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Dr. Bob is Robert Hsiung, MD,
bob@dr-bob.orgShown: posts 35 to 59 of 73. Go back in thread:
Posted by Janelle on April 5, 2002, at 17:48:48
In reply to Re: How can 1/2 life be SAME for DIFF concentrations? » Janelle, posted by IsoM on April 5, 2002, at 15:33:38
Okay, I get that if 500 mg of drug X has the proper effect then at 5-7 half-lives, what's left of it would have little effect on the body & not even be noticed. So, after 5 half-lives, 15.625 would basically have no effect. Heck, after 2-3 half-lives I would think there would not be enough to have a decent effect if 500 mg is needed?
Now, if only 5 mg of drug Y is needed for effectiveness, then with just one half-life, concentration would be at 2.5 mg, which I would think is too little to have an effect?
So, in a way, a med that requires a higher concentration (e.g., the one that requires 500 mg)needs more half-lives (than the one requiring only 5 mg) before it becomes ineffective, with 5-7 half-lives being the max? Is this accurate?ACKKKKKKKK!
I don't even get your comparison of the difference in how much salt as compared to sugar is needed in a cake to be good tasting! All I can think of is that you need a lot more sugar than salt for a cake to taste good, so you need a higher concentration of sugar than of salt.
Posted by Janelle on April 5, 2002, at 18:09:50
I've got info from two different threads that I've gotta combine here to ask my question so please bear with me. Thanks!
Okay, in one thread it said that no matter what your starting concentration is, after 5 half-lives you are at 1/32 of where you started, which is *effectively* gone.
Under another thread it said that after 5 half-lives there is 2^-5 = 1/32 of the original amount
left. Where does this equation come from? Why is it used - is it an equation that some genius came up with to realize that it takes 5 half lives to effectively eliminate a drug? HELP!
Posted by JohnX2 on April 5, 2002, at 18:27:55
In reply to WHY is 2^-5 used to compute max # half-lives?, posted by Janelle on April 5, 2002, at 18:09:50
> I've got info from two different threads that I've gotta combine here to ask my question so please bear with me. Thanks!
>
> Okay, in one thread it said that no matter what your starting concentration is, after 5 half-lives you are at 1/32 of where you started, which is *effectively* gone.
>
> Under another thread it said that after 5 half-lives there is 2^-5 = 1/32 of the original amount
> left. Where does this equation come from? Why is it used - is it an equation that some genius came up with to realize that it takes 5 half lives to effectively eliminate a drug? HELP!The definition of a 1/2 life is that at time t+1 there is 1/2 of the medicine that there was at time t.
so for 5 , 1/2 lifes:
we have:
1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1 / (32) = 1 / ( 2 ^ 5) = 2 ^ -5
No genious. Just math.
John
Posted by Janelle on April 5, 2002, at 19:00:43
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » Janelle, posted by JohnX2 on April 5, 2002, at 18:27:55
Posted by JohnX2 on April 5, 2002, at 19:10:27
In reply to I get the math now, but why 5, it seems arbitrary (nm) » JohnX2, posted by Janelle on April 5, 2002, at 19:00:43
Posted by Janelle on April 5, 2002, at 19:10:51
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » Janelle, posted by JohnX2 on April 5, 2002, at 18:27:55
Am I right in thinking that t + 1 refers to the time the drug was taken (t) and the 1 refers to one half life, so at t+1 50% of the drug would have been eliminated?
Posted by JohnX2 on April 5, 2002, at 19:13:12
In reply to Another (easy!) question re your explanation! » JohnX2, posted by Janelle on April 5, 2002, at 19:10:51
Posted by Janelle on April 5, 2002, at 19:16:48
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » Janelle, posted by JohnX2 on April 5, 2002, at 18:27:55
It has been stated on here numerous places that it takes FIVE half-lives to effectively eliminate a drug from the body.
How did this number of FIVE half-lives to eliminate a drug become a *given* - did someone somehow figure out that it takes 5 half-lives to eliminate a drug?
Next, using 5 as a *given*, how could you plug 6, 7 or whatever number into your example of:
so for 5 , 1/2 lifes:
we have:
1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1 / (32) = 1 / ( 2 ^ 5) = 2 ^ -5If you did 1/2 *1/2 for 6,7,8, whatever number of times you would not get the 1/32 answer that is the amount of the drug left after 5 half-lives.
