Leonid:
Thank you very much for your clear and helpful answer.
May I suggest that the Weibull distribution function might be more
clearly written:
B= IVIVC*PAR1
WDER=(GAMA1/B)*((T/B)**(GAMA1-1))*EXP(-(T/B)**GAMA1)
Be well.
Paul
Leonid Gibiansky wrote:
Paul,
No, this is not a correct way to introduce drug to depot. The idea was:
Step 1. Fit Weibull or something similar to the dissolution data:
time t = 0, 1, 2,...
fraction absorbed: f = 0, 0.1, 0.5 ..
Use model:
f(t)=1-exp(t/to)^gamma
Using observed dissolution data, finds t0 and gamma that would provide
good fit of the dissolution data
If needed, add extra parameter
f(t)=A*(1-exp(t/to)^gamma)
Step 2: Assume some IVIVC model, for example:
in-vivo dissolution is the same as in vitro:
FF=1-exp(t/to)^gamma
or
in-vivo dissolution is faster/slower then in vitro:
FF=1-exp(t/(THETA(IVIVC)*t0))^gamma
where THETA is estimated
or some other model
Step 3:
put drug to depot, but it should be in the $DES block, and it should be
a derivative of FF, not FF itself:
$DES
B=THETA(IVIVC)*t0
WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM)
DADT(1)=F1*DOSE*WDER-KA*A(1)
Here t0 and GAMM are fixed (from in-vitro data fit) while THETA(IVIVC)
corresponds to IVIVC and need to be estimated from the data.
If you would like to stop dissolution at some time TMAX, you can use:
$DES
B=THETA(IVIVC)*t0
WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM)
IF(T.GT.TMAX) WDER=0
DADT(1)=F1*DOSE*WDER-KA*A(1)
If you would like to stop absorption at some time TMAX, you can use:
$DES
B=THETA()*t0
WDER=GAMM/(B**GAMM))*T**(GAMM-1)*EXP(-(T/B)**GAMM)
IF(T.GT.TMAX) KA=0
DADT(1)=F1*DOSE*WDER-KA*A(1)
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566
Paul Hutson wrote:
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
$SUBROUTINES ADVAN6 TOL=3
$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
DADT(1) = RAT1 - A(1)*KA
DADT(2) = A(1)*KA - A(2)*CL/V2
$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: [email protected]
[mailto:[email protected]]
On Behalf Of Leonid Gibiansky
Sent: Friday, 11 December, 2009 6:55
To: [email protected]
Cc: [email protected]
Subject: Re: [NMusers] Duration of Absorption Time From Depot (Gut) as
Covariate
Paul,
You need to rewrite the system using differential equations rather than
ADVAN2 and then use
$DES
FLAG=1
IF(T.GE.TOFF) FLAG=0.0001
KA=TVKA*FLAG
In the PK block, this should not work because your TIME is discrete
while nonmem is trying small variation of TOFF parameter to compute the
gradient (which is indeed zero if you do it in the PK block)
On a different note, you are assuming 1 to 1 IVIVC (in-vitro
dissolution
= in vivo dissolution). It is rarely the case. You may try to describe
your dissolution profile by some function (Weibull is very flexible)
and
then use parametric _expression_ for IVIVC (for example, time scaling) to
insert the dose into the depot compartment (as input rate)
Thanks
Leonid
--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: 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
$SUBROUTINES ADVAN2
; 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
Madison WI 53705-2222
Tel 608.263.2496
Fax 608.265.5421
Pager 608.265.7000, p7856
This message and any attachments are solely for the intended recipient.
If you are not the intended recipient, disclosure, copying, use or
distribution of the information included in this message is prohibited
--- Please immediately and permanently delete.
--
Paul R. Hutson, Pharm.D.
Associate Professor
UW School of Pharmacy
777 Highland Avenue
Madison WI 53705-2222
Tel 608.263.2496
Fax 608.265.5421
Pager 608.265.7000, p7856
--
Paul R.
Hutson, Pharm.D.
Associate
Professor
UW School
of Pharmacy
777
Highland Avenue
Madison
WI 53705-2222
Tel 608.263.2496
Fax
608.265.5421
Pager
608.265.7000, p7856
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