maturation changes improved the predictions (the same
previous paper).
Of course everybody agrees that children are not like test tubes nor should
they be modelled as one-, two- compartmental models. On the other hand, test
tube data can provide very valuable knowledge about compounds that should be
mechanistically incorporated into our models (e.g. whether a compound get
metabolised by CYP2D6, its extent and the likelihood of polymorphism can be
determined using in vitro data).
As you once said at one of the PAGE meetings, it is not possible to imagine
a case where weight doesnt play a role, however this is sometimes taken out
of the context and interpreted as weight is the only player. Then we tend
to model everything using only weight even enzyme/receptor affinity or
absorption rate.
We are in full agreement that the age and size should be integrated to be
able to make sensible predictions and for that reason these two are the
fundamental elements in our bottom-up approach but not the only ones. It
is generally accepted that the metabolic clearance is proportional to the
size of the liver and based on more than 5000 data point a good equation for
predicting the size of the liver is developed (Johnson TN, Tucker GT, Tanner
MS, et al. Changes in liver volume from birth to adulthood: a meta-analysis.
Liver Transpl 2005 Dec; 11(12):1481-93 freely available at:
http://dx.doi.org/10.1002/lt.20519). However, the size of the liver is again
not the only determinant of the metabolic clearance and we need to take into
account other relevant covariates such as the enzyme abundances in the
liver, blood flow, plasma protein biding and the haematocrite level which
can be altered by polymorphism, ethnicity, disease states, etc. For
instance, ignoring renal function maturation can simply bring about
incorrect conclusions:
( http://www.nature.com/doifinder/10.1038/sj.clpt.6100327).
I see lots of common grounds between the bottom-up and top-down
approaches and do not consider these two as competing but complementary
approaches (last few slides of
http://www.emea.europa.eu/pdfs/conferenceflyers/paediatric/19rostami.pdf
show and example of the consistency between the two approaches).
Our argument is, let's mechanistically incorporate our collective knowledge
from all reliable sources as much as and whenever possible into
physiologically based models and use empirical models only when there is not
any other alternatives.
Yours Sincerely
Masoud
PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
whenever it is out please.
Masoud Jamei, PhD, SMIEEE
Senior Scientific Advisor, Head of M&S
Honorary Lecturer, School of Medicine, University of Sheffield
Simcyp Limited
Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK
Tel +44 (0) 114 292 2327
Fax +44 (0) 114 292 2333
www.simcyp.com
real solutions from virtual populations
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
Behalf Of Nick Holford
Sent: 19 September 2008 23:11
To: nmusers
Subject: Re: [NMusers] Scaling for pediatric study planning
Masoud,
I dont know of any good reason to introduce an arbitrary cut-off above
age 2 years for the usefulness of allometric scaling. Allometric theory
is applicable from single cells to very large multicellular organisms.
It should be expected to explain the size related changes in PK
throughout life beginning from conception.
As you point out there are major maturational changes, in addition to
size, which need to be considered and indeed these effects can be
comparable to those of size in young children (less than 1 year of age).
The empirical models used to describe maturation in Johnson et al. 2006
are somewhat limited because they use post-natal age rather than
biological age to describe changes of in vitro enzyme activity. They
also rely on the assumption that children are like test tubes. While it
is can be debated if children are just small adults it seems less likely
they are big test tubes.
Alternative top-down approaches (i.e. based on intact humans not test
tubes), while still being empirical for the description of maturation,
do at least allow plausible extrapolation from conception to the fully
mature adult because they use post-menstrual age in combination with
allometric scaling for size at all ages (see references).
An important practical application of an integrated age and size
approach is the ability to make sensible predictions of drug clearance
in young children when, as is usually the case, there is no reliable
data available. When making extrapolations it is best to rely on
mechanism based theory whenever possible but when forced to be empirical
(all maturation models) then at least the model should extrapolate in a
sensible way.
Best wishes,
Nick
1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y.
Pharmacokinetics of oral acyclovir in neonates and in infants: a
population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7.
2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I.
Maturational pharmacokinetics of single intravenous bolus of propofol.
Paediatr Anaesth. 2007;17(11):1028-34.
3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH.
Vancomycin pharmacokinetics in preterm neonates and the prediction of
adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84.
4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA.
Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates:
Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth.
2008;Epub.
5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in
children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30.
6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
et al. Human renal function maturation a quantitative description
using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
Masoud Jamei wrote:
> I can't agree more with Jeff's comments that we should "pursue more
> physiologic expressions" and this is a "place where "bottom-up"
approaches"
> are advantageous.
>
> The allometric scaling may be useful for children older than 2 years but
for
> younger subjects surely the developmental factors should be considered as
> explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
Prediction
> of the clearance of eleven drugs and associated variability in neonates,
> infants and children. Clin Pharmacokinet 45:931-956.
>
> Regards
> Masoud
>
>
>> -----Original Message-----
>> From: [EMAIL PROTECTED] [mailto:owner-
>> [EMAIL PROTECTED] On Behalf Of Jeffrey Barrett
>> Sent: 19 September 2008 16:54
>> To: [EMAIL PROTECTED]; [EMAIL PROTECTED]
>> Cc: [email protected]
>> Subject: Re: [NMusers] Scaling for pediatric study planning
>>
>> Leonid / Joachim,
>>
>> I think we're pushing the envelope on empiricism here. Two facts of
>> reality prevail here:
>>
>> 1) we seldom collect enough data during the absorption phase to assess
>> any meaningful age/developmental dependencies across the age continuum.
>> The fisrt-order assumption is always bad even in adults but we live
>> with it because we seldom have absorption as a primary phase of
>> interest.
>>
>> 2) a physiologic approach, in addition to a more fundamental
>> approximation of reality also has more options with respect to
>> functional expressions that can accomodate developmental factors such
>> as changes in pH dependency, the surface area of the GI tract, or the
>> site and expression of presystemic P450 enzymes all of which factor
>> into the size surrogacy issue.
>>
>> Hence, I'm not sure that I would consider the allometric
>> characterization of absorption in the same manner as one would treat CL
>> or V considerations as it is indeed a hybrid process. I will defer to
>> Nick's wisdom on this but if I am pressed for a guess, I would not
>> scale but pursue more physiologic expressions. In actuality, this is a
>> place where "bottom-up" approaches would seem to have a decided
>> advantage.
>>
>> Jeff
>>
>>
>>
>> Jeffrey S. Barrett, Ph.D., FCP
>> Research Associate Professor, Pediatrics Director, Pediatric
>> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
>> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
>> Children's Hospital of Philadelphia
>> 3615 Civic Center Blvd.
>> Philadelphia, PA 19104
>>
>> KMAS (Kinetic Modeling & Simulation)
>> Institute for Translational Medicine
>> University of Pennsylvania
>> email: [EMAIL PROTECTED]
>> Ph: (267) 426-5479
>>
>>
>>>>> Leonid Gibiansky <[EMAIL PROTECTED]> 9/19/2008 11:20 AM
>>>>>
>>>>>
>> Just to add:
>>
>> c) how do we allometrically scale a VM rate constant of the Michaelis-
>> Menten elimination model:
>>
>> C1=A(1)/V1
>> DADT(1)= ... -A(1)*VM/(KM+C1)
>>
>> d) do we need to allometrically scale a KM constant of the Michaelis-
>> Menten elimination model ?
