I haven't read the article, so I don't know how the TAD parameter is used. I'm assuming you need to know TAD during the simulation. If you only need it for some sort of post-simulation analysis, I have some ideas for other simpler options.
Your question reminds me of something I implemented in this insulin demo. Look at the first event in this model, and you should be able to do something similar to determine TAD. But I do want to say that this is a little tedious. If this is something that comes up often, I'd like to think of features we could add to make the work easier.
In my case, I also needed to set a parameter in response to a dose. I did that by adding a helper event and a helper species (that is the target of the dose). The basic idea is that the helper species is only there to trigger the event whenever a dose occurs. So the species concentration starts out as zero, and the event detects whenever the species concentration changes (due to a dose). The even then transfers the drug to the "real" target and updates the parameter. One annoying limitation today is that events aren't triggered at time=0, so you have to do a little extra work if you have a dose at time 0. I worked around this by getting the dose to trigger at some small time greater than 0 (effectively making the dose get applied at a time > 0). So to summarize, here's what your event might look like:
- Trigger: time > timeSmall & Dose > 0*Dose
- Event Function 1 (store TAD): paramTAD = time
- Event Function 2 (apply dose): Target = Target + Dose
- Event Function 3 (reset helper species): Dose = 0*Dose
