Understanding Drug Clearance and Kinetics

All right, guys, so now let's talk about drug clearance. Now, when we talk about drug clearance, what is clearance? How do we define clearance? Well, clearance is basically, if you really want to think about it, it's the rate of elimination of a particular drug over the plasma concentration of the drug. And we can actually further define that. We'll do that in just a second. But what I want you to remember is it is equal to, the rate of elimination is equal to the rate, so the clearance is equal to the rate of elimination. Divided by the concentration of the drug within the plasma. So in concentration of the drug within the plasma. That is how we define clearance. Now we can actually further define it if we really wanted to. That it's the volume of plasma that's cleared of a drug. per unit time so it's volume per time you know you know what's interesting about clearance as clearance is actually basically a way of looking at elimination now what is elimination elimination is you're getting rid of the drug you're removing the drug from the body. Now, people may just think, oh, that's just excretion. But excretion and elimination is not necessarily the same thing. Elimination, really, when it comes down to it, is a combination of two particular things. It's the liver being able to metabolize, inactivate the drug that we've already discussed. So it's a combination of metabolism and, to some degree, also excretion. Who's the primary organ that excretes drugs? The kidneys. So the urinary system is responsible for being able to excrete particular drugs into the urine. So elimination is a combination of these two things to be able to remove the drug from the body. There's many different organs that are involved in clearance or elimination of the drug from the body. Do you guys know what those organs are? There's so many of them. But the primary ones that are the most clinically relevant in pharmacokinetics is the kidney and the liver. And we can actually calculate this out. We can say, okay, the liver is responsible for clearing this particular amount. of plasma of a drug per unit time. And so we call that the clearance of the hepatic system. And then we could also take into consideration, let me add that on top of that. I want to figure out the total amount of clearance of a particular volume of plasma that occupies a drug per unit time. I could add up the clearances of each individual organ. So I could take into consideration the hepatic system plus the renal system. And this would give me the total clearance, if you will. Now, there is a lot of other like small, minuscule involved. of clearance from other organs. Can you guys think about some of these? Think about the lungs. The lungs are important for being able to clear like anesthetics, so inhale gases. You also have your GIT can actually potentially eliminate drugs that don't get absorbed across the GI tract into the blood or things that actually are eliminated from the body via breast milk, saliva, lacrimal secretions as well. So many different ways that we can eliminate drugs, but these are the two primary ways. And this is an important topic. You want to know why? Because clearance is obviously not just dependent. upon elimination, but elimination is dependent upon the function of these organs. If someone develops some type of what? Dysfunction of their kidneys or dysfunction of their liver, what happens to the clearance? It would decrease because their ability of that organ to perform the functions of clearing or eliminating the drug is going to decrease. So I want you guys to remember that when someone has renal dysfunction, what would happen to the clearance? The clearance will decrease. If someone has liver dysfunction, what will happen? The clearance will decrease. And this can lead to an accumulation of the drug, especially if that drug is cleared by that particular organ. So for example, I'm taking a drug, drug A. Drug is primarily cleared by the kidney. It takes most of the clearance percentage, let's say 95%. Hepatic, only like 5%. If a patient has chronic kidney disease, now that drug is not being cleared by the kidney primarily, and so the concentration of the drug will start to rise. The rate of elimination is going to decrease. If drug B... is metabolized by the liver. And the liver actually has some type of cirrhosis, acute liver failure, and it's primarily responsible for eliminating 95% of the drug. And you have liver dysfunction, you're not going to be able to clear or eliminate the drug from the body. That rate of elimination decreases, and your clearance will then subsequently do what? It'll also decrease. So it's important to be able to remember that. The other thing that we can actually further go down the line, especially for USMLE, is that sometimes they'll actually further determine, based upon mathematical derivations, another... kind of equivalency with respect to clearance. So we can say that clearance is not just dependent upon rate of elimination and drug concentration in the plasma. It's also dependent upon volume of distribution times a particular constant. We say 0.693. We can round that to 0.7. And here's the big thing, divided by the half-life. So we got to talk a little bit quickly about half-life. We'll talk about it more when we get into elimination kinetics. But what I want you to remember is you can... See, based upon this equation, don't worry about volume of distribution. It's a constant for most, for different types of drugs. And don't worry about this. Focus on the half-life. I want you to think based upon this equation, what would the half-life have to do with the clearance? How would it affect the clearance? And what is half-life? What the heck is that? Half-life is the