>>
>> any experience with these quantities (for example, if they were
>> estimated, what were the estimates, with the precision)?
>>
>>
>> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>>
>> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
>> support those suggestions.
>>
>> Leonid
>> --------------------------------------
>> Leonid Gibiansky, Ph.D.
>> President, QuantPharm LLC
>> web: www.quantpharm.com
>> e-mail: LGibiansky at quantpharm.com
>> tel: (301) 767 5566
>>
>>
>>
>>
>> [EMAIL PROTECTED] wrote:
>>
>>> Dear NM_Users,
>>>
>>> we have all been good students and listened to Nick when he told us
>>> again and again the rock-solid truths of allometry:
>>>
>>> Volume: *(WT/70)
>>>
>>> CL: *(WT/70)**0.75
>>>
>>> any rate constant related to distribution or elimination:
>>>
>> *(WT/70)**(-0.25)
>>
>>> Here my questions:
>>> a) how do we allometrically scale a first-order rate constant of
>>> absorption after oral dosing?
>>>
>>> b) how do we allometrically scale a first-order rate constant of
>>> absorption from a subcutaneous injection site?
>>>
>>> Thank you for your thoughts,
>>>
>>> Joachim
>>>
>>> __________________________________________
>>> Joachim GREVEL, Ph.D.
>>> MERCK SERONO International S.A.
>>> Exploratory Medicine
>>> 1202 Geneva
>>> Tel: +41.22.414.4751
>>> Fax: +41.22.414.3059
>>> Email: [EMAIL PROTECTED]
>>>
>>>
>>>
>> -----------------------------------------------------------------------
>> -
>>
>>> This message and any attachment are confidential, may be privileged
>>>
>> or
>>
>>> otherwise protected from disclosure and are intended only for use by
>>>
>> the
>>
>>> addressee(s) named herein. If you are not the intended recipient, you
>>>
>>> must not copy this message or attachment or disclose the contents to
>>>
>> any
>>
>>> other person. If you have received this transmission in error, please
>>>
>>> notify the sender immediately and delete the message and any
>>>
>> attachment
>>
>>> from your system.
Masoud,
I think we are more in less in agreement on this. I applaud the efforts
built into programs such as SIMCYP which attempts to predict clearance
based on complex physicochemical and physiological models. However my
perspective is that the gold standard 'observations' of clearance come
from observing intact organisms. Predictive models can be evaluated by
procedures such as the visual predictive check which directly compare
distribution percentiles from predictions and observations (Karlsson &
Holford 2008).
The evaluation of the SIMCYP predictions reported in the CPK paper
(Johnson et al 2006) is hard to do. It is left to the reader to compare
apples and oranges (lines and ellipses) to try to imagine how good a
prediction has been made. If we could agree to use the same methods for
evaluation of predictions then we could directly compare the merits of
the different prediction methods. I would be very happy to collaborate
with you on such a project. My colleagues and I have some quite large
collections of individual clearances in paediatric and young adult
populations that could be used as the reference.
Thanks for the reminder about Amin Rostami's comparison of bottom up and
top down approaches. But once again its hard to evaluate because he has
a graph comparing the predictions of an empirical liver volume model
based on BSA with a more theoretically sound allometric model based on
WT but there are no observations to be seen (Slide 21). The same is true
in his other slide 22.
Some bits of SIMCYP are strongly mechanistic while others -- such as the
relationship between age and liver volume are only an empirical
description needed to turn a test tube enzyme activity into a clearance
prediction. There is only an approximate relationship between liver
structure (i.e. liver volume) and liver function based on a one
compartment homogeneous distribution assumption (the same assumption
used by PK compartmental models).
I think your claim that more than 5000 data points were used to build
the age and liver volume model is a bit misleading because the methods
section reads 'A total of 5,036 liver size measurements in subjects from
birth to 18 yr old, from 9 different reference
sources9-11,15,16,18,19,21,22 were included in our analysis. In the
majority of cases the individual data and associated covariates were not
reported, only mean values and variability) stratified for age groups.'.
This seems to be a naive pooled type of analysis and not a mixed effects
analysis based on over 5000 individuals as readers of nmusers might be
expecting.
The weight and post-menstrual age model for GFR that we have reported is
based on 923 individual subjects and 1153 observations. The model is a
mixed effect analysis that was able to identify the fixed effects of age
and weight as well as random effects of between subject variability and
residual error. I will be very happy to send you a copy of the article
as soon as it appears which should be any time now.
Best wishes,
Nick
Karlsson MO, Holford NHG. A Tutorial on Visual Predictive Checks. PAGE
17 (2008) Abstr 1434 [wwwpage-meetingorg/?abstract=1434]. 2008.
Masoud Jamei wrote:
> Dear Nick
>
> Many thanks for your comments. The two years of age is an estimated
> post-natal age when most of the CYP enzymes, serum albumin level and also,
> to some extent, the body composition reach those of adults and the
> incorporation of maturation changes improved the predictions (the same
> previous paper).
>
> Of course everybody agrees that children are not like test tubes nor should
> they be modelled as one-, two- compartmental models. On the other hand, test
> tube data can provide very valuable knowledge about compounds that should be
> mechanistically incorporated into our models (e.g. whether a compound get
> metabolised by CYP2D6, its extent and the likelihood of polymorphism can be
> determined using in vitro data).
>
> As you once said at one of the PAGE meetings, it is not possible to imagine
> a case where weight doesnt play a role, however this is sometimes taken out
> of the context and interpreted as weight is the only player. Then we tend
> to model everything using only weight even enzyme/receptor affinity or
> absorption rate.
>
> We are in full agreement that the age and size should be integrated to be
> able to make sensible predictions and for that reason these two are the
> fundamental elements in our bottom-up approach but not the only ones. It
> is generally accepted that the metabolic clearance is proportional to the
> size of the liver and based on more than 5000 data point a good equation for
> predicting the size of the liver is developed (Johnson TN, Tucker GT, Tanner
> MS, et al. Changes in liver volume from birth to adulthood: a meta-analysis.
> Liver Transpl 2005 Dec; 11(12):1481-93 freely available at:
> http://dx.doi.org/10.1002/lt.20519). However, the size of the liver is again
> not the only determinant of the metabolic clearance and we need to take into
> account other relevant covariates such as the enzyme abundances in the
> liver, blood flow, plasma protein biding and the haematocrite level which
> can be altered by polymorphism, ethnicity, disease states, etc. For
> instance, ignoring renal function maturation can simply bring about
> incorrect conclusions:
> ( http://www.nature.com/doifinder/10.1038/sj.clpt.6100327).
>
> I see lots of common grounds between the bottom-up and top-down
> approaches and do not consider these two as competing but complementary
> approaches (last few slides of
> http://www.emea.europa.eu/pdfs/conferenceflyers/paediatric/19rostami.pdf
> show and example of the consistency between the two approaches).
