Nothing
R/calc_derived.R
In pmxTools: Pharmacometric and Pharmacokinetic Toolkit
Defines functions
calc_derived_3cpt
calc_derived_2cpt
calc_derived_1cpt
calc_derived
Documented in
calc_derived
calc_derived_1cpt
calc_derived_2cpt
calc_derived_3cpt
#' Calculate derived pharmacokinetic parameters for a 1-, 2-, or 3-compartment
#' linear model.
#'
#' @param CL Clearance (volume per time units, e.g. L/h)
#' @param V1,V Central volume of distribution (volume units, e.g. L). Values
#' are synonyms; use only one.
#' @param V2 First peripheral volume of distribution (volume units, e.g. L)
#' @param V3 Second peripheral volume of distribution (volume units, e.g. L)
#' @param Q2,Q Intercompartmental clearance from central to first peripheral
#' compartment (volume per time units, e.g. L/h). Values are synonyms; use
#' only one.
#' @param Q3 Intercompartmental clearance from central to second peripheral
#' compartment (volume per time units, e.g. L/h)
#' @param ka Absorption rate (inverse time units, e.g. 1/h)
#' @param dur Duration of zero-order absorption (time units, e.g. h)
#' @param tlag Absorption lag time (time units, e.g. h)
#' @param tinf Duration of infusion (time units, e.g. h)
#' @param dose Dose (amount units, e.g. mg)
#' @param tau Duration of interdose interval (time units, e.g. h; defaults to 24)
#' @param step Time increment to use when estimating NCA parameters (time units, e.g. h; defaults to 0.1)
#' @param type Parameters to return. Default is \code{"all"}. If not
#' \code{"all"}, this may be a vector from the names of the return value list.
#' @param sigdig Number of significant digits to be returned. Default is
#' \code{5}.
#' @param verbose For \code{calc_derived()}, provide a message indicating the
#' type of model detected.
#' @param ... Passed to the other \code{calc_derived_*()} functions.
#'
#' @return Return a list of derived PK parameters for a 1-, 2-, or 3-compartment
#' linear model given provided clearances and volumes based on the
#' \code{type}. If a dose is provided, estimated non-compartmental analysis (NCA) parameters will
#' be provided as well, based on simulation of single-dose and (if `tau` is specified) steady-state time courses.
#' \itemize{
#' \item \code{Vss}: Volume of distribution at steady state, \eqn{V_{ss}} (volume units, e.g. L); 1-, 2-, and 3-compartment
#' \item \code{k10}: First-order elimination rate, \eqn{k_{10}} (inverse time units, e.g. 1/h); 1-, 2-, and 3-compartment
#' \item \code{k12}: First-order rate of transfer from central to first peripheral compartment, \eqn{k_{12}} (inverse time units, e.g. 1/h); 2- and 3-compartment
#' \item \code{k21}: First-order rate of transfer from first peripheral to central compartment, \eqn{k_{21}} (inverse time units, e.g. 1/h); 2- and 3-compartment
#' \item \code{k13}: First-order rate of transfer from central to second peripheral compartment, \eqn{k_{13}} (inverse time units, e.g. 1/h); 3-compartment
#' \item \code{k31}: First-order rate of transfer from second peripheral to central compartment,\eqn{k_{31}} (inverse time units, e.g. 1/h); 3-compartment
#' \item \code{thalf_alpha}: \eqn{t_{1/2,\alpha}} (time units, e.g. h); 1-, 2-, and 3-compartment
#' \item \code{thalf_beta}: \eqn{t_{1/2,\beta}} (time units, e.g. h); 2- and 3-compartment
#' \item \code{thalf_gamma}: \eqn{t_{1/2,\gamma}} (time units, e.g. h); 3-compartment
#' \item \code{alpha}: \eqn{\alpha}; 1-, 2-, and 3-compartment
#' \item \code{beta}: \eqn{\beta}; 2- and 3-compartment
#' \item \code{gamma}: \eqn{\beta}; 3-compartment
#' \item \code{trueA}: true A; 1-, 2-, and 3-compartment
#' \item \code{trueB}: true B; 2- and 3-compartment
#' \item \code{trueC}: true C; 3-compartment
