Multiple-dose kinetics for two depots

[arindampal1981]

Hi,
I'm struggling with a DDI study code in rxode.
I have provided two separate depot() for the perpetrator and the afflicted drug.
The code run well for single dose, however, could not find a way out for multiple-dose simulation.

I have laid out initial state conditions viz.,

ini <- c(depot1=20000000, depot2=10000000,
centrA=0, periA=0, centrB=0, centrC=0); # A=parent, B=metabolite, C=perpetrator drug

It worked well for single dose:
solve(mod_A, et(amt=0) %>%
et(0,48,length.out=49), theta, ini) %>% plot(A,B,C)

For multiple doses, event for amount only takes dose for A not for C.
For ex., solve(mod_A, et(amt=20000000, ii=12, addl=4) %>%
et(0,48,length.out=49), theta, ini) %>% plot(A,B,C)
Only changes "A" but not "C".

How to include C in the event(amt=, ii=12, addl=4)?

[billdenney]

I'm going to convert this to a discussion. Can you please share your code, if possible?

[arindampal1981]

Sure, suffixes "a", "b", "c" are basically denoting the drug A, metabolite B and perpetrator drug C.
Here is the code:

mod_a <-rxode2({
  alag(depot1) = tlag1;     # lag in A absorpn.
  alag(depot1) = tlag2;     # lag in A absorpn. going to 1st-pass
  alag(depot2) = tlag;     #lag in C absorpn.  
  
  C1 = centra/Va;   # A centr systemic
  C2 = peria/Va2;   # A peri systemic
  
  C3 = centrb/Vb;    # B centr presystemic
  
  C4 = centrc/Vc;       # C centr systemic
  C5 = peric/Vc2;
  Eh = CLmet0/Qh*(1 - Qu^y*Emax/(Qu^y + IC50^y)); # Extraction hepatic
  CLmet = Eh*Qh;                                  # metabolic clearance systemic
  
  d/dt(depot1) =-kaa*(1-f1)*depot1;               # A's PK: direct path to gut
  d/dt(centra) =  - CLa*C1 - Qa*C1 + Qa*C2 + kaa*(1-f1)*depot1 - CLmet*C1;
  d/dt(peria)  = Qa*C1 - Qa*C2;
  
  d/dt(depot1) = -kab*(f1)*depot1;                # A's PK: direct to presys metabolism
  d/dt(centrb) =  kab*(f1)*depot1 - CLb*C3 + CLmet*C1;
  
  d/dt(depot2) = -kac*(depot2);  		 # C's PK
  d/dt(centrc) =  - CLc*C4 - Qc*C4 + Qc*C5 + kac*(depot2);
  d/dt(peric)  = Qc*C4 - Qc*C5;
    });

ini <- c(depot1=20000000, depot2=10000000,
         centra=0, peria=0,centrb=0, centrc=0, peric=0);

theta <- c(tlag=0.36,kac=2.32, CLc=20700,Vc=173000, Vc2=33000,Qc=3020,    # C's parameter
           tlag1=0.6,kaa=0.8, CLa=11700,Va=431000,Va2=409000, Qa=66400,   # A's parameter
           tlag2=1.3,kaa=0.4, CLb=30600, Vb=70000, f1=0.77,               # B's parameter
           CLmet0=55000, IC50=19300, Emax=75, y=1.21, Qh=84000);          # A's metabolism

solve(mod_a, et(amt=0) %>% 
        et(0,48,length.out=49), theta, ini) %>% plot(C1,C3,C4,Eh)

[mattfidler]

I'm unsure what you are trying to do in this model. While you have 2 separate depots you define depot1 one more than once in a couple of ways.

First you have:

  alag(depot1) = tlag1;     # lag in A absorpn.
  alag(depot1) = tlag2;     # lag in A absorpn. going to 1st-pass

Since alag(depot1) is defined twice, only the last value is in effect, that is alag(depot1) = tlag2. This applies for the whole system. The statement alag(depot1) = tlag1 doesn't actually do anything in this model since it is overwritten.

The same is true of the duplicated definition of d/dt(depot), the first defenition is replaced by the second, that is:

  d/dt(depot1) =-kaa*(1-f1)*depot1;               # A's PK: direct path to gut (ignored)
# ...
  d/dt(depot1) = -kab*(f1)*depot1;                # A's PK: direct to presys metabolism (the only that is in effect)

Because these definition overwrite the previous one, it is not surprising you are not getting the results that you are expecting.

[mattfidler]

If you are trying to do different things based on maybe a first-pass flag, you would want to have the flag in the data and combine the definitions, that is

alag(depot1) = alag1*(1-FP) + alag2*FP

d/dt(depot1) = -kaa*(1-f1)*depot1*(1-FP) +  -kab*(f1)*depot1 * FP

Where FP is an indicator of the first pass effect.

[arindampal1981]

Thanks Matt, for correcting this out, I chose f1 as indicator of 1st pass fraction so, FP is not required. It actually solved the multiple lag problem within the same drug. This was a concern too since I tried checking their individual outputs and I saw the difference of conc. over time when combining them in my model.
But then how do I simulate multiple dose profiles at single run for both drugs A (from depot1) and C (from depot2)?
Since in,
solve(mod_a, et(amt=30000000) %>% et(0,48,length.out=49), theta, ini)
"amt" takes the dose from depot1.

[mattfidler]

You have to have f1 as a part of your event table. Covariates are currently not supported by et() so you could ad them with something like:

 et(amt=30000000) %>% et(0,48,length.out=49) %>% dplyr::mutate(f1=ifelse(time >= 1,1, 0))