>
> Our argument is, let's mechanistically incorporate our collective knowledge
> from all reliable sources as much as and whenever possible into
> physiologically based models and use empirical models only when there is not
> any other alternatives.
>
> Yours Sincerely
> Masoud
>
> PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
> whenever it is out please.
>
>
> Masoud Jamei, PhD, SMIEEE
> Senior Scientific Advisor, Head of M&S
> Honorary Lecturer, School of Medicine, University of Sheffield
>
> Simcyp Limited
> Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK
> Tel +44 (0) 114 292 2327
> Fax +44 (0) 114 292 2333
> www.simcyp.com
> real solutions from virtual populations
>
>
Quoted reply history
> -----Original Message-----
> From: owner-nmusers
> Behalf Of Nick Holford
> Sent: 19 September 2008 23:11
> To: nmusers
> Subject: Re: [NMusers] Scaling for pediatric study planning
>
> Masoud,
>
> I dont know of any good reason to introduce an arbitrary cut-off above
> age 2 years for the usefulness of allometric scaling. Allometric theory
> is applicable from single cells to very large multicellular organisms.
> It should be expected to explain the size related changes in PK
> throughout life beginning from conception.
>
> As you point out there are major maturational changes, in addition to
> size, which need to be considered and indeed these effects can be
> comparable to those of size in young children (less than 1 year of age).
>
> The empirical models used to describe maturation in Johnson et al. 2006
> are somewhat limited because they use post-natal age rather than
> biological age to describe changes of in vitro enzyme activity. They
> also rely on the assumption that children are like test tubes. While it
> is can be debated if children are just small adults it seems less likely
> they are big test tubes.
>
> Alternative top-down approaches (i.e. based on intact humans not test
> tubes), while still being empirical for the description of maturation,
> do at least allow plausible extrapolation from conception to the fully
> mature adult because they use post-menstrual age in combination with
> allometric scaling for size at all ages (see references).
>
> An important practical application of an integrated age and size
> approach is the ability to make sensible predictions of drug clearance
> in young children when, as is usually the case, there is no reliable
> data available. When making extrapolations it is best to rely on
> mechanism based theory whenever possible but when forced to be empirical
> (all maturation models) then at least the model should extrapolate in a
> sensible way.
>
> Best wishes,
>
> Nick
>
> 1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y.
> Pharmacokinetics of oral acyclovir in neonates and in infants: a
> population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7.
> 2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I.
> Maturational pharmacokinetics of single intravenous bolus of propofol.
> Paediatr Anaesth. 2007;17(11):1028-34.
> 3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH.
> Vancomycin pharmacokinetics in preterm neonates and the prediction of
> adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84.
> 4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA.
> Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates:
> Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth.
> 2008;Epub.
> 5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in
> children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30.
> 6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
> et al. Human renal function maturation a quantitative description
> using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
>
> Masoud Jamei wrote:
>
>> I can't agree more with Jeff's comments that we should "pursue more
>> physiologic expressions" and this is a "place where "bottom-up"
>>
> approaches"
>
>> are advantageous.
>>
>> The allometric scaling may be useful for children older than 2 years but
>>
> for
>
>> younger subjects surely the developmental factors should be considered as
>> explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
>>
> Prediction
>
>> of the clearance of eleven drugs and associated variability in neonates,
>> infants and children. Clin Pharmacokinet 45:931-956.
>>
>> Regards
>> Masoud
>>
>>
>>
>>> -----Original Message-----
>>> From: owner-nmusers
>>> nmusers
>>> Sent: 19 September 2008 16:54
>>> To: Joachim.Grevel
>>> Cc: nmusers
>>> Subject: Re: [NMusers] Scaling for pediatric study planning
>>>
>>> Leonid / Joachim,
>>>
>>> I think we're pushing the envelope on empiricism here. Two facts of
>>> reality prevail here:
>>>
>>> 1) we seldom collect enough data during the absorption phase to assess
>>> any meaningful age/developmental dependencies across the age continuum.
>>> The fisrt-order assumption is always bad even in adults but we live
>>> with it because we seldom have absorption as a primary phase of
>>> interest.
>>>
>>> 2) a physiologic approach, in addition to a more fundamental
>>> approximation of reality also has more options with respect to
>>> functional expressions that can accomodate developmental factors such
>>> as changes in pH dependency, the surface area of the GI tract, or the
>>> site and expression of presystemic P450 enzymes all of which factor
>>> into the size surrogacy issue.
>>>
>>> Hence, I'm not sure that I would consider the allometric
>>> characterization of absorption in the same manner as one would treat CL
>>> or V considerations as it is indeed a hybrid process. I will defer to
>>> Nick's wisdom on this but if I am pressed for a guess, I would not
>>> scale but pursue more physiologic expressions. In actuality, this is a
>>> place where "bottom-up" approaches would seem to have a decided
>>> advantage.
>>>
>>> Jeff
>>>
>>>
>>>
>>> Jeffrey S. Barrett, Ph.D., FCP
>>> Research Associate Professor, Pediatrics Director, Pediatric
>>> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
>>> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
>>> Children's Hospital of Philadelphia
>>> 3615 Civic Center Blvd.
>>> Philadelphia, PA 19104
>>>
>>> KMAS (Kinetic Modeling & Simulation)
>>> Institute for Translational Medicine
>>> University of Pennsylvania
>>> email: barrettj
>>> Ph: (267) 426-5479
>>>
>>>
>>>
>>>>>> Leonid Gibiansky <LGibiansky
>>>>>>
>>>>>>
>>>>>>
>>> Just to add:
>>>
>>> c) how do we allometrically scale a VM rate constant of the Michaelis-
>>> Menten elimination model:
>>>
>>> C1=A(1)/V1
>>> DADT(1)= ... -A(1)*VM/(KM+C1)
>>>
>>> d) do we need to allometrically scale a KM constant of the Michaelis-
>>> Menten elimination model ?
>>>
>>> any experience with these quantities (for example, if they were
>>> estimated, what were the estimates, with the precision)?
>>>
>>>
>>> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>>>
>>> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
>>> support those suggestions.
>>>
>>> Leonid
>>> --------------------------------------
>>> Leonid Gibiansky, Ph.D.
>>> President, QuantPharm LLC
>>> web: www.quantpharm.com
>>> e-mail: LGibiansky at quantpharm.com
>>> tel: (301) 767 5566
>>>
>>>
>>>
>>>
>>> Joachim.Grevel
>>>
>>>
>>>> Dear NM_Users,
>>>>
>>>> we have all been good students and listened to Nick when he told us
>>>> again and again the rock-solid truths of allometry:
>>>>
>>>> Volume: *(WT/70)
>>>>
>>>> CL: *(WT/70)**0.75
>>>>
>>>> any rate constant related to distribution or elimination:
>>>>
>>>>
>>> *(WT/70)**(-0.25)
>>>
>>>
>>>> Here my questions:
>>>> a) how do we allometrically scale a first-order rate constant of
>>>> absorption after oral dosing?
>>>>
>>>> b) how do we allometrically scale a first-order rate constant of
>>>> absorption from a subcutaneous injection site?