#' \item \code{fracA}: fractional A; 1-, 2-, and 3-compartment
#' \item \code{fracB}: fractional B; 2- and 3-compartment
#' \item \code{fracC}: fractional C; 3-compartment
#' \item \code{AUCinf}: Area under the concentration-time curve to infinity (single dose)
#' \item \code{AUCtau}: Area under the concentration-time curve over the dosing interval at steady state
#' \item \code{Cmax}: Maximum concentration after a single dose
#' \item \code{Cmaxss}: Maximum concentration over the dosing interval at steady state
#' \item \code{Tmax}: Time after dose of maximum concentration
#' \item \code{AUCinf_dose_normalized}: Dose-normalized area under the concentration-time curve to infinity (single dose)
#' \item \code{AUCtau_dose_normalized}: Dose-normalized area under the concentration-time curve over the dosing interval at steady state
#' \item \code{Cmax_dose_normalized}: Dose-normalized maximum concentration after a single dose
#' \item \code{Cmaxss_dose_normalized}: Dose-normalized maximum concentration over the dosing interval at steady state
#' \item \code{step}: Time increment used when estimating NCA parameters.
#' }
#'
#' The input parameters with standardized names (\code{dose}, \code{V1}, \code{V2},
#' \code{V3}, \code{CL}, \code{Q2}, and \code{Q3}) are also returned in the
#' list, and if provided, additional PK parameters of `ka`, `tlag`, `tinf` and `dur` are also
#' returned in the list. All inputs may be scalars or vectors.
#'
#' @author Justin Wilkins, \email{justin.wilkins@@occams.com}
#' @author Bill Denney, \email{wdenney@@humanpredictions.com}
#' @references Shafer S. L. \code{CONVERT.XLS}
#' @references Rowland M, Tozer TN. Clinical Pharmacokinetics and
#' Pharmacodynamics: Concepts and Applications (4th). Lippincott Williams &
#' Wilkins, Philadelphia, 2010.
#'
#' @examples
#' params <- calc_derived(CL=29.4, V1=23.4, V2=114, V3=4614, Q2=270, Q3=73)
#' @importFrom PKNCA pk.calc.auc.all
#' @export
calc_derived <- function(..., verbose=FALSE) {
arg_names <- names(list(...))
if (all(arg_names %in% names(formals(calc_derived_1cpt)))) {
if (verbose) message("Detected 1-compartment model")
calc_derived_1cpt(...)
} else if (all(arg_names %in% names(formals(calc_derived_2cpt)))) {
if (verbose) message("Detected 2-compartment model")
calc_derived_2cpt(...)
} else if (all(arg_names %in% names(formals(calc_derived_3cpt)))) {
if (verbose) message("Detected 3-compartment model")
calc_derived_3cpt(...)
} else {
unknown_params <- setdiff(arg_names, names(formals(calc_derived_3cpt)))
stop(
"Could not determine model type based on argument names. Please check the following argument names: ",
paste(unknown_params, collapse=", ")
)
}
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_1cpt(CL=16, V=25)
#' @export
calc_derived_1cpt <- function(CL, V=NULL, V1=NULL, ka=NULL, dur=NULL, tlag=NULL, tinf=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
k10 <- CL/V1
Vss <- V1
trueA <- 1/V1
thalf <- log(2)/k10
alpha <- k10
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("1-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("1-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("1-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(CL/V1, sigdig),
Vss=signif(Vss, sigdig),
thalf=signif(thalf, sigdig),
alpha=signif(alpha, sigdig),
trueA=signif(1/V1, sigdig),
fracA=1,
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_2cpt(CL=16, V1=25, V2=50, Q=0.5)
#' @export
calc_derived_2cpt <- function(CL, V1=NULL, V2, Q2=NULL, V=NULL, Q=NULL, dur=NULL, tinf=NULL, ka=NULL, tlag=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
if (!xor(is.null(Q), is.null(Q2))) {
stop("Exactly one of Q or Q2 may be provided since they are considered synonyms.")
