Placeholder Image

字幕列表 影片播放

  • So now, we finally get to talk about the half-life or the T 1/2

  • and this is an incredibly important topic so I'm going to put some stars next to it.

  • So what is the elimination half life?

  • Well, the elimination half is the time it takes to eliminate 50% of that drug from your body or from your plasma

  • and the reason we care about this is two-fold.

  • One, we want to know how long it takes to get rid of all of that drug from our body

  • and two, by knowing how quickly we eliminate that drug, it gives us a sense of how frequently we should be dosing that drug.

  • Now what I want to do is kind of front load this lecture and give you the 3 most important points to remember right off the bat

  • and then we'll develop each of these points.

  • So, the first point we've already talked about and that is the definition of half-life.

  • This is the time it takes to go from some initial concentration CNOT to 1/2 of that initial concentration.

  • The second point I want you to remember is that it doesn't matter what your initial dosage is or your initial concentration

  • 95% of that drug will always be eliminated after 4.5 half lives.

  • So, if we're at any sort of steady state, after 4.5 half-lives, 95% of that drug will be eliminated regardless of the initial concentration.

  • The third point I want you to remember is that the half-life is inversely proportional to the rate of drug metabolism.

  • So, if I metabolize the drug faster, we expect the half life to go down

  • Now, we have a term which represents this rate of drug elimination and this is KE or KEL.

  • It's the first order elimination rate constant.

  • first order elimination rate constant

  • Now you don't actually have to memorize this equation but you need to understand what this term is here.

  • So this term represents how quickly we are eliminating the drug and if this increases, we expect the half-life to decrease.

  • Now if you're unfamiliar with this term first order elimination, I'd recommend going back to the last video and watching what that means.

  • In a nutshell, it says that the first order elimination which is happening for most drugs at most dosages,

  • the proportion of drug metabolized over time is constant.

  • So while you don't have to memorize this equation, you need to memorize an equation that is derived from this

  • and that is the half-life is equal to 0.693 x the volume of distribution divided by a term that we haven't heard before

  • called the clearance. This guy is called the clearance.

  • And we'll talk about clearance in a future video but real quick, the clearance is the volume of blood that gets eliminated of drug per unit time.

  • So these are the 3 most important points to remember and if you wanted to stop this video right here and you just learned these 3 points,

  • you would probably be okay but that's not how we roll.

  • We want to really understand things.

  • So, let's work through an example with the table here.

  • So the example that we're going to use is we're going to say that the half life of the drug is equal to 1 hour

  • and that the initial concentration is equal to 8 mg of drug per liter of plasma.

  • So we'll start off by looking at the left hand side of this table.

  • Notice that the time increment is 1 hour and this 1 hour is the half-life of the drug.

  • So every hour that goes by, we expect the concentration of the drug to decrease by 1/2.

  • So let's look at the plasma concentration.

  • If I started at 8 mg/L, after 1 hour I expect to be at 4 and after another hour, I expect to be at 2 and then at 1 and then at 0.5 and then at 0.25.

  • Now, moving on over to the right here. This part is a little more interesting.

  • We have the amount of drug that is remaining and I listed it as fractions and also, as a percentage.

  • So after 1 half-life, we expect 1/2 of the drug to be remaining.

  • After 2 half-lives, I have gone down by 1/2 and by another 1/2.

  • So another way of writing this is I've gone down by 1/2 squared or I have 1/4 of the drug remaining or 25%.

  • and now that means that I've metabolized 75% of the drug.

  • If I go by, if I let another hour go by, another half-life has gone by.

  • So I've gone 1/2 x 1/2 x 1/2 or 1/2 to the 3rd and I have 1/8 remaining.

  • So, notice this trend here.

  • If you want to figure out what fraction of the drug is remaining after a certain number of half-lives,

  • you just take oh 3 half-lives have gone by, it's 1/2 raised to the 3rd or 1/8 of the drug is remaining.

  • Now, let's get to that second point that we've talked about that. That 95% of the drug is always eliminated after around 4.5 half lives.

  • So, at 4 half-lives, I have 6.25% remaining.

  • That means I've metabolized around 94% of the drug.

  • And so, as more time goes by, I'm going to metabolize another half-life right.

  • So if I had 1/16 then I have 1/32 left at 5 hours or 5 half-lives and that's around 97% of that drug has been eliminated.