Ack, this is bugging me out!
Posted by JohnX2 on April 5, 2002, at 19:24:10
In reply to EE-GADS! No, it can't be 6, 7, etc. because: » JohnX2, posted by Janelle on April 5, 2002, at 19:16:48
I don't know who says that "1/32" is some magical barrier? Why not 1/64 , 1/128 ?For 1/32 you DO need exactly 5 half lives.
John
> It has been stated on here numerous places that it takes FIVE half-lives to effectively eliminate a drug from the body.
>
> How did this number of FIVE half-lives to eliminate a drug become a *given* - did someone somehow figure out that it takes 5 half-lives to eliminate a drug?
>
> Next, using 5 as a *given*, how could you plug 6, 7 or whatever number into your example of:
>
> so for 5 , 1/2 lifes:
>
> we have:
> 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = 1 / (32) = 1 / ( 2 ^ 5) = 2 ^ -5
>
> If you did 1/2 *1/2 for 6,7,8, whatever number of times you would not get the 1/32 answer that is the amount of the drug left after 5 half-lives.
>
> Ack, this is bugging me out!
Posted by Janelle on April 5, 2002, at 19:46:44
Just who the heck (some famous pdoc) came up/invented the concept that it takes FIVE half-lives for any med to be effectively gone from a person's body????????
How was this number 5 derived????
Posted by Janelle on April 5, 2002, at 19:50:32
In reply to Re: EE-GADS! No, it can't be 6, 7, etc. because: » Janelle, posted by JohnX2 on April 5, 2002, at 19:24:10
You wrote "For 1/32 you DO need exactly 5 half lives."
How do you go from 1/32 to get the 5 (for number of half lives)??
Posted by JohnX2 on April 5, 2002, at 20:25:44
In reply to JohnX2: how does this work in reverse: » JohnX2, posted by Janelle on April 5, 2002, at 19:50:32
> You wrote "For 1/32 you DO need exactly 5 half lives."
>
> How do you go from 1/32 to get the 5 (for number of half lives)??log2(32) = 5
John
Posted by Janelle on April 5, 2002, at 20:28:22
In reply to Re: JohnX2: how does this work in reverse: » Janelle, posted by JohnX2 on April 5, 2002, at 20:25:44
Posted by Janelle on April 5, 2002, at 20:30:44
nfm
Posted by fachad on April 5, 2002, at 20:40:58
In reply to 1/2 LIFERS:did a famous pdoc invent the following:, posted by Janelle on April 5, 2002, at 19:46:44
Janelle,
It was my pdoc who told me the 5 half-lives thing.
I don't really think it was meant as an absolute; I think he just didn't feel comfortable with only waiting 4, but he knew I was too impatient to wait 6. So 5 it was...and the rest is history.
> Just who the heck (some famous pdoc) came up/invented the concept that it takes FIVE half-lives for any med to be effectively gone from a person's body????????
>
> How was this number 5 derived????
Posted by Dr. Bob on April 5, 2002, at 23:37:23
In reply to WHY is 2^-5 used to compute max # half-lives?, posted by Janelle on April 5, 2002, at 18:09:50
> I've got info from two different threads that I've gotta combine here to ask my question so please bear with me.
It's easier for others, too, if information isn't split up on separate threads...
Bob
Posted by Elizabeth on April 7, 2002, at 22:31:29
In reply to JohnX2: how does this work in reverse: » JohnX2, posted by Janelle on April 5, 2002, at 19:50:32
> You wrote "For 1/32 you DO need exactly 5 half lives."
>
> How do you go from 1/32 to get the 5 (for number of half lives)2^5 = 2 x 2 x 2 x 2 x 2 = 32
2^(-5) = 1/(2^5) = 1/32 = 0.03125 = 3.125%
Someone just must have decided that 3% or so was a nice cut-off for "gone." It's just a matter of where you draw the line, not a law of nature.
(Like I said, 7 half-lives -- by which time 1/128, less than 1%, remains -- is what I was taught.)
