From: Sam Liao <*sliao*>

Date: Sat, 26 Sep 2009 23:29:20 -0400

Dear Katya:

It works, thanks for your advice. The reason I need the equilibrium

compartment is to get PRED estimated.

Best regards,

Sam

*> Sam,
*

*> You do not need an equilibrium compartment, you can solve the equation
*

*> explicitly:
*

*>
*

*> $DES
*

*> K1 = A(1)/V1-A(2)-KD
*

*> C = 0.5*(K1+ SQRT(K1*K1+4*KD*A(1)/V1))
*

*> DADT(1)= -K10*C*V1 - KINT*C*V1*A(2)/(KD+C)
*

*> DADT(2)= KSYN - KDEG*A(2) -(KINT - KDEG)*C*A(2)/(KD+C)
*

*>
*

*>
*

*> If you would like to use the equilibrium compartment just for the sake
*

*> of test, E(3) should denote the equation that needs to be solved as
*

*> E(3)=0. Thus, something like this:
*

*>
*

*> $AESINITIAL
*

*> INIT=1
*

*> A(3)=0.001
*

*> $AES
*

*> K1 = A(1)/V1-A(2)-KD
*

*> E(3) = A(3)-0.5*(K1+ SQRT(K1*K1+4*KD*A(1)/V1))
*

*> $DES
*

*> DADT(1)= -K10*A(3)*V1 - KINT*A(3)*V1*A(2)/(KD+A(3))
*

*> DADT(2)= KSYN - KDEG*A(2) -(KINT - KDEG)*A(3)*A(2)/(KD+A(3))
*

*>
*

*> Regards,
*

*> Katya
*

*>
*

*> -------------------------
*

*> Ekaterina Gibiansky, Ph.D.
*

*> CEO&CSO, QuantPharm LLC
*

*> Web: www.quantpharm.com
*

*> Email: EGibiansky at quantpharm.com
*

*> Tel: (301)-717-7032
*

*>
*

*> Sam wrote:
*

*>> Dear nmusers:
*

*>> I would like to continued this thread started by Robert. I tried the
*

*>> $AES method suggested by Katya in my PK model where the first two
*

*>> compartments are defined in $DES while the third compartment is
*

*>> defined as an equilibrium algebraic equation in $AES. I got error
*

*>> msg shown below. Could anyone tell what is missing in my code?
*

*>>
*

*>> "LUDATN IS UNABLE TO INVERT JACOBIAN (DA) FOR AES
*

*>> VARIABLES
*

*>>
*

*>> ERROR OCURRED WHILE ATTEMPTING TO OBTAIN INITIAL VALUES FOR DY/DT"
*

*>> Sam Liao
*

*>> ===== sim02.lst =====================================================
*

*>> $PROB A TMDD MODEL
*

*>> $INPUT C ID TIME DV AMT RATE DOSE EVID CMT SS
*

*>> $DATA sim01.csv IGNORE=C
*

*>> $SUBROUTINES ADVAN9 TOL=3
*

*>> $MODEL
*

*>> COMP=(CENTRAL)
*

*>> COMP=(RTOT)
*

*>> COMP=(A3 EQUILIBRIUM)
*

*>> $PK
*

*>> CL = THETA(1)* EXP(ETA(1))
*

*>> V1 = THETA(2)* EXP(ETA(2))
*

*>>
*

*>> K10= CL/V1
*

*>>
*

*>> KSYN= THETA(3)* EXP(ETA(3))
*

*>> KDEG= THETA(4)* EXP(ETA(4))
*

*>> KINT= THETA(5)* EXP(ETA(5))
*

*>> KD = THETA(6)* EXP(ETA(6))
*

*>>
*

*>> BL= KSYN/KDEG
*

*>> A_0(2)=BL ;BOUNDARY CONDITION FOR EQUATION 3
*

*>> $AESINITIAL
*

*>> INIT=1
*

*>> A(3)=0.001
*

*>> $AES
*

*>> K1 = A(1)/V1-A(2)-KD
*

*>> E(3) = 0.5*(K1+ SQRT(K1*K1+4*KD*A(1)/V1))
*

*>> $DES
*

*>> DADT(1)= -K10*A(3)*V1 - KINT*A(3)*V1*A(2)/(KD+A(3))
*

*>> DADT(2)= KSYN - KDEG*A(2) -(KINT - KDEG)*A(3)*A(2)/(KD+A(3))
*

*>>
*

*>> .............
*

*>>> Robert,
*

*>>>
*

*>>> You can do it using ADVAN9 with NEQUILIBRIUM option in $MODEL, and
*

*>>> $AESINITIAL and $AES blocks. E.g. (where A(13) is what is F in your
*

*>>> example) :
*

*>>>
*

*>>> $SUBROUTINES ADVAN9 TOL=4
*

*>>> $MODEL NEQUILIBRIUM=1
*

*>>> COMP(COMP1)
*

*>>> ....
*

*>>> COMP(COMP13)
*

*>>>
*

*>>> $PK
*

*>>> ...
*

*>>>
*

*>>> $AESINITIAL
*

*>>> INIT = 0; 0=APPROXIMATE, 1=EXACT
*

*>>> A(13)=0.001
*

*>>> $AES
*

*>>> E(13)=A(9)-A(13)-A(13)*A(10)/(KSS+A(13))-A(13)*A(12)/(KSS2+A(13))
*

*>>>
*

*>>> $DES
*

*>>> ...
*

*>>>
*

*>>> $ERROR
*

*>>> Y = A(13)+EPS(1)
*

*>>>
*

*>>> Regards,
*

*>>> Katya
*

*>>>
*

*>>> --------------------------
*

*>>> Ekaterina Gibiansky, Ph.D.
*

*>>> CEO&CSO, QuantPharm LLC
*

*>>> Web: www.quantpharm.com
*

*>>> Email: EGibiansky *

*>>> Tel: (301)-717-7032
*

*>>>
*

*>>>
*

*>>> Robert Kalicki wrote:
*

*>>>> Dear NMusers,
*

*>>>>
*

*>>>> Most of the models are pre-defined (ADVANx), expressed as a system
*

*>>>> of differential equations or provided in the form of an explicit
*

*>>>> mathematical equation (PRED).
*

*>>>>
*

*>>>> Is it possible to deal with nonlinear inexplicit equations like y =
*

*>>>> f(x,y) where both differential equations and explicit solution
*

*>>>> equation are not known or not obvious.
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>> Concretely, using PRED, one would find F on the both sides:
*

*>>>>
*

*>>>> F = f(X) + g(F)
*

*>>>>
*

*>>>> Y = F+EPS(1)
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>> Many thanks in advance
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>> Best regards,
*

*>>>>
*

*>>>> Robert
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>>
*

*>>>> ___________________________________________
*

*>>>> Robert M. Kalicki, MD
*

*>>>>
*

*>>>> Postdoctoral Fellow
*

*>>>>
*

*>>>> Department of Nephrology and Hypertension
*

*>>>>
*

*>>>> Inselspital
*

*>>>>
*

*>>>> University of Bern
*

*>>>>
*

*>>>> Switzerland
*

*>>>>
*

*>>>>
*

*>>>>
*

*>
*

*>
*

*>
*

Received on Sat Sep 26 2009 - 23:29:20 EDT

Date: Sat, 26 Sep 2009 23:29:20 -0400

Dear Katya:

It works, thanks for your advice. The reason I need the equilibrium

compartment is to get PRED estimated.

Best regards,

Sam

Received on Sat Sep 26 2009 - 23:29:20 EDT