Let’s consider the take-home points from this exercise. First of all, when a loading dose is given to start therapy the usual goal is to achieve a concentration at time zero after the loading dose. That is about the same as the projected stay state concentration. That’s our ultimate goal. Once you have the target concentration at time zero the loading dose is simply the amount of drug that will produce that concentration in the given volume.
It’s filling the tank Let’s consider now a multiple dosing regimen where we’re trying to achieve a specific average steady-state concentration from intermittent dosingㄡ A mainus dosing regimen can either involve the rate of infusion such as a continuous infusion of perhaps twenty milligrams per hour as a continuous infusion or it can be a dose given at certain intervals and the designation that we use for dosing interval is Tau or the Greek letter tau(τ) In this case the example is 200 milligrams every six hours. In either case what we’re concerned about is the rate at which drug is being administered to the patient. So for a continuous infusion it’s fairly obvious we’re giving a rate of so many milligrams per hour.
In the case of a multiple dosing regimen or intermittent dosing regimen, we have to divide the dose by the Tau. So in the case of 200 milligrams every six hours, the average dosing rate would be thirty three point three milligrams per hour. The average steady-state concentration is the dosing rate in milligrams per hour divided by the clearance. So it’s very similar to a continuous infusion where the equation on the Left shows that Css is equal to the rate of infusion divided by clearance.
When we’re talking about the average steady-state concentration during multiple dosing, its dose divided by tau or the dosing rate divided by clearance In a sense both of these equations have the rate out the rate at which drug is being eliminated on the left and the rate in on the right, or the continuous infusion the rate out is the Css times the clearance and that is equal to the rate at which the drug is being infused the Rinf.
For a multiple dosing regimen it’s the average stay state concentration times the clearance is the rate out and the rate in is dose over tau or the dose divided by the dosing interval how many milligrams per hour on average are being administered to the patient. Now when we convert a dosing rate a dose over tau, we complete that calculation we know that a certain number of milligrams per hour need to be given to the patient. If it’s an intermittent dosing regimen, we need to break that down into a specific dose and dosing interval or a dose and a Tau. Now let’s assume for the sake of example that the dosing rate we need to achieve is 50 milligrams per hour.
Now we have to consider what the options are for dosing this drug what strengths is the drug available and is it available in 200 milligrams, 250 milligrams, 300 milligrams, 400 milligrams. We’re going to have to use a dosing rate that’s compatible to the strengths of the drug that are available and there might also be an optimal dosing interval based on the pharmacodynamics or the pharmacokinetics of the drug. That we’re shooting for and that’s going to affect the the specific dosing regimen that we select for a given dosing rate.
But once we know what our limitations are and coming up with a specific dosing regimen, the way to convert a dosing rate in milligrams per hour to a specific regimen is very simple. We assume two options. We’re either going to start with Q six hours or every six hours as our base interval In which case for a 50 milligram per hour dosing rate that would be 300 milligrams every six hours or we try every eight hours in which case a 50 milligram per hour rate would be four milligrams every eight hours.
Now the beauty of going with q6 and q8 is that every possible practical dosing interval is a multiple of one of these two values in the case of q6, if the best dose would be 600 milligrams or the best dosing interval would be Q12, we can go with a 600 milligram dose. Based on just scaling up the 300 milligrams q6, if we scale it from the q8 dose of 400 milligrams we can go with every 4 hours which would be 200 milligrams every 4 hours. Or either the q6 or the q8 regimen would make it easy to determine a q24 regimen either multiplying the 300 milligrams by 4 to get 1200 milligrams or the 400 milligrams by 3.
there’d be three doses once a day versus three one dose once a day being the same as three doses every eight hours at 1200 milligrams. So we can identify the most practical dosing regimen starting with q 6 and q 8 and multiplying them by the dosing rate that we initially determined. Let’s pause again for answering of a question. Okay, you’ve answered this question a dosing regimen of 400 milligrams every eight hours, produces the same C average steady state as a dosing regimen of… Now we know right off the bat that if we’ve got a dosing regimen of 400 milligrams every eight hours we’re talking about a dosing rate of 50 milligrams per hour.
So whatever dosing regimen the patient receives in order to keep the C average steady state the same, we’re gonna have to use the same dosing rate in milligrams per hour. 300 milligrams q 6 is indeed 50 milligrams per hour. Likewise 600 milligrams q 12 is also 50 milligrams per hour but 900 milligrams every 24 hours is not 50 milligrams per it would have to be 1,200 milligrams every 24 hours . So the answer to this question is D. A and B are correct but C is not.
Now let’s explore the challenge of coming up with a multiple dosing regimen that’s based on Cmax and Cmin, in a specific C Max and C min rather than C average steady-state. In order to come up with a multiple dosing regimen shooting for a specific C Max and C min, we first have to know what the target C Max and C min is, and we have to know both the elimination rate constant and the volume.
Now what we’re going to discover as we continue through this course is that K relates more directly to the dosing interval to the tau and volume relates more directly to the dose when we’re looking for a C average steady state and we don’t care about C Max and C men we can use clearance which is the combination of K times V but when we want to tease out a specific C Max and C min we need to keep the elimination rate constant and the volume separateㄡ Such that the elimination rate constant gives us a clue about the best dosing interval and the volume gives us a clue as to the best dose.
So the first thing we would do is calculate the dosing interval and round it to a practical number. Now the equation that we’ve already covered the time is equal to the natural log of c1 over c2 divided by K. Now specifically our time is tiled the dosing interval and c1 and c2 represent the maximum concentration and the minimum concentration. The result during this dosing interval and they’re divided by the patient’s elimination rate constant. So this would give us the dosing interval based on the patient’s K they would achieve the specific C Max and C men that we’re looking for.
We were then round that off to a practical number the closest four six eight twelve 24 hours whatever that may be. We would then calculate the dose. And thedose is represented by the the c-max at steady state is produced by the dose divided by the volume divided by one minus e to the minus K tau. Now let’s take a closer look at that. C at time zero we’ve said is the dose divided by volume. So C max we can think of it as the C at time zero dose divided by volume, divided by one minus e to the minus K tau.
1 minus e to the minus K tau is the factor that determines the comparison between the concentration that results from an individual dose a single dose at time zero to what that same dose given intermittently would produce as a maximum steady state concentration at time tau we see the Tau in the denominator of that equation so whatever time the dosing interval is we plug that in and that would tell us how the extent to which the drug is going to accumulate from the serum concentration after one dose to the multiple dosing an intermittent dosing schedule.
And we can see then that the dose would actually be calculated by taking the C max concentration times the volume times the factor 1 minus e to the minus K tau.