Disso expression not coupling with absorption

[arindampal1981]

Hi rxode team,

Consider me as a new user of rxode2. I tried simulating an autoinduction model, which was satisfactory, however when I coupled a dissolution model with depot, I failed to simulate the change in PK profile from the 2nd dose onward. It seems, the convolution is working for 1st and not for subsequent doses. Your guidance will be very helpful.

Several questions came up:

1. In the Line 6, instead of dose=50000000, I used "depot" but I found no conc. (C1) after 24 h, couldn't reason out why that's happening? If not wrong "amt" in event record supplies the "depot", so changing the no. in amt will change the depot, but that's working.
2. I have tried without an induction model too, it seems the disso. expression (t^b/(MDT^b+t^b)) is not coupling for addl doses.

Here is the model code:

mod1 <-rxode2({
    alag(depot) = tlag;
  C1 = centr/V1;
  C2 = peri/V2;
  diss = (t^b/(MDT^b+t^b));
  CLind = CLindss*((50000000/Dref))*(1-exp(-0.693*t/T50));
  CL = CL0 + CLind;

  d/dt(depot) =-ka*depot*diss;
  d/dt(centr) =  - CL*C1 - Q*C1 + Q*C2 + ka*depot *diss;
  d/dt(peri)  = Q*C1 - Q*C2;
  });

ini <- c(depot=0,centr=0,peri=0);

theta <- c(ka=2,tlag=0.5, CL0 = 16000, CLindss=18000,
           V1 = 80000, V2 = 164000, Q = 4400, T50=72,
           Dref=50000000, b=2.5,MDT=6);

ev <- et(amountUnits="ng", timeUnits="h") %>%
  et(time=0, amt=50000000, ii=12, addl=4) %>%
  add.sampling(time=0:72);

solve(mod1,ev,theta,ini) %>% plot(C1)

[mattfidler]

Hi @arindampal1981,

I think you need to use dose0(depot) and tad0(depot) to make this
work with arbitrary doses and dosing times.

See:

library(rxode2)
#> rxode2 3.0.4 using 10 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`

mod1 <-rxode2({
  alag(depot) = tlag;
  C1 = centr/V1;
  C2 = peri/V2;
  diss = (t^b/(MDT^b+t^b));
  CLind = CLindss*((dose0(depot)/Dref))*(1-exp(-0.693*tad0(depot)/T50))
  CL = CL0 + CLind;

  d/dt(depot) =-ka*depot*diss;
  d/dt(centr) =  - CL*C1 - Q*C1 + Q*C2 + ka*depot *diss;
  d/dt(peri)  = Q*C1 - Q*C2;
});
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’

ini <- c(depot=0,centr=0,peri=0);

theta <- c(ka=2,tlag=0.5, CL0 = 16000, CLindss=18000,
           V1 = 80000, V2 = 164000, Q = 4400, T50=72,
           Dref=50000000, b=2.5,MDT=6);

ev <- et(amountUnits="ng", timeUnits="h") %>%
  et(time=0, amt=50000000, ii=12, addl=4) %>%
  add.sampling(time=0:72);

solve(mod1,ev,theta,ini) %>% plot(C1)

ev <- et(amountUnits="ng", timeUnits="h") %>%
  et(time=0, amt=50000000, ii=12, addl=4, evid=7) %>%
  add.sampling(time=0:72)

^{Created on 2025-02-21 with reprex v2.1.1}

These are discussed in the rxode2 language reference

[arindampal1981]

Thanks Matt,
Unfortunately, I could not understand the function dose0(depot), neither do I find it in the rxode2 language reference.

I thought of changing the dose and tad, but how do I change it since the system throws error if I change tad(2) implying time after 2nd dose?
Can you kindly explain the difference between:
tad() or tad(x) Time after dose (tad()) or time after dose for a compartment tad(cmt); no dose=NA -> selecting this yields no profile
tad0() or tad0(x) Time after dose (tad0()) or time after dose for a compartment tad0(cmt); no dose=0 -> selecting this yields the PK profile.

Moreover, when I add evid=7 in the events with
CLind = CLindss*((depot/Dref))(1-exp(-0.693tad0(depot)/T50)); -> this yields no profile.

If we are using evid=7, what compartment we are considering as transit compartment?
My naivety! I tried to workaround podo(depot) with tad() and tlast() but it doesn’t actually put the dose in the compartment.

Even with adding all these the 2nd dose does not read the dissolution input and still yields the immediate-release input as was the original case (without disso).

Regards
Arindam

[mattfidler]

dose0(depot)

This gives the last dose administered to the depot compartment. Before a dose this has a 0 value.

For dose(depot) on the other hand is NA before a dose is given

You are right both dose() and dose0() are missing from the function reference.

[mattfidler]

I thought of changing the dose and tad, but how do I change it since the system throws error if I change tad(2) implying time after 2nd dose?

tad(depot) gives time after dose in the depot compartment and tad() gives the time after dose to any compartment. There is no function to give time after 2nd dose.

[mattfidler]

Moreover, when I add evid=7

Evid is the "phantom" dose, which means you actually do not dose the ODE system at all, but the tad and other such parameters are updated as if you did update the system.

You would need to create your own dosing inside the ode itself. This is what is done in the transit compartment example here:

https://nlmixr2.github.io/rxode2/articles/rxode2-transit-compartments.html

Which matches the paper where the model was cited.

[mattfidler]

Even with adding all these the 2nd dose does not read the dissolution input and still yields the immediate-release input as was the original case (without disso).

When I look at the ODEs you have, they are not quite the same as what is included in the transit compartment model. To me, reading the model I don't see any reason why there should be anything but an immediate response followed by a slower response.

[mattfidler]

You could do the classic thing:

• Split the dose into two compartments depot1 and depot2
• Model a bioavailbility between each
• Have the depot1 represent the immediate absorption
• Have the depot2 represent the transit compartment absorption

Then when they both feed into the central compartment, you should see the immediate and long term release.

[arindampal1981]

Hi Matt,
I resolved the problem.
I found tad0( ) working to get the profiles I wished for.

But then what is the difference between tad( ) {tad( ) doesn't work} and tad0( )?
evid doesn't seem to play a role here and even it is, it got to be evid=4 (reset+dose).

[mattfidler]

tad() gives the time after dose. When doses have not been administered, this is NA.

tad0(0) also gives the time after dose. Unlike tad() when doses have not been administered this is 0.

When using in the ODE solver, if the tad() is part of the integration tries to use NA or NaN and therefore dosen't work.

However, with tad0() the integration works since it is zero instead of NA or NaN.

However, you cannot distinguish between when there is a zero time after dose vs no dose is adminstered.

You could also use tad() but you would have to use something like ifelse(is.na(tad()), 0, tad()), but it is a bit more verbose.

[arindampal1981]

Thanks Matt! There are insightful learnings.