From: Ekaterina Gibiansky <*EGibiansky*>

Date: Sun, 27 Sep 2009 01:09:02 -0400

Sam,

You can get PRED without the third compartment. Just define the variable that

you need in $ERROR:

$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)

$ERROR (ONLY OBSERVATIONS)

K11 = A(1)/V1-A(2)-KD

C1 = 0.5*(K11+ SQRT(K11*K11+4*KD*A(1)/V1))

Then, use C1 instead of F everywhere where you used F, and output C1 in the

$TABLE.

Regards,

Katya

-------------------------

Ekaterina Gibiansky, Ph.D.

CEO&CSO, QuantPharm LLC

Web: www.quantpharm.com

Email: EGibiansky at quantpharm.com

Tel: (301)-717-7032

Sam Liao wrote:

*> 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 Sun Sep 27 2009 - 01:09:02 EDT

Date: Sun, 27 Sep 2009 01:09:02 -0400

Sam,

You can get PRED without the third compartment. Just define the variable that

you need in $ERROR:

$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)

$ERROR (ONLY OBSERVATIONS)

K11 = A(1)/V1-A(2)-KD

C1 = 0.5*(K11+ SQRT(K11*K11+4*KD*A(1)/V1))

Then, use C1 instead of F everywhere where you used F, and output C1 in the

$TABLE.

Regards,

Katya

-------------------------

Ekaterina Gibiansky, Ph.D.

CEO&CSO, QuantPharm LLC

Web: www.quantpharm.com

Email: EGibiansky at quantpharm.com

Tel: (301)-717-7032

Sam Liao wrote:

Received on Sun Sep 27 2009 - 01:09:02 EDT