This is a real one-compartment pharmacokinetic model with first-order oral absorption. Each dose D is absorbed at rate ka and eliminated at rate ke = CL/Vd, where clearance CL is scaled by the patient's CYP450 activity score. Repeated doses superpose linearly — the concentration at any moment is the sum of every past dose's own decaying contribution:
C(t) = Σₙ D·kₐ / (Vd·(kₐ−kₑ)) · [e^(−kₑ(t−tₙ)) − e^(−kₐ(t−tₙ))]
kₑ = CL / Vd, CL = CL_normal · activity(genotype)
t½ = ln(2) / kₑ
- Genotype — CYP450 activity score: PM 0.25×, IM 0.5×, NM 1.0×, RM 1.75×, UM 3.0× clearance. A poor metabolizer clears the drug slowly and accumulates toward toxicity on a normal-person dose; an ultrarapid metabolizer clears it so fast the concentration can never climb into the window.
- Dose and interval τ — the prescriber's two real levers. The only way to keep a poor metabolizer safe is a smaller dose or a longer interval; the only way to get an ultrarapid metabolizer into the window is a larger dose or a shorter interval.
- Therapeutic window (shaded band) — concentration must clear the effective floor to work and stay under the toxic ceiling to be safe. This is exactly the CPIC dosing-guideline problem for narrow-therapeutic-index drugs like warfarin, clopidogrel and tricyclic antidepressants.
Real-world relevance: identical mg doses of the same drug can leave a poor metabolizer toxic and an ultrarapid metabolizer sub-therapeutic — this is why CYP450 genotyping before prescribing narrow-window drugs changes the actual mg dose ordered, not just a footnote on the label.