In RxODE: Facilities for Simulating from ODE-Based Models

An RxODE model specification consists of one or more statements optionally terminated by semi-colons ; and optional comments (comments are delimited by # and an end-of-line).

A block of statements is a set of statements delimited by curly braces, { ... }.

Statements can be either assignments, conditional if/else if/else, while loops (can be exited by break), special statements, or printing statements (for debugging/testing)

Assignment statements can be:

simple assignments, where the left hand is an identifier (i.e., variable)
special time-derivative assignments, where the left hand specifies the change of the amount in the corresponding state variable (compartment) with respect to time e.g., d/dt(depot):
special initial-condition assignments where the left hand specifies the compartment of the initial condition being specified, e.g. depot(0) = 0
special model event changes including bioavailability (f(depot)=1), lag time (alag(depot)=0), modeled rate (rate(depot)=2) and modeled duration (dur(depot)=2). An example of these model features and the event specification for the modeled infusions the RxODE data specification is found in RxODE events vignette.
special change point syntax, or model times. These model times are specified by mtime(var)=time
special Jacobian-derivative assignments, where the left hand specifies the change in the compartment ode with respect to a variable. For example, if d/dt(y) = dy, then a Jacobian for this compartment can be specified as df(y)/dy(dy) = 1. There may be some advantage to obtaining the solution or specifying the Jacobian for very stiff ODE systems. However, for the few stiff systems we tried with LSODA, this actually slightly slowed down the solving.

Note that assignment can be done by =, <- or ~.

When assigning with the ~ operator, the simple assignments and time-derivative assignments will not be output.

Special statements can be:

Compartment declaration statements, which can change the default dosing compartment and the assumed compartment number(s) as well as add extra compartment names at the end (useful for multiple-endpoint nlmixr models); These are specified by cmt(compartmentName)
Parameter declaration statements, which can make sure the input parameters are in a certain order instead of ordering the parameters by the order they are parsed. This is useful for keeping the parameter order the same when using 2 different ODE models. These are specified by param(par1, par2,...)

An example model is shown below:

   # simple assignment
   C2 = centr/V2;

   # time-derivative assignment
   d/dt(centr) = F*KA*depot - CL*C2 - Q*C2 + Q*C3;

Expressions in assignment and if statements can be numeric or logical, however, no character nor integer expressions are currently supported.

Numeric expressions can include the following numeric operators +, -, *, /, ^ and those mathematical functions defined in the C or the R math libraries (e.g., fabs, exp, log, sin, abs).

You may also access the R's functions in the R math libraries, like lgammafn for the log gamma function.

The RxODE syntax is case-sensitive, i.e., ABC is different than abc, Abc, ABc, etc.

Identifiers

Like R, Identifiers (variable names) may consist of one or more alphanumeric, underscore _ or period . characters, but the first character cannot be a digit or underscore _.

Identifiers in a model specification can refer to:

State variables in the dynamic system (e.g., compartments in a pharmacokinetics model).
Implied input variable, t (time), tlast (last time point), and podo (oral dose, in the undocumented case of absorption transit models).
Special constants like pi or R's predefined constants.
Model parameters (e.g., ka rate of absorption, CL clearance, etc.)
Others, as created by assignments as part of the model specification; these are referred as LHS (left-hand side) variable.

Currently, the RxODE modeling language only recognizes system state variables and "parameters", thus, any values that need to be passed from R to the ODE model (e.g., age) should be either passed in the params argument of the integrator function rxSolve() or be in the supplied event data-set.

There are certain variable names that are in the RxODE event tables. To avoid confusion, the following event table-related items cannot be assigned, or used as a state but can be accessed in the RxODE code:

cmt
dvid
addl
ss
rate
id

However the following variables are cannot be used in a model specification:

evid
ii

Sometimes RxODE generates variables that are fed back to RxODE. Similarly, nlmixr generates some variables that are used in nlmixr estimation and simulation. These variables start with the either the rx or nlmixr prefixes. To avoid any problems, it is suggested to not use these variables starting with either the rx or nlmixr prefixes.

Logical Operators

Logical operators support the standard R operators ==, != >= <= > and <. Like R these can be in if() or while() statements, ifelse() expressions. Additionally they can be in a standard assignment. For instance, the following is valid:

cov1 = covm*(sexf == "female") + covm*(sexf != "female")

Notice that you can also use character expressions in comparisons. This convenience comes at a cost since character comparisons are slower than numeric expressions. Unlike R, as.numeric or as.integer for these logical statements is not only not needed, but will cause an syntax error if you try to use the function.