drug buildup (half life question/discussion)

[~_Hiss_~]

Lets say, someone takes buprenorphine 16mg a day for 10 years. 3652 days, a high but probably often occuring maintenance dose. They have then taken 58 grams. In the 87,648 hours, they have gone through roughly 2369 half lives at 37hrs.

Is a person who takes 100mg methadone for a few years now dependent on a few grams of methadone?

I don't know an equation to figure it out (i was going to try hence the above #s) but wouldn't they have built up a few grams in their system? Are their other factors involved when people take drugs over long periods of time?

Without knowing much about it, i think it is scary when people are prescribed drugs with long half lives, especially ones that cause dependence such as prozac (half life 4-6 days with chronic use), methadone and buprenorphine. How can drugs like this get approved when there is no idea of conseqences of what will happen when people have hundreds of times the prescribed dose floating around in them?

 

[Sturnam]

well, first of all you have to take into account bioavailability. bupe's bioavailability we'll say is 50% sublingually for easy math. that means you only actually get 8mg of that 16mg in your system.

i know there's definitely more to this, but i don't actually know the mechanics of it. but i do know that you don't have to worry about building up grams in your system.

and you don't have to worry about them not knowing the consequences with many times the 'prescribed dose'. I think that many times the prescribed dose is lower because they know that it takes several days/weeks to build up a steady drug level. plus, that's what Phase III trials are for

 

[Beenhead]

Well generall half life is a first order rate equation

• Half-life of a first-order reaction:

T1/2 = ln2 / k

k = the rate constant for the conversion of Methadone to its inactive counterpart.

[M] = [Mi] (e)^-kt

Meaning the molarity of Methadone after time t equals the initial Molarity of Methadone times the natural log e to the negative rate constant k.

 

[Temeraroius]

Helpfull... you know basic chem and math.

 

[nuke]

Generally first order kinetics so the rate of the metabolic reaction and excretion of a drug increases as the concentration of the drug increases (hence the curve rather than line after peak plasma con'cs), so no, you don't get super excessive amounts of drugs building up in your system usually even if they have long half-lives. However, some drugs are very lipophilic and get stuck in fatty tissues for exceptionally long periods of time.

This is why if you eat 8 grams of mushrooms or 2 grams of mushrooms, the effect of 8 grams is only marginally longer in duration than two grams rather than 4 times longer.

 

[~_Hiss_~]

Helpfull... you know basic chem and math.

Heh right off wikipedia. Doesn't mean anything without a rate constant, which they don't happen to put in drug inserts.

This is why if you eat 8 grams of mushrooms or 2 grams of mushrooms, the effect of 8 grams is only marginally longer in duration than two grams rather than 4 times longer.

Excellent analogy, definitely what I was looking for. I didn't think it made sense buildup would go to such high levels without some kind of stronger reducing mechanism taking place.

 

[The Monkey Mantra]

It's not "a stronger reducing mechanism" taking place. It's the same old mechanism, with more substrate to work on. Half the drug is out of your system by the half-life time no matter *how* much you're taking. You'd have to constantly increase your dosage to constantly increase the amount in your system. It's like...

Take 50 mg every day. Every three days, 50 percent is gone. That's 75 mg gone the first time, leaving you with 75 mg. Another three days you're up to 225 but now you're cutting out 112.5. Another three days you're up to 262.5 and then cutting out 131.25. Add 150 again to get 281.25. Take away another half to get to 140.625. Add another 150 over the next three days to get to about 290. Take away half to get 145. Over the next three days add another 150. See how you can never end up gaining past 300 mg? At that point, you're taking away half (150) and then putting 150 back. This is what we refer to as the "steady state" level of the drug, where the same amount is leaving as is coming in. You can't break past it by doing anything short of upping the dose. The longer a half-life, the longer it takes to reach steady state, too. Doctors use steady state calculations to figure out what the actual level of drug in your blood is, and drugs with a long time to steady state don't have to be dosed often to maintain a fairly stable effect.

 

[johanneschimpo]

I'm pretty sure it only reaches twice what your daily dose is, at least when talking about something with a 24 hour half-life. I would draw a graph if I could put it on here, but if you're taking 50mg of "substance X" every day and "substance X" has a 24 hour half-life, the highest concentration you will reach is 100mg.
Here's the math I did very quickly in my head, for the conditions I stated above.
day 1: 50mg
day 2: 75mg
day 3: 87.5mg
day 4: 93.75mg
day 5: 96.625mg
day 6: 98.3125mg
day 7: 99.15625mg
ETC

It looks to asymptotically reach 100 (not 150). Not that I care, got bored.