} else if (!is.null(Q)) {
# Use the preferred synonym
Q2 <- Q
}
### variables
k10 <- CL/V1
k12 <- Q2/V1
k21 <- Q2/V2
a0 <- k10 * k21
a1 <- -(k10 + k12 + k21)
i1 <- (-a1 + sqrt(a1*a1-4*a0))/2
i2 <- (-a1 - sqrt(a1*a1-4*a0))/2
c1 <- (k21 - i1)/(i2 - i1)/V1
c2 <- (k21 - i2)/(i1 - i2)/V1
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("2-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("2-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("2-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(k10, sigdig),
k12=signif(k12, sigdig),
k21=signif(k21, sigdig),
Vss=signif(V1 + V2, sigdig),
thalf_alpha=signif(log(2)/i1, sigdig),
thalf_beta=signif(log(2)/i2, sigdig),
alpha=signif(i1, sigdig),
beta=signif(i2, sigdig),
trueA=signif(c1, sigdig),
trueB=signif(c2, sigdig),
fracA=signif(c1*V1, sigdig),
fracB=signif(c2*V1, sigdig),
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
V2=V2,
Q2=Q2,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_3cpt(CL=29.4, V1=23.4, V2=114, V3=4614, Q2=270, Q3=73)
#' @export
calc_derived_3cpt <- function(CL, V1=NULL, V2, V3, Q2=NULL, Q3, V=NULL, Q=NULL, ka=NULL, dur=NULL, tinf=NULL, tlag=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
if (!xor(is.null(Q), is.null(Q2))) {
stop("Exactly one of Q or Q2 may be provided since they are considered synonyms.")
} else if (!is.null(Q)) {
# Use the preferred synonym
Q2 <- Q
}
### variables
k10 <- CL/V1
k12 <- Q2/V1
k21 <- Q2/V2
k13 <- Q3/V1
k31 <- Q3/V3
a0 <- k10 * k21 * k31
a1 <- (k10 * k31) + (k21 * k31) + (k21 * k13) + (k10 * k21) + (k31 * k12)
a2 <- k10 + k12 + k13 + k21 + k31
p <- a1 - (a2 * a2 / 3)
q <- (2 * a2 * a2 * a2 / 27) - (a1 * a2 / 3) + a0
r1 <- sqrt(-(p * p * p)/27)
phi <- acos((-q/2)/r1)/3
r2 <- 2 * exp(log(r1)/3)
root1 <- -(cos(phi) * r2 - a2/3)
root2 <- -(cos(phi + 2 * pi/3) * r2 - a2/3)
root3 <- -(cos(phi + 4 * pi/3) * r2 - a2/3)
i1 <- pmax(root1, root2, root3)
# There is no pmedian function
i2 <- mapply(FUN=function(...) median(c(...)), root1, root2, root3)
i3 <- pmin(root1, root2, root3)
c1 <- (k21 - i1) * (k31 - i1) / (i1 - i2) / (i1 - i3) / V1
c2 <- (k21 - i2) * (k31 - i2) / (i2 - i1) / (i2 - i3) / V1
c3 <- (k21 - i3) * (k31 - i3) / (i3 - i2) / (i3 - i1) / V1
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("3-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("3-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("3-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(k10, sigdig),
k12=signif(k12, sigdig),
k21=signif(k21, sigdig),
k13=signif(k13, sigdig),
k31=signif(k31, sigdig),
Vss=signif(V1 + V2 + V3, sigdig),
thalf_alpha=signif(log(2)/i1, sigdig),
thalf_beta =signif(log(2)/i2, sigdig),
thalf_gamma=signif(log(2)/i3, sigdig),
alpha=signif(i1, sigdig),
beta =signif(i2, sigdig),
gamma=signif(i3, sigdig),
trueA=signif(c1, sigdig),
trueB=signif(c2, sigdig),
trueC=signif(c3, sigdig),
fracA=signif(c1*V1, sigdig),
fracB=signif(c2*V1, sigdig),
fracC=signif(c3*V1, sigdig),
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
V2=V2,
V3=V3,
Q2=Q2,
Q3=Q3,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
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Defines functions calc_derived_3cpt calc_derived_2cpt calc_derived_1cpt calc_derived
Documented in calc_derived calc_derived_1cpt calc_derived_2cpt calc_derived_3cpt
#' Calculate derived pharmacokinetic parameters for a 1-, 2-, or 3-compartment
#' linear model.
