RxODE-syntax.Rmd
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 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
statements, or printing statements (for debugging/testing). Assignment statements can be:
d/dt(depot)
:depot(0) = 0
f(depot)=1
), lag time (lag(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.cmt(compartmentName)
mtime(var)=time
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 <-
.
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
). 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.
There are certain variable names that are in the RxODE
event tables. To avoid confusion, the following event table-related items cannot be used in a RxODE model specification:
rate
amt
ss
addl
evid
ii
dvid
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:
t
(time), tlast
(last time point), and podo
(oral dose, in the undocumented case of absorption transit models).pi
or R’s predefined constants.ka
rate of absorption, CL
clearance, etc.)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 solve()
or be in the supplied event data-set.
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.
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)
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).
%
is currently unsupported.else if
is not currently supportedifelse
are not currently supported.(cmt==2)*1+(cmt==3)*4
is not supported