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 now 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 maybe people may just think oh that's just excretion but excretion 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 involvement 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 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 the 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 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 us mle is that sometimes they'll actually further determine based upon like 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 it's here's the big thing divided by the half-life so we've got to talk about a little bit quickly about half-life we'll talk about it more 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 remember especially for you and emily 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 all right so we talk about elimination kinetics and we're talking about rate of elimination we're talking about half-lifes 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 elimination all that stuff so i'm going to help you guys out with that so first thing 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 okay the rate of elimination of this drug it can vary according to first order enzymatic kinetics but the fraction of drug that we eliminate every spec 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 a hundred milligrams per liter of drug a to a particular patient assuming it is 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 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 2 hours i should have removed another 50 percent and i'm down to 25 milligrams in the bloodstream at time 3 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 around 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 i 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 100 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 p-e-a 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 our work under the activity of zero-order enzymatic kinetics now here's the interesting thing if you notice here half-life is constant and which one first order it is variable in the zero order the only thing that's constant and zero order is the rate of elimination so the amount of drug the milligram of drug that we were 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 0 100 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 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 0 at 100 then i start at 75 okay one hour i'm going to remove 25 more milligrams and i'd 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 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 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 to 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 drug 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 like 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 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 of 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 in somatic 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 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.
