Question

With repeated dosage of a drug how long in half-lives, when the plasma concentration to reach 95% of the steady state level if the drug shows a non-saturating first-order kinetics? Please calculate the number of half life and show the calculation procedure. It should be a specific number but not a range.

Answer 1

In this case, the drugs follow first-order kinetics. According to this model, a constant fraction of the drug is eliminated in the unit of time, and, in turn, the kinetics is exponential. The rate of elimination is directly proportional to drug concentration that, in turn, decays exponentially.
For most drugs, the time to reach steady state is four to five half-lives if the drug is given at regular intervals—no matter the number of doses, the dose size, or the dosing interval. A half-life is how long it takes for half of the drug to be eliminated from the body.

For simplicity, let’s assume we administer a dose every half-life. If a single dose is given every half-life, half of the first dose will be cleared from the body before the next dose.

So, after the second dose, there will be 1.5 doses in the body. Half of that is eliminated and then the next dose is given, meaning there are now 1.75 doses in the body. At dose #5 (after five half-lives), there will be close to two doses in the body, which means one entire dose is eliminated each dosing interval. If we continue dosing at the same frequency, the amount we dose will be eliminated during each dosing interval. As a result, drug concentrations in the body remain constant (steady).

Another way to think about steady state:

• After Dose 1: There are 0.5 doses left at the end of the dosing interval. This means we’re at 50% steady state.
• After Dose 2: There are 1.5 doses in the body, then half is eliminated to leave 0.75 doses (75% steady state).
• After Dose 3: There are 1.75 doses in the body, then half is eliminated to leave 0.875 doses (88% steady state).
• After Dose 4: There are 1.875 doses in the body, then half is eliminated to leave 0.9375 doses (94% steady state).
• After Dose 5: There are 1.9375 doses in the body, then half is eliminated to leave 0.96875 (97% steady state).

At 97% we’re considered to be at approximate steady state, where the rate of input equals the rate of elimination at one dose per dosing interval.

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