# Re: Duration of Absorption Time From Depot (Gut) as Covariate

From: Paul Hutson <prhutson>
Date: Tue, 15 Dec 2009 16:52:36 -0600
Leonid & Jeroen:
Thank you for your suggestions.  I incorporated Jeroen's suggestion of using MTIME below, with a slight modification (KA = TVKA *(1-MPAST(1))), since I want to turn KA off, not on, at TOFF.

I try below to use Leonid's suggestion of a Weibull distribution to describe the dissolution of the oral product, rather than using multiple AMT & RATE inputs corresponding to the dissolution data for the product.  My fit deteriorates both by OBj Func and VPC.  Does the code below appear to be appropriate for introducing the oral drug in A(1) using a Weibull distribution?
Thanks very much
Paul

\$MODEL COMP=(DEPOT, DEFDOSE) COMP=(CENTRAL, DEFOBS)
\$PK
callfl=-2
CL=THETA(1)*EXP(ETA(1)); CLEARANCE
V2=THETA(2)*EXP(ETA(2)); V2
TOFF=THETA(3)*EXP(ETA(3)); DURATION OF PRESENCE IN ABSORPTION SEGMENT
K=CL/V2
AUC=AMT/CL
S2=V2/1000

;CLOSE ABSORPTION AFTER SOME TIME TOFF
TVKA=THETA(4)*EXP(ETA(4))
MTIME(1)=TOFF
KA=TVKA*(1.001-MPAST(1)); MPAST(1) = O UNTIL MTIME(1)(TOFF) IS REACHED, THEN IS 1

;DRUG APPEARANCE
PAR1=THETA(5); SCALING CONSTANT FOR TIME
GAMA1=THETA(6); SLOPE FUNCTION FOR WEIBULL
WB1=1-EXP(-((TIME/PAR1)**GAMA1))
RAT1 = AMT*WB1

\$DES

\$ERROR
IPRE = F
W1=F
DEL   = 0
IF(IPRE.LT.0.001) DEL = 1
IRES  = DV-IPRE;  NEGATIVE TREND IS OVERESTIMATING IPRED WRT DV
IWRE = IRES/(W1+DEL)
Y=F*(1+ERR(1))+ERR(2)

\$THETA  (0.1,1.23, 50);      CL
\$THETA  (0.10,97.8,1000);    V2
\$THETA  (0.1,86.5,1000);      TOFF
\$THETA  (0.0001, .7, 4); KA
\$THETA  176.1 FIXED; PAR1
\$THETA    1.033 FIXED ; SLOPE

\$OMEGA   0.5; CL
\$OMEGA   0.3; V2
\$OMEGA   0.6; TOFF
\$OMEGA   0.3; ka

\$SIGMA  .5;         SIG1
\$SIGMA  .1;         SIG2

\$ESTIMATION METH=1 INT SIGDIGITS=3 MAXEVAL=9999 PRINT=10 NOABORT

Elassaiss - Schaap, J. (Jeroen) wrote:
```Leonid, Paul,

Alternatively one may use the MTIME function in NM6 so the algebraic
solutions in eg. ADVAN2 are still applicable:

\$PK
....
MTIME(1)=TOFF
KA=TVKA*MPAST(1)

Best regards,
Jeroen

Jeroen Elassaiss-Schaap, PhD
Modeling & Simulation Expert
Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3)
Early Clinical Research and Experimental Medicine
Schering-Plough Research Institute
T: +31 41266 9320

-----Original Message-----
From: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel:    (301) 767 5566

Paul Hutson wrote:
```
```I have been asked to look at data that suggest a dependence of AUC and
```
```
```
```Cmax upon transit time in the gut.  The elimination rates for the one
compartment model are quite similar, suggesting that the variability
lies in bioavailability.  Preliminary data suggest that the absorption
```
```
```
```of this drug from the gut is transporter-limited, and may be dependent
```
```
```
```upon the duration of time that the drug is exposed to a specific
portion of the duodenum or jejunum.  Drug is observed at the earliest
sampling time, so I am not including a Tlag at this point.

I have in vitro dissolution data for this (hopefully) extended release
```
```
```
```formulation, which I am introducing to the gut compartment for the
human subject PK data as events of AMT and RATE corresponding to each
measured point in the dissolution curve.  Thus I am fixing it as a
time-dependent inputs over the 12 hour period following the single
dose and during the plasma sampling.  Because of the non-instantaneous
```
```
```
```input function, I understand I cannot use Savik's TRANSIT model
```
```(2007).
```
```I have tried the code below to try to turn off Ka after some time
TOFF, the point at which the drug is estimated to have moved past the
section of absorption.  There is no change in the gradient for TOFF,
and the fit is not improved over a simple 1 compartment absorption
```
```model (ADVAN2).
```
```I cannot turn off compartment 1 (-1) in my INPUT, since I do not know
when to turn it off (I am trying to determine this in the model).
There is extensive first pass of the compound - I do not know of any
auto-inhibition of metabolism.  I suppose that I could try to trip F1
to null at some TOFF, but tripping Ka to Null seems more physiologic.

Can anyone suggest a snippet of code that might close Ka based upon a
covariate THETA corresponding to the time required to move past the
intestinal segment of absorption?
Thanks very much.
Paul

; 1 COMPARTMENT MODEL, NO LAG, NO LIMIT TO ABSORPTION PERIOD

\$PK
TVKA=THETA(1); ABSORPTION RATE FROM GUT CL=THETA(2)*EXP(ETA(1));
CLEARANCE V2=THETA(3)*EXP(ETA(2)); V2 TOFF=THETA(4)*EXP(ETA(3));
DURATION OF PRESENCE IN ABSORPTION SEGMENT
K=CL/V2
DOSE=5; MG TABLET
AUC=DOSE/CL
S2=V2/1000

FLAG=1
IF(TIME.GE.TOFF) FLAG=0.0001
KA=TVKA*FLAG

\$ERROR
IPRE = F
W1=F
DEL   = 0
IF(IPRE.LT.0.001) DEL = 1
IRES  = DV-IPRE;  NEGATIVE TREND IS OVERESTIMATING IPRED WRT DV
IWRE = IRES/(W1+DEL)
Y=F*(1+ERR(1))+ERR(2)

\$THETA  (0.1,1.23, 50);      KAGUT
\$THETA  (0.10,97.8,1000);      CL
\$THETA  (0.1,86.5,1000);      V2
\$THETA  (0.001, 1, 24); DUR

;\$OMEGA   0.3; KA
\$OMEGA   0.5; CL
\$OMEGA   0.3; V2
\$OMEGA   0.6; TOFF
--

Paul R. Hutson, Pharm.D.

Associate Professor

UW School of Pharmacy

777 Highland Avenue

Tel  608.263.2496

Fax 608.265.5421

Pager 608.265.7000, p7856

```
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--
Paul R

Paul R. Hutson, Pharm.D.

Associate Professor

UW School of Pharmacy

777 Highland Avenue