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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