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 <- seq(1, 0.25, -0.25) # fractions absorbed
kel <- 0.15 # elimination rate constant
kabs <- 1 # IR: absorption rate constant
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 * c(1, f) / V / kel
x.int <- 4
y.int <- 25
xs <- seq(0, 24, x.int)
ys <- seq(0, 100, y.int)
main <- bquote(italic(k)[abs] * ", " * italic(k)[el]== . ((sprintf("%.3g, %.3g", kabs, kel))))
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 = main) # 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(f) + 1))[-1]
C <- D / V * (exp(-kel * t)) # IV
lines(t, C, col = "red", lwd = 3, lty = 2)
for (i in seq_along(f)) { # EV
if (!isTRUE(all.equal(kabs, kel))) { # common: kabs # kel
C <- D * f[i] * kabs / (V * (kabs - kel)) * (exp(-kel * t) - exp(-kabs * t))
} else { # flip flop: kabs = kel
k <- kel
C <- D * f[i] / V * k * t * exp(-k * t)
tmax[i] <- 1 / k
Cmax[i] <- D * f[i] / V * k * tmax[i] * exp(-k * tmax[i])
}
lines(t, C, col = clr[i], lwd = 3, lend = "round", ljoin = "round")
}
lgd <- c("1*", sprintf("%.3f", f))
legend("top", inset = 0.05, box.lty = 0, bg = "white", lwd = 3, col = c("red", clr), title.cex = 1.25, title = expression(italic(f)), legend = lgd, lty = c(2, rep(1, seg.len = 4)
lgd <- sprintf("%.0f", AUC)
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[1] / V, 0))))
for (i in seq_along(f)) {
lgd[i + 1] <- bquote(.((sprintf("%4.1f (%.2f)", Cmax[i], tmax))))
}
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(f))), form = c("IV", rep("IR", length(f))), f = c(1, f), D = D, V = V, kel = kel, kabs = c(NA, rep(kabs, length(f))), tmax = c(0, rep(tmax, length(f))), Cmax = c(D * f[1] / 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, 7)] <- rep("–", 2)
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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