  • So somewhere between 4 and 5 half-lives, we expect 95% of that drug to be eliminated and this does not depend on the initial concentration.

  • If I would've started at 32 then I would've been at 16, then at 8, then at 4, then at 2, then at 1

  • and somewhere between here, I would've also eliminated 95% of the drug.

  • So that is 0.2.

  • And the 3rd point has to do with the first order elimination rate constant and how it relates to the half-life

  • and to do that, we need to graph a first order elimination rate graph using a linear plot and then using a semi-log plot.

  • So, using a linear plot, remember that the half life is 1 hour and so if I started at 8 mg/L, after an hour, I'd be around 4

  • and then I'd be around 2 and then I'd be around 1 and then I'd be around 0.5

  • and if I wanted to graph this, I get this exponential graph.

  • Now, as scientists right, we want to be able to describe this graph

  • and if I wanted to know the plasma concentration at any point, it can be given by this equation.

  • and that is that the concentration at any time (T) is equal to your initial concentration x E raised to the -KT

  • where K is that first order elimination rate constant.

  • Now, you don't have to memorize this equation but from this equation, I can solve this for the half-life

  • and if I do that, that's where I get the T 1/2 is equal to 0.693 over that first order elimination rate constant.

  • Now, maybe what I'll do in a future video is just talk about how this is derived but let's be on the scope of what we're talking about now.

  • The bigger point is to understand this inverse relationship between the half-life and the elimination rate constant.

  • Now, the best way to do that is by looking at a semi-log graph.

  • And so, what is a semi-log graph?

  • It's probably been awhile since people have used this.

  • So, when I say semi-log, half of the graph is a logarithmic graph or half of the scale and that's the Y axis is logarithmic

  • where the other half is linear.

  • and so notice the units here.

  • I start at 0.25 and then I double 0.5 and then I double to 1 and then a 2, 4, 8

  • or another way of thinking of this is that the concentration is decreasing by 1/2 each time.

  • So, this is the perfect graph to graph the half-life.

  • So, if I started at 8 after a certain period of time, 1 half-life I would be at 4 and then at 2 and then at 1 and then at 0.5

  • and if I went to another one, I would be at 0.25.

  • Now there is no way this graph is going to be exponential. It is a linear graph and that is because I'm using a logarithmic scale.

  • Now, this graph helps us in a couple of ways.

  • First off, I want you to note that this slope correlates very well.

  • Let's just write correlates with that first order elimination rate constant.

  • And maybe in that future video were I talk about how half-life is derived, I'll tell you how you can solve for K but just know that it correlates with it.

  • And for your purposes, you can just say, the slope is K.

  • And so, the point here is that the steeper the slope, this increases the first order elimination rate constant K

  • and as a result, I'm eliminating faster and I decrease the half-life.

  • Remember, there is an inverse relationship between the 2.

  • So, what I'll do here is I'm just going to graph a new plot.

  • So this new plot, I'm still starting at 8 but after 3 hours, I've gotten rid of most of that drug.

  • So using this graph, if I wanted to solve for the half-life, I just take 2 points that I have half the concentration of 1 another.

  • So, let's just say here at you know at 2. What I meant is value of 2 for the plasma concentration. 2 mg/L, I was at 1 hour

  • and half of that would be when I'm at 1 and that looks like I'm at about 1 1/2 hours. 1.5.

  • So the time it takes to go from an initial concentration to 1/2 your initial concentration is the half-life.

  • So, the T 1/2 here is equal to 0.5 hours.

  • And so, as this graph is becoming steeper, as I'm increasing the rate of elimination, the half-life is going down.

  • It went from 1 to 0.5.

  • And so, the point is that you need to remember this inverse relationship between the rate of metabolism and the drug half-life.

  • Now, you should walk away from this with these 3 main points that we've listed up here.

  • Maybe what I'll do in the next video is just quickly cover some of the math for all of us nerds who like this very much

  • but the next big topic we're going to talk about is drug clearance and really, we'll get into excretion.

  • So, make sure to subscribe in my channel to see whenever new videos become available.

  • I hope you enjoyed.

So now, we finally get to talk about the half-life or the T 1/2

字幕與單字

單字即點即查 點擊單字可以查詢單字解釋

B1 中級

藥物半衰期概述 - 藥學講座 10 (Drug Half-life | An Overview - Pharm Lect 10)

  • 64 7
    Yu Syuan Luo 發佈於 2021 年 01 月 14 日
影片單字