#'
#' @param CL Clearance (volume per time units, e.g. L/h)
#' @param V1,V Central volume of distribution (volume units, e.g. L). Values
#' are synonyms; use only one.
#' @param V2 First peripheral volume of distribution (volume units, e.g. L)
#' @param V3 Second peripheral volume of distribution (volume units, e.g. L)
#' @param Q2,Q Intercompartmental clearance from central to first peripheral
#' compartment (volume per time units, e.g. L/h). Values are synonyms; use
#' only one.
#' @param Q3 Intercompartmental clearance from central to second peripheral
#' compartment (volume per time units, e.g. L/h)
#' @param ka Absorption rate (inverse time units, e.g. 1/h)
#' @param dur Duration of zero-order absorption (time units, e.g. h)
#' @param tlag Absorption lag time (time units, e.g. h)
#' @param tinf Duration of infusion (time units, e.g. h)
#' @param dose Dose (amount units, e.g. mg)
#' @param tau Duration of interdose interval (time units, e.g. h; defaults to 24)
#' @param step Time increment to use when estimating NCA parameters (time units, e.g. h; defaults to 0.1)
#' @param type Parameters to return. Default is \code{"all"}. If not
#' \code{"all"}, this may be a vector from the names of the return value list.
#' @param sigdig Number of significant digits to be returned. Default is
#' \code{5}.
#' @param verbose For \code{calc_derived()}, provide a message indicating the
#' type of model detected.
#' @param ... Passed to the other \code{calc_derived_*()} functions.
#'
#' @return Return a list of derived PK parameters for a 1-, 2-, or 3-compartment
#' linear model given provided clearances and volumes based on the
#' \code{type}. If a dose is provided, estimated non-compartmental analysis (NCA) parameters will
#' be provided as well, based on simulation of single-dose and (if `tau` is specified) steady-state time courses.
#' \itemize{
#' \item \code{Vss}: Volume of distribution at steady state, \eqn{V_{ss}} (volume units, e.g. L); 1-, 2-, and 3-compartment
#' \item \code{k10}: First-order elimination rate, \eqn{k_{10}} (inverse time units, e.g. 1/h); 1-, 2-, and 3-compartment
#' \item \code{k12}: First-order rate of transfer from central to first peripheral compartment, \eqn{k_{12}} (inverse time units, e.g. 1/h); 2- and 3-compartment
#' \item \code{k21}: First-order rate of transfer from first peripheral to central compartment, \eqn{k_{21}} (inverse time units, e.g. 1/h); 2- and 3-compartment
#' \item \code{k13}: First-order rate of transfer from central to second peripheral compartment, \eqn{k_{13}} (inverse time units, e.g. 1/h); 3-compartment
#' \item \code{k31}: First-order rate of transfer from second peripheral to central compartment,\eqn{k_{31}} (inverse time units, e.g. 1/h); 3-compartment
#' \item \code{thalf_alpha}: \eqn{t_{1/2,\alpha}} (time units, e.g. h); 1-, 2-, and 3-compartment
#' \item \code{thalf_beta}: \eqn{t_{1/2,\beta}} (time units, e.g. h); 2- and 3-compartment
#' \item \code{thalf_gamma}: \eqn{t_{1/2,\gamma}} (time units, e.g. h); 3-compartment
#' \item \code{alpha}: \eqn{\alpha}; 1-, 2-, and 3-compartment
#' \item \code{beta}: \eqn{\beta}; 2- and 3-compartment
#' \item \code{gamma}: \eqn{\beta}; 3-compartment
#' \item \code{trueA}: true A; 1-, 2-, and 3-compartment
#' \item \code{trueB}: true B; 2- and 3-compartment
#' \item \code{trueC}: true C; 3-compartment
#' \item \code{fracA}: fractional A; 1-, 2-, and 3-compartment
#' \item \code{fracB}: fractional B; 2- and 3-compartment
#' \item \code{fracC}: fractional C; 3-compartment
#' \item \code{AUCinf}: Area under the concentration-time curve to infinity (single dose)
#' \item \code{AUCtau}: Area under the concentration-time curve over the dosing interval at steady state
#' \item \code{Cmax}: Maximum concentration after a single dose
#' \item \code{Cmaxss}: Maximum concentration over the dosing interval at steady state
#' \item \code{Tmax}: Time after dose of maximum concentration
#' \item \code{AUCinf_dose_normalized}: Dose-normalized area under the concentration-time curve to infinity (single dose)
#' \item \code{AUCtau_dose_normalized}: Dose-normalized area under the concentration-time curve over the dosing interval at steady state
#' \item \code{Cmax_dose_normalized}: Dose-normalized maximum concentration after a single dose
#' \item \code{Cmaxss_dose_normalized}: Dose-normalized maximum concentration over the dosing interval at steady state
#' \item \code{step}: Time increment used when estimating NCA parameters.