time it takes to go from 100% of the drug to 50% of the drug. However long it takes to get to that point, that is the half-life of the drug. If the half-life of the drug is high, increase, very long. So let's actually use a different color here. Let's say that the half-life of a particular drug is very long. It takes a long time to drop the amount of the drug to 50% from 100%. What happens to the clearance based upon this equation? Well, the denominator is going to be high. That's going to lower the overall number. So the clearance will subsequently decrease. So remember that half-life and clearance are inversely proportional. In the same way, if I have a drug that has a very short half-life, it takes very little time for it to be able to go from 100% to 50%. I'm clearing it very quickly. If that's the case then, half-life goes down, what happens to the clearance? The clearance will subsequently go up. So remember, clearance, half-life, inversely proportional type of relationship. Let's write that down. So clearance is inversely proportional to half-life. That's an important concept to remember, especially for USMLE. All right, so now, when we talk about half-life and rate of elimination, we're using all these different types of terms, we have to really quickly talk about something called elimination kinetics. Alright, so when we talk about elimination kinetics, and we're talking about rate of elimination, we're talking about half-lives and things like that, most drugs, when we think about them with respect to their biochemical type of profile, work under what's called first-order enzymatic kinetics. Now, you probably thought biochemistry would never come back again, but unfortunately it is coming back a little bit. So first-order kinetics, we have to talk about this one, and then we'll talk afterwards. about the less common situation we don't really want most drugs as clinicians to act under zero order and you'll see why in a second. When we talk about first order enzymatic kinetics and zero order enzymatic kinetics, you guys will get questions probably on your test about either comparing the graphs, knowing specific types of terminologies of which things are constant, what's the proportion of drug to rate of elimination, all that stuff. So I'm going to help you guys out with that. So first thing that I want you guys to remember for first order enzymatic kinetics, most drugs, thank goodness, operate under first order. enzymatic kinetics. I want you to remember that most drugs will operate under first order enzymatic kinetics. When you think about this, here's what's really interesting. Let's say that we take a drug that operates under what's called first order enzymatic kinetics. One of the cool things about this drug is we think about its rate of elimination. The rate of elimination of this drug, it can vary according to first order enzymatic kinetics, but the fraction of drug that we eliminate per unit time. The fraction of drug that we eliminate per unit time is constant. And you know what that's interesting is? We can use this concept of half-life of that fraction of per unit time. And we can say that in first-order enzymatic kinetics, half-life is, very, very important here, guys, constant. What the heck does that mean? What that means is I can say that, let's say I have a drug. Here is drug A. And I'm going to deliver 100 milligrams per liter. of drug A to a particular patient. Assuming it has 100% bioavailability, I give it IV, gets into the bloodstream, 100% of the drug is there. What's going to happen to that drug is over time, if I'm not giving any more of the drug, so there's no increase in the dosing, it's going to become eliminated over time. The way that it gets eliminated is very, very dependent upon its half-life. And so what I can say is the half-life is constant. So what I'm going to say is, just to make this up, I'm going to say I'm going to remove... 50% of the drug, 50% of the drug is going to be eliminated per hour. So I'm going to put E for elimination. I'm going to eliminate 50%. The fraction of drug removed every per unit time is constant. So for example, I start off at 100 milligrams. Then I go to half of that 50 milligrams. Then I half to 50 to go to 25. Half 25, that gets me to 12.5. Half 12.5, I had to get to 6.25. You get the point. I'll just keep coming down. What I expect is every hour I'm going to go to each one of these percentages or milligram amount because the fraction of the proportionality factor is going to be constant every single hour. So for example, at time zero, when I give the drug, there's 100 milligrams. At one hour, there should be approximately 50 milligrams left. At time two hours, I should have removed another 50%, and I'm down to 25 milligrams in the bloodstream. At time three, I'm down to about... 12.5. At the fourth hour, I'm down to about 6.25. And if I were to really be particular, if I could get it somewhere in there, like three point something, I'd probably be around the fifth hour, like somewhere on like 3.2 something. All right. So if I kind of. Look at this graph. What I notice out of this graph is that it moves in a very type of interesting fashion. You see how it kind of comes down like this? This is what's called an exponential graph. So an exponential curve. So what sometimes you may be asked is, is you get a graph and you say okay this drug is operating under what type of enzymatic kinetics? You would say first order because it's an exponential graph. If we're to say okay what drugs operate under first order enzymatic kinetics? You say I got you boo, it's most drugs. And you know why? is because the half-life is constant every single hour removing 50% of the drug. Now, here's what's really interesting. The amount of drug that you give to the