-elizabeth
Posted by 2sense on April 8, 2002, at 19:56:30
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » Janelle, posted by JohnX2 on April 5, 2002, at 18:27:55
John --
Math yes -- but don't sell yourself short on the genius thing. A Beautiful Mind is an excellent example of (as was Einstein and many others) of individuals with brains that were highly intelligent and creative and gave society many wonderful things; and yet they suffered from issues dealing with their mental health. I wish the stigma could be explained? If one has a physical problem people sympathize, etc. if someone has a mental issue, they are shunned -- I realize it is changing and the stigma is more political (my opinion) and having to do with $$ (again my opinion) -- but the sad fact I believe is that there will always be a stigma attached to those who have the courage to deal with their mental/emotional health as well as their physical health. Interestingly enough I wonder how many shun those who deal with their health in a complete fashion, do not deal with the big blue elephant in their own life?
Just my 2Sense
Posted by Elizabeth on April 10, 2002, at 12:03:43
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » JohnX2, posted by 2sense on April 8, 2002, at 19:56:30
> Math yes -- but don't sell yourself short on the genius thing.
I didn't get the impression that John was selling himself short. I'm sure we can all name many clever and creative people who were or are afflicted with mental illness.
But this stuff *is* just arithmetic!
-elizabeth
Posted by 2sense on April 10, 2002, at 13:06:42
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » 2sense, posted by Elizabeth on April 10, 2002, at 12:03:43
> > Math yes -- but don't sell yourself short on the genius thing.
>
> I didn't get the impression that John was selling himself short. I'm sure we can all name many clever and creative people who were or are afflicted with mental illness.
>
> But this stuff *is* just arithmetic!
>
> -elizabeth
Elizabeth -->> I didn't get the impression that John was selling himself short.
>
I simply was trying to pay John a complement; truly nothing else was intended by what I wrote him.
>
>
>> I'm sure we can all name many clever and creative people who were or are afflicted >> with mental illness.
>
Point taken. I am sure you are most correct that a lot of people could list off individuals who are bright and creative, with or without mental health issues. It has been my own experience in encountering smart (for that matter any and all kinds of) people who know arithmetic that not all of them would understand what John was explaining. My mother would be one of them. She was a straight A student in high school, she choose to stay at home and raise 5 of us. She knows arithmetic, but she would not comprehend what John was explaining. In my mom’s case it might be due to the fact she has no interest in understanding it. In my own humble opinion, it could be less about the arithmetic that could potentially confuse people (someone did ask the question in the first place) and more the context of the arithmetic that John was explaining in this case.Thanks for letting me know you opinion on the matter; I appreciate yours and others taking the time to be so responsive to others’ postings.
Sue
Posted by Adam on April 10, 2002, at 23:03:12
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » JohnX2, posted by 2sense on April 8, 2002, at 19:56:30
I always think that any discussion of this kind benefits from some understanding of some simple math and physical principles.
You can, if you know the half-life, calculate the amount of drug you are going to have around at any point in the future. You can also determine the half life of something by watching it dissapear over any span of time.
It all can be explained in the law of exponential decay, expressed thusly:
At=Ai * e^kt
(Ai = initial amount, At equals amount at time t, k is the "decay constant")If I don't know what k was, I can find out: Say at the beginning of the experiment I had 50g of stuff in a box, and when I looked 100 min later, I had only 30g of stuff left. Using the formula above...
30g = 50g * e^(k*100 min)
Now solve for k...
ln(30g/50g) / 100min = k = -0.005108
(k is in units min^-1 in this case)Now I can calculate the half life of stuff. Since the half life is the time it takes for half of the stuff to disappear...
0.5 = e^-0.005108t
Solve for t...
ln0.5/-0.005108 = t = 135.7 minutes
This is kind of cool: If I know what k is, I can calculate the half life (t(1/2)) of anything just by using the formula ln0.5 / k = t(1/2)
Conversely, if I know the half life of something, I can always find k:
k = ln0.5 / t(1/2)
And if I know k, I can calculate how much of something there will be at any time in the future if I know how much is around now.
