Re: arterio-venous modeling

From: Peter Wright <p.m.c.wright@ncl.ac.uk> Subject: Re: arterio-venous modeling Date: 30 Sep 1997 08:49:31 -0400 Rik and other NMusers >The TCI means that I cannot do ordinary PK modeling because of the >continuously varying input rate and I hoped to be able to model using >ordinary linear interpolation, specifying slope and intercept of the >interpolating segments. This works very well for an ordinary effect >compartment situation with hysteresis. However, I have venous >concentrations and (especially for propofol) proteresis which I assume >is due to arterio-venous differences. > >The problem is (I assume) that for hysteresis the measured concentrations >drive the hypothetical effect compartment concentrations that are related >to the effect while in this case the arterial concentrations that drive the >venous concentrations are related to the effect. > >Do you agree about the assumption of arterio-venous differences and >does anyone have suggestions for modeling this specific situation? > I have faced these problems and dealt with them in the following ways. After an experiment conducted using target controlled infusions I created data files with multiple dosing events reconstructed from the output of Stanpump. This is rather crude and run times were slow as might be expected. However it worked. I believe there is a utility on the Stanford PK/PD server which can create a list of dose events from a Stanpump output in a relatively easy way (though I have not myself seen it). A fairly simple way to model arterio-venous differences in a quasi compartmental fashion is to create an effect type compartment (which follows arterial concentration via a rate constant). I call this the gradient compartment. Then model venous concentrations as being contributed to by arterial concentrations and concentrations in the gradient compartment such that the relative proportions add up to 1. This models venous concentrations as initially less then arterial then later greater than arterial, but with AUC identical. There are two parameters in the model. In the situation of peripheral elimination (e.g. nitroglygerin,atracurium) an additional parameter will be required to adjust the " total proportion" down from 1. In the situation desribed above this will only work if PK and PD are modeled simultaneously because you have data only from the arterial side. The code to achieve this model when data are available for from both artery and vein is as follows. Arterial concentrations are compartment 1. The "gradient" compartment is 4. Since you have concentrations only from the venous side you will be able to simplify this somewhat. $ERROR Y1 = F * (1+ERR(1)) Cp = A(1)/V1 Cg = A(4)/V4 PROPG = THETA(8) PROPA = (1 - THETA(8)) Cv = (Cg * PROPG) + (Cp * PROPA) Y2 = Cv * (1+ERR(2)) Q1 = 0 Q2 = 0 IF (CMT.EQ.1) Q1 = 1 IF (CMT.EQ.4) Q2 = 1 Y = Q1*Y1 + Q2*Y2 If there are any mistakes in this please let me know. Peter Wright University of Newcastle upon Tyne