patient is directly proportional to the rate of elimination. And this is important only in first order enzymatic kinetics. This is the only time that drug concentration and rate of elimination is directly proportional. So if I decide to increase the concentration of my drug, and I'll explain it down here in just a second. If I increase the concentration of my drug, I will subsequently increase the concentration of its rate of elimination. These are directly proportional. This is the only situation. It's not that way. in zero order. What that means is here I have drug concentration on the x-axis, here I have rate of elimination on the y-axis. What would this say? As I go towards the right, what would I expect my rate of elimination to do? Increase. So if I use that color here, blue, as I increase my drug concentration I expect my rate of elimination to increase. You want to know why? I have enzyme sites that are available for the drug. If I give this hundred milligrams of the drug, It can bind onto the active site of the enzyme, be metabolized. Once it's metabolized or excreted, it can then actually go through this reaction process. So as I increase the concentration of my drug, I will increase the rate of it being eliminated. So I'm going to see this kind of increase in the graph. Now watch what happens for zero order. For zero order enzymatic kinetics, thank goodness there's not many drugs that undergo zero order kinetics. The ones that I want you to remember is remember PEA. So phenotone, which you're going to abbreviate PHT. E for the next one is ethanol. So alcohol, we'll put E-T-O-H. And the last one is aspirin. We'll put A-S-A. These are the primary drugs that you guys will potentially be tested on that act or work under the activity of zero-order enzymatic kinetics. Now, here's the interesting thing. If you notice here, half-life is constant in which one? First order. It is variable in the zero-order. The only thing that's constant in zero-order is the rate of elimination. So the amount of drug, the milligram of drug that we actually eliminate per hour is constant. So rate of elimination is constant. Not the half-life. in zero order. Meaning, if I have drug A, same situation here, I'm going to administer 100 milligrams per liter of a drug intravenously. So that means that I have 100% bioavailability, all the drug is going to get into the bloodstream. How much time is it going to take for me to be able to eliminate most of that drug or completely all of the drug, as long as I'm not giving more of it? Well, the rate of elimination of that drug is constant, meaning that I'm going to remove, let's just pretend here, 25 milligrams of drug every hour. That's my elimination rate. You see how it's constant? It's not a percentage. The percentage that I will remove every single time is actually going to vary. But the rate that I remove drug is constant. So for example, I start off here at time zero, 100 milligrams. At the second point here, if I keep going down here, 100 milligrams, I got to subtract 25, that's 75. Subtract another 25, that's going to be 50. Subtract another 25, that'll be 50. it'll be 25 and then come completely down to zero here. Okay. So every hour I'm going to remove 25 milligrams. That's my rate of elimination. So I start off here at time zero at a hundred. Then I start at 75. Okay. One hour, I'm going to remove 25 more milligrams. And at set two hours off 50 milligrams left at three hours, I will remove another 25 and I'm left with 25 milligrams. And then at time zero, I'm sorry, at a zero milligrams, which is about four hours later, I would remove all of the drug. It should be completely gone. So what do you notice about this particular curve here if we do it like in a different color here? What do you guys notice here? Not perfect, but it's linear. It's not exponential that you would see in a first order. In zero order, this is what's called a linear type of curve or a linear graph if you will. So sometimes what they may say is you get this graph and say okay, this is a particular drug that you guys see. What is kind of what order kinetics is it operating under? And you would say it's zero order because it's linear. And I can tell that the rate of elimination is constant. What kind of drugs would do this? Only these particular drugs. And now, the last comparison is that we said that in first order, as you increase drug concentration, you increase rate of elimination. That's not the case in this situation. So we can say that these two, let's actually say, are not proportional. They are, let's say, independent. of one another. This is an extremely important concept. Watch this. Here I have the same thing, drug concentration x-axis, rate of elimination on the y-axis. If I give, if I increase the concentration of the drug in... First order, it increased the rate of elimination. As I increase the concentration of the drug, it will not increase the rate of elimination. What is the rate of elimination? Constant. That means that what happens is I can keep giving more. and more and more and more drugs. But guess what happens to the rate of elimination on the Y-axis? It's not going to keep going up. It's going to stay flat because it's constant at this particular amount, at this particular concentration, it is going to be constant. That's an important concept. And the reason why is if you look at this enzymatically, is if I have a drug here, what's happening is this drug, I give a hundred milligrams of this drug. And if I continue to to keep trying to increase the concentration of the drug, it's supposed to interact with enzymes. But this enzyme is occupied with so much drug. It's completely saturated. It's at what's called V max. You probably thought that would never come back. But this is when