I modeling a compound using pop PK which follows a non linear absorption. For dose dependent Ka, could you please confirm if the following syntax is correct?
The model is not working so I would appreciate it if you help me to troubleshoot the problem.
Is that correct to introduce D50 as a param?
Is that correct to map Dose in Aa and also as covariate or I should separate them?
if you are interested in modeling nonlinear absorption, I would kindly refer you to exercise PK42 from the Gabrielsson book: “Pharmacokinetic and Pharmacodynamic Data Analysis - Concepts and Applications, 5th Edition, by Gabrielsson Johan and Daniel Weiner”
His implementation uses a different approach, e.g. saturating the amount of compound in the absorption compartment:
deriv(Aa = - Vm * Aa / (Km + Aa))
You could define Vm and Km as population parameters, e.g. with random effects included.
I would suggest you apply this approach first and see whether it helps to represent your data.
As Bernd suggested, the G&B book has use of an MM model for this (PK42).
The parameterization you are using (1-Dose/(Dose+D50)) is more often used for modeling bioavailability (F). There are a few problems with your attempt at using this for Ka. The nonlinear function needs to be a structural parameter, not an eta (n). The function you are using is unitless, but Ka has units 1/time. Lastly, you are using 1’s (the default) for initial estimates, and that is often a problem.
Thanks for your recommendations, I will certainly try that. However, I have a problem with the model running.
The problem is same as when I try to define transit compartment in the model (below).
The model starts running but after the first iteration for a few seconds it turns back with terrible fitting. I am a bit in doubt in the model building for nonlinear Ka, so I asked you, but the same trend happened for transit compartment and delay function. Do you think that there is a problem or it is normal?