From: Paul Hutson prhutson@pharmacy.wisc.edu
Subject:[NMusers] Fx
Date: 5/24/2004 7:22 PM

I am modeling an oral drug with both parent and metabolite plasma concentrations available.
When using ADVAN6 with differential equations for such extravascular dosing, I understand
F2 to represent the bioavailability of the drug in the depot compartment (#1) moving to
the central (sampled) compartment (#2).  However, it is not clear to me from the manual
whether I need to explicitly include F2 in $PK or whether it is inferred..

eg.
TVCL=THETA(1)
TVV=THETA(2)
F2=THETA(3)
V2=TVV/F2
S2=V2/1000

VS

TVCL=THETA(1)
TVV=THETA(2)
F2=THETA(3)
V2=TVV
S2=V2/1000

Also, should the parameter V2 or S2 be used in the differential (or, adjusting
for the 10^3 difference, does it matter?)...

S2=V2/1000 ; Scaling for parent
$DES
DADT(1)=-A(1)*KA
DADT(2)=A(1)*KA-(A(2)*(CL+CLM))/V2  (S2?) ; eq for parent
DADT(3)=(A(2)*CLM-A(3)*CLME)/V2  (S2?)     ; eq for METABOLITE

Thanks.
Paul
(P.S. Nice paper on morphine PK in kids in BJA, Nick.)

Paul Hutson, Pharm.D.
Associate Professor (CHS)
UW School of Pharmacy
777 Highland Avenue
Madison, WI 53705-2222
Tel:    (608) 263-2496
FAX:    (608) 265-5421
Pager: (608) 265-7000, #7856
_______________________________________________________

From Nick Holford
Subject: RE: [NMusers] Fx
Date: 5/24/2004 5:01 PM

Paul, 

F2 is the bioavailability of AMT (specified in the data file)
into CMT 2. It is not the fraction of drug moving from depot (CMT=1)
to central (CMT=2). For your oral dosing data set you can only
meaningfully apply F1 to describe bioavailability from the depot. 

I don't recommend using V2 in the $DES. The DADT means dAMT/time
so stick to thinking in amount not conc for these equations. 

Finally, you need to be aware of identifiability issues. Given
oral drug you cannot estimate F1 (but you can estimate between
subject variability in F1). Similary you cannot estimate V3
(metabolite volume) without assuming all the parent goes to the
metabolite. Usual thing to do is to assume all clearance goes to
metabolite and forget about trying to distinguish CL from CLM or
you can assume and FIX V3 to some plausible value e.g. same as V2.
Then you can distinguish CL from CLM. 

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

_______________________________________________________

From: Bachman, William (MYD) bachmanw@iconus.com
Subject: RE: [NMusers] Fx
Date: Tue, May 25, 2004 7:51 am 

F2 must be explicitly included:

TVCL=THETA(1)
TVV=THETA(2)
F2=THETA(3)
V2=TVV
S2=V2/1000
 
(also, remember that, the volume AND the clearance are both
apparent, if you don't include F2)


With respect to " should the parameter V2 or S2 be used in the
differential (or, adjusting for the 10^3 difference, does it matter?)...":
 
They have different functions,  S2 should be defined in $PK because
it converts the second compartment amounts to concentrations (NONMEM
calculates amounts whereas we generally observe concentrations).  V2 or
S2 can be used in $DES (IF THERE WAS NOT ALSO A UNIT ADJUSTMENT FACTOR)
because they WOULD be equivalent (and are used to calculate the rate
constant needed in the differential equation, CL/V2.)
 
William J. Bachman, Ph.D. 
Manager, Pharmacometrics Research and Development 
GloboMax® 
The Strategic Pharmaceutical Development Division of ICON plc 
7250 Parkway Drive, Suite 430 
Hanover, MD 21076 
410-782-2212 
bachmanw@iconus.com 

_______________________________________________________

From: Ekaterina Gibiansky GibianskyE@guilfordpharm.com  
Subject: RE: [NMusers] Fx
Date:Tue, May 25, 2004 9:28 am

Paul,

F2 is a fraction of dose amount in your data file  that is transfered in compartment
2. That's it, NONMEM does not know anything else about it. By default it is 1. So
you do not need to mention F2 in the code (and yes, volume and clearance are then
apparent values CL/F, V/F) unless you want to estimate F or fix it to some specific
value. However, with oral dosing and linear model you cannot estimate F, it is not
identifiable. So, no need for F2 in the model you have now.
If you were to have a nonlinear model (say, relative F2 is dose dependent), where
you need THETA(s) for F2, CL and V would not be apprarent values, and you should not
divide them by F2. S2 is a scaling parameter that NONMEM uses to convert PREDICTED
amount in the compartment into predicted concentration to then compare it with the
observed value. That predicted amount is computed using the dose that entered the
compartment, i.e. with F2 already figured in. You should not include it in the
scaling again.

