From: Johan.Rosenborg@astrazeneca.com 
Subject: [NMusers] Concentration dependent volume of distribution 
Date: Monday, 18 March 2002 17:47 

All, 

I would like to model concentration or possibly amount dependent volume of 
distribution, using ADVAN8. Does anyone have a suggestion on how to deal 
with this problem? I have tried to introduce VD, VMAX and A50 as shown 
below, but it did not work. 

/ Johan 

$PROBLEM 
$INPUT ID AMT SS II RATE TIME EVID CMT DV FLAG STUD 
$DATA  dat.prn IGNORE=# 
$SUBROUTINES  ADVAN8 TOL=4 
$MODEL 
  COMP=(CENTRAL) 
  COMP=(PERIPHL) 
  COMP=(PERIPHC) 
$PK 
  K10 =THETA(1)*(1+ETA(1)) 
  K12 =THETA(2) 
  K21 =THETA(3) 
  K13 =THETA(4)*(1+ETA(2)) 
  K31 =THETA(5) 
;------------ Volume------------------------- 
  VD  =THETA(6)*(1+ETA(3)) 
  VMAX=THETA(9)*(1+ETA(5)) 
  A50 =THETA(10)*(1+ETA(6)) 
;-------------------------------------------- 
  F0   =THETA(7)*(1+ETA(4)) 
$DES 
  S1  =VD+VMAX*A(1)/(A50+A(1)) 
  C1  =A(1)/S1 
 DADT(1)=K41*A(4)-(K10+K12+K13)*C1*S1+K21*A(2)+K31*A(3) 
 DADT(2)=K12*C1*S1-K21*A(2) 
 DADT(3)=K13*C1*S1-K31*A(3) 
$ERROR 
  IF (EVID.EQ.0.AND.F.GT.0) THEN 
  IPRED=LOG(F) 
  ELSE 
  IPRED=LOG(F+0.001) 
  ENDIF 
  IRES=DV-IPRED 
  IWRES=IRES 
  X6=0 
  X7=0 
  IF(CMT.EQ.1)X6=1 
  IF(CMT.EQ.(-5))X7=1 
  Y=IPRED+X6*ERR(1)+X7*ERR(2) 


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From: Piotrovskij, Vladimir [PRDBE] [mailto:VPIOTROV@PRDBE.jnj.com]
Subject: RE: [NMusers] Concentration dependent volume of distribution
Date: Tuesday, March 19, 2002 5:04 AM

Johan, 
I don't think making V explicitly dependent on conc of amount is a right way to follow.
If V is concentration-dependent it indicates nonlinear distribution caused by, eg, saturable
protein binding. You'd better explore nonlinear binding in the central or peripheral compartment,
or, alternatively, a saturable transport to (one of the) peripheral compartments, etc.

Best regards, 
Vladimir


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From: "Wang, Bing" 
Subject: FW: [NMusers] Concentration dependent volume of distribution
Date: Tue, 19 Mar 2002 09:45:44 -0800


John,
 
This is a loop - the calculation of Conc depends on Vc while in your model
Vc is Conc-dependent. It will confuse NONMEM...
 
Most likely the observed conc-dependent Vc is caused by the nonlinear protein
binding at (extremely?) low dose levels. A saturable binding compartment (e.g., COMP 2)
may be introduced:
 
K12=KON*(RMAX-A(2))                             ; RMAX is the maximum number of binding sites. 
K21=KOFF
.... then use K12 and K21 in your DES.
 
It is possible that you have to fix KOFF=1 to avoid overparameterization...
 
Regards.
 
Bing Wang 
 



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From: "Bachman, William" 
Subject: RE: [NMusers] Concentration dependent volume of distribution
Date: Tue, 19 Mar 2002 11:08:23 -0500

Johan,
 
Aside from Vladimir's biological objections (which have merits), from a strictly modeling viewpoint,
you seem to have an undefined fourth compartment (as evidenced by DADT(1)=K41*A(4) ... )
unless I'm missing something here.  What is this term supposed to represent?
 
Bill
 


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