Mathematical Notes

One-compartment PK

For first-order absorption and elimination:

$$ C(t) = \frac{F \cdot D \cdot k_a}{V_d(k_a-k_e)}\left(e^{-k_e t} - e^{-k_a t}\right) $$

Where:

• $F$ is bioavailability

• $D$ is dose

• $k_a$ is absorption rate

• $k_e$ is elimination rate

• $V_d$ is apparent volume of distribution

AUC

Without physical decay, an analytical approximation is:

$$ \mathrm{AUC}_{0\to\infty} \approx \frac{F \cdot D}{CL} $$

For scenarios with physical decay and/or multi-compartment dynamics, OpenDose-PopPK computes AUC numerically from the simulated profile.