all of the enzymes completely saturated. So no matter how much more you give the drug, it's not going to increase the rate of the reaction. And so this rate of the reaction will not proportionally increase. It's going to stay constant. It's just going to do it at the rate that it wants to. And that's an important thing. So whenever you look at this on this aspect of the graph, this is first order. this my friends is zero order and the problem with this is that you can see toxicity with this aspect of zero order that's why we don't like as clinicians to see zero order enzymatic kinetics with a particular drug all right the last thing that i want you guys to remember here is that when we talk about a drug sometimes you can actually use something that we call talk about called steady state and we're going to talk about that with dosage regimens but what's really important is half-life is very important for the time it takes to get to steady state and the steady state basically definition definition is the amount that you're giving is equal to the amount that you're eliminating. So that's the steady state concentration. It's when you're at an equilibrium between the amount that you're putting into the body is equal to the amount that the body is getting rid of. That's dependent upon the half-life. And the same concept, the amount of time it takes for you to completely eliminate the drug from the body according to first order kinetics is dependent upon the half-life. And you know how much time it takes? If you kind of look at here, let's say I have 100 milligrams of the drug, what does it take for me to get to about 95% of the drug eliminated? So at 6.25, I have like 93, 94%. If I were to go here, I'd be somewhere around like approximately three something, right? Approximately three something. something. Well, that means that I've metabolized at least 97% of the drug. So in between, what half-life was this at? So this was one, two, three, four, the fourth half-life. And then around this one, right, you get to about three, three point something milligrams that are left. You're at about five half-lives. That means somewhere around approximately 95% of the drug being eliminated is equal to about four to five. half-lives. So that's an important thing to remember because guess how many half-lives it takes to get to steady state concentration? The same amount for it actually to eliminate 95% for the body, four to five half-lives. All right, guys, let's do some questions about clearance. So we got a 55-year-old woman brought to the ED, had some seizures. She has a history of renal disease undergoing dialysis. She gets an intravenous infusion of an anti-seizure drug, which the following is likely to be observed with the use of drug ninja in this patient. So when we think about this patient here, what do we know? Well, we know that they have renal disease. Well, we only... you think about clearance, clearance is really dependent upon renal function and liver function as the primary organs here. So because she has an underlying renal disease, what do you think is going to happen to the clearance of that drug? It's likely going to decrease. And when we think about clearance, clearance is really dependent upon half-life, right? So clearance and half-life have a very strong relationship with one another. So what we know is, is that as clearance decreases, the half-life of that drug is going to significantly increase. And as the half-life a drug increases, that means it can concentrate within the body and it can actually start to have potential side effects if you can't clear the drug from the body. And so because of that, one of the important things to understand is that as the half-life of a drug really, really increases, because you can't clear it. because you have an underlying renal disease here, what would I want to do to the dosage of the next dose that I give for this drug? Or if I actually think about this now, what kind of dosage would I want to give? Would I want to give a very low dose, a normal dose, or a high dose if they have renal disease causing decreased clearance and an increase in half-life? I probably want to, because I have a very high half-life now, I probably would want to drop the dosage here. So because of that situation where half Half-life is increasing, dosage should subsequently decrease as well. So that is what I would actually pick for this particular answer here. All right, guys, so here's the next question. We got a pharmacokinetic study of a new antihypertensive drug. It's being conducted in some healthy human volunteers. The half-life of the drug after administration by continuous infusion is about 12 hours. That's the half-life. What do we know about half-life? Which, again, is very, very important. How many half-lives does it take for the drug to be able to reach steady state? Do you guys remember? We said it takes about four to five half-lives for a drug to be able to reach steady state concentration. If the half-life for the infusion is 12 hours, about four half-lives will get me close to the steady state, four to five. So what's 12 times four? It's about 48. So it might be just a little bit greater than 48 hours, but at least 48 hours is going to be the minimum that I need. And so look here, 48 hours would definitely be our answer because we know four to five half-lives would help us to be able to reach steady state concentration if we're giving it via continuous infusion. So I would expect this to be 48 hours. All right, guys, that covers this section here on the concept of clearance. In the next video, what we're going to do is we're going to start talking a little bit more about the dosages of drugs, the regimens of drugs, and get a little bit of detail into that. See you guys there.

