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

From: Leonid Gibiansky <LGibiansky>
Date: Tue, 15 Dec 2009 19:14:21 -0500

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
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)

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

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

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
>
> \$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: owner-nmusers
>> On Behalf Of Leonid Gibiansky
>> Sent: Friday, 11 December, 2009 6:55
>> To: prhutson
>> Cc: NMUSERS
>> Subject: Re: [NMusers] Duration of Absorption Time From Depot (Gut) as
>> Covariate
>>
>> Paul,
>> You need to rewrite the system using differential equations rather than
>>
>> \$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
>>>
>>
>>> 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. Hutson, Pharm.D.
>
> Associate Professor
>
> UW School of Pharmacy
>
> 777 Highland Avenue
>