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