#' }
#'
#' The input parameters with standardized names (\code{dose}, \code{V1}, \code{V2},
#' \code{V3}, \code{CL}, \code{Q2}, and \code{Q3}) are also returned in the
#' list, and if provided, additional PK parameters of `ka`, `tlag`, `tinf` and `dur` are also
#' returned in the list. All inputs may be scalars or vectors.
#'
#' @author Justin Wilkins, \email{justin.wilkins@@occams.com}
#' @author Bill Denney, \email{wdenney@@humanpredictions.com}
#' @references Shafer S. L. \code{CONVERT.XLS}
#' @references Rowland M, Tozer TN. Clinical Pharmacokinetics and
#' Pharmacodynamics: Concepts and Applications (4th). Lippincott Williams &
#' Wilkins, Philadelphia, 2010.
#'
#' @examples
#' params <- calc_derived(CL=29.4, V1=23.4, V2=114, V3=4614, Q2=270, Q3=73)
#' @importFrom PKNCA pk.calc.auc.all
#' @export
calc_derived <- function(..., verbose=FALSE) {
arg_names <- names(list(...))
if (all(arg_names %in% names(formals(calc_derived_1cpt)))) {
if (verbose) message("Detected 1-compartment model")
calc_derived_1cpt(...)
} else if (all(arg_names %in% names(formals(calc_derived_2cpt)))) {
if (verbose) message("Detected 2-compartment model")
calc_derived_2cpt(...)
} else if (all(arg_names %in% names(formals(calc_derived_3cpt)))) {
if (verbose) message("Detected 3-compartment model")
calc_derived_3cpt(...)
} else {
unknown_params <- setdiff(arg_names, names(formals(calc_derived_3cpt)))
stop(
"Could not determine model type based on argument names. Please check the following argument names: ",
paste(unknown_params, collapse=", ")
)
}
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_1cpt(CL=16, V=25)
#' @export
calc_derived_1cpt <- function(CL, V=NULL, V1=NULL, ka=NULL, dur=NULL, tlag=NULL, tinf=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
k10 <- CL/V1
Vss <- V1
trueA <- 1/V1
thalf <- log(2)/k10
alpha <- k10
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("1-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("1-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("1-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("1-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_1cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_1cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(CL/V1, sigdig),
Vss=signif(Vss, sigdig),
thalf=signif(thalf, sigdig),
alpha=signif(alpha, sigdig),
trueA=signif(1/V1, sigdig),
fracA=1,
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_2cpt(CL=16, V1=25, V2=50, Q=0.5)
#' @export
calc_derived_2cpt <- function(CL, V1=NULL, V2, Q2=NULL, V=NULL, Q=NULL, dur=NULL, tinf=NULL, ka=NULL, tlag=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
if (!xor(is.null(Q), is.null(Q2))) {
stop("Exactly one of Q or Q2 may be provided since they are considered synonyms.")