All right, guys, so now let's talk about drug clearance. Now, when we talk about drug clearance, what is clearance? How do we define clearance?

Well, clearance is basically, if you really want to think about it, it's the rate of elimination of a particular drug over the plasma concentration of the drug. And we can actually further define that. We'll do that in just a second. But what I want you to remember is it is equal to, the rate of elimination is equal to the rate, so the clearance is equal to the rate of elimination. Divided by the concentration of the drug within the plasma.

So in concentration of the drug within the plasma. That is how we define clearance. Now we can actually further define it if we really wanted to. That it's the volume of plasma that's cleared of a drug.

per unit time so it's volume per time you know you know what's interesting about clearance as clearance is actually basically a way of looking at elimination now what is elimination elimination is you're getting rid of the drug you're removing the drug from the body. Now, people may just think, oh, that's just excretion. But excretion and elimination is not necessarily the same thing.

Elimination, really, when it comes down to it, is a combination of two particular things. It's the liver being able to metabolize, inactivate the drug that we've already discussed. So it's a combination of metabolism and, to some degree, also excretion. Who's the primary organ that excretes drugs?

The kidneys. So the urinary system is responsible for being able to excrete particular drugs into the urine. So elimination is a combination of these two things to be able to remove the drug from the body.

There's many different organs that are involved in clearance or elimination of the drug from the body. Do you guys know what those organs are? There's so many of them.

But the primary ones that are the most clinically relevant in pharmacokinetics is the kidney and the liver. And we can actually calculate this out. We can say, okay, the liver is responsible for clearing this particular amount. of plasma of a drug per unit time.

And so we call that the clearance of the hepatic system. And then we could also take into consideration, let me add that on top of that. I want to figure out the total amount of clearance of a particular volume of plasma that occupies a drug per unit time.

I could add up the clearances of each individual organ. So I could take into consideration the hepatic system plus the renal system. And this would give me the total clearance, if you will. Now, there is a lot of other like small, minuscule involved.

of clearance from other organs. Can you guys think about some of these? Think about the lungs.

The lungs are important for being able to clear like anesthetics, so inhale gases. You also have your GIT can actually potentially eliminate drugs that don't get absorbed across the GI tract into the blood or things that actually are eliminated from the body via breast milk, saliva, lacrimal secretions as well. So many different ways that we can eliminate drugs, but these are the two primary ways.

And this is an important topic. You want to know why? Because clearance is obviously not just dependent.

upon elimination, but elimination is dependent upon the function of these organs. If someone develops some type of what? Dysfunction of their kidneys or dysfunction of their liver, what happens to the clearance? It would decrease because their ability of that organ to perform the functions of clearing or eliminating the drug is going to decrease. So I want you guys to remember that when someone has renal dysfunction, what would happen to the clearance?

The clearance will decrease. If someone has liver dysfunction, what will happen? The clearance will decrease.

And this can lead to an accumulation of the drug, especially if that drug is cleared by that particular organ. So for example, I'm taking a drug, drug A. Drug is primarily cleared by the kidney.

It takes most of the clearance percentage, let's say 95%. Hepatic, only like 5%. If a patient has chronic kidney disease, now that drug is not being cleared by the kidney primarily, and so the concentration of the drug will start to rise.

The rate of elimination is going to decrease. If drug B... is metabolized by the liver. And the liver actually has some type of cirrhosis, acute liver failure, and it's primarily responsible for eliminating 95% of the drug.

And you have liver dysfunction, you're not going to be able to clear or eliminate the drug from the body. That rate of elimination decreases, and your clearance will then subsequently do what? It'll also decrease. So it's important to be able to remember that.

The other thing that we can actually further go down the line, especially for USMLE, is that sometimes they'll actually further determine, based upon mathematical derivations, another... kind of equivalency with respect to clearance. So we can say that clearance is not just dependent upon rate of elimination and drug concentration in the plasma.

It's also dependent upon volume of distribution times a particular constant. We say 0.693. We can round that to 0.7.

And here's the big thing, divided by the half-life. So we got to talk a little bit quickly about half-life. We'll talk about it more when we get into elimination kinetics.

But what I want you to remember is you can... See, based upon this equation, don't worry about volume of distribution. It's a constant for most, for different types of drugs. And don't worry about this.

Focus on the half-life. I want you to think based upon this equation, what would the half-life have to do with the clearance? How would it affect the clearance? And what is half-life? What the heck is that?

Half-life is the time it takes to go from 100% of the drug to 50% of the drug. However long it takes to get to that point, that is the half-life of the drug. If the half-life of the drug is high, increase, very long.

