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Model

Source: vignettes/model.Rmd
model.Rmd
install.packages("PKPDsim")

Introduction

new_ode_model is the function that creates a new ODE model that can be used in the sim() command. It defines the ODE system and sets some attributes for the model. The model can be specified in three different ways:

  • model: a string that references a model from the library included in PKPDsim. Examples in the current library are e.g. pk_1cmt_oral, pk_2cmt_iv. To show the available models, run new_ode_model() without any arguments.
  • code: using code specifying derivatives for ODE specified in pseudo-R code
  • file: similar to code, but reads the code from a file

Model from library

For example, a 1-compartment oral PK model can be obtained using:

pk1 <- new_ode_model(model = "pk_1cmt_oral")

Run the new_ode_model() function without arguments to see the currently available models:

## Error in new_ode_model(): Either a model name (from the PKPDsim library), ODE code, an R function, or a file containing code for the ODE system have to be supplied to this function. The following models are available:
##   pk_1cmt_iv
##   pk_1cmt_iv_auc
##   pk_1cmt_iv_mm
##   pk_2cmt_iv
##   pk_2cmt_iv_auc
##   pk_3cmt_iv
##   pk_1cmt_oral
##   pk_2cmt_oral
##   pk_3cmt_oral

Custom model from code

The custom model needs to be specified as a string or text block:

pk1 <- new_ode_model(code = "
  dAdt[1] = -KA * A[1]
  dAdt[2] = +KA * A[1] -(CL/V) * A[2]
")

The input code should adhere to the following rules:

  • the derivatives in the ODE system are defined using dAdtomputate
  • array indices for the derivatives and compartments are indicated with [ ]. Compartments indices can start at either 0 or 1. If the latter, all indices will be reduced by 1 in the translation to C++ code.
  • equations are defined using =
  • power functions need to be written out as pow(base,exp).
  • force any numbers to be interpreted as real, to avoid them being interpreted as integer. So if an equation involves the real number 3, it is usually safer to write this as 3.0 in code.

The input code is translated into a C++ function. You can check that the model compiled correctly by typing the model name on the R command line, which prints the model information:

pk1
## ODE definition: 
## 
##   dAdt[1] = -KA * A[1];
##   dAdt[2] = +KA * A[1] -(CL/V) * A[2];
## ;
##  
## Required parameters: KA, CL, V 
## Covariates:  
## Variables:  
## Fixed parameters:  
## Number of compartments: 2 
## Observation variable: 
## Observation scaling: 1
## Lag time: none
## IOV CV: {}
## IOV bins: 1
## Comments: 
##  -

If you’re interested, you can also output the actual C++ function that is compiled by specifying the cpp_show_code=TRUE argument to the new_ode_model() function.

More custom model options

You can introduce new variables in your code, but you will have to define them using declare_variables argument too:

pk1 <- new_ode_model(code = "
  KEL = CL/V
  dAdt[1] = -KA * A[1]
  dAdt[2] = +KA * A[1] -KEL * A[2]
", declare_variables = c("KEL"))

Also, when you want to use covariates in your ODE system (more info on how to define covariates is in the Covariates vignette), you will have to define them, both in the code and in the function call:

pk1 <- new_ode_model(code = "
  CLi = WT/70
  KEL = CLi/V
  dAdt[1] = -KA * A[1]
  dAdt[2] = +KA * A[1] -(CL*(WT/70)/V) * A[2]
", declare_variables = c("KEL", "CLi"), covariates = c("WT"))

One exception to the input code syntax is the definition of power functions. PKPDsim does not translate those from the pseudo-R code to valid C++ syntax automatically. C/C++ does not use the ^ to indicate power functions, but uses the pow(value, base) function instead, so for example an allometric PK model should be written as:

pk1 <- new_ode_model(code = "
  CLi = CL * pow((WT/70), 0.75)
  dAdt[1] = -KA * A[1]
  dAdt[2] = +KA * A[1] -(CLi/V) * A[2]
", declare_variables = c("CLi"))

Dosing / bioavailability

The default dosing compartment and bioavailability can be specified using the dose argument. By default, the dose will go into compartment 1, with a bioavailability of 1. The bioav element in the list can be either a number or a character string referring a parameter.

pk1 <- new_ode_model(code = "
    dAdt[1] = -KA * A[1]
    dAdt[2] = +KA * A[1] -(CL/V) * A[2]
  ",
  dose = list(cmt = 1, bioav = "F1"),
  parameters = list(KA = 1, CL = 5, V = 50, F1 = 0.7)
)

Bioavailability can also be used for dosing based on mg/kg, since that is not supported in new_regimen(). The way to implement this is by scaling the dose by the “weight” covariate using the bioavailability:

mod <- new_ode_model(code = "
    dAdt[1] = -(CL/V)*A[1];
  ",
  dose = list(cmt = 1, bioav = "WT"),
  obs = list(cmt = 1, scale = "V"),
  covariates = list("WT" = new_covariate(value = 70))
)

Observations

The observation compartment can be set by specifying a list to the obs argument, with either the elements cmt and scale, or variable.

pk1 <- new_ode_model(code = "
    dAdt[1] = -KA * A[1]
    dAdt[2] = +KA * A[1] -(CL/V) * A[2]
  ", 
  obs = list(cmt = 2, scale = "V")
)

The scale can be either a parameter or a number, the cmt can only be a number.

Note that the variables specified inside the differential equation block are not available as scaling parameters. E.g. for allometry you will have to redefine the scaled volume as follows:

pk1 <- new_ode_model(code = "
    Vi = V * (WT/70)
    dAdt[1] = -KA * A[1]
    dAdt[2] = +KA * A[1] -(CL/Vi) * A[2]
  ", 
  obs = list(cmt = 2, scale = "V * (WT/70)")
)

Or define the observation using a variable:

pk1 <- new_ode_model(code = "
    dAdt[1] = -KA * A[1]
    dAdt[2] = +KA * A[1] -(CL/V) * A[2]
    CONC = A[2]
  ", 
  obs = list(variable = "CONC"),
  declare_variables = "CONC"
)

Custom model from file

Using the file argument, the model code is read from the specified files. This is just a convenience function, i.e. it allows you to separate models from R code more easily.

pk1 <- new_ode_model(
  file = "pk_1cmt_oral_nonlin_v1.txt",
  declare_variables = c("KEL", "CLi")
)