Which formula represents a loading dose used to quickly achieve target drug concentration?

• A. LD = Css × Vd
• B. LD = Css × Cl
• C. LD = Dose × F
• D. LD = Vd / Css

Answer: (A)

To rapidly reach a target drug level, you give a loading dose that fills the body’s distribution space, captured by the volume of distribution (Vd). Right after an IV bolus with instantaneous distribution, the plasma concentration equals Dose/Vd. To hit the desired concentration Css, set Dose/Vd = Css and solve for Dose, giving Dose = Css × Vd. This directly links the amount you give to both the target concentration and how widely the drug distributes.

If the drug is given orally, you’d adjust for incomplete absorption with F (bioavailability): Dose = Css × Vd / F, which reduces to Css × Vd for IV administration where F = 1.

The other formulas don’t reflect how much needs to be given to achieve the target concentration quickly. Dose × F isn’t the correct relationship for a loading dose, and Vd/Css would give an incorrect unit and meaning, while Css × Cl relates to elimination rate, not the initial amount needed.