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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
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: 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
>> 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
>
Received on Tue Dec 15 2009 - 19:14:21 EST

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