Combined exponential + differential equations in $DES for post-SS concentrations
From: "Kazimierz H.Kozlowski" khkoz@czd.waw.pl
Subject: [NMusers] Combined exponential + differential equations in $DES for post-SS concentrations
Date: Wed, June 16, 2004 2:53 pm
Dear NONMEM users,
I have some problem in post-infusion exponential equations and $DES.
It is single subject, steady-state R1 defined in $PK and lasting at TIME=0,
2-compartment model. In the case of post-steady-state infusion
stoping, first
distribution phase could be much shallowed in comparison to single i.v.
dose.
When using combined exponential and differential equation I would like to
compare this 2 method as well as accelerete computation time in the next
population PK/PD analysis. Has any person has experienced with such
problem?
#1. Concerning central compartment I obtained identical values for A(1)
computed
by $DES and exponential equation computed by $ERROR, however, only
similar values when computed by exponential equation computed by
$DES.
#2. Concerning peripherial compartment they were not acceptable differences
(errous equation?) between A(2) from $DES and exponential equations.
#3. It is possible resolve 2-compartment model in the case shallowed ALPHA
phase when data are from post-infusion only?
sincerely
Kazimierz H. Kozlowski
Laboratory of Pharmacokinetics
The Children's Memorial Health Institute
04-736 Warsaw, Poland
E-mail: khkoz@czd.waw.pl
$PK
.
.
IF (EVID.EQ.1) THEN
.
.
PR1=RR*.......
ENDIF
K21=ALPHA*BETA/K10
K12=ALPHA+BETA-K21-K10
CC1A=(K21-ALPHA)/(BETA-ALPHA) ;C1' (E1=K21)
CC1B=(K21-BETA)/(ALPHA-BETA) ;C2'
CC2A=(K12+K10-ALPHA)/(BETA-ALPHA) ;T1' (E2=K12+K10)
CC2B=(K12+K10-BETA)/(ALPHA-BETA) ;T2'
AUCC=CC1A/ALPHA+CC1B/BETA ;
FC1=(CC1A/ALPHA)/AUCC ;f1 for Cp equation
(exponential)
FC2=(CC1B/BETA)/AUCC ;f2 for Cp equation
AUCT=CC2A/ALPHA+CC2B/BETA ;
FT1=(CC2A/ALPHA)/AUCT ;f1 for Ct equation
(also 2-exponential)
FT2=(CC2B/BETA)/AUCT ;f2 for Ct equation
R1=PR1* ..... ;
R1 computed using RR from $DATA
IF (TIME.GT.0) R1=0
$DES
C1=PR1*FC1*EXP(-ALPHA*T)+PR1*FC2*EXP(-BETA*T) ; post-SS infusion end
Cp (correct)
C2=PR1*FT1*EXP(-ALPHA*T)+PR1*FT2*EXP(-BETA*T) ; post- SS infusion
end Ct (errous?)
DADT(1)=K12*(A(2)-A(1))-K10*A(1) ; Cp
DADT(2)=K21*(A(1)-A(2)) ; Ct
DADT(3)=............ ; Ce
effect compartment model
$ERROR
A1=A(1) ; S1=1
A2=A(2)
A3=A(3)
CPP1=PR1*FC1*EXP(-ALPHA*TIME)+PR1*FC2*EXP(-BETA*TIME)
CPP2=PR1*FT1*EXP(-ALPHA*TIME)+PR1*FT2*EXP(-BETA*TIME)
.
.
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