![[dr. bob]](/dr-bob-sm.gif)
Dr. Bob is Robert Hsiung, MD,
bob@dr-bob.orgShown: posts 49 to 73 of 73. Go back in thread:
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
Posted by 2sense on April 11, 2002, at 7:07:51
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
*** EXCELLENT ***I like you're style!
Posted by 2sense on April 11, 2002, at 7:10:55
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
It is pretty cool -- imagine harnessing all
the brains on this board?
Posted by Elizabeth on April 11, 2002, at 8:39:31
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
Damn, I was going to make that joke!
Posted by Elizabeth on April 11, 2002, at 8:41:15
In reply to Re: How'd We Manage To Share the Same Brain? :-) » IsoM, posted by 2sense on April 11, 2002, at 7:10:55
> It is pretty cool -- imagine harnessing all the brains on this board?
[insert diabolical laughter here]
-e
Posted by Elizabeth on April 11, 2002, at 9:02:26
In reply to How to get a half-life..., posted by Adam on April 10, 2002, at 23:03:12
> I always think that any discussion of this kind benefits from some understanding of some simple math and physical principles.
Yes, that's my feeling. This isn't complicated stuff, although the inability to use proper notation on this board makes it look kind of messy and cluttered. Also, resorting to expressing stuff in terms of logs might be intimidating to some.
> 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.
This is true in some cases. I should point out, though, that with many drugs, the concentration isn't always the same in all parts of the body. (Adam mentions this at the end of his post but doesn't go into detail; personally I think it's pretty important, even more important than guppies -- maybe.) If you're dealing with a drug that occurs in different concentrations in different places, the elimination half-life isn't such a good model. If the concentration is the same everywhere, a "one-compartment model" is adequate. There are also two- and three-compartment models for calculating this kind of thing when the concentration isn't the same in different places; the "compartments" might be sites like the brain, for example (particularly important when dealing with psychoactive drugs).
> It doesn't make much sense, under normal circumstances, to talk about the half-life of guppies.
I dunno -- maybe in some models it does!
> 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
Ahh, my favorite kind.
You know, if yesterday someone told me that today I would read a post here in which someone compared medications to fish, I wouldn't have believed it.
-elizabeth
Posted by IsoM on April 11, 2002, at 10:39:40
In reply to Re: How'd We Manage To Share the Same Brain? :-) » IsoM, posted by 2sense on April 11, 2002, at 7:10:55
Posted by Adam on April 11, 2002, at 14:50:01
In reply to Re: How to get a half-life... » Adam, posted by Elizabeth on April 11, 2002, at 9:02:26
>
> Yes, that's my feeling. This isn't complicated stuff, although the inability to use proper notation on this board makes it look kind of messy and cluttered. Also, resorting to expressing stuff in terms of logs might be intimidating to some.
>
Yeah, but I had a bit of an agenda here, a little paen to reductionism, if you will. One could easily just plug something into a calculator using these equations and have fun with it, and not worry about Vd's and AUC's and compartments and all that, or even the algebra.Suffice to say, the classic exponential rate law only works perfectly in a single compartment where distribution is instantaneous. I think, however, you could say it's also a good approximation for plasma levels from a single dose over time frames on the order of a half-life. Of course, elimination rates would tell you nothing about sertraline's effects on the CNS if it did not cross the blood-brain barrier, for instance. But, luckily, it does!
As for my being fond of reductionism, I guess it's my hope that someone might find as interesting as I do the fact that this simplified rate law is also the same for radioactive decay, or for guppies. I must confess I learned about many things and their rate of change in their own context without realising the connection was more than a kind of coincidence. When I understood the connection, I understood that many important processes in the world are ruled, fundamentally, by chance. So you can reduce many seemingly disparate phenomena down to the result of probability. The chance that a sertraline molecule will encounter a liver enzyme and be demethylated, the chance that an alpha particle will tunnel far enough out of a uranium nucleus that electrical forces overpower nuclear forces, and so on. All yield the same curve, basically.
> You know, if yesterday someone told me that today I would read a post here in which someone compared medications to fish, I wouldn't have believed it.
>
Good! I think things like this are fun.Just as an aside, my fondness for guppies is personal: Whenever I had to go to the lab on a weekend, nixing some other plan, my S.O. would say "Oh, you have to feed the guppies." So now, any lab-related duty that interferes with my life is called "feeding the guppies." I wind up explaining all kinds of things in terms of guppies due to this association, and I find their pedagogical uses are quite impressive, as well as what I gain heuristically in trying to construct ever-more elaborate guppy analogies. Guppies have been more helpful to me than zebrafish ever could be!