So let's actually use a different color here. Let's say that the half-life of a particular drug is very long. It takes a long time to drop the amount of the drug to 50% from 100%.

What happens to the clearance based upon this equation? Well, the denominator is going to be high. That's going to lower the overall number.

So the clearance will subsequently decrease. So remember that half-life and clearance are inversely proportional. In the same way, if I have a drug that has a very short half-life, it takes very little time for it to be able to go from 100% to 50%. I'm clearing it very quickly. If that's the case then, half-life goes down, what happens to the clearance?

The clearance will subsequently go up. So remember, clearance, half-life, inversely proportional type of relationship. Let's write that down. So clearance is inversely proportional to half-life.

That's an important concept to remember, especially for USMLE. All right, so now, when we talk about half-life and rate of elimination, we're using all these different types of terms, we have to really quickly talk about something called elimination kinetics. Alright, so when we talk about elimination kinetics, and we're talking about rate of elimination, we're talking about half-lives and things like that, most drugs, when we think about them with respect to their biochemical type of profile, work under what's called first-order enzymatic kinetics. Now, you probably thought biochemistry would never come back again, but unfortunately it is coming back a little bit. So first-order kinetics, we have to talk about this one, and then we'll talk afterwards.

about the less common situation we don't really want most drugs as clinicians to act under zero order and you'll see why in a second. When we talk about first order enzymatic kinetics and zero order enzymatic kinetics, you guys will get questions probably on your test about either comparing the graphs, knowing specific types of terminologies of which things are constant, what's the proportion of drug to rate of elimination, all that stuff. So I'm going to help you guys out with that. So first thing that I want you guys to remember for first order enzymatic kinetics, most drugs, thank goodness, operate under first order.

enzymatic kinetics. I want you to remember that most drugs will operate under first order enzymatic kinetics. When you think about this, here's what's really interesting. Let's say that we take a drug that operates under what's called first order enzymatic kinetics.

One of the cool things about this drug is we think about its rate of elimination. The rate of elimination of this drug, it can vary according to first order enzymatic kinetics, but the fraction of drug that we eliminate per unit time. The fraction of drug that we eliminate per unit time is constant.

And you know what that's interesting is? We can use this concept of half-life of that fraction of per unit time. And we can say that in first-order enzymatic kinetics, half-life is, very, very important here, guys, constant. What the heck does that mean?

What that means is I can say that, let's say I have a drug. Here is drug A. And I'm going to deliver 100 milligrams per liter. of drug A to a particular patient. Assuming it has 100% bioavailability, I give it IV, gets into the bloodstream, 100% of the drug is there.

What's going to happen to that drug is over time, if I'm not giving any more of the drug, so there's no increase in the dosing, it's going to become eliminated over time. The way that it gets eliminated is very, very dependent upon its half-life. And so what I can say is the half-life is constant.

So what I'm going to say is, just to make this up, I'm going to say I'm going to remove... 50% of the drug, 50% of the drug is going to be eliminated per hour. So I'm going to put E for elimination.

I'm going to eliminate 50%. The fraction of drug removed every per unit time is constant. So for example, I start off at 100 milligrams.

Then I go to half of that 50 milligrams. Then I half to 50 to go to 25. Half 25, that gets me to 12.5. Half 12.5, I had to get to 6.25. You get the point.

I'll just keep coming down. What I expect is every hour I'm going to go to each one of these percentages or milligram amount because the fraction of the proportionality factor is going to be constant every single hour. So for example, at time zero, when I give the drug, there's 100 milligrams. At one hour, there should be approximately 50 milligrams left. At time two hours, I should have removed another 50%, and I'm down to 25 milligrams in the bloodstream.

At time three, I'm down to about... 12.5. At the fourth hour, I'm down to about 6.25. And if I were to really be particular, if I could get it somewhere in there, like three point something, I'd probably be around the fifth hour, like somewhere on like 3.2 something.

All right. So if I kind of. Look at this graph. What I notice out of this graph is that it moves in a very type of interesting fashion. You see how it kind of comes down like this?

This is what's called an exponential graph. So an exponential curve. So what sometimes you may be asked is, is you get a graph and you say okay this drug is operating under what type of enzymatic kinetics? You would say first order because it's an exponential graph.

If we're to say okay what drugs operate under first order enzymatic kinetics? You say I got you boo, it's most drugs. And you know why?

is because the half-life is constant every single hour removing 50% of the drug. Now, here's what's really interesting. The amount of drug that you give to the patient is directly proportional to the rate of elimination. And this is important only in first order enzymatic kinetics. This is the only time that drug concentration and rate of elimination is directly proportional.

