Fx

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: 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: 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: 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 _______________________________________________________

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