R: Create an ODE-based model specification

RxODE {RxODE} | R Documentation

## Create an ODE-based model specification

### Description

Create a dynamic ODE-based model object suitably for translation into fast C code

### Usage

    RxODE(
      model,
      modName = basename(wd),
      wd = getwd(),
      filename = NULL,
      extraC = NULL,
      debug = FALSE,
      calcJac = NULL,
      calcSens = NULL,
      collapseModel = FALSE,
      package = NULL,
      ...,
      linCmtSens = c("linCmtA", "linCmtB", "linCmtC"),
      indLin = FALSE,
      verbose = FALSE
    )

### Arguments

`model` | This is the ODE model specification. It can be: a string containing the set of ordinary differential equations (ODE) and other expressions defining the changes in the dynamic system. a file name where the ODE system equation is contained An ODE expression enclosed in `\{\}` (see also the `filename` argument). For details, see the sections “Details” and `RxODE Syntax` below.
`modName` | a string to be used as the model name. This string is used for naming various aspects of the computations, including generating C symbol names, dynamic libraries, etc. Therefore, it is necessary that `modName` consists of simple ASCII alphanumeric characters starting with a letter.
`wd` | character string with a working directory where to create a subdirectory according to `modName`. When specified, a subdirectory named after the “`modName.d`” will be created and populated with a C file, a dynamic loading library, plus various other working files. If missing, the files are created (and removed) in the temporary directory, and the RxODE DLL for the model is created in the current directory named `rx_????_platform`, for example `rx_129f8f97fb94a87ca49ca8dafe691e1e_i386.dll`
`filename` | A file name or connection object where the ODE-based model specification resides. Only one of `model` or `filename` may be specified.
`extraC` | Extra c code to include in the model. This can be useful to specify functions in the model. These C functions should usually take `double` precision arguments, and return `double` precision values.
`debug` | is a boolean indicating if the executable should be compiled with verbose debugging information turned on.
`calcJac` | boolean indicating if RxODE will calculate the Jacobain according to the specified ODEs.
`calcSens` | boolean indicating if RxODE will calculate the sensitivities according to the specified ODEs.
`collapseModel` | boolean indicating if RxODE will remove all LHS variables when calculating sensitivities.
`package` | Package name for pre-compiled binaries.
`...` | ignored arguments.
`linCmtSens` | The method to calculate the linCmt() solutions
`indLin` | Calculate inductive linearization matrices and compile with inductive linearization support.
`verbose` | When `TRUE` be verbose with the linear compartmental model

### Details

The `Rx` in the name `RxODE` is meant to suggest the abbreviation Rx for a medical prescription, and thus to suggest the package emphasis on pharmacometrics modeling, including pharmacokinetics (PK), pharmacodynamics (PD), disease progression, drug-disease modeling, etc.

The ODE-based model specification may be coded inside a character string or in a text file, see Section RxODE Syntax below for coding details. An internal `RxODE` compilation manager object translates the ODE system into C, compiles it, and dynamically loads the object code into the current R session. The call to `RxODE` produces an object of class `RxODE` which consists of a list-like structure (environment) with various member functions (see Section Value below).

For evaluating `RxODE` models, two types of inputs may be provided: a required set of time points for querying the state of the ODE system and an optional set of doses (input amounts). These inputs are combined into a single event table object created with the function `eventTable()` or `et()`.

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.

### Value

An object (environment) of class `RxODE` (see Chambers and Temple Lang (2001)) consisting of the following list of strings and functions:

    * `model` a character string holding the source model specification.
    * `get.modelVars`a function that returns a list with 3 character
        vectors, `params`, `state`, and `lhs` of variable names used in the model
        specification. These will be output when the model is computed (i.e., the ODE solved by integration).

      * `solve`{this function solves (integrates) the ODE. This
          is done by passing the code to [rxSolve()].
          This is as if you called `rxSolve(RxODEobject, ...)`,
          but returns a matrix instead of a rxSolve object.

          `params`: a numeric named vector with values for every parameter
          in the ODE system; the names must correspond to the parameter
          identifiers used in the ODE specification;

          `events`: an `eventTable` object describing the
          input (e.g., doses) to the dynamic system and observation
          sampling time points (see  [eventTable()]);

          `inits`: a vector of initial values of the state variables
          (e.g., amounts in each compartment), and the order in this vector
          must be the same as the state variables (e.g., PK/PD compartments);

          `stiff`: a logical (`TRUE` by default) indicating whether
          the ODE system is stiff or not.

