indirect PK-PD model and lag-time

From: alison@c255.ucsf.EDU (ABoeckmann) Subject: indirect PK-PD model and lag-time Date: 24 Sep 1998 14:13:17 -0400 PREDPP is not able to model intercompartmental lag. It can only model absorption lag, i.e., it can delay the dose from entering the system. In Guide VIII, there is an example " PK PD SEQUENTIAL 1 EXAMPLE ". In this example, the PK data is fit first, then the PK parameters are held fixed and the PD data is fit. We say in this example: If, moreover, an absorption lag (ALAG1) parameter is modeled in $PK with parameters estimated from the PD data only, then this introduces a lag in the dose - Ce relationship. Since this lag was not present in the dose - Cp relationship, it may be interpreted as a lag in the Cp - Ce relationship. In Sylvie's control stream, ALAG1 could be used in the second run, when the PD data is fit, and would provide the desired lag. However, the $DES block does not look right: $DES DADT(1)=-(K12+K)*A(1) ; PK model 1st cpt DADT(2)= K12*A(1)-K21*A(2) ; PK model 2nd cpt EFF=C50/(C50+A(1)/S1) DADT(3)=KIN*EFF-KOUT*A(3) ; PTR model I would expect the first DE to include the K21 term, returning drug from periperal to central: DADT(1)=-(K12+K)*A(1)+K21*A(2) ; PK model 1st cpt Lewis Sheiner also suggests the following approach, which allows simultaneous fit of PK and PD data: If you want a lag time, it would be on the compartment into which you put the dose, presumably CENTRAL. This will simply cause all the PK and PD events to be delayed relative to the time of the dose. If you prefer a 'real' lag; that is, more equilibration time between PK (compt 1) and effect, you could use a catenary chain leading to the 'effect' site. That is, interpose say 2 delay (DLY1, DLY2) compartments between CENTRAL and EFFECT, with the transfer rate from CENTRAL to DLY1 equal to that from DLY1 to DLY2. Don't bother with an eta on this rate. You'll have to choose the number of delay compartments arbitrarily since it's much harder to try to estimate how many of these you need. This is equivalent to having an 'Erlang' disposition function for the delay... see papers by Jim Matis in JPB several years ago. By the way, why do you have an eta on the input rate constant for the bioeffector compartment, rather than on C50; and why no eta on the exit rate for the bioeffector? Alison Boeckmann