} else if (!is.null(Q)) {
# Use the preferred synonym
Q2 <- Q
}
### variables
k10 <- CL/V1
k12 <- Q2/V1
k21 <- Q2/V2
a0 <- k10 * k21
a1 <- -(k10 + k12 + k21)
i1 <- (-a1 + sqrt(a1*a1-4*a0))/2
i2 <- (-a1 - sqrt(a1*a1-4*a0))/2
c1 <- (k21 - i1)/(i2 - i1)/V1
c2 <- (k21 - i2)/(i1 - i2)/V1
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("2-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("2-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("2-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1, V2=V2, Q=Q)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("2-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_2cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_2cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, Q=Q, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(k10, sigdig),
k12=signif(k12, sigdig),
k21=signif(k21, sigdig),
Vss=signif(V1 + V2, sigdig),
thalf_alpha=signif(log(2)/i1, sigdig),
thalf_beta=signif(log(2)/i2, sigdig),
alpha=signif(i1, sigdig),
beta=signif(i2, sigdig),
trueA=signif(c1, sigdig),
trueB=signif(c2, sigdig),
fracA=signif(c1*V1, sigdig),
fracB=signif(c2*V1, sigdig),
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
V2=V2,
Q2=Q2,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
#' @rdname calc_derived
#' @examples
#' params <- calc_derived_3cpt(CL=29.4, V1=23.4, V2=114, V3=4614, Q2=270, Q3=73)
#' @export
calc_derived_3cpt <- function(CL, V1=NULL, V2, V3, Q2=NULL, Q3, V=NULL, Q=NULL, ka=NULL, dur=NULL, tinf=NULL, tlag=NULL, dose=NULL, tau=NULL, step=0.1, type="all", sigdig=5) {
if (!xor(is.null(V), is.null(V1))) {
stop("Exactly one of V or V1 may be provided since they are considered synonyms.")
} else if (!is.null(V)) {
# Use the preferred synonym
V1 <- V
}
if (!xor(is.null(Q), is.null(Q2))) {
stop("Exactly one of Q or Q2 may be provided since they are considered synonyms.")
} else if (!is.null(Q)) {
# Use the preferred synonym
Q2 <- Q
}
### variables
k10 <- CL/V1
k12 <- Q2/V1
k21 <- Q2/V2
k13 <- Q3/V1
k31 <- Q3/V3
a0 <- k10 * k21 * k31
a1 <- (k10 * k31) + (k21 * k31) + (k21 * k13) + (k10 * k21) + (k31 * k12)
a2 <- k10 + k12 + k13 + k21 + k31
p <- a1 - (a2 * a2 / 3)
q <- (2 * a2 * a2 * a2 / 27) - (a1 * a2 / 3) + a0
r1 <- sqrt(-(p * p * p)/27)
phi <- acos((-q/2)/r1)/3
r2 <- 2 * exp(log(r1)/3)
root1 <- -(cos(phi) * r2 - a2/3)
root2 <- -(cos(phi + 2 * pi/3) * r2 - a2/3)
root3 <- -(cos(phi + 4 * pi/3) * r2 - a2/3)
i1 <- pmax(root1, root2, root3)
# There is no pmedian function
i2 <- mapply(FUN=function(...) median(c(...)), root1, root2, root3)
i3 <- pmin(root1, root2, root3)
c1 <- (k21 - i1) * (k31 - i1) / (i1 - i2) / (i1 - i3) / V1
c2 <- (k21 - i2) * (k31 - i2) / (i2 - i1) / (i2 - i3) / V1
c3 <- (k21 - i3) * (k31 - i3) / (i3 - i2) / (i3 - i1) / V1
AUCinf <- NULL
AUCtau <- NULL
Cmax <- NULL
Cmaxss <- NULL
Tmax <- NULL
AUCinf_dose_normalized <- NULL
AUCtau_dose_normalized <- NULL
Cmax_dose_normalized <- NULL
Cmaxss_dose_normalized <- NULL
guess_tmax <- 0
if(!is.null(ka)) guess_tmax <- 1/ka
if(!is.null(dur)) guess_tmax <- dur
if(!is.null(tinf)) guess_tmax <- tinf
tend <- 24
while(tend<guess_tmax) {
tend <- tend*2
}
if(!is.null(dose)) {
message("dose present. NCA parameters will be estimated.")
if(!is.null(tau)) message("tau present. Steady state NCA parameters will be estimated.")