          For stiff ODE systems (`stiff = TRUE`), `RxODE` uses
          the LSODA (Livermore Solver for Ordinary Differential Equations)
          Fortran package, which implements an automatic method switching
          for stiff and non-stiff problems along the integration interval,
          authored by Hindmarsh and Petzold (2003).

          For non-stiff systems (`stiff = FALSE`), `RxODE` uses `DOP853`,
          an explicit Runge-Kutta method of order 8(5, 3) of Dormand and Prince
          as implemented in C by Hairer and Wanner (1993).

          `trans_abs`: a logical (`FALSE` by default) indicating
          whether to fit a transit absorption term
          (TODO: need further documentation and example);

          `atol`: a numeric absolute tolerance (1e-08 by default);

          `rtol`: a numeric relative tolerance (1e-06 by default).e

          The output of \dQuote{solve} is a matrix with as many rows as there
          are sampled time points and as many columns as system variables
          (as defined by the ODEs and additional assignments in the RxODE model
              code).}

      * `isValid` a function that (naively) checks for model validity,
          namely that the C object code reflects the latest model
          specification.
      * `version` a string with the version of the `RxODE`
          object (not the package).
      * `dynLoad` a function with one `force = FALSE` argument
          that dynamically loads the object code if needed.
      * `dynUnload` a function with no argument that unloads
          the model object code.
      * `delete` removes all created model files, including C and DLL files.
          The model object is no longer valid and should be removed, e.g.,
          `rm(m1)`.
      * `run` deprecated, use `solve`.
      * `get.index` deprecated.
      * `getObj` internal (not user callable) function.

### Author(s)

Melissa Hallow, Wenping Wang and Matthew Fidler

### References

Chamber, J. M. and Temple Lang, D. (2001) Object Oriented Programming in R. R News, Vol. 1, No. 3, September 2001. https://cran.r-project.org/doc/Rnews/Rnews_2001-3.pdf.

Hindmarsh, A. C. ODEPACK, A Systematized Collection of ODE Solvers. Scientific Computing, R. S. Stepleman et al. (Eds.), North-Holland, Amsterdam, 1983, pp. 55-64.

Petzold, L. R. Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations. Siam J. Sci. Stat. Comput. 4 (1983), pp. 136-148.

Hairer, E., Norsett, S. P., and Wanner, G. Solving ordinary differential equations I, nonstiff problems. 2nd edition, Springer Series in Computational Mathematics, Springer-Verlag (1993).

Plevyak, J. `dparser`, http://dparser.sourceforge.net. Web. 12 Oct. 2015.

### See Also

`eventTable()`, `et()`, `add.sampling()`, `add.dosing()`

### Examples

    # Step 1 - Create a model specification
    ode <- "
       # A 4-compartment model, 3 PK and a PD (effect) compartment
       # (notice state variable names 'depot', 'centr', 'peri', 'eff')

       C2 = centr/V2;
       C3 = peri/V3;
       d/dt(depot) =-KA*depot;
       d/dt(centr) = 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;
    "

    m1 <- RxODE(model = ode)
    print(m1)

    # Step 2 - Create the model input as an EventTable,
    # including dosing and observation (sampling) events

    # QD (once daily) dosing for 5 days.

    qd <- eventTable(amount.units = "ug", time.units = "hours")
    qd$add.dosing(dose = 10000, nbr.doses = 5, dosing.interval = 24)

    # Sample the system hourly during the first day, every 8 hours
    # then after

    qd$add.sampling(0:24)
    qd$add.sampling(seq(from = 24 + 8, to = 5 * 24, by = 8))

    # Step 3 - set starting parameter estimates and initial
    # values of the state

    theta <-
      c(
        KA = .291, CL = 18.6,
        V2 = 40.2, Q = 10.5, V3 = 297.0,
        Kin = 1.0, Kout = 1.0, EC50 = 200.0
      )

    # init state variable
    inits <- c(0, 0, 0, 1)
    # Step 4 - Fit the model to the data

    qd.cp <- m1$solve(theta, events = qd, inits)

    head(qd.cp)

    # This returns a matrix.  Note that you can also
    # solve using name initial values. For example:

    inits <- c(eff = 1)
    qd.cp <- solve(m1, theta, events = qd, inits)
    print(qd.cp)

    plot(qd.cp)

[Package RxODE version 1.1.4 Index]