From: Johan.Rosenborg@astrazeneca.com 
Subject: [NMusers] Model estimate of dose 
Date:  Mon, November 29, 2004 5:41 am 

Dear NMusers,

I have a dataset with observations both at site of absorption and in plasma.
The system must be initialized with a bolus dose in the depot compartment at
time zero to establish the initial condition. I would like to use the data
at the absorption site to estimate the actual dose given;  A(depot
compartment)=THETA(X) at time zero - does anyone know how to do this?

/ Johan

> Johan Rosenborg
> AstraZeneca R&D Lund
> Experimental Medicine, S-221 87 Lund, Sweden
> Tel: +46 46 33 65 99 Fax: +46 46 33 71 91
> E-mail: johan.rosenborg@astrazeneca.com
_______________________________________________________

From: "Sam Liao"  
Subject: RE: [NMusers] Model estimate of dose
Date: Mon, November 29, 2004 10:27 am 

Hi Johan:

One alternative to solve this is by estimate of F in your PK model

Sam
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From:  "Nick Holford" n.holford@auckland.ac.nz
Subject: RE: [NMusers] Model estimate of dose
Date: Mon, November 29, 2004 1:53 pm 

Johan,

I have some difficulty understanding what you are trying to do. 

The situation is exactly comparable to giving a parenteral bolus dose into the
central compartment and measuring drug in the central compartment and the peripheral
compartment (with elimination from the peripheral compartment). In this situation
one would not typically try to estimate bioavailability. It would be assumed to be
one.

The dose is usually treated as a known quantity in pharmacokinetics. If the amount
reaching the systemic circulation is less than the dose then it is usual to estimate
the extent of bioavailability. This can be done easily by estimating F1, the
bioavailability fraction for a dose entering compartment 1 (assuming this is where
you have put the dose specified by the AMT data item).

In your case if you have some other data e.g. concentrations after a parenteral dose
to the central compartment then under the usual assumption that clearance does not
change then you can estimate F1 by fitting the two sets of data simultaneously.
Unlike the usual oral plus IV dose experiment, because you have absorption
compatment concs you will be able to estimate the apparent volume of the absorption
compartment in addition to other parameters such as KA.

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/

_______________________________________________________

From: Johan.Rosenborg@astrazeneca.com
Subject: RE: [NMusers] Model estimate of dose
Date: Tue, December 7, 2004 9:39 am 

Dear Anthe, Sam and Nick,

Thank you for your concern in this matter and your suggestion to moderate
the measured dose via F (Sorry for my late feedback!). A further
clarification to my question may be appropriate. A radiactive substance was
administered via the lungs. Radiactivity was measured at 2-min intervals
with a gamma camera on several occasions up to a few hours post-dose; the
primary estimate of the amount deposited in the airways - the dose - was
based on the first measurement. What I would like to do is to fit a model to
the gamma camera measurements as a means to estimate the amount at time zero
by back extrapolation, so to say. If the radioactive tracer is deposited in
CMT=n, it should be possible to estimate the amount - the dose - at time
zero as follows:

A(n) = THETA(X)*EXP(ETA(Y)) x AMT 

(a unit dose is assigned to the deposition compartment in the data file,
i.e. AMT=1 in the record where CMT=n, TIME=0 and EVID=4)

Any suggestion on how to proceed with this idea?

/ Johan 

> Johan Rosenborg
> AstraZeneca R&D Lund
> Experimental Medicine, S-221 87 Lund, Sweden
> Tel: +46 46 33 65 99 Fax: +46 46 33 71 91
> E-mail: johan.rosenborg@astrazeneca.com

_______________________________________________________

From: "Bachman, William (MYD)" bachmanw@iconus.com
Subject: RE: [NMusers] Model estimate of dose
Date:  Tue, December 7, 2004 10:57 am 

Maybe I'm missed something in the previous discussions but I still think
Nick's explanation still holds.  Put your unit dose in the data file and
estimate Fn.

e.g. if you assume, dose goes to CMT=1

$INPUT C ID TIME DV AMT CMT
$SUBROUTINE ADVAN2 TRANS2 
$PK
  TVCL=THETA(1)
  CL=TVCL*EXP(ETA(1))
  TVV=THETA(2)
  V=TVV*EXP(ETA(2))
  TVKA=THETA(3)
  KA=TVKA*EXP(ETA(3))
  S2=V
TVF1=THETA(4)
F1=TVF1*EXP(ETA(4))