In the differential equation block, V2 and S2 are equivalent (as Bill says) only in
the sense that NONMEM will not complain and will spit the estimates just fine (if
the model is linear). But the estimate of CL will be in different (inconsistent)
units than V, if V/1000 is used for estimation. For a nonlinear model (depending on
how it is written) using S2 may lead to problems/errors.

Katya

*--------------------
Ekaterina Gibiansky, PhD
Head, Pharmacometrics & Principal Scientist
Guilford Pharmaceuticals Inc
Phone: (410)-631-6828
Fax:   (410)-631-6828
E-mail: gibianskye@guilfordpharm.com

_______________________________________________________

From: Bachman, William (MYD) bachmanw@iconus.com
Subject: RE: [NMusers] Fx
Date: Tue, May 25, 2004 9:56 am  

Yes!  that's right!  only include F2 if you want to estimate it.  Sometimes
you read things that are not there.  I swore the original said oral and IV
(not parent and metabolite like it really did).  comments about V2 in $DES
are also more accurate than mine which only applied to the case at hand.
Katya, thanks for the clarifications.

William J. Bachman, Ph.D. 
Manager, Pharmacometrics Research and Development 
GloboMax® 
The Strategic Pharmaceutical Development Division of ICON plc 
7250 Parkway Drive, Suite 430 
Hanover, MD 21076 
410-782-2212 
bachmanw@iconus.com 
_______________________________________________________

From: Paul Hutson prhutson@pharmacy.wisc.edu
Subject: RE: [NMusers] Fx
Date: Tue, May 25, 2004 12:47 pm  

Dear Katya, Nick and Bill:
Let us assume another case to test my understanding of your explanation.
Let us assume an orally administered controlled release system...
F1 would represent the bioavailability of the nominal dose of the product 
that was delivered to the lumen of the gut.(yes?)
Let us assume the fraction released is 0.6

A fraction of this released, intraluminal drug is then absorbed into the 
systemic circulation (let's ignore about first pass).
Let us assume that the fraction of intraluminal drug absorbed is 0.7.

I would normally consider F2 to be 0.7, however from your explanations, F2 
would appear to be 0.6 x 0.7 = 0.42.  (The relative amount of the dose 
(AMT) that enters systemic circulation, CMT2). In a sense, the contribution 
of F1 is hidden, which is typically the case in evaluating the relative 
bioavailability of different products, in difference subjects.  However, if 
I could collect the oral dosage delivery device :-(  and determine the 
residual drug for that dose in that patient, I would then know by 
difference the F1.  Hence, my interest in whether F2 is specifically the 
overall fraction of AMT that enters CMT2, or whether it is the fraction of 
the amount in the CMT1 depot compartment (AMT*F1) that enters CMT2.   It 
strikes me than another example of this being relevant is in an animal 
model with simultaneous sampling of the portal and hepatic veins modeling 
the Fx associated with hepatic extraction.

Thanks!
Paul

Paul Hutson, Pharm.D.
Associate Professor (CHS)
UW School of Pharmacy
777 Highland Avenue
Madison, WI 53705-2222
Tel:    (608) 263-2496
FAX:    (608) 265-5421
Pager: (608) 265-7000, #7856

_______________________________________________________

From: Bachman, William (MYD) bachmanw@iconus.com
Subject: RE: [NMusers] Fx
Date: Tue, May 25, 2004 2:34 pm  

F2 is the fraction of "the DOSE that enters into CMT2" that would be
"available" for transfer into a subsequent compartment (not "the fraction of
the DOSE in the CMT1 depot compartment (AMT*F1) that enters CMT2", that's
F1).  Nick's points on identifiability with respect to parent-metabolite
modeling are also well taken.  I don't believe I would try to model F2
personally in this situation unless I could separately administer the
metabolite.  Even then ...

However, I don't quite follow his logic about the use of V2 in $DES (units
of CL/V are inverse time, so you end up with amount per time.)  And it
allows you to parameterize the model in terms of useful parameters.

William J. Bachman, Ph.D. 
Manager, Pharmacometrics Research and Development 
GloboMax® 
The Strategic Pharmaceutical Development Division of ICON plc 
7250 Parkway Drive, Suite 430 
Hanover, MD 21076 
410-782-2212 
bachmanw@iconus.com 
_______________________________________________________

From:  	Nick Holford n.holford@auckland.ac.nz
Subject: RE: [NMusers] Fx
Date:  Wed, 26 May 2004 09:01:00 +1200

Bill, Paul,

To clarify my remarks about using V2 in $DES. I was really referring to
eqn 3 where the whole expression is divided by V2 and thus DADT is the
deriv of conc wrt time. I think is is best to avoid this although with
proper thought and when necessary suitable initialization of the compartment
it can be used to get the correct solution. The eqn 3 below is wrong because
it is inappropriateley scaled by V2 instead of V3 and A(2) needs to be
divided by V2.

