`<- modlib("pk1", end = 120) mod `

`. Building pk1 ... done.`

```
<- ev(amt = 100, ii = 12, addl = 4, ss = 1)
dose
mrgsim(mod, dose, recsort = 3) %>% plot()
```

Keep reading for all the details; I’m including this brief list of key items up front for your convenience.

- Use
`ss_rtol`

and`ss_atol`

arguments to`mrgsim()`

to control the local error estimate when`mrgsolve`

is finding steady state - Use
`ss_n`

to limit the number of doses that will be administered when advancing to steady state; if the number of doses exceeds`ss_n`

then a warning is issued and`mrgsolve`

moves on - Use
`ss_fixed = TRUE`

to silence the warning when`ss_n`

is exceeded; you are essentially saying dose up to`ss_n`

and then give up and move on without warning - Use
`SS_ADVANCE`

in`$ODE`

to check if the system is currently being advanced - Use
`ss_cmt`

in`[ set ]`

(inside your model) to select the compartments to be considered when finding steady state; you might have better success / efficiency if you focus on key compartments (or exclude unhelpful compartments like a depot compartment)

Within mrgsolve, the term “steady state” (`SS`

) applies specifically to the pharmacokinetic dosing system and indicates that the rate of drug administration is equal to the rate of drug elimination. Steady state dosing can take the form of repeated intermittent doses (bolus or infusion, administered intermittently at a given dosing interval) or a continuous infusion administered to steady state.

The user can direct mrgsolve to advance the system to steady state for intermittent dosing by including `ss=1`

in an event object or input data set. For example:

`<- modlib("pk1", end = 120) mod `

`. Building pk1 ... done.`

```
<- ev(amt = 100, ii = 12, addl = 4, ss = 1)
dose
mrgsim(mod, dose, recsort = 3) %>% plot()
```

In this example, the `ss=1`

flag tells mrgsolve to advance the system to steady state under a dosing regimen of 100 mg every 12 hours (and then give a total of 5 doses). When using the `ss=1`

flag, the user is required to indicate the dosing interval (here every 12 hours) and additional doses are optional. Similar behavior can be achieved for intermittent infusions by setting the infusion `rate`

.

A continuous infusion can be dosed to steady state by including the `ss=1`

flag, a value for `rate`

(any positive rate or -1 if the rate is being modeled), and setting the dose amount (`amt`

/`AMT`

) to zero:

```
<- ev(amt = 0, rate = 5, ss = 1, cmt = "CENT")
infus
mrgsim(mod, infus, recsort = 3) %>% plot()
```

Because `CL`

is equal to 1 in this model, we see that the continuous (never-ending) infusion was started at steady state with a value of 5.

It’s important to recognize that `SS`

is related to the PK dosing system; it is finding the state of the system after an infinite number of doses have been administered under a certain regimen. And this is essentially how mrgsolve goes about finding steady state: when the `ss=1`

flag is encountered, mrgsolve starts repeatedly administering doses and advancing the system to the next dose according to the inter-dose interval (`ii`

). Once mrgsolve determines that the amounts in the system at any dose are the same as they were at the preceding dose, mrgsolve declares that `SS`

has been achieved.

mrgsolve uses a local error estimate to determine the degree to which concentrations are changing or not changing between doses on the way to `SS`

. This is determined by a relative tolerance parameter (`ss_rtol`

) and an absolute tolerance parameter (`ss_atol`

). As of mrgsolve version 0.10.3, these tolerances are distinct from the tolerances used for solving the differential equations (`rtol`

and `atol`

, respectively). Note that when advancing to `SS`

in an ODE model, `ss_rtol`

(the relative tolerance for determining `SS`

) must be larger (less precise) than `rtol`

(the relative tolerance used by the ODE solver). Once the difference between two trough concentrations is less than A\(_{trough}\) * `ss_rtol`

+ `ss_atol`

, then the system is said to be at steady state. By default, this calculation is done for every single compartment in the model and all compartments have to meet this criteria before the system is said to be at steady state. So, increasing `ss_rtol`

(say from 1e-8 to 1e-3) will also allow us to call it “good” with respect to steady state sooner.

Both tolerances for steady state are stored in the model object and can be set with the update method. For example,

```
<- house()
mod
<- update(mod, ss_rtol = 1e-5, ss_atol = 1e-8) mod
```

It was noted above that mrgsolve advances the system to steady state with a brute force approach: doses are repeatedly administered at a regular interval (for intermittent `SS`

) until pre-dose concentrations are the same dose to dose. mrgsolve sets an upper limit (equal to 500) to the number of doses that will be administered before giving up on trying to find steady state. Once this maximum number of doses is exceeded, mrgsolve will issue a warning that steady state was not achieved and continue on with the problem. For example:

```
<- ev(amt = 100, ii = 12, ss = 1, VC = 800)
dose
<- mrgsim(house(), dose) out
```

```
. Warning in (function (x, data, idata = no_idata_set(), carry_out = carry.out, : [steady_bolus] ID 1 failed to reach steady state
. ss_n: 500, ss_rtol: 1e-08, ss_atol: 1e-08
```

Here, mrgsolve administered 500 doses and the pre-dose concentrations were still not similar enough to declare the system to be at steady state.

The maximum dose number can be set with the `ss_n`

argument to `mrgsim`

(or one of the variants; see `?do_mrgsim`

help topic). This number can be increased to prevent the warning:

`<- mrgsim(house(), dose, ss_n = 1000) out `

Alternatively, the `ss_fixed`

argument to mrgsim (see `?do_mrgsim`

) can be set to `TRUE`

to silence the warning. In this case, **up to** `ss_n`

doses will be administered and if `SS`

is not achieved with that many doses, the problem will continue with no warning.

Sometimes it might be sufficient to only consider one compartment when determining `SS`

(e.g. the central compartment in a PK model). Other times, it might be helpful to exclude a compartment when determining `SS`

(e.g. a depot dosing compartment when concentrations can get very small toward the end of the dosing interval).

mrgsolve allows the user to identify compartments to include or exclude in determining `SS`

. This is done through the `ss_cmt`

option in `$SET`

. To only consider the `CENT`

compartment, write the following in the model file:

`[ set ] ss_cmt = "CENT"`

This says to **only** look at the `CENT`

compartment when determining `SS`

.

Alternatively, you can exclude certain compartments like this:

`[ set ] ss_cmt = "-GUT,DEPOT"`

This says to ignore the `GUT`

and `DEPOT`

compartments when determining `SS`

.

As another example, you might want to exclude an accumulator compartment when calculating `SS`

```
[ set ] ss_cmt = "-AUC"
[ ode ]
= -kel * CENT;
dxdt_CENT
= CENT/VC; dxdt_AUC
```

This is just a partial model snippet, but it shows how you might exclude the AUC compartment when determining `SS`

.

mrgsolve also provides an `SS_ADVANCE`

indicator that is passed into `$ODE`

and evaluates to `true`

when the system is being advanced to steady state. So a better way to exclude the accumulator compartment from being considered for `SS`

calculation would be this:

```
[ ode ]
= CENT/VC;
dxdt_AUC
if(SS_ADVANCE) dxdt_AUC = 0;
```

This code prevents the `AUC`

compartment from changing during the advance to `SS`

and the dose to dose difference in `AUC`

will always be zero, effectively excluding this compartment from factoring into the `SS`

determination. This should be the preferred approach to dealing with an `AUC`

compartment.