Posted by Larry Hoover on May 13, 2006, at 9:10:50
In reply to What does half-life really mean?, posted by flip_flop on May 13, 2006, at 1:51:10
> Let's say I take 100 mg of some drug that has a half-life of 6 hours. Does this mean that after 6 hours, 50 mg of the drug is still active? This drug would need to be taken at least 2 times/day, but why couldn't I just take twice the dosage only once/day?
The target you're shooting for is stable blood concentration. Your last example would be an extreme roller coaster. Ideally, you dose at half the intended blood concentration, with a frequency equal to the half life. Let's use your numbers, and work out the math.
Time zero: First dose, 100 mg.
Time +6: 50 mg remaining from first dose, plus 100 mg more = 150 mg. Symbolically, you now have in your blood 1 + 1/2 doses.
Time +12: 75 mg remaining from before, 25 from Tzero, 50 from T6, plus 100 mg more. You now have 1 + 1/2 + 1/4 doses in your blood.
Time +18: 87.5 mg remaining from before, 12.5 from Tzero, 25 from T6, and 50 from T12, plus 100 mg more. You now have 1 + 1/2 + 1/4 + 1/8 doses in your blood.
T24: 93.75 remaining from before.....1 + 1/2 + 1/4 + 1/8 + 1/16The limiting value of the first series is 1 (dose), and that of the second series is 2. I.e. the sum of those fractions that make up each series approaches infinitely close to the numbers 1 and 2. So, a doctor sets the dose at half the expected peak plasma concentration, and sets the dosing frequency so that the interval between doses is the half-life of the drug. Blood concentrations oscillate between 1 and 2 times the dose, with a period of the half life.
It is generally assumed that five half-lives are required to reach fairly stable blood levels, but there are a lot of assumptions being made, and I don't want to go into those too much, yet. Not all drugs work by half-lives. Alcohol is metabolized at a fixed rate, independent of any concept such as half-life, for example (zeroth order rate law).
This example, as hypothesized, would be true for well over 90% of the drugs commonly used. There are some important exceptions, and even doctors screw up on those exceptions.
I hope this helps your understanding. Feel free to ask more questions.
Lar
poster:Larry Hoover
thread:643354
URL: http://www.dr-bob.org/babble/20060510/msgs/643401.html