I think we are actually along the same line overall. What we got into below are some technical trivials, although very fundamental. For the model used in the poster, it is simplified, trying to show what's the problem and how it could be handled rather than intending to mimic all possibilities in reality, as you can understand. Alan
-----Original Message----- From: Shi, Jun [mailto:[EMAIL PROTECTED] Sent: Wednesday, February 14, 2007 12:19 PM To: Xiao, Alan; [EMAIL PROTECTED]; Nmusers (E-mail); [EMAIL PROTECTED] Cc: Shi, Jun 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 -----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] 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] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
