RxODE Modeling Syntax

Introduction

This vignette 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.

Example

   # 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;

Syntax

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 or conditional if statements. Assignment statements can be either simple assignments, where the left hand is an identifier (i.e., variable), or 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):

   # 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). Notice that the modulo operator % is currently unsupported.

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

Identifiers

Identifiers (variable names) may consist of one or more alphanumeric and underscore _ characters, but the first character cannot be a digit. NB: The dot . character may not be used as part of an identifier.

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().

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.

Bugs and/or deficiencies

Comments are not allowed inside statements, therefore the following code is syntactically incorrect:

 # incorrect syntax (comments not allowed inside statements)
 S2 = 1.0    # scaler for the central compartment ;

 # correct syntax
 S2 = 1.0;   # scaler for the central compartment

The modulo operator % is currently unsupported. Similarly, the old-style exponentiation operator ** is unsupported (use ^).