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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=#
\$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
\$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)

*******

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,

*******

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

*******

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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