How to Calculate Half-Life
The half-life of a substance is calculated using the formula t₁/₂ = ln(2)/k, where k is the elimination rate constant. 1, 2
Understanding Half-Life
Half-life (t₁/₂) is defined as the time required for the plasma or blood concentration of a drug to decrease by 50% 2. This pharmacokinetic parameter is crucial for:
- Determining appropriate dosing intervals 2
- Predicting time to steady state concentrations 2
- Estimating drug washout periods 1
- Planning perioperative medication management 1
The Mathematical Formula
The formula for calculating half-life consists of:
- t₁/₂ = ln(2)/k ≈ 0.693/k 2, 3
- Where k is the elimination rate constant (the fraction of drug eliminated per unit time) 4, 3
Practical Application
For medications like metformin:
- The elimination rate constant (k) can be determined from plasma concentration measurements 4, 5
- For metformin specifically, the elimination half-life is approximately 5 hours in patients with normal renal function 4
- This means after 5 hours, the plasma concentration of metformin decreases by 50% 4
Factors Affecting Half-Life
Several factors can influence a drug's half-life:
- Renal function (particularly important for drugs like metformin and dabigatran) 1, 4
- Hepatic function (for drugs metabolized by the liver) 2
- Age (pediatric and geriatric populations often have altered half-lives) 1, 2
- Drug interactions (can inhibit or induce metabolizing enzymes) 2
- Genetic variations in drug transporters (e.g., OCT1 variants affecting metformin) 4
Clinical Significance
Understanding half-life has important clinical applications:
- For medications with short half-lives (e.g., fentanyl: 2-4 hours), more frequent dosing is required to maintain therapeutic levels 1
- Drugs with longer half-lives (e.g., methadone: 15-60 hours) require less frequent dosing 1
- When discontinuing medications before procedures, timing depends on the half-life 1
- For example, dabigatran (t₁/₂ = 14-17 hours) should be stopped 3-5 days before high bleeding risk surgery 1
Advanced Concepts: Context-Sensitive Half-Time
For intravenous medications administered by continuous infusion:
- The context-sensitive half-time may be more relevant than elimination half-life 6
- This represents the time required for plasma concentration to decrease by 50% after terminating an infusion of specific duration 6
- For example, fentanyl's context-sensitive half-time increases significantly with longer infusions (200 minutes after 6-hour infusion, 300 minutes after 12-hour infusion) 1
Practical Estimation Methods
When multiple blood samples are difficult to obtain (e.g., in critically ill patients):
- A single blood sample method can be used to estimate half-life 5
- This approach uses known pharmacokinetic parameters combined with the single measurement 5
- The formula can be calculated using standard computing tools at the bedside 5
Understanding and correctly calculating half-life is essential for appropriate medication dosing, particularly for drugs with narrow therapeutic windows or in patients with altered drug clearance.