Which factor(s) impacts the loading dose ?

Let’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.

So 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

Now 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.

Now 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.

We 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.

So 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.

So 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.

If 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.

The zero serum concentration that existed at the start of the infusion would be halfway to steady-state or halfway to 32 so it would also be 16 milligrams per liter. At any point in time if we add the concentration on the red curve to the concentration on the blue curve, we’re going to achieve a concentration of 32 milligrams per liter. This is ideally the way it works when we give a loading dose that’s perfectly matched with a continuous infusion where the loading dose is designed to achieve the same concentration of x zero as the continuous infusion at steady state . So let’s pause for you to answer this question please pause the video and answer this one.

A patient receives a loading dose. The size of the loading dose depends on V. That’s a true statement. Remember there’s there’s two factors that determine the size of a loading dose. And that’s the volume and the desired concentration we want to achieve. B is false. The size of a dose depends on The half-life has nothing to do with a loading dose. Loading dose only depends on the the concentration we want to achieve in the size of the tank. Half-life determines how much drug is going to need to be administered thereafter but has nothing to do with the loading dose. And C is also false. The size of the dose depends on the clearance. That’s similar to B.

Clearance 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?

Now 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.

We 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