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Welcome to clinical applications of
pharmacokinetic dosing and monitoring.
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This is session 2.
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Dosing basics-how to determine the right amount of drug for a patient.
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In this video we're gonna try to answer the question.
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How can we determine the safest and most effective dose of drug for a specific patient?
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By the time you complete this lesson,
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you should be able to determine a loading dose to start therapy;
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to calculate the rate of infusion; to achieve a desired steady-state concentration
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and predictthe steady-state concentration from a given infusion.
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Calculate a dosing regimen to achieve a desired average steady-state concentration C max at steady-state
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or C min at steady-state
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and identify how serum concentrations
accumulate during an infusion
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or a multiple dosing regimen.
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And the role of one minus e to the minus KT.
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Lastly to adjust dosing regimens, based on first-order linearity.
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We're going to explore three major types of dosing.
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The first is the loading dose .
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This is a single dose designed to achieve a desired concentration at time 0
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We also consider continuous infusions that are designed to achieve a desired steady-state concentration
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once the concentration plateaus.
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And lastly we'll look at intermittent dosing,
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multiple doses to achieve a desired C average steady state
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and also multiple doses to achieve a specific maximum and minimum concentration.
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Let's start with serum concentrations from a continuous infusion.
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Now you can see that the rate of infusion in this example is 100 milligrams per hour
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with a clearance of 4 liters per hour.
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The patient has a k' of 0.2 per hour and a volume of 20 liters.
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This yields a steady-state concentration of 25 milligrams per liter
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Now once the serum concentration plateaus
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when steady-state has been achieved.
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That concentration remains consistent.
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and at that point we can say that the steady-state concentration from this continuous infusion
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is equal to the rate of the infusion divided by the clearance.
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Or we can always break up clearance into its component parts K times V
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based on the equations that we talked about in Lesson one.
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But primarily we're concerned about the rate of infusion
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divided by the clearance to determine the steady-state concentration during a continuous infusion.
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Now let's take a look at the concept of percent lost as an accumulation factor
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the supplies during continuous infusion but also during multiple dosing regimens
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if our elimination rate constant is 0.2 per hour
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and the time interval is 4 hours
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then e to the minus KT is 0.45
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as we said in Lesson one that represents the percent remaining.
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So 45 percent of the drug under those circumstances would be remaining after 4 hours.
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but what that also means is that 55 percent of the drug would be lost.
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So e to the minus KT represents percent remaining after time T during an elimination phase of drug.
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Therefore the value 1 minus e to the minus KT is the percent that was lost during time T.
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Now 1 minus e to the minus K T where T is the time of infusion
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or percent lost during the time of infusion
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what that defines is the accumulation to steady state
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during a continuous infusion.
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Let me illustrate this concept,
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if we look at the concentration from infusion,
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we can see that it's steady state.
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The rate of infusion divided by clearance gives us that steady-state concentration.
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However, we need to be able to identify what the serum concentration might be
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at some time prior to achieving steady-state
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as the drug is accumulating during the continuous infusion.
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This is represented by the rate of infusion
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divided by clearance which would give us steady-state
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but now we introduce this one minus e to the minus KT factor
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as an accumulation factor
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where T in that equation is the time of infusion .
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So the longer the infusion has been running ,the larger the concentration from the infusion would be.
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If we think of it in terms of relationship to the concentration at steady state,
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the concentration at any point in time prior to steady state
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is equal to the concentration that would
exist at steady state times 1 minus e to the minus KT.
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Now when you look at this this equation, it should be fairly obvious to you that as T becomes large.
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The fact that e to the minus KT is a negative exponent
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as T becomes very large e to the minus KT becomes very small
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and the value 1 minus e to the minus KT, essentially approaches 1.
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so when T is large such that the time is enough for the patient to have reached steady state,
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then the concentration of infusion is essentially equal to the concentration at steady state.
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But when the time of infusion is relatively short and compared to what it would take to reach steady state,
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then, the concentration at time T is going to be equal to the steady-state concentration
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times 1 minus e to the minus KT, where T
is the time of infusion.
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Let's consider how drug relates drug
dosing relates to clearance.
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If we have a patient with a volume of 20 liters and a clearance of 4 liters per hour
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and the steady-state concentration we're
shooting for is 10 milligrams per liter,
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well, this means is we have a 20 liter
tank.
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4 liters of that tank are cleared of drug per hour.
