WEBVTT
Kind: captions
Language: en
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Taking a closer look at the elimination
rate constant
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we can identify a different perspective for defining what the elimination rate constant is
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It's the fraction of drug volume cleared per
unit time.
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It's typically represented by the equation clarence equal K times V
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elimination rate constant times the volume of distribution.
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Another way to represent that equation just algebraically rearranging it
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as K equals clearance over volume which actually is a better representation of what's occurring physiologically
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between the clearance and the volume.
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Let me illustrate this.
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If the K or the elimination rate constant is point 20 per hour
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which we can also designate as 0.20 hours to the -1,
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what this tells us is that 20% of the volume is cleared of drug every hour.
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It's illustrated in the schematic below
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where 4 liters per hour as indicated in yellow are cleared by the net that we pull through the tank
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and since we have a tank of 20 litres 4 litres represents point 2
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so every hour, if we pull the net through the tank at that rate,
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removing the fish from those those yellow liters,
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we have 20% of the volume of the tank being cleared
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Now if we represent this by actual serum
concentrations.
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If we start with 10 and we have a K of 0.2 hours to the minus 1
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and then have 1 hour we will have a concentration of 8.2
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then of 2 hours six point seven
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and the end of three hours 5 point 5.
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Now what's interesting is that
if we plot the natural log of those serum concentrations,
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we get two point three, two point one, one point nine and one point seven.
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So the elimination rate constant can be considered from two different angles.
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If we're considering the plot of natural log versus time,
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it represents the decline in the natural log of the concentration per hour.
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Note that every hour, the natural log
concentration drops by point two
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which is the value of K. That's the slope of the line.
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But it also represents the 20% of the volume is eliminated or excuse me cleared not eliminated
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but cleared every hour.
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So let's illustrate how this relates, the volume the clearance, and the elimination rate constant.
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Keeping in mind our equation K is the proportion of volume
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that is cleared per unit time.
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Why does an increase in volume cause K to decrease?
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We can illustrate that very clearly.
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There's our schematic showing a clearance of 4 liters per hour
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a volume of 20 liters and we have a concentration of 8 milligrams per liter
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such that K is 0.2 because 20% of 20 is 4
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4% excuse me
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20% of that 20 liter tank is cleared
every hour.
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Now if we double the volume without changing the clearance
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our clearance is still 4 liters per hour.
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Now our volume is 40 liters.
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Our concentration has dropped to 4 milligrams per liter
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and the K has dropped to 0.1 hours to the minus 1
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because now it's 4 in relation to 40
liters rather than 20 liters.
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So when volume changes, K will change even though clearance does not change.
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We can also pose the question why does an increase in clearance also cause an increase in K?
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Well, they're directly related.
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If we double the clearance to 8 liters per hour
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and we don't change the volume of
distribution.
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We still have a 20 liter tank but now every hour we're clearing 8 liters instead of only 4.
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So K has now doubled to 40% or 0.4 hours to the minus 1.
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So let's pause for another brain check here.
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According to the fishtank model k is ______.
Pause the video and answer that question.
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Well, if we look at our answers,
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according to the fishtank model K is the slope of concentration versus time curve.
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No, K is the slope of the natural log of concentration versus time curve.
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The concentration versus time curve isn't even a straight line.
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B says the fraction of volume cleared to the total volume of the tank
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that is our definition of K using the fishtank model.
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C says it's inversely proportional to clearance.
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No, K is directly proportional to clearance as we Illustrated on the previous slide.
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So our answer is B.
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Let's try an exercise to see if you can answer this question.
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Patient is taking a renal-excreted
drug and develops renal failure.
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Which of the following would definitely change in this patient?
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Consider our equation K representing the fact that elimination rate constant
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is the fraction of volume
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that is cleared per unit time.
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Our answer is both clearance and K when a patient's renal function
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or for adequately metabolized drug liver function changes.
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Clarence will change and when clearance changes because the organ that eliminates the drug changes.
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K will also change.
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Volume is not going to change and since K represents the relationship between clearance and volume.
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K must change if the clearance changes.
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Take home points from that exercise.
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Changes in renal function directly affect clearance of really excreted drugs
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that's an important point to keep in mind.
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Secondly, when clearance changes, the K
will change in direct proportion.
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A change in clearance will not cause a change in V.
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K is simply the fraction of two other parameters: Clarence and volume.
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It cannot change anything.
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However, if clearance doesn't change, a change in volume will cause an inversely proportional change.
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Okay it's important to remember here in the relationship between clearance volume and emission rate constant.
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That the elimination rate constant is simply a representation of relationship between
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two other important variables: clearance and volume.
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The clearance is inherently dependent on
what's taking place in the body.
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How the drug is being eliminated by the body?
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Volume is also dependent on things taking place in the body,
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but changes involume and clearance may be independent of each other.
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But the elimination rate constant is nothing more than an indication of the relationship
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between clearance and volume.
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so you can't look at this equation from a purely mathematical perspective
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and assume that if K changes that clearance or volume would have to change in response.
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No it's the other way around.
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A change in clearance or volume will cause a change in K.