So if I decide to increase the concentration of my drug, and I'll explain it down here in just a second. If I increase the concentration of my drug, I will subsequently increase the concentration of its rate of elimination. These are directly proportional.

This is the only situation. It's not that way. in zero order. What that means is here I have drug concentration on the x-axis, here I have rate of elimination on the y-axis. What would this say?

As I go towards the right, what would I expect my rate of elimination to do? Increase. So if I use that color here, blue, as I increase my drug concentration I expect my rate of elimination to increase.

You want to know why? I have enzyme sites that are available for the drug. If I give this hundred milligrams of the drug, It can bind onto the active site of the enzyme, be metabolized. Once it's metabolized or excreted, it can then actually go through this reaction process. So as I increase the concentration of my drug, I will increase the rate of it being eliminated.

So I'm going to see this kind of increase in the graph. Now watch what happens for zero order. For zero order enzymatic kinetics, thank goodness there's not many drugs that undergo zero order kinetics. The ones that I want you to remember is remember PEA.

So phenotone, which you're going to abbreviate PHT. E for the next one is ethanol. So alcohol, we'll put E-T-O-H.

And the last one is aspirin. We'll put A-S-A. These are the primary drugs that you guys will potentially be tested on that act or work under the activity of zero-order enzymatic kinetics. Now, here's the interesting thing.

If you notice here, half-life is constant in which one? First order. It is variable in the zero-order.

The only thing that's constant in zero-order is the rate of elimination. So the amount of drug, the milligram of drug that we actually eliminate per hour is constant. So rate of elimination is constant. Not the half-life. in zero order.

Meaning, if I have drug A, same situation here, I'm going to administer 100 milligrams per liter of a drug intravenously. So that means that I have 100% bioavailability, all the drug is going to get into the bloodstream. How much time is it going to take for me to be able to eliminate most of that drug or completely all of the drug, as long as I'm not giving more of it? Well, the rate of elimination of that drug is constant, meaning that I'm going to remove, let's just pretend here, 25 milligrams of drug every hour.

That's my elimination rate. You see how it's constant? It's not a percentage.

The percentage that I will remove every single time is actually going to vary. But the rate that I remove drug is constant. So for example, I start off here at time zero, 100 milligrams. At the second point here, if I keep going down here, 100 milligrams, I got to subtract 25, that's 75. Subtract another 25, that's going to be 50. Subtract another 25, that'll be 50. it'll be 25 and then come completely down to zero here. Okay.

So every hour I'm going to remove 25 milligrams. That's my rate of elimination. So I start off here at time zero at a hundred. Then I start at 75. Okay.

One hour, I'm going to remove 25 more milligrams. And at set two hours off 50 milligrams left at three hours, I will remove another 25 and I'm left with 25 milligrams. And then at time zero, I'm sorry, at a zero milligrams, which is about four hours later, I would remove all of the drug.

It should be completely gone. So what do you notice about this particular curve here if we do it like in a different color here? What do you guys notice here? Not perfect, but it's linear. It's not exponential that you would see in a first order.

In zero order, this is what's called a linear type of curve or a linear graph if you will. So sometimes what they may say is you get this graph and say okay, this is a particular drug that you guys see. What is kind of what order kinetics is it operating under? And you would say it's zero order because it's linear.

And I can tell that the rate of elimination is constant. What kind of drugs would do this? Only these particular drugs.

And now, the last comparison is that we said that in first order, as you increase drug concentration, you increase rate of elimination. That's not the case in this situation. So we can say that these two, let's actually say, are not proportional.

They are, let's say, independent. of one another. This is an extremely important concept.

Watch this. Here I have the same thing, drug concentration x-axis, rate of elimination on the y-axis. If I give, if I increase the concentration of the drug in...

First order, it increased the rate of elimination. As I increase the concentration of the drug, it will not increase the rate of elimination. What is the rate of elimination?

Constant. That means that what happens is I can keep giving more. and more and more and more drugs. But guess what happens to the rate of elimination on the Y-axis? It's not going to keep going up.

It's going to stay flat because it's constant at this particular amount, at this particular concentration, it is going to be constant. That's an important concept. And the reason why is if you look at this enzymatically, is if I have a drug here, what's happening is this drug, I give a hundred milligrams of this drug.

And if I continue to to keep trying to increase the concentration of the drug, it's supposed to interact with enzymes. But this enzyme is occupied with so much drug. It's completely saturated. It's at what's called V max.

