2.3

## Taipei Medical University

Skip to 0 minutes and 14 secondsLet's consider how a loading dose relates to the volume of distribution. Using our example again of a volume of 20 liters clearance of 4 liters per hour, that's a K of 0.2 per hour and we have a desired concentration of 10 milligrams per liter. If the patient has a volume of distribution of 20 liters. We can treat the patient as a 20 liter tank filled imagine ously with blood. Now, in the case of an 80 kilogram patient, we often represent value that you would obtain from the literature in terms of liters per kilogram. So let's say a patient has a volume of 0.25 liters per kilogram, we determined that the patient's volume therefore is 20 liters.

Skip to 1 minute and 0 secondsSo using the fishtank model that we learned in Lesson one, we can we can assume that this patient is going to function when we give a dose as if the patient were a tank filled with nothing but blood in that tank has a volume of 20 liters. So it should be fairly obvious that if we want to achieve a concentration of 10 milligrams per liter and our tank contains 20 liters, we're going to have to give 200 milligrams as a loading dose to achieve that concentration of 10 milligrams per liter. So our loading dose is simply the desired concentration times the volume of the tank

Skip to 1 minute and 40 secondsNow let's go behind the scenes and take a look again at that perfect loading dose. Now we know that when we give a dose of 200 milligrams and place that into a tank of 20 liters we're going to get a concentration at time zero of 10 milligrams per liter. So concentration at time zero equals dose over volume Again I'm showing you these equations but what's more important as you understand the relationships between the variables contained in the equation. It should be intuitively obvious to you that in order to determine the concentration at time zero we need to know the dose that goes into the tank and the volume of the tank.

Skip to 2 minutes and 20 secondsNow let's consider relating a loading nose to a steady-state concentration. So, let's use a different example. Now we've got a drug that has a half-life of 5.8 hours which is based on an elimination rate constant of 0.12 hours to the minus 1. Remember half-life is 0.693 divided by K. The volume is 25 liters and the clearance is 3.0 liters per hour. If we want to achieve a steady-state concentration from a continuous infusion of 32 milligrams per liter, we will need a rate of infusion of 96 milligrams per hour and when we ultimately reach steady state based on the equation steady state concentration is equal to the rate of infusion divided by Clarence.

Skip to 3 minutes and 13 secondsWe will achieve a steady-state concentration of 32 milligrams per liter. Now if we give a loading dose. Let's say we don't want to wait until a state's a concentration of 32 milligrams per liter is achieved. We need a therapeutic effect before that time. So we're going to give a loading dose . Ultimately we would like that loading dose to achieve a concentration of 32 milligrams per liter, then we start the infusion that would ultimately take us to a steady-state concentration of 32 milligrams per liter. and that should give us a nice consistent serum concentration of 32. That would take 800 milligrams. Based on our relationship of dose to volume giving us the concentration at time 0.

Skip to 4 minutes and 1 secondSo a dose of 800 milligrams in a volume of 25 liters would give us a concentration of 32 milligrams per liter but let's take a look at the dynamics between those two different doses. Because there's a relationship between the elimination of drug after we give a loading dose and the accumulation of drug the results from a continuous infusion. And what's called the superposition principle tells us that the body can't tell the source of a drug molecule from one dose or another. All the drug molecules for a given drug appear to be the same thing from the body's perspective. So whether that molecule of drug came from a loading dose or continuous infusion, the body can't tell the difference.

Skip to 4 minutes and 52 secondsSo you theoretically, and from practical perspective as well, could determine what the serum concentration would be at any point in time from a loading dose. Determining what the serum concentration would be from any point in time from the start of an infusion, add those two values together, and that would be the patient's actual serum concentration. In this case, we start by giving the patient an 800 milligram loading dose to achieve concentration at time 0 of 32 milligrams per liter. And from that point, the concentration declines such that 32 times e to the minus KT would tell us what the sermon level would be at any time T.

Skip to 5 minutes and 34 secondsIf we start a continuous infusion at the same time and the concentration at steady state that would ultimately be achieved is also 32 milligrams per liter and the serum concentration at any point in time prior to achieving steady-state would be equal to 32 milligrams per liter times 1 minus e to the minus KT where T is the time of infusion. Now know remember we said on the previous slide that the half-life is 5.8 hours. So at that half-life at that point of time 5.8 hours, that 32 milligrams per liter there that we achieved from the loading dose would have dropped in half to 16 milligrams per liter.

Skip to 7 minutes and 49 secondsClearance has nothing to do with what it would take to achieve a certain concentration at time 0. The only two factors that determine the dose to determine to achieve a concentration at time 0 are the concentration we're trying to achieve and the volume of distribution. So the answer is A. Now let's try an exercise. Patient is about to start continuous infusion that's intended to produce a serum concentration of 80 milligrams per liter. Patient has a clearance of 5 liters per hour and a K of 0.2 hours to the minus 1. And also has a volume of 25 liters. What loading dose would you recommend?

Skip to 8 minutes and 35 secondsNow based on what we just discussed on the previous slide, you should know that the clearance and the K are represent extraneous information that you really don't need to answer this this question. We know that we want to achieve a serum concentration of 80 milligrams per liter and that the patient has a tank of 25 liters. So how many milligrams is it going to take to add to that tank of 25 liters such that the concentration that results is 80 milligrams per liter and the answer is... There it is 2,000 milligrams. 2,000 milligrams placed into a tank of 25 liters will give you a concentration of 80 milligrams per liter.

Skip to 9 minutes and 19 secondsWe can see the diagram of this on the right the loading dose, if it's if it's perfect would be achieving a serum concentration of 80 milligrams per liter and now if we started a continuous infusion at the same time that was designed to provide a steady-state serum concentration of 80 milligrams per liter. Then we would maintain that concentration from the very beginning from the time of the loading dose until the patient got to steady state. But again we have no way of knowing that we accomplished that until steady state conditions were actually achieved

Continuing from the previous video, Prof. Brown specifies how a loading dose relates to the volume of distribution (V).

He shows the relationship between elimination and accumulation during a drug infusion, which is important for this lesson.

Can you tell which factor(s) impacts the loading dose for a patient? Is it the volume of distribution (V), clearance (CL), k, or half-life? This concept is explained further in two brain exercises in this video.

What do you think of the relationship between elimination and accumulation during a drug infusion? Please share your thoughts below.

##### Educator:

Prof. Daniel L. Brown