From: "Jim Jiang" 
Subject: [NMusers] PD lag time in $DES
Date: Wed, November 17, 2004 7:02 pm 

Dear All,

I am using NONMEM to estimate PKPD parameters simultaneously. But the drug 
I am studying has indirect PD response. I would like to know how to 
estimate PD lag-time while using differential equation.

Many Thanks

Jim

Dr. Jim Xuemin Jiang
N415, Faculty of Pharmacy, Building A15,
The University of Sydney, NSW, 2006
Telephone: 61 2 90365025
Fax: 61 2 93514391
Email: xuemin@pharm.usyd.edu.au
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From: "mathangi" mathangi@msn.com
Subject: RE: [NMusers] PD lag time in $DES
Date:  Thu, November 18, 2004 10:02 am 

Dr.Jiang,

If I understand your question correctly, I am assuming you want to model the
delay in your pharmacodynamic response using an indirect response model.
If it is so, below is an example and part of the code for an iv bolus - one
compartment model and inhibitory indirect response model .

$SUBROUTINE ADVAN6  TRANS1 TOL=3

$MODEL
   COMP = CENTRAL
   COMP = EFFECT

$PK
   CL    = CLI                                           ; INDIVIDUAL
CLEARANCE IN L/HR
   V     = VI                                              ; INDIVIDUAL
VOLUME OF DISTRIBUTION IN L
   KIN   = THETA(1)*EXP(ETA(1))       ; BASAL ZERO ORDER PRODUCTION RATE OF
BIOMARKER
   KOUT  = THETA(2)*EXP(ETA(2))    ; BASAL FIRST ORDER RATE CONSTANT FOR
ELIMINATION
                                                                ; OF
BIOMARKER
   IC50  = THETA(3)*EXP(ETA(3))        ;CONCENTRATION OF DRUG AT 50% OF
MAXIMUM OF INHIBITION
   S1    = V
   S2    = 1
   F2    = KIN/KOUT                               ;BASELINE RESPONSE; R0 =
KIN/KOUT


$DES
   DADT(1) = -CL/V*A(1)              ;PLASMA COMPARTMENT
   INH     = A(1)/(IC50+A(1))         ;INHIBITORY FUNCTION
   DADT(2) = KIN*(1-INH)-KOUT*A(2)   ; INDIRECT RESPONSE MODEL I


And accordingly, the data file can be arranged by including AMT=1 for CMT=2
at
TIME=0 to initialise the response compartment.

Please let me know, if this is what you wanted.

Thanks
Mathangi

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From: Perez Ruixo, Juan Jose [PRDBE]  JPEREZRU@PRDBE.jnj.com
Subject: RE: [NMusers] PD lag time in $DES
Date: Thursday, 18 November 2004 11:33

Dear Jim, 

You may want to have a look to a recent PAGE presentation,
"NONMEM Implementation of Cell Lifespan Models for Hematological
Drug Effects".

http://www.page-meeting.org/page/page2004/Kimko.pdf 

Juan Jose Perez Ruixo, PhD. 
Advanced PK/PD Modelling & Simulation, 
Johnson & Johnson Pharmaceutical Research & Development, 
Beerse (Belgium). 
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From: mark.e.sale@gsk.com 
Subject: RE: [NMusers] PD lag time in $DES
Date: Thu, November 18, 2004 10:46 am 

Jim, 

This isn't easy.  In simulation packages, a "pipe" is created
by a long series of concatenated compartments (in ACSL is was 50),
as in: 

DADT(1) = -K*A(1) 
DADT(2) = K*A(1)-K*A(2) 
DADT(3) = K*A(2)-K*A(3) 
. 
. 
. 
DADT(50) = K*A(49)-K*A(50) 

50 compartments will give a very nice "square wave" delay effect, but
is numerically very difficult for estimation, even though there is only
one parameter, which describes the delay.  I've used a smaller number of
compartments (2 or 3), but that doesn't really give a lag/delay, more of
smudging sort of effect. 

In $PRED, you can just do 
LAG = THETA() 
the use T-LAG 

But, there is not, as far as I know, an (easy) way to store what the value was at (T-LAG) using $DES. 

Mark Sale M.D.
Global Director, Research Modeling and Simulation
GlaxoSmithKline
919-483-1808
Mobile 
919-522-6668
_______________________________________________________

From:  "Nick Holford" n.holford@auckland.ac.nz
Subject: RE: [NMusers] PD lag time in $DES
Date:  Thu, November 25, 2004 4:20 am 

Mark,

mark.e.sale@gsk.com wrote:
> 
> But, there is not, as far as I know, an (easy) way to store what the value was at
(T-LAG) using $DES.
> 

The value of a response at T-LAG can be obtained by creating a model with a
duplicate set of compartments. One set of compartments is used to predict the
response at T and the other at T-LAG. You need to replicate the dosing history for
each set of compartments. e.g. for the simple case of a one compartment disposition
with first order absorption:

ID TIME AMT CMT DV
1   0   100 1   .
1   0   100 3   .
...

$MODEL
   COMP (GUT)
   COMP (CP)
   COMP (GUTLAG)
   COMP (CPLAG)

$PK
  ALAG3=THETA(lag)
  ...

$DES
  DGUT=A(1)
  DCP=A(2) ; the value of the non-lagged conc
  RATEIN=KA*GUT
  DADT(1)=-RATEIN
  DADT(2)=RATEIN - DCP*CL

  DGUTL=A(3)
  DCPLAG=A(4)  ; the value of the lagged conc
  RATELG=KA*GUTL
  DADT(3)=-RATELG
  DADT(4)=RATELG - DCPLAG*CL

This DE model can be easily extended to describe a turnover model (aka indirect
effect) to create a lagged effect. This code gives you simultaneous access to both
the current conc/effect and the lagged conc/effect in $DES. The only tricky part of
this model is the need to keep track of any time varying covariates that you might
be using so that you use the correct time associated value of the covariate to
influence the current or lagged compartment parameters.

Nick
--
Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x86730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/
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