RE: Simultaneous drug and metabolite POPPK
I think this is the central point ( and the reason I brought it up): you
may have a very good fit to the data, but the parameters could be
completely meaningless. Although occasionally that may not matter, I
would worry about the validity of any extrapolation I did with a model
whose parameters did not have a biological meaning. If we did not care
about the biology, we could just fits splines to the data and take the
rest of the day off...
Mike
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Michael J. Fossler, Pharm. D., Ph. D., F.C.P.
Director
Clinical Pharmacokinetics, Modeling & Simulation
GlaxoSmithKline
(610) 270 - 4797
FAX: (610) 270-5962
Cell: (443) 350-1194
[EMAIL PROTECTED]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
"Shi, Jun" <[EMAIL PROTECTED]>
Sent by: [EMAIL PROTECTED]
14-Feb-2007 12:18
To
"Xiao, Alan" <[EMAIL PROTECTED]>, [EMAIL PROTECTED],
"Nmusers (E-mail)" <[email protected]>, [EMAIL PROTECTED]
cc
"Shi, Jun" <[EMAIL PROTECTED]>
Subject
RE: [NMusers] Simultaneous drug and metabolite POPPK
Alan,
Let's make sure what we agree and what we don't agree. Frankly, I am not
clear where we disagree (until I saw your poster).
O.K., let's do conversion of concentration of P and Mets to molar unit
(this makes chemical sense ? we agreed), and fix Vd of met to be 1 (this
is the trick in coding, but couldn?t resolve the fundamental issue of
lacking of info?we agreed).
What we may have talked differently is the definition of KMP, which is not
the K12 in your poster. In the model I am referring to, KMP is
?disconnected? from any of k for parent. In the real world, parent does
not only form one metab, metab does not always behave in formation rate
being the rate limiting, and metab does not always sequentially formed
from one to another? Your model appeared to simply some of the real world
issues ? it is fine when your data gives the justifications.
As we both know there are many unidentifiable factors in modeling P and
Metab simultaneously (F, Fm, Vd?), I hope that you could agree with me
that one should always be cautious when interpret parameter obtained from
such a model (i.e., modeling P and Met after oral administration of P) on
its physiological meaning. The key issue to me here, is that whether the
model offers good predictivity and under what underlying conditions.
Jun
Quoted reply history
-----Original Message-----
From: Xiao, Alan [mailto:[EMAIL PROTECTED]
Sent: Wed 2/14/2007 9:31 AM
To: Shi, Jun; [EMAIL PROTECTED]; Nmusers (E-mail);
[EMAIL PROTECTED]
Subject: RE: [NMusers] Simultaneous drug and metabolite POPPK
I know your Equs 1-3 are talking the SAME thing since they are all about
the metabolite. But my question is the physical meaning of the term in the
equation for the parent (which you did not show) and in the equation for
the metabolite. After a closer look to your equations below, I have a
question related to the fundamental science - chemistry. That is, your KMP
term in the mass balance differential equations for the metabolite refers
to the mass (production) rate of the metabolite. The same term in the
equation for the parent refers to the mass (elimination) rate of the
parent (to the metabolite). Unless the metabolite and the parent have
exactly the same molecular weight (MW), these two mass rates that this
same term refers to are different. That's the fundamental chemistry behind
the discussion about whether or not concentrations should be in molar
units. Or you have to use molecular weight to correct the parameter
estimates after modeling if you have to use weight concentration units as
Serge mentioned in another email. Based on the equations below, I think
you'll have to re-define/interpret your parameter in a way different from
what is normally taught in class.
By the way, in equation 3 below, it is equivalent to fix V3=1, which I
don't think can really resolve the overparameterization problem. The
following poster in the 2002 ASCPT meeting might be able to help a little
on this. Also, can you give the steps to derive how volume ratios become a
part of KMP?
Thanks,
Alan
-----Original Message-----
From: Shi, Jun [mailto:[EMAIL PROTECTED]
Sent: Tuesday, February 13, 2007 8:09 PM
To: Xiao, Alan; [EMAIL PROTECTED]; Nmusers (E-mail);
[EMAIL PROTECTED]
Subject: RE: [NMusers] Simultaneous drug and metabolite POPPK
Alan,
I am afraid that you didn't read my code carefully enough. Actually, Eqs
1-3 are talking about the SAME thing, ie, metabolite rate. I started out
with the full data, i.e., with IV info available (Eq1), then, tried to
illustrate the issue when IV data is not available (Eq2) and finally, show
how this can be coded in NONMEM in view of the constraint in order to fit
the data (Eq3).
