The half-life (T₁/₂) of a drug is the time it takes for the concentration of the drug in the body to reduce by half. It is an important parameter in pharmacokinetics because it helps determine dosing intervals and drug clearance.

Formula to Calculate T₁/₂

The half-life depends on the order of reaction:

1. First-Order Kinetics (Most Common)

For most drugs, elimination follows first-order kinetics, meaning a constant fraction of the drug is eliminated per unit time. The formula is:

T1/2=0.693kT_{1/2} = \frac{0.693}{k}

Where:

• T₁/₂ = Half-life of the drug
• k = Elimination rate constant (per hour or per minute)

To find k, use:

k=ln2T1/2=0.693T1/2k = \frac{\text{ln}2}{T_{1/2}} = \frac{0.693}{T_{1/2}}

Or, if drug concentration at two time points is known:

k=ln⁡(C1/C2)t2−t1k = \frac{\ln(C_1 / C_2)}{t_2 – t_1}

where C₁ and C₂ are drug concentrations at times t₁ and t₂.

2. Zero-Order Kinetics (Rare, e.g., Alcohol)

In zero-order kinetics, a constant amount of drug is eliminated per unit time. The half-life formula is:

T1/2=0.5C0k0T_{1/2} = \frac{0.5 C_0}{k_0}

Where:

• C₀ = Initial drug concentration
• k₀ = Zero-order elimination rate (amount per time)

Practical Example (First-Order)

If a drug has an elimination rate constant k = 0.1 hr⁻¹, then:

T1/2=0.6930.1=6.93 hoursT_{1/2} = \frac{0.693}{0.1} = 6.93 \text{ hours}

So, after 6.93 hours, half of the drug will be gone.

Key Takeaways

• First-order drugs: Use T₁/₂ = 0.693/k.
• Zero-order drugs: Use T₁/₂ = 0.5 C₀ / k₀.
• Knowing T₁/₂ helps in designing proper dosing regimens to maintain effective drug levels.