PharmacologyTier 1Medical Sciences concept

Half-life calculation from clearance and volume of distribution

Core concept

t1/2 = 0.693 x Vd / CL -- half-life is determined by clearance and volume of distribution, it is not an independent primary parameter
Rearranged, this means CL = 0.693 x Vd / t1/2, and Vd = CL x t1/2 / 0.693 -- any one of the three can be derived if the other two are known
A drug's half-life can be prolonged either by decreased clearance (renal/hepatic impairment) or increased Vd (e.g. oedema, obesity for lipophilic drugs) -- same observed effect, opposite underlying cause

Steady state is reached after ~4-5 half-lives regardless of dose or dosing interval -- this is the fact she will be asked to apply, not just define
Time to eliminate a drug (e.g. after overdose or before restarting an interacting drug) also follows ~4-5 half-lives to reach <10% of original level
Fraction of drug excreted unchanged in urine, combined with total clearance, allows calculation of the renal clearance component (renal CL = total CL x fraction excreted unchanged) -- distinguishes renal vs hepatic elimination for a given drug

A common trap: assuming a longer half-life always means "more drug in the body" -- it may instead mean a larger Vd (drug distributed into tissue, less in plasma) with unchanged total clearance
When comparing two drugs by a Vd/CL table, the one with the shorter calculated t1/2 reaches steady state fastest and is cleared fastest after stopping -- useful for choosing an agent when rapid offset is needed (e.g. critical illness)
Dosing interval should be chosen relative to t1/2, not to Vd or CL alone -- a drug with a short t1/2 needs frequent dosing or a sustained-release formulation to maintain a steady concentration

Loading dose calculation depends on Vd alone (see separate note) -- independent of half-life
Maintenance dose/clearance-based dosing (e.g. in renal impairment) depends on CL alone -- again independent of Vd
This is the standard one-compartment model; drugs with multi-compartment kinetics (e.g. early distribution phase) have a more complex, biphasic decline not captured by a single t1/2

3 more sections, plus exam facts

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