All I tried to say is that there are many other identifiability issues can
NOT be addressed with this type of data by modeling (i.e., model P and Met
when only P is administrated, and more than one metabs are formed). Given
this fact, conversion to molar unit becomes less critical (although it is
a good practice). One should be always cautious when interpret the
parameter obtained on its physiological meaning (even if you have
concerted to molar unit).
Jun
-----Original Message-----
From: Xiao, Alan [ mailto:[EMAIL PROTECTED]
Sent: Tue 2/13/2007 5:22 PM
To: Shi, Jun; [EMAIL PROTECTED]; Nmusers (E-mail);
[EMAIL PROTECTED]
Subject: RE: [NMusers] Simultaneous drug and metabolite POPPK
Hmm,
I wonder how you write the mass balance equation for the parent and how to
define parameter KMP. If you use the same term KMP(iv)*A(2) in both
equations for the parent [DADT(2)=...-KMP(iv)*A(2)] and the metabolite
(DADT(3)=...], then this same term have different physical meaning in two
equations if weight concentrations are used. I think you don't want to use
the same term to represent two different things (and two different
quantities) in your mass balance equations although you may still get
fitting perfect.
In addition, for simultaneously modeling parent/metabolite data, yes, if
you don't have iv data for metabolite, you can not get a unique set of
parameter estimates for metabolites because of overparameterization.
However, if you have prior information about metabolic ratios, you can fix
that into your model, such as Kel_met_parent / Kel_tot_parent=R (e.g.
0.5), where Kel_met_parent is elimination rate constant of the parent
through metabolism of interest and Kel_tot_parent is the total elimination
rate constant of the parent, so R is called metabolic ratio. Once this
ratio is available, volume of distribution for metabolites are estimable
if data is informative.
They might be other options to handle the issue as well.
Alan
-----Original Message-----
From: [EMAIL PROTECTED] [ mailto:[EMAIL PROTECTED]
]On Behalf Of Shi, Jun
Sent: Tuesday, February 13, 2007 10:50 AM
To: [EMAIL PROTECTED]; Nmusers (E-mail);
[EMAIL PROTECTED]
Subject: RE: [NMusers] Simultaneous drug and metabolite POPPK
Mike,
This depends on the purpose of the modeling and the information available.
Usually, we only have Parent and Met concentration data after oral
administration, therefore, we can't estimate the true disposition
parameters. We can get CL/F and V/F for parent, but we can get nothing
more than apparent Production rate constant and Elimination rate constant
for Met. In this case, converting the data to micromolar unit or not is
not critical.
e.g.
Let's begin from the differential equation below:
DADT(3)=KMP(iv)*A(2)-KME*A(3) Eq 1
where A(2) is the amount of parent (mg), A(3) is the amount of metabolite
(mg). KmP is the production rate of the metabolite.
Because the distribution volume of Met (V3) is unobtainable (no IV data of
Met), we have to convert dA/dt to dC/dt and divide both sides of Eq 1 by
V3 as follows:
DADT(3)/V3=KMP(iv)*A(2)/V3-KME*A(3)/V3 Eq 2
In NONMEM, we coded this as follows:
DADT(3)=KMP *A(2)/V2-KME*A(3) Eq 3
Please note that DADT(3) in Eq 3, actually, is dC3/dt (a rate of
concentration instead of amount), and KMP in Eq 3 = KMP(iv) x V2/V3 in Eq
1. In other words, KMP is a composite parameter of both volumn ratio and
molecular weight ratio.
If there are IV data for both parent and metabolite after administrations
of parent and metabolite seperately, the true disposition parameters can
be estimated for both. By converting the concentration unit to molar, we
can estimate formation fraction of parent to metabolite.
Jun Shi
Clinical Pharmacology and Drug Dynamics
Forest Research Institute
Rm18-35
Harborside Financial Center-Plaza V
Jersey City, NJ 07311
Tel: 201-427-8044
Fax: 201-427-8498
Email: [EMAIL PROTECTED]
-----Original Message-----
From: [EMAIL PROTECTED] [ mailto:[EMAIL PROTECTED]
On Behalf Of [EMAIL PROTECTED]
Sent: Tuesday, February 13, 2007 9:02 AM
To: Nmusers (E-mail); [EMAIL PROTECTED]
Subject: RE: [NMusers] Simultaneous drug and metabolite POPPK
I have a question for those who submitted these two examples - Did you
transform the data into micromolar quantities? It is not clear from the
examples. I have not done much parent/metabolite modeling (just lucky I
guess) but it seems to me that one would have to work in molar units for
these models to be valid. Can someone comment on this?
Mike
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Michael J. Fossler, Pharm. D., Ph. D., F.C.P.
Director
Clinical Pharmacokinetics, Modeling & Simulation
GlaxoSmithKline
(610) 270 - 4797
FAX: (610) 270-5962
Cell: (443) 350-1194
[EMAIL PROTECTED]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~