>>>>
>>>> Thank you for your thoughts,
>>>>
>>>> Joachim
>>>>
>>>> __________________________________________
>>>> Joachim GREVEL, Ph.D.
>>>> MERCK SERONO International S.A.
>>>> Exploratory Medicine
>>>> 1202 Geneva
>>>> Tel: +41.22.414.4751
>>>> Fax: +41.22.414.3059
>>>> Email: joachim.grevel
>>>>
>>>>
>>>>
>>>>
>>> -----------------------------------------------------------------------
>>> -
>>>
>>>
>>>> This message and any attachment are confidential, may be privileged
>>>>
>>>>
>>> or
>>>
>>>
>>>> otherwise protected from disclosure and are intended only for use by
>>>>
>>>>
>>> the
>>>
>>>
>>>> addressee(s) named herein. If you are not the intended recipient, you
>>>>
>>>> must not copy this message or attachment or disclose the contents to
>>>>
>>>>
>>> any
>>>
>>>
>>>> other person. If you have received this transmission in error, please
>>>>
>>>> notify the sender immediately and delete the message and any
>>>>
>>>>
>>> attachment
>>>
>>>
>>>> from your system.
Masoud,
I think we are more in less in agreement on this. I applaud the efforts built into programs such as SIMCYP which attempts to predict clearance based on complex physicochemical and physiological models. However my perspective is that the gold standard 'observations' of clearance come from observing intact organisms. Predictive models can be evaluated by procedures such as the visual predictive check which directly compare distribution percentiles from predictions and observations (Karlsson & Holford 2008).
The evaluation of the SIMCYP predictions reported in the CPK paper (Johnson et al 2006) is hard to do. It is left to the reader to compare apples and oranges (lines and ellipses) to try to imagine how good a prediction has been made. If we could agree to use the same methods for evaluation of predictions then we could directly compare the merits of the different prediction methods. I would be very happy to collaborate with you on such a project. My colleagues and I have some quite large collections of individual clearances in paediatric and young adult populations that could be used as the reference.
Thanks for the reminder about Amin Rostami's comparison of bottom up and top down approaches. But once again its hard to evaluate because he has a graph comparing the predictions of an empirical liver volume model based on BSA with a more theoretically sound allometric model based on WT but there are no observations to be seen (Slide 21). The same is true in his other slide 22.
Some bits of SIMCYP are strongly mechanistic while others -- such as the relationship between age and liver volume are only an empirical description needed to turn a test tube enzyme activity into a clearance prediction. There is only an approximate relationship between liver structure (i.e. liver volume) and liver function based on a one compartment homogeneous distribution assumption (the same assumption used by PK compartmental models).
I think your claim that more than 5000 data points were used to build the age and liver volume model is a bit misleading because the methods section reads 'A total of 5,036 liver size measurements in subjects from birth to 18 yr old, from 9 different reference sources9-11,15,16,18,19,21,22 were included in our analysis. In the majority of cases the individual data and associated covariates were not reported, only mean values and variability) stratified for age groups.'. This seems to be a naive pooled type of analysis and not a mixed effects analysis based on over 5000 individuals as readers of nmusers might be expecting.
The weight and post-menstrual age model for GFR that we have reported is based on 923 individual subjects and 1153 observations. The model is a mixed effect analysis that was able to identify the fixed effects of age and weight as well as random effects of between subject variability and residual error. I will be very happy to send you a copy of the article as soon as it appears which should be any time now.
Best wishes,
Nick
Karlsson MO, Holford NHG. A Tutorial on Visual Predictive Checks. PAGE 17 (2008) Abstr 1434 [wwwpage-meetingorg/?abstract=1434]. 2008.
Masoud Jamei wrote:
> Dear Nick
>
> Many thanks for your comments. The two years of age is an estimated
> post-natal age when most of the CYP enzymes, serum albumin level and also,
> to some extent, the body composition reach those of adults and the
> incorporation of maturation changes improved the predictions (the same
> previous paper).
>
> Of course everybody agrees that children are not like test tubes nor should
>
> they be modelled as one-, two- compartmental models. On the other hand, test
> tube data can provide very valuable knowledge about compounds that should be
> mechanistically incorporated into our models (e.g. whether a compound get
> metabolised by CYP2D6, its extent and the likelihood of polymorphism can be
> determined using in vitro data).
>
> As you once said at one of the PAGE meetings, it is not possible to imagine
>
> a case where weight doesn’t play a role, however this is sometimes taken out
> of the context and interpreted as “weight is the only player”. Then we tend
> to model everything using only weight even enzyme/receptor affinity or
> absorption rate.
>
> We are in full agreement that the age and size should be integrated to be
>
> able to make sensible predictions and for that reason these two are the
> fundamental elements in our “bottom-up” approach but not the only ones. It
> is generally accepted that the metabolic clearance is proportional to the
> size of the liver and based on more than 5000 data point a good equation for
> predicting the size of the liver is developed (Johnson TN, Tucker GT, Tanner
> MS, et al. Changes in liver volume from birth to adulthood: a meta-analysis.
> Liver Transpl 2005 Dec; 11(12):1481-93 – freely available at:
> http://dx.doi.org/10.1002/lt.20519). However, the size of the liver is again
> not the only determinant of the metabolic clearance and we need to take into
> account other relevant covariates such as the enzyme abundances in the
> liver, blood flow, plasma protein biding and the haematocrite level which
> can be altered by polymorphism, ethnicity, disease states, etc. For
> instance, ignoring renal function maturation can simply bring about
> incorrect conclusions:
> ( http://www.nature.com/doifinder/10.1038/sj.clpt.6100327).
>
> I see lots of common grounds between the “bottom-up” and “top-down”
>
> approaches and do not consider these two as competing but complementary
> approaches (last few slides of
> http://www.emea.europa.eu/pdfs/conferenceflyers/paediatric/19rostami.pdf
> show and example of the consistency between the two approaches).
>
> Our argument is, let's mechanistically incorporate our collective knowledge
>
> from all reliable sources as much as and whenever possible into
> physiologically based models and use empirical models only when there is not
> any other alternatives.
>
> Yours Sincerely
> Masoud
>
> PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
> whenever it is out please.
>
> Masoud Jamei, PhD, SMIEEE
>
> Senior Scientific Advisor, Head of M&S Honorary Lecturer, School of Medicine, University of Sheffield Simcyp Limited Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK Tel +44 (0) 114 292 2327 Fax +44 (0) 114 292 2333 www.simcyp.com real solutions from virtual populations
>
Quoted reply history
> -----Original Message-----
> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On
> Behalf Of Nick Holford
> Sent: 19 September 2008 23:11
> To: nmusers
> Subject: Re: [NMusers] Scaling for pediatric study planning
>
> Masoud,
>
> I dont know of any good reason to introduce an arbitrary cut-off above age 2 years for the usefulness of allometric scaling. Allometric theory is applicable from single cells to very large multicellular organisms. It should be expected to explain the size related changes in PK throughout life beginning from conception.
>
> As you point out there are major maturational changes, in addition to size, which need to be considered and indeed these effects can be comparable to those of size in young children (less than 1 year of age).
