Question

So for the following question I really want to understand how to approach the problem. I'm having a really hard time understanding the concept so a detailed answer (that's also dumbed down) will be much appreciated!

If a drug has a half-life of 10 hours and is taken orally, how long will it take until the subject achieves a steady state drug concentration?

Answer 1

The steady state is defined as when the rate if input of the drug equals to the rate of elimination of the drug, then steady state has been achieved.

To explain this lets take an example of a cartoon of eggs in kitchen. Every morning you utilize two eggs to prepare breakfast. Someone who notice this, buy eggs and fill the cartoon. After few days, this will appear as if the cartoon was never empty. Thus it can be said the eggs are in steady state as the rate of elimination is equal to rate of input.

The half life of a drug is the time it takes for the plasma concentration of the drug of reach half of its origional concentration.

• If the half life of the drug is 10 hours and 5 half lives are required, then it will take 50 hours to achieve steady state concentration.
• If the half life of the drug is 10 hours and 4 half lives are required, then it will take 40 hours to achieve steady state concentration.
• If the half life of the drug is 10 hours and 3 half lives are required, then it will take 30 hours to achieve steady state concentration.
• If the half life of the drug is 10 hours and 2 half lives are required, then it will take 20 hours to achieve steady state concentration.
• If the half life of the drug is 10 hours and 1 half lives are required, then it will take 10 hours to achieve steady state concentration.

Here the number of half live required indicated how much percentage of steady state concentration is to be achieved. That means:

• 1 half life means 50% of steady state is achieved.
• 2 Half life means 75 % of steady state is achieved.
• 3 Half life means 87.5 % of steady state is achieved.
• 4 Half life means 93.8 % of steady state is achieved.
• 5 Half life means 96.9 % of steady state is achieved.

This is called rule of thumb which states that the steady state will be achieved after 4-5 half lives.