Time dependent input in transit compartment model

[Murali-Ramanathan]

Hello everyone

New to mrgsolve here. I am trying to code a time-dependent input into a transit compartment model.

I am trying to modify the example model code from Kyle Baron #4. I also have the very similar code from https://github.com/mrgsolve/gallery/blob/master/absorption/transit.md

I do not have any bolus inputs or constant rate infusion dosing events. The only input to the system is the time-dependent input.

What is the best way to implement this? I was considering adding a new depot compartment "newcomp" whose differential equation that would receive the time-dependent input and transfer that input into the original "depot" compartment with the gamma distribution.

I am assuming that it would be inappropriate to simply add the new time-dependent input to the rate_in term.

Any help is appreciated

[kylebaron]

Hi @Murali-Ramanathan -

I'm wondering: do you know when the changes happen for the time-dependent input? Or is that determined "inside the model"?

Kyle

[Murali-Ramanathan]

Hi @kylebaron

Thanks for getting back!
The time-dependent function is continuous [0, Inf). In principle, it can be determined inside the model.
Murali

[Murali-Ramanathan]

@kylebaron:

I am thinking that for the special case of the transit compartment model, it may be okay to place the time-dependent rate function in a dosing compartment that is functionally the first transit compartment and have it transit to the next transit compartment with rate constant of ktr.

Not sure that approach is general though or if there is a better way.
Murali

[kylebaron]

I'm not sure what the right answer is here. It might be more straightforward in the end to just code up each compartment explicitly. I'm afraid I can't help much without playing around with it a bit myself.

[Murali-Ramanathan]

I am first trying to insert a time-dependent input function into a simple one compartment model before I tackle its integration with the transit compartment model. CAPTURE indicates the input function (ggval), which resembles the gamma distribution, computes fine. However, it does not seem to behave within the ODE. Other simple functions do fine. Here's the code..

code3ggmin <- '
[ param ]
KTR=1
Q=-.2, mu=0.5,sig=1

[ cmt ] GGCMT
[ global ]
[ main ]
[ ode ]

// Preliminaries for time-dependent input function
double qsq=pow(Q,-2.0);
double qw=(log(SOLVERTIME)-mu)/sig;
double qxp = qsq*(Qqw-exp(Qqw));

// Log of time-dependent input first
double lgggval = log(abs(Q))+qsq*log(qsq)+qxp-lgamma(qsq)-log(sig)-log(SOLVERTIME);
// This is the time-dependent input function
double ggval = exp(lgggval);

dxdt_GGCMT=ggval -KTR*GGCMT;

$CAPTURE ggval
'
mod3ggmin <- mcode("transit", code3ggmin, delta = 0.1, end = 32)
mrgsim(mod3ggmin, ev(amt = 0)) %>% plot()

[kylebaron]

I think this will be a problem:

log(SOLVERTIME)

Maybe

if(SOLVERTIME <= 0) ggval = 0;

dxdt_GGCMT=ggval -KTR*GGCMT;

to get over this for now; I'd probably refactor the code to avoid that computation altogether.

[Murali-Ramanathan]

Thanks! That patch worked. I should have caught that. Will look at ways to eliminate the log(SOLVERTIME) term.