R-script to reproduce the graphics and additional data frame of results
# CC-BY Helmut Schütz 2024
op <- par()
par("mar" = c(4.1, 4.6, 1, 0), ljoin = "mitre", lend = "square", font.main = 1, cex.main = 1.25, cex.axis = 1.5, cex.lab = 1.5, las = 1)
D <- 100 # dose
V <- 1 # volume of distribution
f <- 1 # fraction absorbed
kel <- 0.15 # elimination rate constant
kabs <- c(2, 1, 0.5, 0.25) # IR: absorption rate constants
kabs <- c(kabs, kel / 3) # MR: abs. slower than el.
t <- seq(0, 24, length.out = 5001) # times
# one-compartment model, zero-order input, first-order elimination
tmax <- log(kabs / kel) / (kabs - kel)
Cmax <- D * f * kabs / (V * (kabs - kel)) * exp(-kel * tmax) - exp(-kabs * tmax))
AUC <- D * f / V / kel
x.int <- 4
y.int <- 25
xs <- seq(0, 24, x.int)
ys <- seq(0, 100, y.int)
plot(1, 1, xlim = c(0, 24), ylim = c(0, 100), type = "n", axes = FALSE, xlab = expression(italic(t) * " [h]"), ylab = expression(italic(C) * " [m / V]"), main = bquote(italic(k)[el] == . ((sprintf("%.3g", kel))))) # empty plot
for (i in seq_along(xs)) { # x-grid
lines(x = rep(xs[i], 2), y = c(0, 100), col = "gray50", lty = 3, lwd = 1.25)
}
for (i in seq_along(ys)) { # y-grid
lines(x = c(0, 24), y = rep(ys[i], 2),col = "gray50", lty = 3, lwd = 1.25)
}
axis(side = 1, at = seq(0, 24, by = 4), lwd = 2.5)
axis(side = 1, at = 0:24, lwd = 1.25, tcl = -0.35, labels = FALSE)
axis(side = 2, at = seq(0, 100, by = 25), lwd = 2.5)
axis(side = 2, at = seq(0, 100, by = 5), lwd = 1.25, tcl = -0.35, labels = FALSE)
clr <- colorRampPalette(c("red", "blue"))((length(kabs) + 1))[-1]
C <- D / V * (exp(-kel * t)) # IV
lines(t, C, col = "red", lwd = 3, lty = 2)
for (i in seq_along(kabs)) { # EV
if (!isTRUE(all.equal(kabs[i], kel))) { # common: kabs # kel
C <- D * f * kabs[i] / (V * (kabs[i] - kel)) * (exp(-kel * t) - exp(-kabs[i] * t))
} else { # flip flop: kabs = kel
k <- kel
C <- D * f / V * k * t * exp(-k * t)
tmax[i] <- 1 / k
Cmax[i] <- D * f / V * k * tmax[i] * exp(-k * tmax[i])
}
lines(t, C, col = clr[i], lwd = 3, lend = "round", ljoin = "round")
}
lgd <- c(" –", sprintf("%.3f", kabs))
legend("top", inset = 0.05, box.lty = 0, bg = "white", lwd = 3, col = c("red", clr), title.cex = 1.25, title = expression(italic(k)[abs]), legend = lgd, lty = c(2, rep(1, length(f))), seg.len = 4)
lgd <- sprintf("%.0f", rep(AUC, length(kabs) + 1))
legend("topright", inset = 0.05, box.lty = 0, bg = "white", col = c("red", clr), title.cex = 1.25, title = expression(italic(AUC)), legend = lgd, pch = 19, pt.cex = 1)
lgd[1] <- bquote(.((sprintf("%.0f (%.0g)", D * f / V, 0))))
for (i in seq_along(Cmax)) {
lgd[i + 1] <- bquote(.((sprintf("%.1f (%5.1f)", Cmax[i], tmax[i]))))
}
legend("right", inset = 0.05, box.lty = 0, bg = "white", col = c("red", clr), title.cex = 1.25, title = expression(italic(C)[max]*" "*(italic(t)[max])), legend = lgd, pch = 19, pt.cex = 1)
par<- op
PK <- data.frame(admin = c("IV", rep("PO", length(kabs))), form = c("IV", rep("IR", length(kabs) - 1), "MR"), f = f, D = D, V = V, kel = kel, kabs = c(NA, kabs), tmax = c(0, tmax), Cmax = c(D * f / V, Cmax), AUC = AUC)
PK[, c(3:5, 7:10)] <- signif(PK[, c(3:5, 7:10)], 3)
PK[, 7] <- sprintf("%.3f", PK[, 7])
PK[1, c(2:3, 7)] <- rep("–", 3)
txt <- paste("admin : Mode of administration", "\nform  : Formulation", "\nf  : Fraction absorbed", "\nD  : Dose", "\nV  : Volume of distribution", "\nkabs  : Absorption rate constant [1 / h]", "\nkel  : Elimination rate constant [1 / h]", "\ntmax  : Time of maximum concentration [h]", "\nCmax  : Maximum concentration [m / V]", "\nAUC  : Area Under the Curve [h × m / V]\n")
print(PK, row.names = FALSE); cat(txt)

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