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: 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 >>>> >>>> >>>> > > >