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