DADT(1)=-A(1)*KA
DADT(2)=A(1)*KA-(A(2)*(CL+CLM))/V2  (S2?) ; eq for parent
DADT(3)=(A(2)*CLM-A(3)*CLME)/V2  (S2?)     ; eq for METABOLITE

I recommend this style:

;First compute quantities once for efficiency and clarity:
RATEIN=A(1)*KA
DC2=A(2)/V2
DC3=A(3)V3

;Define DES in units of amount/time and products of conc*clearance
DADT(1)=-RATEIN
DADT(2)=RATEIN - DC2*(CL+CLM) ; eq for parent
DADT(3)=DC2*CLM - DC3*CLME    ; eq for METABOLITE

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

From: Ekaterina Gibiansky GibianskyE@guilfordpharm.com  
Subject: RE: [NMusers] Fx
Date: Tue, May 25, 2004 5:03 pm  

Paul,

I feel, with our sloppy explanations we do not make your life easier.
Nick is right, F1, not F2, is what we are talking about. F2 would only
be defined if you place a dose directly in compartment 2. With dose
placed in compartment 1, only F1 make sense, and it is AMT*F1 what
NONMEM sees in compartment 1. With your example F1=0.42, if your AMT is
the total dose administered, and F1=0.7 if you manage to subtract the
unreleased dose from your AMT in the data file.

As to using V2 in $DES, I do not see any problem there as long as you
keep units consistent for all parameters.

From the two solutions of dealing with metabolite bioavailability,
assuming everything is going into compartment 3 (i.e. forget about CLM)
versus fixing V3=V2 (like you have), I would prefer the former only
because it can not create a false impression of knowledge of fraction
metabolized. 

Katya
*--------------------
Ekaterina Gibiansky, PhD
Head, Pharmacometrics & Principal Scientist
Guilford Pharmaceuticals Inc
Phone: (410)-631-6828
Fax:   (410)-631-6828
E-mail: gibianskye@guilfordpharm.com

_______________________________________________________

From: Xiao, Alan alan_xiao@merck.com
Subject: RE: [NMusers] Fx
Date: Wed, May 26, 2004 8:23 am  

Paul,

I believe F2 can not help you in your case. 

Parameter identifiability (or overparameterization) problem related to
modeling metabolite (or multicompartment) data, when neither excretion data
is available nor separate metabolite administration is conducted, could be
fixed by fixing the metabolic ratio. This metabolic ratio could either be
from prior studies or derived from preclinical data or derived from other
drugs with similar molecular structure and/or similar metabolic pathways.

When your system is linear in PK, you could directly fix the metabolic ratio
through K values, such as K23/(K20+K23). If your system is nonlinear, you
might want to add an excretion compartment and fix the ratio at some value
at time infinity (theoretically). If your metabolism is reversible directly
or indirectly, the equation to express the metabolic ratio will be a little
bit more complicated. By the way, although your metabolic ratio is fixed,
the interindividual variability could still be estimated if it's estimable
from the data. 

Whether you use volume of distribution  or not in your $DES will not change
anything. It's just a matter of reparameterization in the mass balance
differential equations. However, if you fix the volume of distribution to a
certain value, you might want to be careful because it could be misleading.
On the other hand, I doubt you could really solve the overparameterization
problem by fixing the volume of distribution. The reason is simple, control
volume of distribution can not control the metabolic ratio (or relative mass
transport in terms of mass balance).

S3 should be scaled consistently as S2 for the purpose of mass balance. Just
one point, if your metabolite concentration and parent drug concentration
are expressed in weight unit such as ng/mL, you need set up a reference for
both using their molecular weight to calibrate their concentrations.

Hope this helps.

Alan


_______________________________________________________

From: Bachman, William (MYD) bachmanw@iconus.com
Subject: RE: [NMusers] Fx
Date: Wed, May 26, 2004 8:21 am  

Katya et al.,

I think we have beaten one this to death, but, the way I read it, Paul
really does want F2 (or the fraction of metabolite "available"), not F1 (the
fraction of parent "available").  He has just not done the experiments or
collected the appropriate data to get that parameter.  I also can't quite
yet understand why he wants that parameter or if it even makes any sense.
(The metabolite in the central compartment, in my way of thinking, is 100%
"available" or is it that Paul is considering that the conversion from
parent to metabolite occurs in some other location and we want to know the
fraction of the AMT converted in the location that is seen in the central
compartment?) 

This also has confused at least one other person who contacted me off-line.
For the record, if you are doing the typical oral and IV experiment (parent
only) and you want to estimate bioavailability, you will want to model F1.  

Nick is correct that DADT(3)was scaled incorrectly for the volume in Paul's
original code.  Paul would either have to define a new parameter for V3 or
else CLME becomes a parameter with units of inverse time (KME).  If he chose
the former, (identifiability not withstanding):

DADT(3)=(A(2)*CLM))/V2-(A(3)*CLME)/V3

My apologies for my contribution to the confusion.  Mea culpa.
;)
Bill

William J. Bachman, Ph.D. 
Manager, Pharmacometrics Research and Development 
GloboMax® 
The Strategic Pharmaceutical Development Division of ICON plc 
7250 Parkway Drive, Suite 430 
Hanover, MD 21076 
410-782-2212 
bachmanw@iconus.com 
_______________________________________________________