Drug Half-Life and Dosing
How elimination half-life determines dosing frequency, time to steady state, and drug accumulation during chronic therapy.
## What Is Half-Life?
The elimination half-life (t1/2) is the time required for the plasma concentration of a drug to decrease by 50%. It is determined by two fundamental parameters:
**t1/2 = (0.693 x Vd) / CL**
Where Vd is volume of distribution and CL is clearance. A drug with a large Vd or low clearance will have a long half-life.
## Half-Life and Dosing Frequency
The goal of repeated dosing is to maintain plasma concentrations within the therapeutic window — above the minimum effective concentration (MEC) and below the toxic concentration. General guidelines:
- **Short half-life drugs** (< 4 hours): require frequent dosing or sustained-release formulations. Example: immediate-release morphine (t1/2 ~2-3 hours) dosed every 4 hours.
- **Moderate half-life drugs** (4-12 hours): typically dosed 2-3 times daily. Example: metoprolol (t1/2 ~3-7 hours).
- **Long half-life drugs** (> 24 hours): once-daily or less frequent dosing. Example: amlodipine (t1/2 ~35 hours) dosed once daily.
## Time to Steady State
During repeated dosing at regular intervals, drug accumulates until the rate of administration equals the rate of elimination. This equilibrium is called **steady state** and is reached after approximately **5 half-lives**, regardless of dose or dosing interval.
| Half-Lives Elapsed | % of Steady State |
|-------------------|-------------------|
| 1 | 50% |
| 2 | 75% |
| 3 | 87.5% |
| 4 | 93.75% |
| 5 | 96.875% |
A drug with a 12-hour half-life reaches steady state in about 2.5 days. Amiodarone (t1/2 ~40-55 days) takes 6-9 months without a loading dose.
## Loading Doses
When immediate therapeutic levels are needed and the half-life is long, a **loading dose** rapidly achieves target concentrations:
**Loading dose = Vd x Cp(target) / F**
Examples include digoxin (t1/2 ~36 hours), phenytoin (t1/2 ~22 hours), and amiodarone. The maintenance dose then sustains the concentration.
## Accumulation Factor
During chronic dosing, the accumulation factor predicts how much higher steady-state concentrations will be compared to the first dose:
**Accumulation factor = 1 / (1 - e^(-0.693 x tau/t1/2))**
Where tau is the dosing interval. Drugs dosed at intervals shorter than their half-life accumulate more.
## Key Takeaways
- Half-life depends on both volume of distribution and clearance
- Dosing interval is guided by half-life to maintain therapeutic concentrations
- Steady state is reached after approximately 5 half-lives
- Loading doses are used when the half-life is too long to wait for steady state
- Drug accumulates more when the dosing interval is shorter than the half-life