>
> The empirical models used to describe maturation in Johnson et al. 2006 are somewhat limited because they use post-natal age rather than biological age to describe changes of in vitro enzyme activity. They also rely on the assumption that children are like test tubes. While it is can be debated if children are just small adults it seems less likely they are big test tubes.
>
> Alternative top-down approaches (i.e. based on intact humans not test tubes), while still being empirical for the description of maturation, do at least allow plausible extrapolation from conception to the fully mature adult because they use post-menstrual age in combination with allometric scaling for size at all ages (see references).
>
> An important practical application of an integrated age and size approach is the ability to make sensible predictions of drug clearance in young children when, as is usually the case, there is no reliable data available. When making extrapolations it is best to rely on mechanism based theory whenever possible but when forced to be empirical (all maturation models) then at least the model should extrapolate in a sensible way.
>
> Best wishes,
>
> Nick
>
> 1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y. Pharmacokinetics of oral acyclovir in neonates and in infants: a population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7. 2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I. Maturational pharmacokinetics of single intravenous bolus of propofol. Paediatr Anaesth. 2007;17(11):1028-34. 3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH. Vancomycin pharmacokinetics in preterm neonates and the prediction of adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84. 4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA. Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates: Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth. 2008;Epub. 5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30. 6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M, et al. Human renal function maturation – a quantitative description using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
>
> Masoud Jamei wrote:
>
> > I can't agree more with Jeff's comments that we should "pursue more
> > physiologic expressions" and this is a "place where "bottom-up"
>
> approaches"
>
> > are advantageous.
> >
> > The allometric scaling may be useful for children older than 2 years but
>
> for
>
> > younger subjects surely the developmental factors should be considered as
> > explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
>
> Prediction
>
> > of the clearance of eleven drugs and associated variability in neonates,
> > infants and children. Clin Pharmacokinet 45:931-956.
> >
> > Regards
> >
> > Masoud
> >
> > > -----Original Message-----
> > > From: [EMAIL PROTECTED] [mailto:owner-
> > > [EMAIL PROTECTED] On Behalf Of Jeffrey Barrett
> > > Sent: 19 September 2008 16:54
> > > To: [EMAIL PROTECTED]; [EMAIL PROTECTED]
> > > Cc: [email protected]
> > > Subject: Re: [NMusers] Scaling for pediatric study planning
> > >
> > > Leonid / Joachim,
> > >
> > > I think we're pushing the envelope on empiricism here. Two facts of
> > > reality prevail here:
> > >
> > > 1) we seldom collect enough data during the absorption phase to assess
> > > any meaningful age/developmental dependencies across the age continuum.
> > > The fisrt-order assumption is always bad even in adults but we live
> > > with it because we seldom have absorption as a primary phase of
> > > interest.
> > >
> > > 2) a physiologic approach, in addition to a more fundamental
> > > approximation of reality also has more options with respect to
> > > functional expressions that can accomodate developmental factors such
> > > as changes in pH dependency, the surface area of the GI tract, or the
> > > site and expression of presystemic P450 enzymes all of which factor
> > > into the size surrogacy issue.
> > >
> > > Hence, I'm not sure that I would consider the allometric
> > > characterization of absorption in the same manner as one would treat CL
> > > or V considerations as it is indeed a hybrid process. I will defer to
> > > Nick's wisdom on this but if I am pressed for a guess, I would not
> > > scale but pursue more physiologic expressions. In actuality, this is a
> > > place where "bottom-up" approaches would seem to have a decided
> > > advantage.
> > >
> > > Jeff
> > >
> > > Jeffrey S. Barrett, Ph.D., FCP
> > > Research Associate Professor, Pediatrics Director, Pediatric
> > > Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
> > > Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
> > > Children's Hospital of Philadelphia
> > > 3615 Civic Center Blvd.
> > > Philadelphia, PA 19104
> > >
> > > KMAS (Kinetic Modeling & Simulation)
> > > Institute for Translational Medicine
> > > University of Pennsylvania
> > > email: [EMAIL PROTECTED]
> > > Ph: (267) 426-5479
> > >
> > > > > > Leonid Gibiansky <[EMAIL PROTECTED]> 9/19/2008 11:20 AM
> > >
> > > Just to add:
> > >
> > > c) how do we allometrically scale a VM rate constant of the Michaelis-
> > > Menten elimination model:
> > >
> > > C1=A(1)/V1
> > > DADT(1)= ... -A(1)*VM/(KM+C1)
> > >
> > > d) do we need to allometrically scale a KM constant of the Michaelis-
> > > Menten elimination model ?
> > >
> > > any experience with these quantities (for example, if they were
> > > estimated, what were the estimates, with the precision)?
> > >
> > > My suggestion would be NOT to scale a), b) and d), and scale VM as the
> > >
> > > rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
> > > support those suggestions.
> > >
> > > Leonid
> > > --------------------------------------
> > > Leonid Gibiansky, Ph.D.
> > > President, QuantPharm LLC
> > > web: www.quantpharm.com
> > > e-mail: LGibiansky at quantpharm.com
> > > tel: (301) 767 5566
> > >
> > > [EMAIL PROTECTED] wrote:
> > >
> > > > Dear NM_Users,
> > > >
> > > > we have all been good students and listened to Nick when he told us
> > > > again and again the rock-solid truths of allometry:
> > > >
> > > > Volume: *(WT/70)
> > > >
> > > > CL: *(WT/70)**0.75
> > > >
> > > > any rate constant related to distribution or elimination:
> > >
> > > *(WT/70)**(-0.25)
> > >
> > > > Here my questions:
> > > > a) how do we allometrically scale a first-order rate constant of
> > > > absorption after oral dosing?
> > > >
> > > > b) how do we allometrically scale a first-order rate constant of
> > > > absorption from a subcutaneous injection site?
> > > >
> > > > Thank you for your thoughts,
> > > >
> > > > Joachim
> > > >
> > > > __________________________________________
> > > > Joachim GREVEL, Ph.D.
> > > > MERCK SERONO International S.A.
> > > > Exploratory Medicine
> > > > 1202 Geneva
> > > > Tel: +41.22.414.4751
> > > > Fax: +41.22.414.3059
> > > > Email: [EMAIL PROTECTED]
> > >
> > > -----------------------------------------------------------------------
> > > -
> > >
> > > > This message and any attachment are confidential, may be privileged
> > >
> > > or
> > >
> > > > otherwise protected from disclosure and are intended only for use by
> > >
> > > the
> > >
> > > > addressee(s) named herein. If you are not the intended recipient, you
> > > >
> > > > must not copy this message or attachment or disclose the contents to
> > >
> > > any
> > >
> > > > other person. If you have received this transmission in error, please
> > > >
> > > > notify the sender immediately and delete the message and any
> > >
> > > attachment
> > >
> > > > from your system.
