PK model with transit compartments for absorption

1

I am new to Pumas and modeling - killer combo! I have seen some recent posts on LinkedIn about you, so I thought I could ask for your advice. Not sure if this is the right way to approach this forum. I guess other experts can weigh in as well. I wanted to check if you can confirm is the following model syntax looks right. My model has a one compartment disposition, a slow absorption. Tlag was deemed to inappropriate so I was trying a transit compartment absorption model.

My code begins here

ka_transit2_1cmt = @model begin  
    @param begin
      tvmtt          ∈ RealDomain(lower=5, upper=100.0)
      tvcl              ∈ RealDomain(lower=0.001)
      tvvc             ∈ RealDomain(lower=0.001)
      σ²_add       ∈ RealDomain(lower=0.001)
    end
    
    @pre begin
      CL            = tvcl 
      Vc            = tvvc 
      ktr           = 1/tvmtt
    end
  
    @dynamics begin
      Depot'         = -ktr * Depot_slow 
      Transit1'     = ktr * (Depot_slow - Transit1)
      Transit2'     = ktr * (Transit1 - Transit2)
      Central'      = ktr * Transit2 - CL/Vc * Central 
    end
  
    @derived begin
      cp            = @. (Central/Vc)
      conc       ~ @. Normal(cp, sqrt(σ²_add))
    end
end

My code ends here

2

hi Bob,

Welcome to the community and we are glad to have you on board!

You can take a look at some of the absorption model examples here Absorption models

Just looking at the code (on my phone), it seems correct what you have coded up there.

Best,
Vijay

3

Dr Vijay - Thank you very much. May be you or some other expert can help me with understanding the statistical implications of my parameterization - ktr vs mtt. Would there be any preference in adding a between-subject variability on one over the other? Typically kinetic models are specified from first principles in rates and rate-constants; and not in terms of time (except for tlag). Would the community recommend specifying the BSV on ktr; and derive mtt from the reciprocal individual estimate of ktr? Or directly specify the variance on mtt? Hope I am not asking a very silly question. I do not want to take undue advantage of you; so if you think I should write to another expert, please suggest.
Bob

4

Feel free to ask away. This is an open inclusive community for everyone to learn and contribute :slight_smile:

Not sure if there is a preference one way or the other. MTT seems like a parameter that has a better interpretation than ktr in my opinion. I would add BSV there. However, these are just a play of numerical arrangements at the end of the day. We should use something that helps us articulate our results better.

5

I absolutely agree with @vijay. One thing you could do is try it both ways (BSV on ktr and BSV on MTT) and see if one of the 2 models seems better (e.g. lower OFV), or the distribution of the random effects looks more normal or one or the other parameter (maybe look at QQ-plots). Just a suggestion.