The Half-Life Formula in Pharmacokinetics
The half-life (t₁/₂) of a drug is defined as the time taken for the plasma concentration to decrease by 50%, and is calculated using the formula t₁/₂ = 0.693 × Vd/CL, where Vd is the volume of distribution and CL is clearance. 1
Understanding Half-Life
Half-life is one of the most important pharmacokinetic parameters with significant clinical implications. It determines:
- How frequently a medication needs to be dosed
- Time to reach steady state (approximately 5 half-lives)
- Time for drug elimination (approximately 5 half-lives for 97% elimination)
- Risk of drug accumulation
Basic Formula Components
The standard half-life formula consists of:
- t₁/₂ = 0.693 × Vd/CL
Where:
- 0.693 is the natural logarithm of 2 (ln 2)
- Vd is the volume of distribution (in L/kg or L)
- CL is the clearance (in L/h or mL/min)
Alternative Expressions
In a one-compartment model, the half-life can also be expressed as:
- t₁/₂ = ln(2)/k
Where:
- k is the elimination rate constant
For drugs following first-order kinetics (most drugs), the elimination rate is proportional to the drug concentration.
Clinical Applications of Half-Life
Dosing Implications
- Drugs with short half-lives (< 8 hours) typically require multiple daily doses
- Drugs with half-lives of 12-48 hours are ideal for once-daily dosing 2
- Drugs with very long half-lives (> 24 hours) may allow for less frequent dosing
Perioperative Management
The half-life formula is crucial for determining when to stop medications before procedures:
- For direct oral anticoagulants (DOACs), discontinuation timing is based on half-lives:
Drug Accumulation
The half-life determines drug accumulation at steady state. For drugs with longer half-lives, the time to reach steady state is prolonged, which affects:
- Time to maximum therapeutic effect
- Risk of adverse effects
- Time to drug elimination after discontinuation
Factors Affecting Half-Life
Several factors can alter a drug's half-life:
- Renal function: Impaired kidney function increases the half-life of renally eliminated drugs
- Hepatic function: Liver disease prolongs half-life of hepatically metabolized drugs
- Age: Elderly patients often have longer half-lives due to reduced clearance
- Drug interactions: Medications affecting metabolism can alter half-life
- Protein binding: Changes in protein binding can affect the free fraction available for elimination
Common Pitfalls in Half-Life Calculation
Multi-Compartment Models
The simple half-life formula assumes a one-compartment model, which may underestimate the true half-life by:
- Up to 25% for humans
- Up to 26% for dogs
- Up to 20% for monkeys 4
For drugs with multi-compartment distribution, the terminal half-life (t₁/₂,z) is most clinically relevant, representing the elimination phase after distribution equilibrium.
Operational vs. Terminal Half-Life
The terminal half-life may overpredict drug accumulation at steady state. For some drugs, the "operational multiple dosing half-life" (t₁/₂,op) better predicts actual accumulation behavior, especially for extended-release formulations 5.
Active Metabolites
When calculating a drug's effective half-life, active metabolites must be considered. For example, some drugs have active metabolites with longer half-lives than the parent compound, extending the duration of action beyond what the parent drug's half-life would suggest 1.
Practical Application
For accurate half-life determination:
- Use the appropriate model (one-compartment vs. multi-compartment)
- Consider both distribution and elimination phases
- Account for patient-specific factors affecting clearance and volume of distribution
- Remember that for most drugs, 5 half-lives are required for:
- Reaching steady state when starting therapy
- Nearly complete elimination (97%) when discontinuing therapy 6
The half-life formula provides essential information for optimizing drug dosing regimens, managing perioperative medication adjustments, and predicting drug behavior in various clinical scenarios.