The tci package can be used to apply target-controlled infusion (TCI) algorithms to 1-, 2-, and 3-compartment pharmacokinetic (PK) models with intravenous drug administration. Three-compartment PK models with an effect-site compartment are also supported. TCI algorithms incorporated in the package permit plasma or effect-site targeting and incorporation of closed-form pharmacodynamic (PD) models. Alternate user-defined PK models, population PK models, or TCI algorithms can additionally be specified.
The tci package can be installed from GitHub using the devtools package and loaded as follows.
PK models can be evaluated by the predict.pkmod method in combination with a dosing schedule. Dosing schedules should indicate infusion starting times and rates, with the infusion termination time specified with rate 0.
# e.g. infusion rates of 100 mg/hr for 30 sec intervals at 0, 4 minutes.
dose <- create_intvl(
as.matrix(cbind(time = c(0.5,4,4.5,10),
infrt = c(100,0,100,0)))
)
dose## infrt begin end
## [1,] 100 0.0 0.5
## [2,] 0 0.5 4.0
## [3,] 100 4.0 4.5
## [4,] 0 4.5 10.0# model parameters
pars_3cpt <- c(k10=1.5,k12=0.15,k21=0.09,k13=0.8,
k31=0.8,v1=10,v2=15,v3=100,ke0=1)
# predict concentrations of a three-compartment model with effect-site at
# times 1, 2, 8 minutes
predict(pkmod3cptm,
pars = pars_3cpt,
inf = dose,
tms = c(1,2,8))## time c1 c2 c3 c4
## [1,] 1 1.0812467 0.1708101 0.09872216 1.1317615
## [2,] 2 0.3558635 0.2129614 0.07501638 0.7619403
## [3,] 8 0.1675395 0.3914383 0.03653374 0.3157391# plot concentrations
plot(pkmod3cptm, inf = dose, pars = pars_3cpt,
title = "Concentrations for a 3 compartment model with an effect site")
Closed-form PK model solutions for 1-, 2-, and 3-compartment models are provided by the tci package based on solutions and code in Abuhelwa, Foster, and Upton (2015). Custom user-defined PK models, potentially using ODE solvers available in other packages, can be specified and used. See the vignette on user-defined PK functions for an example.
TCI algorithms are iteratively applied through the function ‘tci’. Times and target concentrations are passed as arguments along with a PK model, PK model parameters, and (optional) initial concentrations. Times and targets should include the time/concentration associated with the end of the infusion schedule. Plasma or effect-site targeting is specified through the “tci_alg” argument, or a custom TCI algorithm is provided through the argument “tci_custom.”
# target concentrations of 2 for 0-5 minutes and 3 for 5-10 minutes.
tci_times <- c(0,5,10,10)
tci_targets <- c(2,3,3,3)
# plasma-targeting
inf_3cpt_plasma <- tci(Ct = tci_targets,
tms = tci_times,
pkmod = pkmod3cptm,
pars = pars_3cpt,
tci_alg = "plasma")
# infusions for effect-site targeting
inf_3cpt_effect <- tci(Ct = tci_targets,
tms = tci_times,
pkmod = pkmod3cptm,
pars = pars_3cpt,
tci_alg = "effect",
cptol = 0.2)
head(inf_3cpt_effect)## infrt begin end dt Ct c1_start c2_start c3_start
## [1,] 521.59270 0.0000000 0.1666667 0.1666667 2 0.000000 0.00000000 0.00000000
## [2,] 0.00000 0.1666667 0.3333333 0.1666667 2 7.157983 0.06327658 0.04862527
## [3,] 0.00000 0.3333333 0.5000000 0.1666667 2 4.856783 0.16024552 0.11615645
## [4,] 0.00000 0.5000000 0.6666667 0.1666667 2 3.382646 0.22508402 0.15220327
## [5,] 0.00000 0.6666667 0.8333333 0.1666667 2 2.430990 0.26923296 0.16893074
## [6,] 43.81325 0.8333333 1.0000000 0.1666667 2 1.809977 0.29993095 0.17395669
## c4_start c1_end c2_end c3_end c4_end
## [1,] 0.0000000 7.157983 0.06327658 0.04862527 0.6010525
## [2,] 0.6010525 4.856783 0.16024552 0.11615645 1.4129871
## [3,] 1.4129871 3.382646 0.22508402 0.15220327 1.8170870
## [4,] 1.8170870 2.430990 0.26923296 0.16893074 1.9771107
## [5,] 1.9771107 1.809977 0.29993095 0.17395669 1.9944762
## [6,] 1.9944762 2.000000 0.32708413 0.17612465 1.9820862Infusion schedules are provided in the output of ‘tci’ along with predicted concentrations and can be plotted with the “plot.tciinf” method.
