```From:"Nandy, Partha"
Subject:[NMusers] Modeling of Blood flow data
Date:Tue, February 19, 2002 4:50 pm

Hi,

I am trying to model plasma concentration-time data for a topically
administered drug.   From the data it is apparent that the rate of
absorption and hence the systemic exposure to the drug is dependent on the
blood flow at the site of administration.  The PK data was modeled using the
following assumptions: 1 compartment linear kinetics with lag time.  The
blood flow in this case is measured by laser Doppler and the data are
available at each sampling time point.

The data set looks as follows:

ID        Time (hrs)        DV (ng/ml)        Flow

1        0                0                2.52
1        0.5                0                3.58
1        1                0.5                4.58
1        2                1.85                2.38

etc...

Can someone help me with suggestions of incorporating the blood-flow
information into the PK model?

Warm Regards

Partha Nandy Ph.D.

PURDUE PHARMA L.P.
One Stamford Forum
Stamford, CT 06901-3431

Tel:  (203) 588-8320
FAX: (203) 588-6328
E-mail: Partha.Nandy@pharma.com

*******

From: Nick Holford
Subject: Re: [NMusers] Modeling of Blood flow data
Date: Tue, February 19, 2002 5:50 pm

Partha,

Its hard to tell from the fragment of data if there is much information in blood
flow about the absorption process (When does the conc peak?). However, the data
looks rather sparse and so I would guess you can only hope to learn a little bit.

I would start out using a simple empirical model in ADVAN2 eg.

KA = POPKA * EXP(KFLOW*FLOW)

This will increase absorption rate as FLOW increases when KFLOW>0. This model has
the useful property that it cannot predict negative values of KA and if KFLOW is
"small" then it approximates the linear function:

KA = POPKA * (1 + SLOPE*FLOW)

This linear form is usually easier to explain to your pharmacometrically challenged
clinical colleagues.

If you can detect an improvement in the fit then you could make the model more
sophisticated by using a DE defined model and having KA vary continuously with FLOW
by using a linear interpolation between the observed flow values during the times
between the observations.

There are more physiologically based representations of drug absorption across the
skin involving various skin compartments, permeability factors and blood flow but I
doubt if your data can identify the various components involved.

I note you say that "the rate of absorption and hence the systemic exposure to the
drug is dependent on the blood flow at the site of administration". If you are
thinking of extent of absorption when you say systemic exposure I would point out
that the model I have proposed above would not be expected to change extent.
Changing the rate of absorption does not change extent of absorption unless you have
a more complex model with rate dependent extraction of drug before it reaches the
systemic circulation.

Nick

Nick Holford, Divn Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556
http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

*******

From:"Sam Liao"
Subject:RE: [NMusers] Modeling of Blood flow data
Date: Tue, February 19, 2002 6:15 pm

Hi Partha:

I am not sure how to tell that the rate of absorption is blood flow
dependent.
I expect the rate-limiting step is the skin-permeation rather than the blood
flow.

But, if you want to incorporate the blood flow (BFLW) in your model, I would
suggest to use ADVAN8 and define your model in differntial equations as
follow, good luck!
===============================================
\$MODEL
NCOMP=2
COMP=(ABS)
COMP=(CENTRAL)

\$PK

TVKA = THETA1(1)*BFLW/(THETA(2)*BFLW)
CL   = THETA(3)*EXP(ETA(1))
V    = THETA(4)*EXP(ETA(2))
KA   = TVKA*EXP(ETA(3))

S2=V

\$DES

===============================================

Best regards,

Sam Liao, Ph.D.
PharMax Research
270 Kerry Lane,
Blue Bell, PA 19422
phone: 215-6541151
efax: 1-720-2946783

*******

From:LSheiner
Subject:Re: [NMusers] Modeling of Blood flow data
Date:Tue, February 19, 2002 6:04 pm

Depends on what you mean by "exposure" - rate of absorption does not
affect AUC, for example ...

> The PK data was modeled using the
> following assumptions: 1 compartment linear kinetics with lag time.  The
> blood flow in this case is measured by laser Doppler and the data are
> available at each sampling time point.
>
> The data set looks as follows:
>
> ID      Time (hrs)      DV (ng/ml)      Flow
>
> 1       0               0               2.52
> 1       0.5             0               3.58
> 1       1               0.5             4.58
> 1       2               1.85            2.38
>
> etc...
>
> Can someone help me with suggestions of incorporating the blood-flow
> information into the PK model?

Seems like a natural for 1st order absorption, as transfer rate (Ka) out
of the
depot and into the systemic circulation, if it is not diffusion-limited,
should be linearly proportional to blood flow to/from the site of
absorption.  So

KA = THETA(1) + THETA(2)*FLOW

seems a good place to start. (The FLOW at any given time should be
the average flow during the time since the last flow was recorded and
the time
that this one was recorded; i.e., strictly speaking not the same time
as the event record on which it is recorded.  If your data require
a better approximation to the continuously changing absorption rate,
then you'll have to use differential equations and
interpolate the flow in \$DES)

With diffusion limitation, an Emax-type model for flow's effect
on KA would be natural.

Lag time can be added if need be.

_/  _/  _/_/ _/_/_/ _/_/_/ Professor Lewis B Sheiner, MD
_/  _/ _/    _/_    _/_/    mail:    Box 0626, UCSF, SF, CA,94143
_/  _/ _/        _/ _/       courier: Rm C255,  UCSF, SF, CA,94122
_/_/   _/_/ _/_/_/ _/        415-476-1965 (v), 415-476-2796 (fax)

*******

From:"Bachman, William"
Subject:RE: [NMusers] Modeling of Blood flow data
Date:Wed, February 20, 2002 10:21 am

Sam's model for TVKA reduces to TVKA=THETA(1)/THETA(2)  {BFLW in numerator &
denominator cancel out and no need to introduce another parameter).  I
suspect he's just trying to incorporate BFLW as a covariate:

TVKA = THETA1(1)*BFLW
KA   = TVKA*EXP(ETA(1))

Also, there is no reason to use ADVAN8, you can do this with any of the
library models.

Bill

*******

From:"Williams, Gene M"
Subject:RE: [NMusers] Modeling of Blood flow data
Date:Wed, February 20, 2002 11:03 am

I also noticed the apparent algebraic error. Perhaps Sam meant for the "*"
in the denominator to be a "+"?:

TVKA = THETA1(1)*BFLW/(THETA(2)+ BFLW)

Hopefully Sam will clarify.

*******

From:"Sam Liao"
Subject:RE: [NMusers] Modeling of Blood flow data
Date:Wed, February 20, 2002 12:07 pm

Hi Gene:

Yes,it should be a "+" sign.  It is a Emax model.  When blood flow increase,
skin-penetration become a rate-limiting step.

Best regards,

Sam Liao, Ph.D.
PharMax Research
270 Kerry Lane,
Blue Bell, PA 19422
phone: 215-6541151
efax: 1-720-2946783

*******

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