#' Concentration predictions for 1-compartmental oral PK model after single or multiple bolus doses
#'
#' @param t vector of time
#' @param dose dose
#' @param tau dosing interval
#' @param KA absorption rate
#' @param CL clearance
#' @param V volume of distribution
#' @param F bioavailability, commonly between 0 an 1.
#' @param ruv residual error (list)
#'
#' @references Garrett ER. The Bateman function revisited: a critical reevaluation of the quantitative expressions to characterize concentrations in the one compartment body model as a function of time with first-order invasion and first-order elimination. J Pharmacokinet Biopharm (1994) 22(2):103-128.
#' @references Bialer M. A simple method for determining whether absorption and elimination rate constants are equal in the one-compartment open model with first-order processes. J Pharmacokinet Biopharm (1980) 8(1):111-113
#' @references Nielsen JC, Hutmacher MM et al. J Pharmacokinet Pharmacodyn. 2012 Dec;39(6):619-34. doi: 10.1007/s10928-012-9274-0. Epub 2012 Sep 23.
#' @references https://static-content.springer.com/esm/art%3A10.1007%2Fs10928-012-9274-0/MediaObjects/10928_2012_9274_MOESM1_ESM.docx
#'
#' @examples
#' pk_1cmt_oral(dose = 500, tau = 12, CL = 5, V = 50, KA = 1)
#'
#' @export
pk_1cmt_oral <- function(
t = c(0:24),
dose = 100,
tau = 12,
KA = 1,
CL = 3,
V = 30,
F = 1,
ruv = NULL
) {
k <- CL / V
tmp <- c()
dat <- data.frame(cbind(t = t, dv = 0))
t_dos <- t %% tau
n_dos <- floor(t/tau)
unq_dos <- unique(n_dos) + 1
if(KA == k) {
Tmax <- 1/k
Cmax <- F*dose / (V*exp(1))
V_tmp <- F*dose / (Cmax * exp(1))
}
for(i in seq(unq_dos)) {
sel <- n_dos >= i-1
tmp <- dat[sel,]
tmp$t <- tmp$t - (i-1)*tau
if(KA == k) {
tmp$dv <- (Cmax * exp(1) * tmp$t / Tmax) * exp(-tmp$t / Tmax)
} else {
tmp$dv <- (F*dose*KA/(V*(KA-k)))*(exp(-k*tmp$t) - exp(-KA*tmp$t))
}
dat[sel,]$dv <- dat[sel,]$dv + tmp$dv
}
if(!is.null(ruv)) {
dat$dv <- add_ruv (dat$dv, ruv)
}
return(dat)
}
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