ptci_2ug_plasma <- plot(inf_3cpt_plasma,
title = "Plasma targeting for three-compartment model",
display = FALSE)
ptci_2ug_effect <- plot(inf_3cpt_effect,
title = "Effect-site targeting for three-compartment model",
display = FALSE)
grid.arrange(ptci_2ug_plasma, ptci_2ug_effect)
Functions implementing the Marsh, Schnider, and Eleveld population PK models for propofol (PK-PD for Eleveld model) are currently provided and can be used to calculate PK and PK-PD parameters at patient covariates or to simulate parameters for new patients given inter-patient parameter variability.
patient_dat <- data.frame(AGE = c(20,40,65),
TBM = c(50,70,90),
HGT = c(150,170,200),
MALE = c(TRUE,FALSE,TRUE))
# evaluate at covariate values and return clearance parameters
patient_pk <- schnider_poppk(patient_dat, rand = FALSE, rate = FALSE)
patient_pk## AGE TBM HGT MALE LBM V1 V2 V3 CL Q2 Q3 KE0
## 1 20 50 150 TRUE 40.77778 4.27 31.803 238 1.186933 0.498 0.836 0.456
## 2 40 70 170 FALSE 49.80657 4.27 23.983 238 2.012072 0.978 0.836 0.456
## 3 65 90 200 TRUE 73.08000 4.27 14.208 238 2.131152 1.578 0.836 0.456# evaluate TCI for patient 1
tci_patient1 <- tci(Ct = tci_targets,
tms = tci_times,
pkmod = pkmod3cptm,
pars = patient_pk[1,],
tci_alg = "effect")
head(tci_patient1)## infrt begin end dt Ct c1_start c2_start c3_start
## [1,] 159.1048 0.0000000 0.1666667 0.1666667 2 0.000000 0.000000000 0.000000000
## [2,] 0.0000 0.1666667 0.3333333 0.1666667 2 5.914495 0.007837502 0.001759305
## [3,] 0.0000 0.3333333 0.5000000 0.1666667 2 5.360630 0.022498661 0.005055038
## [4,] 0.0000 0.5000000 0.6666667 0.1666667 2 4.859024 0.035747266 0.008040233
## [5,] 0.0000 0.6666667 0.8333333 0.1666667 2 4.404746 0.047716670 0.010744190
## [6,] 0.0000 0.8333333 1.0000000 0.1666667 2 3.993330 0.058527644 0.013193442
## c4_start c1_end c2_end c3_end c4_end
## [1,] 0.0000000 5.914495 0.007837502 0.001759305 0.2227103
## [2,] 0.2227103 5.360630 0.022498661 0.005055038 0.6183984
## [3,] 0.6183984 4.859024 0.035747266 0.008040233 0.9465626
## [4,] 0.9465626 4.404746 0.047716670 0.010744190 1.2157835
## [5,] 1.2157835 3.993330 0.058527644 0.013193442 1.4336701
## [6,] 1.4336701 3.620730 0.068289564 0.015412023 1.6069638tci functions are compatible with other user-specified population PK models provided that they return parameters with either elimination rate-constants named “k10”, “k12”, etc. (capitalization optional), or as clearance parameters “CL”, “Q2”, etc.
Abuhelwa, Ahmad Y., David J R Foster, and Richard N. Upton. 2015. “ADVAN-style analytical solutions for common pharmacokinetic models.” Journal of Pharmacological and Toxicological Methods 73: 42–48. https://doi.org/10.1016/j.vascn.2015.03.004.