For an IV infusion, what is the relationship between Css,avg, dose rate, and clearance?

• A. Css,avg = Rate_in × Cl.
• B. Css,avg = Dose/τ.
• C. Css,avg = Rate_in / Cl; Rate_in = Dose/τ.
• D. Css,avg = Cl / Rate_in.

Answer: (C)

At steady state during an IV infusion, the rate at which drug enters the body must equal the rate at which it is eliminated. The elimination rate is the product of clearance and the average steady-state concentration, so Rate_in = Cl × Css,avg. Rearranging gives Css,avg = Rate_in / Cl.

Rate_in is the constant infusion rate, which equals Dose divided by the dosing interval τ (Rate_in = Dose/τ). Substituting this into the previous relation yields Css,avg = (Dose/τ) / Cl = Dose / (τ × Cl).

This makes the option that expresses Css,avg as Rate_in divided by Cl and Rate_in as Dose/τ the correct one. The other forms either multiply by Cl, ignore clearance, or invert the relationship, which don’t describe the steady-state infusion correctly.