FRCA Primary Question Bank

The apparent volume of distribution (Vd) is calculated as dose divided by the plasma concentration extrapolated to time zero (C0): Vd = dose / C0 = 50 mg / 10 mg/L = 5 L (answer B).

Vd is a theoretical (apparent) volume relating the total amount of drug in the body to the measured plasma concentration. A Vd of approximately 5 L approximates the intravascular (blood) volume of a 70 kg adult, a pattern seen with drugs largely confined to the vasculature because of high plasma protein binding or large molecular size (e.g. heparin, warfarin).

The other values do not fit the calculation: 3.5 L underestimates the result, while 7 L, 10 L and 14 L would imply distribution into the extracellular fluid or beyond. Understanding Vd is essential for calculating loading doses, since loading dose = Vd x target plasma concentration. This is core content of the RCoA Primary FRCA pharmacology curriculum.

Remember: Vd = dose / C0; a Vd of around 5 L indicates a drug largely confined to the intravascular compartment, and Vd drives the loading dose calculation (loading dose = Vd x target concentration).

A volume of distribution exceeding total body water (approximately 42 L in a 70 kg adult) indicates extensive tissue sequestration. Vd is an apparent volume - it does not correspond to a real physiological space. When Vd is very large, it means the drug is extensively bound to tissues relative to plasma. The relationship is described by Vd = Vp + Vt × (fu/fut), where Vp is plasma volume, Vt is tissue volume, fu is the fraction unbound in plasma, and fut is the fraction unbound in tissues. Extensive tissue binding lowers fut, which raises the fu/fut ratio and therefore increases Vd.

Amiodarone (Vd ~70 L/kg) and chloroquine (Vd ~200 L/kg) are classic examples of drugs with very large Vd values; the BNF reflects this in amiodarone's need for a prolonged loading regimen and its very long elimination half-life owing to accumulation in lipid-rich tissues. A drug confined to the intravascular compartment would have a Vd of approximately 3-5 L. High plasma protein binding would reduce Vd, not increase it.

Remember: Volume of distribution is an apparent, not real, volume - values exceeding total body water indicate extensive tissue binding relative to plasma binding.

The elimination half-life is approximately 345 minutes (about 5.8 hours). Half-life is derived from the relationship t½ = 0.693 × Vd ÷ clearance, where 0.693 is the natural logarithm of 2 (ln2), the constant that links the first-order elimination rate constant to the time taken for the plasma concentration to halve.

Converting to consistent units, a volume of distribution of 50 L equals 50,000 mL and the clearance is 100 mL/min. Substituting gives t½ = 0.693 × 50,000 ÷ 100 = 346 minutes, which rounds to the 345-minute option. The distractors do not satisfy the equation: 115 and 230 minutes underestimate the half-life, while 500 and 693 minutes overestimate it (693 minutes would arise only if the 0.693 constant were erroneously omitted from the numerator).

This calculation assumes a single-compartment model with first-order elimination. A large volume of distribution prolongs half-life because drug sequestered in peripheral tissues is unavailable to the clearing organs, whereas a high clearance shortens it. Half-life is therefore a hybrid (dependent) variable governed by both Vd and clearance rather than an independent property of the drug - a distinction emphasised in the RCoA Primary FRCA pharmacokinetics curriculum and standard texts.

Remember: t½ = 0.693 × Vd ÷ clearance - always reconcile units (Vd in mL, clearance in mL/min). Half-life is a derived parameter determined jointly by volume of distribution and clearance, so changes in either alter it.