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RE: Identifiablity of parent / metabolite PK with interconversion

From: Dong-Seok Yim <yimds>
Date: Wed, 4 Feb 2009 11:44:00 +0900

Thank you for your comprehensive comment.
Once I raised this, I wish to ask the question in a different way.

Suppose we measured concentrations of CMT2 (parent) and CMT3 (metabolite).
In a situation where K20 comparable to K30 > K23 >> K32 near to 0, can
NONMEM give reliable estimates of K20 and K23 ?
As long as the sum of rate constants going out of CMT2 (K23 + K20) remain
unchanged, any pair of estimates of K23 and K20 may be given by NONMEM, I am
concerned. Then, K20 may be underestimated near to 0 with K23 and K30
overestimated accordingly; some flip-flop like situation.
Is fixing V3 identical to that of V2 good enough to prevent this kind of
erroneous NONMEM results ?


-----Original Message-----
From: Leonid Gibiansky [mailto:LGibiansky
Sent: Monday, February 02, 2009 11:46 PM
To: yimds
Cc: nmusers
Subject: Re: [NMusers] Identifiablity of parent / metabolite PK with

Hi Dong-Seok Yim,
If equilibration rates (K23, K32) are much larger than the elimination
rates, then parent and metabolite will be at equilibrium (K23 A2 = K23
A3), and you will not be able to estimate K23, K32 separately, only K23
to K32 ratio. If this is true, you can see it on the plot of parent vs.
metabolite concentrations (by subject): the plot should show strong

If you have enough data in the range where the parent and drug
concentrations are not proportional, you should be able to estimate all
the parameters.

One visual test that may help is to plot scatter-plot matrix of random
effects (ETAs vs. ETAs) and look for strong correlations. Also, you may
check correlation of parameter estimates.
should give you the eigenvalues of the correlation matrix. If the ratio
of the largest to the smallest is above 1000, parameters may not be
trusted. Correlation matrix itself may help to identify correlated
parameters, so look on the correlation between K23 and K32, in particular.

A helpful way to visualize parameter correlations is to do a bootstrap,
and then look at the scatter plot matrix of the parameters vs.
parameters plots. For example, you may be interested in K32 vs K23 (for
all bootstrap samples) plot. If the run time is short, use 1000 samples.
If it is long, 100 should give you a general idea of what is going on.

Also, the code that you show us should not compile since VS and VA are
not defined. I guess, it is just a typo, but you are missing VS=V2,
VA=V3 somewhere.


Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
e-mail: LGibiansky at
tel: (301) 767 5566

Dong-Seok Yim wrote:
> Hi, colleagues,
> I am currently trying to model plasma concentrations of parent and
> metabolite with interconversion. (nmtran code is in the bottom).
> The data came from a densely sampled PK study in healthy subjects. I put
> the metabolite Vd identical to the parent Vd as recommended. Then, I
> managed to obtain some estimates that make the individual plots look nice.
> However, I doubt whether we can get reliable estimates for K23 or K32
> and (hence, even K20 and K30 ) without urine concentration data and
> without any priori knowledge on the metabolic ratios etc.
> I suspect that the estimates of K23, K32, K20, K30 and V2 are all
> interconnected as the Ka and Ke are in the flip-flop phenomenon - Am I
> wrong ?
> Searching for some references for the metabolite PK modeling using
> NONMEM, I found an article reporting detailed pop PK parameters of
> CPT-11 and its metaolites in patients (Rujia Xie, Ron H.J. Mathijssen,
> Alex Sparreboom, Jaap Verweij, and Mats O. Karlsson. Journal of
> Clinical Oncology, Vol 20, No 15 (August 1), 2002: pp 3293-3301)
> In the paper, interconversion rate constants of interconverted
> forms (CPT-11 lactone and CPT-11 carboxylate / SN-38 lactone and SN-38
> carboxylate ) were tabulated without using any urine data. -
> If any of the authors comment on the method to obtain reliable values
> using plasma concenentrations only, I would appreciate.
> Any comments from nmusers other than above authors are also much welcomed
> Thanks !
> Dong-Seok Yim
> ----------------------------------------
> $PK
> KA = THETA(1)*EXP(ETA(1))
> K20 = THETA(2)*EXP(ETA(2))
> V2 = THETA(3)*EXP(ETA(3)) ; V2 = parent Vd
> K30 = THETA(4)*EXP(ETA(4))
> V3 = V2 ; V3 = metabolite Vd
> K23 = THETA(5)*EXP(ETA(5))
> K32 = THETA(6)*EXP(ETA(6))
> CL20 = K20*VS
> CL30 = K30*VA
> S2=VS
> S3=VA
> $DES
> DADT(1)=-KA*A(1)
> DADT(2)=KA*A(1)-K23*A(2)+K32*A(3)-K20*A(2)
> DADT(3)=K23*A(2)-K32*A(3)-K30*A(3)
> Dong-Seok Yim M.D., Ph.D.
> Associate Professor
> Department of Pharmacology
> College of Medicine
> The Catholic University of Korea
> 505 Banpo-Dong, Seocho-Gu, Seoul 137-701, Korea
> Tel +82-2-590-1201
> Fax +82-2-536-2485
> yimds

Received on Tue Feb 03 2009 - 21:44:00 EST

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