F1 is then the estimated dose.  (appropriate constraints of parameter
estimates may be needed, but, there is nothing that inherently dicates F1
can't be greater than 1)

Bill
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From: "Nick Holford" n.holford@auckland.ac.nz
Subject: RE: [NMusers] Model estimate of dose
Date: Tue, December 7, 2004 3:13 pm

Johan,

With the additional information you provide then it seems the problem is quite
simple. But it does depend on what assumptions you make about what the gamma camera
is measuring. If the gamma camera is calibrated in such a way that it measures the
total AMOUNT of radioactivity in the same units as the actually administered dose
(e.g. Curies or Bequerels or whatever ...) then the problem can be solved using
$PRED:

$PRED
   K=THETA(k)*EXP(ETAk)
   DOSE=THETA(dose)*EXP(ETAdose)
   Y=DOSE*EXP(-K*TIME) + EPS

If the gamma camera is not calibrated in units that involve the actual dose then
there is no way to compute the actual dose from the gamma camera data.

Nick

_______________________________________________________

From: Johan.Rosenborg@astrazeneca.com 
Subject: RE: [NMusers] Model estimate of dose
Date: Wed, December 8, 2004 6:07 am 

Nick,

Thank you for your prompt reply! The gamma camera is calibrated in such a
way that it measures the total AMOUNT of radioactivity in the same units as
the actually administered dose, corrected for decay of the tracer during the
course of the experiment. The string you suggest seems to be exactly what I
need - if you have time, some additional crucial technical follow-up
questions: 

1) The data file: shall I enter a unit dummy-dose under AMT at time zero in
conjunction with administration via the lungs (CMT=3)?
2) The model file: how do I assign the dose based on the estimate of "DOSE"
in your string and incorporate it in an ADVAN8-based model as specified
below?

.
.
.
.
$SUBROUTINES ADVAN8 TOL=4
$MODEL
 COMP=(DEFOBS1) ; plasma
 COMP=(PERIPH1) ; peripheral cmt
 COMP=(DEFOBS2) ; lung
$PK
;---------------------------------------------------------------------------
-
;SYSTEMIC PK
;---------------------------------------------------------------------------
-
 CL=THETA(1)*EXP(ETA(1))
 K12=THETA(2)*EXP(ETA(2))
 K21=THETA(3)
 S1 =THETA(4)*EXP(ETA(3))
 K10=CL/S1
 K31=THETA(5)*EXP(ETA(4)))
;---------------------------------------------------------------------------
-
$DES
  DADT(1)=K31*A(3)-(K12+K10)*A(1)+K21*A(2)
  DADT(2)=K12*A(1)-K21*A(2)
  DADT(3)=-K31*A(3)
;---------------------------------------------------------------------------
-
$ERROR  
.
.
.
.

/ Johan

> Johan Rosenborg
> AstraZeneca R&D Lund
> Experimental Medicine, S-221 87 Lund, Sweden
> Tel: +46 46 33 65 99 Fax: +46 46 33 71 91
> E-mail: johan.rosenborg@astrazeneca.com
_______________________________________________________

From: Johan.Rosenborg@astrazeneca.com
Subject: RE: [NMusers] Model estimate of dose
Date:  	Thu, 9 Dec 2004 9:28 am

Bill,

Thank you for your contribution on this issue, too! Indeed, the use of an
unconstrained value of F is a way to moderate the measured dose value.
However, I would like to balance two processes using rate constants,
absorption into the systemic circulation and extravascular elimination from
the airways, and at the same time try to avoid the constraint of a fixed
dose value since I have data on the amount of tracer in the lungs. In that
case isn't it better not to use the bioavailability factor?

/ Johan


>> Johan Rosenborg
>> AstraZeneca R&D Lund
>> Experimental Medicine, S-221 87 Lund, Sweden
>> Tel: +46 46 33 65 99 Fax: +46 46 33 71 91
>> E-mail: johan.rosenborg@astrazeneca.com

_______________________________________________________