AUCinf <- dose/CL
AUCinf_dose_normalized <- AUCinf/dose
# IV bolus
if(is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment bolus detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_bolus(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_bolus(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# IV infusion
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tinf)) {
message("3-compartment infusion detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_infusion(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tinf = tinf)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & !is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_infusion(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tinf=tinf)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order
if(is.null(dur) & !is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment first-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_1(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_1(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral first-order lag
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("3-compartment first-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_1_lag(t=t, dose=dose, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(is.null(dur) & !is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_1_lag(tad = t, dose=dose, tau=tau, ka=ka, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order
if(!is.null(dur) & is.null(ka) & is.null(tlag) & is.null(tinf)) {
message("3-compartment zero-order oral detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_0(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_0(tad = t, dose=dose, tau=tau, dur=dur, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
# oral zero-order lag
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & is.null(tinf)) {
message("3-compartment zero-order oral with lag time detected.")
t <- seq(0, tend, by=step)
C <- calc_sd_3cmt_linear_oral_0_lag(t=t, dose=dose, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag, dur=dur)
Cmax <- max(C)
Tmax <- t[C==Cmax]
Cmax_dose_normalized <- Cmax/dose
}
if(!is.null(dur) & is.null(ka) & !is.null(tlag) & !is.null(tau) & is.null(tinf)) {
t <- seq(0, tau, by=step)
C <- calc_ss_3cmt_linear_oral_0_lag(tad = t, dose=dose, tau=tau, CL=CL, V1=V1, V2=V2, V3=V3, Q2=Q2, Q3=Q3, tlag=tlag, dur=dur)
Cmaxss <- max(C)
AUCtau <- PKNCA::pk.calc.auc.all(conc = C, time = t)
AUCtau_dose_normalized <- AUCtau/dose
Cmaxss_dose_normalized <- Cmaxss/dose
}
}
out <-
list(
k10=signif(k10, sigdig),
k12=signif(k12, sigdig),
k21=signif(k21, sigdig),
k13=signif(k13, sigdig),
k31=signif(k31, sigdig),
Vss=signif(V1 + V2 + V3, sigdig),
thalf_alpha=signif(log(2)/i1, sigdig),
thalf_beta =signif(log(2)/i2, sigdig),
thalf_gamma=signif(log(2)/i3, sigdig),
alpha=signif(i1, sigdig),
beta =signif(i2, sigdig),
gamma=signif(i3, sigdig),
trueA=signif(c1, sigdig),
trueB=signif(c2, sigdig),
trueC=signif(c3, sigdig),
fracA=signif(c1*V1, sigdig),
fracB=signif(c2*V1, sigdig),
fracC=signif(c3*V1, sigdig),
tau=tau,
AUCinf=AUCinf,
AUCtau=AUCtau,
Cmax=Cmax,
Cmaxss=Cmaxss,
Tmax=Tmax,
AUCinf_dose_normalized=AUCinf_dose_normalized,
AUCtau_dose_normalized=AUCtau_dose_normalized,
Cmax_dose_normalized=Cmax_dose_normalized,
Cmaxss_dose_normalized=Cmaxss_dose_normalized,
step=step,
# Include the macro parameters
CL=CL,
V1=V1,
V2=V2,
V3=V3,
Q2=Q2,
Q3=Q3,
ka=ka,
tlag=tlag,
dur=dur,
tinf=tinf,
dose=dose
)
if(type=="all") {
o <- out
} else {
o <- out[[type]]
if (is.null(o)) {
stop("Invalid value for `type`: ", type)
}
}
o[sapply(o, is.null)] <- NULL # drops NULL values
if(!is.null(ka)) {
if(ka < k10) {
warning("Flip-flop kinetics detected. ka is lower than k10, and half-life may therefore not be similar to the half-life calculated by typical NCA.\n")
}
}
o
}
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