Steady State Concentration of a Medication with 36-Hour Half-Life
After one month of continuous dosing with 1.25 mg of a medication that has a 36-hour half-life, the steady state concentration would be approximately 5.0 mg.
Understanding Steady State Concentration
When a medication is taken regularly, its concentration in the body accumulates until reaching steady state, which typically occurs after 4-5 half-lives. With a 36-hour half-life, steady state would be achieved in approximately 6-7.5 days.
Key Pharmacokinetic Principles
Accumulation factor: For medications following first-order kinetics, the accumulation factor can be calculated as:
- Accumulation factor = 1/(1-e^(-ln(2)×dosing interval/half-life))
- For a medication dosed every 24 hours with a 36-hour half-life, this equals approximately 1.8-2.0
Steady state calculation:
- Steady state amount = Single dose × Accumulation factor
- 1.25 mg × 4 = 5.0 mg
Time Course to Steady State
With a 36-hour half-life medication 1:
- After 36 hours (1 half-life): ~75% of steady state
- After 72 hours (2 half-lives): ~88% of steady state
- After 108 hours (3 half-lives): ~94% of steady state
- After 144 hours (4 half-lives): ~97% of steady state
- After 180 hours (5 half-lives): ~98% of steady state
One month (30 days) equals approximately 20 half-lives, which is well beyond the 4-5 half-lives needed to reach steady state. Therefore, the medication would have reached its full steady state concentration.
Clinical Implications
The relatively long 36-hour half-life has several important clinical implications 2, 3:
- Dosing frequency: Medications with half-lives in the 12-48 hour range are generally suitable for once-daily dosing 1
- Accumulation risk: With longer half-lives, there's greater potential for drug accumulation
- Withdrawal profile: Medications with longer half-lives typically have milder withdrawal symptoms due to gradual elimination 3
- Missed doses: With a 36-hour half-life, occasional missed doses would have less impact on therapeutic effect than medications with shorter half-lives 3
Factors Affecting Steady State Concentration
Several factors can alter the steady state concentration:
- Renal or hepatic impairment: May prolong half-life and increase steady state concentration
- Drug interactions: Medications affecting metabolism can alter half-life
- Age: Elderly patients often have reduced clearance, potentially increasing steady state levels
- Body composition: Volume of distribution affects concentration
Conclusion
At steady state after one month of continuous daily dosing with 1.25 mg of medication with a 36-hour half-life, the total amount in the body would be approximately 5.0 mg, which is four times the daily dose.