Besides all the valuable suggestions/opinions raised in the discussion,
there is another point that need to keep in mind in scaling: the unit used
in the parameters. For example, if the absorption rate constant is 1/hr,
this absorption rate is the total mass transfer through the membrane at
the absorption site per unit time. Therefore, the size of the body
matters. If the abosrption rate is 1/hr/cm2 (for example), then the rate
is independent to the body size
Xiaofeng Wang, PhD
Oncology, Novartis
(862)778-8856 (o)
"Masoud Jamei" <masoud.jamei
Sent by: owner-nmusers
09/20/2008 12:07 PM
To
"nmusers" <nmusers
cc
Subject
RE: [NMusers] Scaling for pediatric study planning
Dear Nick
Many thanks for your comments. The two years of age is an estimated
post-natal age when most of the CYP enzymes, serum albumin level and also,
to some extent, the body composition reach those of adults and the
incorporation of maturation changes improved the predictions (the same
previous paper).
Of course everybody agrees that children are not like test tubes nor
should
they be modelled as one-, two- compartmental models. On the other hand,
test
tube data can provide very valuable knowledge about compounds that should
be
mechanistically incorporated into our models (e.g. whether a compound get
metabolised by CYP2D6, its extent and the likelihood of polymorphism can
be
determined using in vitro data).
As you once said at one of the PAGE meetings, it is not possible to
imagine
a case where weight doesn?t play a role, however this is sometimes taken
out
of the context and interpreted as ?weight is the only player?. Then we
tend
to model everything using only weight even enzyme/receptor affinity or
absorption rate.
We are in full agreement that the age and size should be integrated to be
able to make sensible predictions and for that reason these two are the
fundamental elements in our ?bottom-up? approach but not the only ones. It
is generally accepted that the metabolic clearance is proportional to the
size of the liver and based on more than 5000 data point a good equation
for
predicting the size of the liver is developed (Johnson TN, Tucker GT,
Tanner
MS, et al. Changes in liver volume from birth to adulthood: a
meta-analysis.
Liver Transpl 2005 Dec; 11(12):1481-93 ? freely available at:
http://dx.doi.org/10.1002/lt.20519). However, the size of the liver is
again
not the only determinant of the metabolic clearance and we need to take
into
account other relevant covariates such as the enzyme abundances in the
liver, blood flow, plasma protein biding and the haematocrite level which
can be altered by polymorphism, ethnicity, disease states, etc. For
instance, ignoring renal function maturation can simply bring about
incorrect conclusions:
( http://www.nature.com/doifinder/10.1038/sj.clpt.6100327).
I see lots of common grounds between the ?bottom-up? and ?top-down?
approaches and do not consider these two as competing but complementary
approaches (last few slides of
http://www.emea.europa.eu/pdfs/conferenceflyers/paediatric/19rostami.pdf
show and example of the consistency between the two approaches).
Our argument is, let's mechanistically incorporate our collective
knowledge
from all reliable sources as much as and whenever possible into
physiologically based models and use empirical models only when there is
not
any other alternatives.
Yours Sincerely
Masoud
PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
whenever it is out please.
Masoud Jamei, PhD, SMIEEE
Senior Scientific Advisor, Head of M&S
Honorary Lecturer, School of Medicine, University of Sheffield
Simcyp Limited
Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK
Tel +44 (0) 114 292 2327
Fax +44 (0) 114 292 2333
www.simcyp.com
real solutions from virtual populations
Quoted reply history
-----Original Message-----
From: owner-nmusers
On
Behalf Of Nick Holford
Sent: 19 September 2008 23:11
To: nmusers
Subject: Re: [NMusers] Scaling for pediatric study planning
Masoud,
I dont know of any good reason to introduce an arbitrary cut-off above
age 2 years for the usefulness of allometric scaling. Allometric theory
is applicable from single cells to very large multicellular organisms.
It should be expected to explain the size related changes in PK
throughout life beginning from conception.
As you point out there are major maturational changes, in addition to
size, which need to be considered and indeed these effects can be
comparable to those of size in young children (less than 1 year of age).
The empirical models used to describe maturation in Johnson et al. 2006
are somewhat limited because they use post-natal age rather than
biological age to describe changes of in vitro enzyme activity. They
also rely on the assumption that children are like test tubes. While it
is can be debated if children are just small adults it seems less likely
they are big test tubes.
Alternative top-down approaches (i.e. based on intact humans not test
tubes), while still being empirical for the description of maturation,
do at least allow plausible extrapolation from conception to the fully
mature adult because they use post-menstrual age in combination with
allometric scaling for size at all ages (see references).
An important practical application of an integrated age and size
approach is the ability to make sensible predictions of drug clearance
in young children when, as is usually the case, there is no reliable
data available. When making extrapolations it is best to rely on
mechanism based theory whenever possible but when forced to be empirical
(all maturation models) then at least the model should extrapolate in a
sensible way.
Best wishes,
Nick
1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y.
Pharmacokinetics of oral acyclovir in neonates and in infants: a
population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7.
2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I.
Maturational pharmacokinetics of single intravenous bolus of propofol.
Paediatr Anaesth. 2007;17(11):1028-34.
3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH.
Vancomycin pharmacokinetics in preterm neonates and the prediction of
adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84.
4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA.
Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates:
Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth.
2008;Epub.
5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in
children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30.
6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
et al. Human renal function maturation ? a quantitative description
using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
Masoud Jamei wrote:
> I can't agree more with Jeff's comments that we should "pursue more
> physiologic expressions" and this is a "place where "bottom-up"
approaches"
> are advantageous.
>
> The allometric scaling may be useful for children older than 2 years but
for
> younger subjects surely the developmental factors should be considered
as
> explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
Prediction
> of the clearance of eleven drugs and associated variability in neonates,
> infants and children. Clin Pharmacokinet 45:931-956.
>
> Regards
> Masoud
>
>
>> -----Original Message-----
>> From: owner-nmusers
>> nmusers
>> Sent: 19 September 2008 16:54
>> To: Joachim.Grevel
>> Cc: nmusers
>> Subject: Re: [NMusers] Scaling for pediatric study planning
>>
>> Leonid / Joachim,
>>
>> I think we're pushing the envelope on empiricism here. Two facts of
>> reality prevail here:
>>
>> 1) we seldom collect enough data during the absorption phase to assess
>> any meaningful age/developmental dependencies across the age continuum.
>> The fisrt-order assumption is always bad even in adults but we live
>> with it because we seldom have absorption as a primary phase of
>> interest.
>>
>> 2) a physiologic approach, in addition to a more fundamental
>> approximation of reality also has more options with respect to
>> functional expressions that can accomodate developmental factors such
>> as changes in pH dependency, the surface area of the GI tract, or the
>> site and expression of presystemic P450 enzymes all of which factor
>> into the size surrogacy issue.
>>
>> Hence, I'm not sure that I would consider the allometric
>> characterization of absorption in the same manner as one would treat CL
>> or V considerations as it is indeed a hybrid process. I will defer to
>> Nick's wisdom on this but if I am pressed for a guess, I would not
>> scale but pursue more physiologic expressions. In actuality, this is a
>> place where "bottom-up" approaches would seem to have a decided
>> advantage.
>>
>> Jeff
>>
>>
>>
>> Jeffrey S. Barrett, Ph.D., FCP
>> Research Associate Professor, Pediatrics Director, Pediatric
>> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
>> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
>> Children's Hospital of Philadelphia
>> 3615 Civic Center Blvd.
