Modeling of Blood flow data

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? Thanks in advance for your suggestions. 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: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:"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! =============================================== $SUBROUTINES ADVAN8 TOL=6 $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 DADT(1)=-KA*A(1) DADT(2)= KA*A(1)-CL/V*A(2) =============================================== Best regards, Sam Liao, Ph.D. PharMax Research 270 Kerry Lane, Blue Bell, PA 19422 phone: 215-6541151 efax: 1-720-2946783

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 *******