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README

tci

Thetci package implements target-controlled infusion(TCI) algorithms to calculate infusion schedules for compartmentalpharmacokinetic (PK) and pharmacokinetic-pharmacodynamic (PK-PD) models.Using these infusion schedules, functions intci can beused to simulate PK or PK-PD responses with or without modelmisspecification. Generated responses can be used to simulateclosed-loop control by implementing Bayesian updates to the PK or PK-PDmodel based on the “observed” (i.e., simulated) data.

Closed-form solutions are provided for one, two, or three compartmentmammillary models (i.e., all peripheral compartments are joined to acentral compartment), as well as a three-compartment model with anadjoining effect-site. Alternative models, potentially based on ordinarydifferential equations (ODE), can be specified using other R packagesand adapted for use withtci functions (see the “Custom PKmodels and algorithms” vignette).

tci implements both plasma-and effect-site targeting TCIalgorithms based on work by Jacobs (1990) and Shafer and Gregg (1992),respectively. Users can implement alternative user-defined TCIalgorithms, however. Again, see the “Custom PK models and algorithms”vignette for further details.

Several population PK models commonly used for TCI are implemented intci. These include the Marsh, Schnider, and Eleveld modelsfor propofol, and the Minto, Kim, and Eleveld models for remifentanil.Use of these models is illustrated in the “Population PK models”vignette.

Installation

Thetci package can be installed from CRAN using thecommand.

install.packages("tci")

The most recent version can be downloaded from GitHub using thedevtools package and loaded as follows.

devtools::install_github("jarretrt/tci")

library(tci)library(ggplot2)# for plotting

Examples

Equations implementing 1-, 2-, 3-compartment and 3-compartment-effectstructural PK models are included in thetci package. Thefunctionpkmod will automatically infer the correctstructure based on the parameter names.

# 3-compartment model with effect site(mod3ecpt<-pkmod(pars_pk =c(cl =10,q2 =2,q3 =20,v =15,v2 =30,v3 =50,ke0 =1.2)))

## tci pkmod object## See ?update.pkmod to modify or add elements## ## PK model ##  4-compartment PK model ##  PK parameters: cl = 10, q2 = 2, q3 = 20, v = 15, v2 = 30, v3 = 50, ke0 = 1.2 ##  Initial concentrations: (0,0,0,0) ##  Plasma compartment: 1 ##  Effect compartment: 4 ## ## Simulation##  Additive error SD: 0 ##  Multiplicative error SD: 0 ##  Logged response: FALSE

Acceptable parameter names can be viewed by callinglist_parnms(). Less-commonly used parameters, such asclearance from a peripheral compartment, are also permissible.

# acceptable parameter nameslist_parnms()

## Acceptable names for 'pars_pk' vector (case-insensitive) ## ## First compartment options##  Central volume: 'v','v1' ##  Elimination: 'cl','cl1','k10','ke' ## ## Second compartment options##  Peripheral volume: 'v2' ##  Transfer: 'q','q2','k12','k21' ##  Elimination: 'cl2','k20' ## ## Third compartment options##  Second peripheral volume: 'v3' ##  Transfer: 'q3','k13','k31' ##  Elimination: 'cl3','k30' ## ## Effect-site##  Elimination: 'ke0'

Elements ofpkmod objects can be modified through anupdate.pkmod method. Perhaps most usefully, this allows forpartial modifications to PK-PD parameters. For example, the effect-siteequilibrium constant can be easily updated.

update(mod3ecpt,pars_pk =c(ke0 =0.9),init =c(1,0.2,0.3,1))

## tci pkmod object## See ?update.pkmod to modify or add elements## ## PK model ##  4-compartment PK model ##  PK parameters: cl = 10, q2 = 2, q3 = 20, v = 15, v2 = 30, v3 = 50, ke0 = 0.9 ##  Initial concentrations: (1,0.2,0.3,1) ##  Plasma compartment: 1 ##  Effect compartment: 4 ## ## Simulation##  Additive error SD: 0 ##  Multiplicative error SD: 0 ##  Logged response: FALSE

Most functions in thetci package pass additionalarguments toupdate.pkmod allowing for easy modification ofpkmod objects as needed.

TCI Infusion schedules

TCI algorithms are implemented using the functiontci_inf (manual infusions are implemented byinf_manual). The user supplies a set of targets, times atwhich the target is set, and apkmod object. The TCIalgorithm (defaults totype = "plasma") is iterativelyapplied to calculate infusion rates required to reach each target inturn. By default, infusion rates are updated in increments of 1/6,corresponding to every 10-second intervals if infusions rate units arein amount per minute. Infusion rates themselves must have the same unitsas the PK elimination parameters. If elimination rates are in differentunits, such as hours, then the TCI update frequency should be modifiedby the argumentdtm.

