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I have an interesting problem and hope that there may be a relatively
simple solution. I'm attempting to model drug input (zero order for 6
-12 hr) into a peripheral compartment and have concentration data for
that compartment as well as for plasma.
Assuming linear PK, I tried the following model in WinNonlin.
Unfortunately, it doesn't converge. I was able to model the peripheral
compartment data alone, but have problems after adding the second
compartment. Any thoughts or help would be greatly appreciated.
Best regards,
Pat
MODEL
remark ******************************************************
remark Developer:
remark Model Date: 10-01-2009
remark Model Version: 1.0
remark ******************************************************
remark
remark - define model-specific commands
COMMANDS
NCON 1
NFUNCTIONS 2
NDERIVATIVES 2
NPARAMETERS 6
PNAMES 'VT', 'V1', 'Tabs', 'KO1', 'K12', 'K20'
END
remark - define temporary variables
TEMPORARY
T = X
DOSE = CON(1)
K0 = DOSE/Tabs
END
remark - define differential equations starting values
START
Z(1) = 0
Z(2) = 0
END
remark - define differential equations
DIFFERENTIAL
IF T <= Tabs THEN
K01 = K0
ENDIF
IF T > Tabs THEN
K01 = 0
ENDIF
DZ(1)=K01-VT*K12*Z(1)
DZ(2)=K12*Z(1)*VT-K20*Z(2)*V1
END
remark - define algebraic functions
FUNCTION 1
F= Z(1)
END
FUNCTION 2
F= Z(2)
END
remark - define any secondary parameters
remark - end of model
EOM
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Patrick
Looking at the code, i see that K21 is missing. Also, K01 and Tabs are
entered as a parameters. For controlling the rate of input, Tabs may
coded as constant and K01 is calculated by the program. Also, can you
share the error message that you are get when you try to fit both
central and peripheral compartment data simultaneously.
Thanks
Sridhar
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The following message was posted to: PharmPK
Pat,
There are a lot of small errors in the code. Try this code, it should
work:
> NCON 1
> NFUNCTIONS 2
> NDERIVATIVES 2
> NPARAMETERS 5
> PNAMES 'VT', 'V1', 'Tabs', 'K12', 'K20'
> END
> remark - define temporary variables
> TEMPORARY
> T = X
> DOSE = CON(1)
> K0 = DOSE/Tabs
> END
> remark - define differential equations starting values
> START
> Z(1) = 0
> Z(2) = 0
> END
> remark - define differential equations
> DIFFERENTIAL
> IF T <= Tabs THEN
> K01 = K0
> ENDIF
> IF T > Tabs THEN
> K01 = 0
> ENDIF
> DZ(1)=K01-K12*Z(1)
> DZ(2)=K12*Z(1)-K20*Z(2)
> END
> remark - define algebraic functions
> FUNCTION 1
> F= Z(1)/VT
> END
> FUNCTION 2
> F= Z(2)/V1
> END
--
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
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The following message was posted to: PharmPK
Dear Pat,
It looks like your derive equations are inconsistent. Are the units
on Z supposed to be mass or concentration. Since you state that you
have concentration data, the units on your functions (F1, F2) need to
be concentrations. So your model implies that Z is concentration as
well. But the derive equations:
DZ(1)=K01-VT*K12*Z(1)
DZ(2)=K12*Z(1)*VT-K20*Z(2)*V1
....take Z and multiply Volume, giving a mass. K01 is Dose/Tabs, so it
is a mass as well. So, Z is treated as a mass in your derivs and as a
concentration elsewhere.
May I suggest changing your equations slightly:
DZ(1)=K01-VK12*Z(1)
DZ(2)=K12*Z(1)-K20*Z(2)
And
F1 = Z(1)/VT
F2 = Z(2)/V1
Let me know how that works for you, or if I've misunderstood your
problem.
Jason Chittenden, MS
Director, Product Quality
Pharsight - A Certara(tm) Company
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The following message was posted to: PharmPK
Pat,
First, you want to make sure you have tried different minimization
algorithms, e.g., Nelder-Mead vs. Marquardt-Levenberg, while paying
attention to the time required for the failure in convergence. If it
takes
while, you may have the appropriate structural model, however your
initial
estimates may be causing the program to get lost, and you should try
expanding or narrowing your limits with "deliberately off" initial
estimates. If the run terminates quickly, the model may be too
constrained
for the simultaneous fit, and after testing for various weighting
schemes,
there may be a mass balance problem. You can try adding a parallel
first
order loss (K10) of drug from your peripheral compartment which will
allow
the central compartment data some room to be fit with the peripheral
compartment, and/or alternatively, the dose may be taken for granted,
and
you should be adding a bioavailability parameter. In the end, its
relatively difficult to diagnose over the boards due to the assortment
of
factors involved, for example, whether you are using pooled data from
several subjects or not, can also contribute to difficulties in
getting the
fitting parameters.
Good luck,
-Shawn
Shawn D. Spencer, Ph.D., R.Ph.
Assistant Professor of Biopharmaceutics
Florida A&M College of Pharmacy
Tallahassee, FL 32307
shawn.spencer.-a-.famu.edu
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