Re: inexplicit equations in PRED

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