Model estimate of dose

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

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

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 _______________________________________________________