This briefly describes the syntax used to define models that RxODE will translate into R-callable compiled code. It also describes the communication of variables between R and the RxODE modeling specification.


   # An RxODE model specification (this line is a comment).

   if(comed==0){   # concomitant medication (con-med)?
      F = 1.0;     # full bioavailability w.o. con-med
   else {
      F = 0.80;    # 20% reduced bioavailability

   C2 = centr/V2;  # concentration in the central compartment
   C3 = peri/V3;   # concentration in the peripheral compartment

   # ODE describing the PK and PD

   d/dt(depot) = -KA*depot;
   d/dt(centr) = F*KA*depot - CL*C2 - Q*C2 + Q*C3;
   d/dt(peri)  =                      Q*C2 - Q*C3;
   d/dt(eff)   = Kin - Kout*(1-C2/(EC50+C2))*eff;


An RxODE model specification consists of one or more statements 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 statements, or printing statements (for debugging/testing). Assignment statements can be:

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

Additionally, assignment can be done with the ~ operator, which causes RxODE to use the variable/expression while solving but suppress output to either the matrix or data-frame returned in R. The suppression works with simple assignments and time-derivative assignments. All other variable/assignments do not produce output, but are used for the solving.

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). In addition, the factorial operator and function (either ! or factorial as in R) can be used. Notice that the modulo operator % is currently unsupported.

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.


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:

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 passed in the params argument of the integrator function solve().

Sometimes RxODE generates variables that are fed back to RxODE. These variables start with the rx prefix. To avoid any problems, it is suggested to not use these variables starting with the rx prefix.

Interface and data handling between R and the generated C code

Users specify which variables are the dynamic system's state variables via the d/dt(identifier) operator as part of the model specification, and which are model parameters via the params= argument in RxODE solve() method:

m1 <- RxODE(model = ode, modName = "m1")

# model parameters -- a named vector is required
theta <- 
   c(KA=0.29, CL=18.6, V2=40.2, Q=10.5, V3=297, Kin=1, Kout=1, EC50=200)

# state variables and their amounts at time 0 (the use of names is
# encouraged, but not required)
inits <- c(depot=0, centr=0, peri=0, eff=1)

# qd1 is an eventTable specification with a set of dosing and sampling 
# records (code not shown here)

m1$solve(theta, event = qd1, inits = inits)

The values of these variables at pre-specified time points are saved during model fitting/integration and returned as part of the fitted values (see the function eventTable, in particular its member function add.sampling function to define a set of time points when to capture the values of these variables) and returned as part of the modeling output.

The ODE specification mini-language is parsed with the help of the open source tool DParser, Plevyak (2015).

Bugs and/or deficiencies

The modulo operator % is currently unsupported.