>> Philadelphia, PA 19104
>>
>> KMAS (Kinetic Modeling & Simulation)
>> Institute for Translational Medicine
>> University of Pennsylvania
>> email: barrettj
>> Ph: (267) 426-5479
>>
>>
>>>>> Leonid Gibiansky <LGibiansky
>>>>>
>>>>>
>> Just to add:
>>
>> c) how do we allometrically scale a VM rate constant of the Michaelis-
>> Menten elimination model:
>>
>> C1=A(1)/V1
>> DADT(1)= ... -A(1)*VM/(KM+C1)
>>
>> d) do we need to allometrically scale a KM constant of the Michaelis-
>> Menten elimination model ?
>>
>> any experience with these quantities (for example, if they were
>> estimated, what were the estimates, with the precision)?
>>
>>
>> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>>
>> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
>> support those suggestions.
>>
>> Leonid
>> --------------------------------------
>> Leonid Gibiansky, Ph.D.
>> President, QuantPharm LLC
>> web: www.quantpharm.com
>> e-mail: LGibiansky at quantpharm.com
>> tel: (301) 767 5566
>>
>>
>>
>>
>> Joachim.Grevel
>>
>>> Dear NM_Users,
>>>
>>> we have all been good students and listened to Nick when he told us
>>> again and again the rock-solid truths of allometry:
>>>
>>> Volume: *(WT/70)
>>>
>>> CL: *(WT/70)**0.75
>>>
>>> any rate constant related to distribution or elimination:
>>>
>> *(WT/70)**(-0.25)
>>
>>> Here my questions:
>>> a) how do we allometrically scale a first-order rate constant of
>>> absorption after oral dosing?
>>>
>>> b) how do we allometrically scale a first-order rate constant of
>>> absorption from a subcutaneous injection site?
>>>
>>> Thank you for your thoughts,
>>>
>>> Joachim
>>>
>>> _______________________
___________________
>>> Joachim GREVEL, Ph.D.
>>> MERCK SERONO International S.A.
>>> Exploratory Medicine
>>> 1202 Geneva
>>> Tel: +41.22.414.4751
>>> Fax: +41.22.414.3059
>>> Email: joachim.grevel
>>>
>>>
>>>
>> -----------------------------------------------------------------------
>> -
>>
>>> This message and any attachment are confidential, may be privileged
>>>
>> or
>>
>>> otherwise protected from disclosure and are intended only for use by
>>>
>> the
>>
>>> addressee(s) named herein. If you are not the intended recipient, you
>>>
>>> must not copy this message or attachment or disclose the contents to
>>>
>> any
>>
>>> other person. If you have received this transmission in error, please
>>>
>>> notify the sender immediately and delete the message and any
>>>
>> attachment
>>
>>> from your system.
Besides all the valuable suggestions/opinions raised in the discussion,
there is another point that need to keep in mind in scaling: the unit used
in the parameters. For example, if the absorption rate constant is 1/hr,
this absorption rate is the total mass transfer through the membrane at
the absorption site per unit time. Therefore, the size of the body
matters. If the abosrption rate is 1/hr/cm2 (for example), then the rate
is independent to the body size
Xiaofeng Wang, PhD
Oncology, Novartis
(862)778-8856 (o)
"Masoud Jamei" <[EMAIL PROTECTED]>
Sent by: [EMAIL PROTECTED]
09/20/2008 12:07 PM
To
"nmusers" <[email protected]>
cc
Subject
RE: [NMusers] Scaling for pediatric study planning
Dear Nick
Many thanks for your comments. The two years of age is an estimated
post-natal age when most of the CYP enzymes, serum albumin level and also,
to some extent, the body composition reach those of adults and the
incorporation of maturation changes improved the predictions (the same
previous paper).
Of course everybody agrees that children are not like test tubes nor
should
they be modelled as one-, two- compartmental models. On the other hand,
test
tube data can provide very valuable knowledge about compounds that should
be
mechanistically incorporated into our models (e.g. whether a compound get
metabolised by CYP2D6, its extent and the likelihood of polymorphism can
be
determined using in vitro data).
As you once said at one of the PAGE meetings, it is not possible to
imagine
a case where weight doesn?t play a role, however this is sometimes taken
out
of the context and interpreted as ?weight is the only player?. Then we
tend
to model everything using only weight even enzyme/receptor affinity or
absorption rate.
We are in full agreement that the age and size should be integrated to be
able to make sensible predictions and for that reason these two are the
fundamental elements in our ?bottom-up? approach but not the only ones. It
is generally accepted that the metabolic clearance is proportional to the
size of the liver and based on more than 5000 data point a good equation
for
predicting the size of the liver is developed (Johnson TN, Tucker GT,
Tanner
MS, et al. Changes in liver volume from birth to adulthood: a
meta-analysis.
Liver Transpl 2005 Dec; 11(12):1481-93 ? freely available at:
http://dx.doi.org/10.1002/lt.20519). However, the size of the liver is
again
not the only determinant of the metabolic clearance and we need to take
into
account other relevant covariates such as the enzyme abundances in the
liver, blood flow, plasma protein biding and the haematocrite level which
can be altered by polymorphism, ethnicity, disease states, etc. For
instance, ignoring renal function maturation can simply bring about
incorrect conclusions:
( http://www.nature.com/doifinder/10.1038/sj.clpt.6100327).
I see lots of common grounds between the ?bottom-up? and ?top-down?
approaches and do not consider these two as competing but complementary
approaches (last few slides of
http://www.emea.europa.eu/pdfs/conferenceflyers/paediatric/19rostami.pdf
show and example of the consistency between the two approaches).
Our argument is, let's mechanistically incorporate our collective
knowledge
from all reliable sources as much as and whenever possible into
physiologically based models and use empirical models only when there is
not
any other alternatives.
Yours Sincerely
Masoud
PS: I'd greatly appreciate receiving a print out of the Rhodin et al paper
whenever it is out please.
Masoud Jamei, PhD, SMIEEE
Senior Scientific Advisor, Head of M&S
Honorary Lecturer, School of Medicine, University of Sheffield
Simcyp Limited
Blades Enterprise Centre, John Street, Sheffield, S2 4SU, UK
Tel +44 (0) 114 292 2327
Fax +44 (0) 114 292 2333
www.simcyp.com
real solutions from virtual populations
Quoted reply history
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]
On
Behalf Of Nick Holford
Sent: 19 September 2008 23:11
To: nmusers
Subject: Re: [NMusers] Scaling for pediatric study planning
Masoud,
I dont know of any good reason to introduce an arbitrary cut-off above
age 2 years for the usefulness of allometric scaling. Allometric theory
is applicable from single cells to very large multicellular organisms.
It should be expected to explain the size related changes in PK
throughout life beginning from conception.
As you point out there are major maturational changes, in addition to
size, which need to be considered and indeed these effects can be
comparable to those of size in young children (less than 1 year of age).
