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: [email protected]
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