There's a neat physical concept in all of this: The statitistical nature of exponential decay. When you think about it, molecules of a drug aren't like, say, guppies. It doesn't make much sense, under normal circumstances, to talk about the half-life of guppies. Say you had a bowl of ten guppies, all the same age. If you watched the bowl of guppies day after day for months, the number probably wouldn't change much. Then one day there'd be one dead guppy. Maybe the next day, there'd be three. By the end of the week, maybe, they'd all be dead. What happened? They got old and died. Guppies have a "life span". That's a lot different than a "half life". The guppies swim along happily for however long their life span allows, and then, all of the sudden, they die.
Now let's imagine a rather perverse scenerio, to illustrate the concept of half life. Say I have a tank full of 100 guppies. Let's just ignore life span, since the time-frame of the experiment is so much shorter than the life of a guppy...for our puroposes, guppies live forever, undisturbed. Now, into that tank, I throw a blind pirhanna. The voracious pirhanna swims about randomly, and when he encounters a guppy, he eats it.
Now imagine the scene in the tank. The pirhanna begins in an environment dense with guppies. He can't see them, but by random chance, he's bound to bump into one eventually, and he eats them as soon as he does. In the beginning, finding guppies is easy, since there are so many around to bump into. As time goes by, and the guppies become more sparse, the rate that the pirhanna eats them slows, as he is less likely with each guppy he eats to bump into another. Say you counted guppies in the tank each half hour after you introduced the pirhanna. To make it easy, in 30 min. there are 50 guppies (the half life of guppies with the pirhanna around is thus 30 min.) After an hour, there are 25, in two hours there are only six or seven, and so on. You could plot out the disappearance of guppies over time on a graph, and what you would see is an exponential decay curve.
You might notice that the life of the poor guppy in this experiment is determined only by chance. If you watch any individual guppy, it might live only a few minutes, or it might evade the pirhanna for hours if it was lucky. On average, though, you might say in half an hour, any individual guppy has a 50-50 chance of survival. Given those odds, in half an our, you would expect 50% of the guppies to be gone.
In a way, the same goes for molecules. If you took a tab of sertraline, the sertraline doesn't "get old" in your body. Molecules of sertraline float about essentially randomly until something happens. It's theoretically possible that a molecule of sertraline that entered your body could still be there a year from now. It would be exactly the same as it was when you ingested it. The elimination half life of sertraline is about 26 hours. That means that on average, half of the sertraline molecules you ingested will have been excreted, or reacted with something, or been converted by an enzyme, etc. You could also say that any given molecule of sertraline has a 50% chance of being excreted by or chemically altered in your body after 26 hours. It's purely statistical, and exponential decay is just the cumulative result of the chance of something happening once to a single representative entity in a collection of such entities over time.
A funny thing about exponential decay: You never reach zero. When somebody says five or ten half-lives is enough to eliminate something, they just mean for practical purposes. In reality, some portion of that tab of sertraline you took last tuesday could be with you for the rest of your life...even if it's just a molecule. Something only has a chance of disappearing in a given number of half-lives...never a certainty!
(Of course, the mathematical expressions for drug clearance in standard pharmicokinetics can look different even when equivalent to the simple decay law given above, and they becomes a bit more complicated with distribution time, number of compartments, etc. This is the basic idea, though.)
Posted by JohnX2 on April 11, 2002, at 0:33:04
In reply to Re: WHY is 2^-5 used to compute max # half-lives? » 2sense, posted by Elizabeth on April 10, 2002, at 12:03:43
> > Math yes -- but don't sell yourself short on the genius thing.
>
> I didn't get the impression that John was selling himself short. I'm sure we can all name many clever and creative people who were or are afflicted with mental illness.
>
> But this stuff *is* just arithmetic!
>
> -elizabethDitto.
It is just arithmetic. There are a lot of clever people posting to this newsgroup.
John
Posted by Ron Hill on April 11, 2002, at 0:55:08
In reply to How to get a half-life..., posted by Adam on April 10, 2002, at 23:03:12
Posted by IsoM on April 11, 2002, at 1:41:11
In reply to Forget half-life. How do I get a life? (nm) » Adam, posted by Ron Hill on April 11, 2002, at 0:55:08
Posted by Ron Hill on April 11, 2002, at 2:21:19
In reply to How'd We Manage To Share the Same Brain? :-) (nm) » Ron Hill, posted by IsoM on April 11, 2002, at 1:41:11
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