The empirical models used to describe maturation in Johnson et al. 2006
are somewhat limited because they use post-natal age rather than
biological age to describe changes of in vitro enzyme activity. They
also rely on the assumption that children are like test tubes. While it
is can be debated if children are just small adults it seems less likely
they are big test tubes.
Alternative top-down approaches (i.e. based on intact humans not test
tubes), while still being empirical for the description of maturation,
do at least allow plausible extrapolation from conception to the fully
mature adult because they use post-menstrual age in combination with
allometric scaling for size at all ages (see references).
An important practical application of an integrated age and size
approach is the ability to make sensible predictions of drug clearance
in young children when, as is usually the case, there is no reliable
data available. When making extrapolations it is best to rely on
mechanism based theory whenever possible but when forced to be empirical
(all maturation models) then at least the model should extrapolate in a
sensible way.
Best wishes,
Nick
1. Tod M, Lokiec F, Bidault R, De Bony F, Petitjean O, Aujard Y.
Pharmacokinetics of oral acyclovir in neonates and in infants: a
population analysis. Antimicrob Agents Chemother. 2001;45(1):150-7.
2. Allegaert K, de Hoon J, Verbesselt R, Naulaers G, Murat I.
Maturational pharmacokinetics of single intravenous bolus of propofol.
Paediatr Anaesth. 2007;17(11):1028-34.
3. Anderson BJ, Allegaert K, Van den Anker JN, Cossey V, Holford NH.
Vancomycin pharmacokinetics in preterm neonates and the prediction of
adult clearance. Br J Clin Pharmacol. 2007;63(1):75-84.
4. Anand KJS, Anderson BJ, Holford NHG, Hall RW, Young T, Barton BA.
Morphine Pharmacokinetics and Pharmacodynamics in Preterm Neonates:
Secondary Results from the NEOPAIN Multicenter Trial Br J Anaesth.
2008;Epub.
5. Potts AL, Warman GR, Anderson BJ. Dexmedetomidine disposition in
children: a population analysis. Paediatr Anaesth. 2008;18(8):722-30.
6. Rhodin MM, Anderson BJ, Peters AM, Coulthard MG, Wilkins B, Cole M,
et al. Human renal function maturation ? a quantitative description
using weight and postmenstrual age. Pediatr Nephrol. 2008. In Press.
Masoud Jamei wrote:
> I can't agree more with Jeff's comments that we should "pursue more
> physiologic expressions" and this is a "place where "bottom-up"
approaches"
> are advantageous.
>
> The allometric scaling may be useful for children older than 2 years but
for
> younger subjects surely the developmental factors should be considered
as
> explained in: Johnson TN, Rostami-Hodjegan A and Tucker GT (2006)
Prediction
> of the clearance of eleven drugs and associated variability in neonates,
> infants and children. Clin Pharmacokinet 45:931-956.
>
> Regards
> Masoud
>
>
>> -----Original Message-----
>> From: [EMAIL PROTECTED] [mailto:owner-
>> [EMAIL PROTECTED] On Behalf Of Jeffrey Barrett
>> Sent: 19 September 2008 16:54
>> To: [EMAIL PROTECTED]; [EMAIL PROTECTED]
>> Cc: [email protected]
>> Subject: Re: [NMusers] Scaling for pediatric study planning
>>
>> Leonid / Joachim,
>>
>> I think we're pushing the envelope on empiricism here. Two facts of
>> reality prevail here:
>>
>> 1) we seldom collect enough data during the absorption phase to assess
>> any meaningful age/developmental dependencies across the age continuum.
>> The fisrt-order assumption is always bad even in adults but we live
>> with it because we seldom have absorption as a primary phase of
>> interest.
>>
>> 2) a physiologic approach, in addition to a more fundamental
>> approximation of reality also has more options with respect to
>> functional expressions that can accomodate developmental factors such
>> as changes in pH dependency, the surface area of the GI tract, or the
>> site and expression of presystemic P450 enzymes all of which factor
>> into the size surrogacy issue.
>>
>> Hence, I'm not sure that I would consider the allometric
>> characterization of absorption in the same manner as one would treat CL
>> or V considerations as it is indeed a hybrid process. I will defer to
>> Nick's wisdom on this but if I am pressed for a guess, I would not
>> scale but pursue more physiologic expressions. In actuality, this is a
>> place where "bottom-up" approaches would seem to have a decided
>> advantage.
>>
>> Jeff
>>
>>
>>
>> Jeffrey S. Barrett, Ph.D., FCP
>> Research Associate Professor, Pediatrics Director, Pediatric
>> Pharmacology Research Unit, Laboratory for Applied PK/PD Clinical
>> Pharmacology & Therapeutics Abramson Research Center, Rm 916H The
>> Children's Hospital of Philadelphia
>> 3615 Civic Center Blvd.
>> Philadelphia, PA 19104
>>
>> KMAS (Kinetic Modeling & Simulation)
>> Institute for Translational Medicine
>> University of Pennsylvania
>> email: [EMAIL PROTECTED]
>> Ph: (267) 426-5479
>>
>>
>>>>> Leonid Gibiansky <[EMAIL PROTECTED]> 9/19/2008 11:20 AM
>>>>>
>>>>>
>> Just to add:
>>
>> c) how do we allometrically scale a VM rate constant of the Michaelis-
>> Menten elimination model:
>>
>> C1=A(1)/V1
>> DADT(1)= ... -A(1)*VM/(KM+C1)
>>
>> d) do we need to allometrically scale a KM constant of the Michaelis-
>> Menten elimination model ?
>>
>> any experience with these quantities (for example, if they were
>> estimated, what were the estimates, with the precision)?
>>
>>
>> My suggestion would be NOT to scale a), b) and d), and scale VM as the
>>
>> rate constant (~ WT**(-0.25)) but I do not have "rock-solid" data to
>> support those suggestions.
>>
>> Leonid
>> --------------------------------------
>> Leonid Gibiansky, Ph.D.
>> President, QuantPharm LLC
>> web: www.quantpharm.com
>> e-mail: LGibiansky at quantpharm.com
>> tel: (301) 767 5566
>>
>>
>>
>>
>> [EMAIL PROTECTED] wrote:
>>
>>> Dear NM_Users,
>>>
>>> we have all been good students and listened to Nick when he told us
>>> again and again the rock-solid truths of allometry:
>>>
>>> Volume: *(WT/70)
>>>
>>> CL: *(WT/70)**0.75
>>>
>>> any rate constant related to distribution or elimination:
>>>
>> *(WT/70)**(-0.25)
>>
>>> Here my questions:
>>> a) how do we allometrically scale a first-order rate constant of
>>> absorption after oral dosing?
>>>
>>> b) how do we allometrically scale a first-order rate constant of
>>> absorption from a subcutaneous injection site?
>>>
>>> Thank you for your thoughts,
>>>
>>> Joachim
>>>
>>> __________________________________________
>>> Joachim GREVEL, Ph.D.
>>> MERCK SERONO International S.A.
>>> Exploratory Medicine
>>> 1202 Geneva
>>> Tel: +41.22.414.4751
>>> Fax: +41.22.414.3059
>>> Email: [EMAIL PROTECTED]
>>>
>>>
>>>
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