You probably thought that would never come back. But this is when all of the enzymes completely saturated. So no matter how much more you give the drug, it's not going to increase the rate of the reaction.

And so this rate of the reaction will not proportionally increase. It's going to stay constant. It's just going to do it at the rate that it wants to.

And that's an important thing. So whenever you look at this on this aspect of the graph, this is first order. this my friends is zero order and the problem with this is that you can see toxicity with this aspect of zero order that's why we don't like as clinicians to see zero order enzymatic kinetics with a particular drug all right the last thing that i want you guys to remember here is that when we talk about a drug sometimes you can actually use something that we call talk about called steady state and we're going to talk about that with dosage regimens but what's really important is half-life is very important for the time it takes to get to steady state and the steady state basically definition definition is the amount that you're giving is equal to the amount that you're eliminating. So that's the steady state concentration. It's when you're at an equilibrium between the amount that you're putting into the body is equal to the amount that the body is getting rid of.

That's dependent upon the half-life. And the same concept, the amount of time it takes for you to completely eliminate the drug from the body according to first order kinetics is dependent upon the half-life. And you know how much time it takes?

If you kind of look at here, let's say I have 100 milligrams of the drug, what does it take for me to get to about 95% of the drug eliminated? So at 6.25, I have like 93, 94%. If I were to go here, I'd be somewhere around like approximately three something, right? Approximately three something.

something. Well, that means that I've metabolized at least 97% of the drug. So in between, what half-life was this at?

So this was one, two, three, four, the fourth half-life. And then around this one, right, you get to about three, three point something milligrams that are left. You're at about five half-lives. That means somewhere around approximately 95% of the drug being eliminated is equal to about four to five.

half-lives. So that's an important thing to remember because guess how many half-lives it takes to get to steady state concentration? The same amount for it actually to eliminate 95% for the body, four to five half-lives.

All right, guys, let's do some questions about clearance. So we got a 55-year-old woman brought to the ED, had some seizures. She has a history of renal disease undergoing dialysis.

She gets an intravenous infusion of an anti-seizure drug, which the following is likely to be observed with the use of drug ninja in this patient. So when we think about this patient here, what do we know? Well, we know that they have renal disease. Well, we only... you think about clearance, clearance is really dependent upon renal function and liver function as the primary organs here.

So because she has an underlying renal disease, what do you think is going to happen to the clearance of that drug? It's likely going to decrease. And when we think about clearance, clearance is really dependent upon half-life, right?

So clearance and half-life have a very strong relationship with one another. So what we know is, is that as clearance decreases, the half-life of that drug is going to significantly increase. And as the half-life a drug increases, that means it can concentrate within the body and it can actually start to have potential side effects if you can't clear the drug from the body.

And so because of that, one of the important things to understand is that as the half-life of a drug really, really increases, because you can't clear it. because you have an underlying renal disease here, what would I want to do to the dosage of the next dose that I give for this drug? Or if I actually think about this now, what kind of dosage would I want to give? Would I want to give a very low dose, a normal dose, or a high dose if they have renal disease causing decreased clearance and an increase in half-life? I probably want to, because I have a very high half-life now, I probably would want to drop the dosage here.

So because of that situation where half Half-life is increasing, dosage should subsequently decrease as well. So that is what I would actually pick for this particular answer here. All right, guys, so here's the next question.

We got a pharmacokinetic study of a new antihypertensive drug. It's being conducted in some healthy human volunteers. The half-life of the drug after administration by continuous infusion is about 12 hours. That's the half-life. What do we know about half-life?

Which, again, is very, very important. How many half-lives does it take for the drug to be able to reach steady state? Do you guys remember? We said it takes about four to five half-lives for a drug to be able to reach steady state concentration. If the half-life for the infusion is 12 hours, about four half-lives will get me close to the steady state, four to five.

So what's 12 times four? It's about 48. So it might be just a little bit greater than 48 hours, but at least 48 hours is going to be the minimum that I need. And so look here, 48 hours would definitely be our answer because we know four to five half-lives would help us to be able to reach steady state concentration if we're giving it via continuous infusion.

So I would expect this to be 48 hours. All right, guys, that covers this section here on the concept of clearance. In the next video, what we're going to do is we're going to start talking a little bit more about the dosages of drugs, the regimens of drugs, and get a little bit of detail into that.

See you guys there.

Transcript for:Understanding Drug Clearance and Kinetics

Transcript for:
Understanding Drug Clearance and Kinetics