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So it's steady state now picture this .
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If this makes sense to you then dosing drugs at steady state becomes relatively easy.
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At steady state, this patient needs to have a concentration of 10 milligrams per liter
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and we know that the clearance of drug
is 4 liters every hour.
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So what that means is that under steady state conditions
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40 milligrams of drug are going to be eliminated from those 4 liters every hour.
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Therefore, the dosing that this patient needs to receive is 40 milligrams per hour
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to keep the steady-state concentration at 10
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So once a patient is at steady state, if we know the clearance
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and we know the concentration,
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that's maintained at steady state
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that makes it very clear to to identify the rate at which drug has to be administered.
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Because we've essentially identified the rate at which drug is being eliminated.
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Let's pause for a brain exercise question see if you can answer this one.
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If a patient receives a drug by continuous infusion
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the concentration of infusion at the time T of infusion
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will be equal to the Css times e to the minus K T where T is the time of infusion.
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That's a false statement .
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The concentration of infusion is going to be equal to the Css times 1 minus e to the minus KT.
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Not e to the minus KT.
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B is also false. The rate of the infusion is the infraction is the fraction of concentration
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at the time T as compared to Css
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that is not that is a false statement as well.
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Let's consider C.
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C is true. The Css will be twenty milligrams per liter if the rate of infusion is 100 milligrams per hour
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and the clearance is 5 liters per hour
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because we said Css is equal to the rate of infusion divided by clearance.
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So the answer in this question is C.
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Applications of a loading dose.
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Now let's shift gears from a continuous infusion to a loading dose.
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A loading dose is simply used to rapidly achieve a therapeutic effect
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by filling the tank with however much drug is needed to get the the serum concentration up to a certain level.
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It's a means of rapidly achieving a serum concentration that would otherwise take longer to achieve
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as we wait for steady-state conditions to be established.
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Clearance has no effect on the size of a loading dose.
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Loading dose depends only on the volume and the desired concentration at time 0.
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You can think of this in relation to filling your the gas tank of your car with gas.
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When you're going to determine how much gas to put into your tank,
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the only thing that matters is the size of
the tank if you're going to try to fill it.
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The mileage that the car gets has nothing to do with how much gas it takes to fill the tank.
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However, when you're considering how much gas it's going to take to to replenish gas that's being used,
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then you would have to consider the mileage.
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Similarly, if we're simply going to give enough drug with a loading dose
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to increase the patient's serum level to a certain value,
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all we're concerned about is the volume of the tank,
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the rate at which the drug is eliminated from the tank is inconsequential.
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So we're not at all concerned about the clearance or the elimination rate constant of the patient ,
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only the size of the tank and the concentration that we desire to achieve with a loading dose.
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There are three possible results from a loading dose.
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If we've given too high a loading dose or a loading dose that achieves a concentration at time zero,
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that's greater than what the eventual steady-state concentration is going to be,
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then the concentration will gradually decline from the initial concentration
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down to the steady state level that exists during an infusion.
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This is in a situation in which we give a loading dose and
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then right when we give the loading dose we start a continuous infusion.
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We might also give a loading dose that's a little bit too low.
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It's below what the steady-state concentration will eventually become.
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So the serum level gradually increases from that loading dose until it gets to the steady state level.
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We can also nail the loading dose get it exactly right
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such that the concentration at times zero from the loading dose is exactly equivalent
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to what the ultimate steady-state concentration will be from the continuous infusion.
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Now you might have learned that the time it takes to achieve steady-state
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depends on the half-life of the drug,
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but if we give a loading dose that's just right,
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we might achieve a concentration at time zero that's exactly equivalent to the steady-state concentration.
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So under these circumstances such as the curve on the right,
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couldn't we say that steady state conditions have been achieved right off the bat
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as a result of the loading dose and then giving the infusion of the continuous infusion?
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The answer is no.
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Because even though it turned out to be perfect,
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there's no way to tell that it was perfect
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until the patient has achieved steady-state.
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In other words, we can't possibly know that the loading dose that achieved a concentration at time zero.
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What's equal to the steady-state concentration until we get to steady-state it can measure that concentration.
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So it's a theoretical perfection that we can't possibly identify until after steady-state has been achieved.
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So the idea that it takes a certain number of half-lives to achieve steady-state still applies
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even if we give a loading dose and that loading dose is right on.