Posted by Dr. Bob on April 11, 2002, at 15:59:32
In reply to Harnessed PB Brains = Massive Implosion [oops!] (nm), posted by IsoM on April 11, 2002, at 10:39:40
Posted by Jonathan on April 11, 2002, at 18:27:03
In reply to How to get a half-life..., posted by Adam on April 10, 2002, at 23:03:12
Posted by jane d on April 12, 2002, at 11:47:41
In reply to Re: How to get a half-life... » Elizabeth, posted by Adam on April 11, 2002, at 14:50:01
> Just as an aside, my fondness for guppies is personal: Whenever I had to go to the lab on a weekend, nixing some other plan, my S.O. would say "Oh, you have to feed the guppies." So now, any lab-related duty that interferes with my life is called "feeding the guppies." I wind up
So you're saying that this fantasy of dropping a shark in the guppy tank is a long standing one? Seriously, it's a beautiful (if perverse) explanation.
Jane
Posted by Janelle on April 13, 2002, at 1:45:04
In reply to How to get a half-life..., posted by Adam on April 10, 2002, at 23:03:12
Posted by Adam on April 15, 2002, at 11:07:23
In reply to Adam, I have no idea what you did! what is ''e''? (nm) » Adam, posted by Janelle on April 13, 2002, at 1:45:04
Hi, Janelle,
e is the base of the "natural logarithms" and is sometimes called "Euler's number". It has a value of aprox. 2.7183. When you write ln, that's just the symbol or "operator", which tells you to take the "natural log" of something. Any scientific calculator will allow you to take the natural log of a number just by hitting the ln key after entering that number.
So, if I write something like e^kt, that means I'm taking 2.7183 to the power of whatever kt is. If k equals 3 and t equals 2, then e^kt equals 2.7183 to the power of 6, or 403.445. Now, if I entered ln 403.445 into a calculator and hit the ln key, the answer would be very close to six (it's not quite six because I've rounded off a few numbers to the right of the decimal point...otherwise, it would be exactly six).
So, taking e to the power of some number is sort of the reverse of taking the natural log of the result of that calculation. For example, let's use the "base-ten" logs. 10^2 equals 100. The log(10) of 100 is 2. Now again for the natural logs: e^2 equals 7.3892, and ln 7.3892 = 2.
OK, so why would you take the "natural log" of something when you could use a more convenient log system, like base ten? That's kind of a complicated question to answer. I bet Elizabeth could do a better job than me. Anyway, in calculus, you can do operations on equations following certain rules, which give you, say, the area under the curve described by that equation. This works in a relatively straightforward manner except for equations like 1/x (equations where x is to the -1 power). For those equations, taking the log base e of x from 1 to whatever the value of x is gives you this information. Euler's number is kind of this amazing tool, then, for doing such calculations, that arises naturally, if you will. I suppose the value of e means something deep about the universe, but it is well beyond my intelligence to fathom what that could be.
Posted by Adam on April 15, 2002, at 13:00:23
In reply to Half life of guppies » Adam, posted by jane d on April 12, 2002, at 11:47:41
Well, that particular scenerio was an ad hoc creation, and I suppose I could have thought of something more informative if I spent more time on it. My g.f. seems to like guppies more than icky science, though, so I find myself thinking of guppies a lot when I try to explain things. Just a habit I've gotten into.
>
> So you're saying that this fantasy of dropping a shark in the guppy tank is a long standing one? Seriously, it's a beautiful (if perverse) explanation.
>
> Jane
Posted by 2sense on April 15, 2002, at 14:32:48
In reply to Re: Adam, I have no idea what you did! what is ''e''? » Janelle, posted by Adam on April 15, 2002, at 11:07:23
I shouldn't but I am going to.... here is the definition of “half-life” (not nearly as entertaining or intellectually informative and, no I am not being glib or sarcastic or belittling previous posts regarding this good question) that comes from the Nurse's PDR in chapter one under ACTION/KINETICS: The action portion describes the mechanism(s) by which a drug achieves its therapeutic effect; not all mechanisms of action are known. The kinetics portion provides information about the rate of drug absorption, distribution, minimum effective serum or plasma level, biologic half-life, duration of action, metabolism and excretion.
The time it takes for HALF THE DRUG TO BE EXCRETED OR REMOVED FROM THE BLOOD, t1/2, (i.e., the drug’s half-life) is important in determining how often a drug is to be administered and how long to assess for side effects. Therapeutic serum or plasma levels indicate the desired concentration for the drug to exert its beneficial effect and is helpful in predicting the possible onset of side effects, as well as achievement of the desired drug effects.
Just my 2sense ... back to the taxes ...
This is the end of the thread.
Psycho-Babble Medication | Extras | FAQ
Dr. Bob is Robert Hsiung, MD,
bob@dr-bob.org
Script revised: February 4, 2008
URL: http://www.dr-bob.org/cgi-bin/pb/mget.pl
Copyright 2006-17 Robert Hsiung.
Owned and operated by Dr. Bob LLC and not the University of Chicago.