# effect-site targeting for three-compartment effect site modelinf_3ecpt<-inf_tci(target_vals =c(2,3,4,4),target_tms =c(0,2,3,10),pkmod = mod3ecpt,type ="effect")head(inf_3ecpt)

##        begin     end inf_rate Ct c1_start   c2_start  c3_start  c4_start## [1,] 0.00000 0.16667 643.6921  2 0.000000 0.00000000 0.0000000 0.0000000## [2,] 0.16667 0.33333   0.0000  2 6.033672 0.03532348 0.2079682 0.5966263## [3,] 0.33333 0.50000   0.0000  2 4.301795 0.09138590 0.5235366 1.4096671## [4,] 0.50000 0.66667   0.0000  2 3.136188 0.13103476 0.7267367 1.8178340## [5,] 0.66667 0.83333  19.3835  2 2.350071 0.15960595 0.8548449 1.9785480## [6,] 0.83333 1.00000   0.0000  2 2.000000 0.18174014 0.9390928 2.0109479##        c1_end     c2_end    c3_end    c4_end## [1,] 6.033672 0.03532348 0.2079682 0.5966263## [2,] 4.301795 0.09138590 0.5235366 1.4096671## [3,] 3.136188 0.13103476 0.7267367 1.8178340## [4,] 2.350071 0.15960595 0.8548449 1.9785480## [5,] 2.000000 0.18174014 0.9390928 2.0109479## [6,] 1.586605 0.19939667 0.9931813 1.9678507

Population PK models

Population PK models are implemented by the functionpoppkmod. The user must supply a data frame with the set ofcovariates (e.g., weight, age) required by the model. Several publishedpopulation PK models are currently implemented intci. Forpropofol, these include the Marsh, Schnider, and Eleveld models. Forremifentanil, they include the Minto, Kim, and Eleveld models. See?poppkmod or the population PK model vignette for details.list_pkmods() will list available population PK models andcovariates required by each.

# data frame of patient covariatesdata<-data.frame(ID =1:5,AGE =seq(20,60,by=10),TBW =seq(60,80,by=5),HGT =seq(150,190,by=10),MALE =c(TRUE,TRUE,FALSE,FALSE,FALSE))# Eleveld population PK model for propofolpkpd_elvd<-poppkmod(data = data,drug ="ppf",model ="eleveld")

As with thepkmod class,poppkmod objectscan be used byinf_tci and havepredict andsimulate methods to predict and simulate PK-PD responses,respectively.

PK-PD parameter values can be drawn at random from theinter-/intra-individual variability distribution, as described by thepkmod Omega matrix, by either 1) setting the argumentsample = TRUE when callingpoppkmod, or 2) byusing the functionsample_iiv.

set.seed(1)pkpd_elvd_iiv<-sample_iiv(pkpd_elvd)

Simulations

Simulations are best implemented through the functionsimulate_tci, which allows for model misspecification aswell as Bayesian updates to model parameters based on previouslyobserved data (i.e., “closed-loop” control).simulate_tcican be used for bothpkmod orpoppkmodclasses. Required arguments tosimulate_tci are 1) a priorPK model (pkmod_prior) that is used to calculate infusionrates and may be updated throughout the simulation if update times areprovided, 2) a true PK model (pkmod_true) that is used tosimulate observations, 3) TCI target values, 4) TCI target times, and 5)times to simulate observations.

# TCI target values (PD response)target_vals<-c(75,60,50,50)# values are in terms of minutes. 1/6 = 10 seconds# TCI target timestarget_tms<-c(0,3,6,10)# observation timesobs_tms<-seq(1/6,10,1/6)# simulate without updates ("open-loop")sim_ol<-simulate_tci(pkmod_prior = pkpd_elvd,pkmod_true = pkpd_elvd_iiv,             target_vals, target_tms, obs_tms,type ="effect",seed =1)

simulate_tci returns an object with classsim_tci that can be plotted using theggplot2library.

plot(sim_ol)

Modifications can be made to the plot to show a subset of responses,concentrations instead of PD response values, infusion rates, andsimulated data.

plot(sim_ol,yvar ="c4",id =c(1,3,5),show_inf =TRUE,wrap_id =TRUE)

Closed-loop simulations can be implemented by specifying a set ofupdate times. We illustrate this with updates each minute and aprocessing delay of 20 seconds.

sim_cl<-simulate_tci(pkmod_prior = pkpd_elvd,pkmod_true = pkpd_elvd_iiv,             target_vals, target_tms, obs_tms,update_tms =1:10,delay =1/3,type ="effect",seed =1)

## [1] "Simulating ID=1"## [1] "Simulating ID=2"## [1] "Simulating ID=3"## [1] "Simulating ID=4"## [1] "Simulating ID=5"

Sinceplot.sim_tci returns aggplot2object, it is easy to modify aspects such as titles and axis labelsusingggplot2 functions.

plot(sim_cl)+xlab("Minutes")+ylab("Bispectral Index")+ggtitle("Closed-loop simulation of Eleveld propofol model",subtitle ="Minute updates, processing delay of 20 seconds")