How to predict changes in serum concentration?

Welcome to clinical applications of pharmacokinetic dosing and monitoring. This is session 3 the ups and downs of predicting changes in drug concentration. In this video, we’ll try to answer the question how can we predict changes in serum concentrations before they occur. You see good pharmacists can identify when something goes wrong with a drug regimen when the serum concentrations start to go too high or perhaps fall too low. To the point where the patient is not being treated adequately or perhaps may be subject to toxicity. But great pharmacists can anticipate problems with serum concentrations before they even occur simply by recognizing some of the tell-tale signs when pharmacokinetic parameters are starting to get out of whack.

That’s what we want to explore in this video. This session 3 is how can pharmacists identify when serum concentrations might be changing in such a way that the patient will be subject to either toxicity or sub-therapeutic CIRM levels. When you finish this session our goal is that you’ll be able to explain the timing of serum levels as they were late to absorption and distribution. To determine how a change in dose or the dosing interval affects Cmax, at steady state Cmin, at steady state Caverage, at steady state in the area under the curve.

To predict how a change in volume of distribution elimination rate constant or clearance effects C max, C min, C average all at steady state and also the area under the curve. To determine how a change in the fraction unbound affects the total concentration or the unbound concentration of drug both acutely and after steady state is reestablished. First let’s consider when to measure serum levels. Now the first consideration is always that of steady state. We have to make sure that the patient is steady state and a drug in order to evaluate serum concentrations the result from that drug regimen.

Have life of the drug in the examples shown is 17.3 hours so we know that 95% steady-state is four point three half-lives which for this drug in this situation would be eighty hours and the consideration here is that to measure a serum concentration before we get to 95% steady-state. Risks the possibility that the serum concentration is not truly representative of the drug regimen. If the serum level has grown much earlier than steady-state is achieved then we might make a misinterpretation of the suitability of the drug regimen perhaps assume that the serum levels are appropriate when the dosing regimen really needs to be changed. So it’s very important to wait until we’re very close to steady-state conditions.

That’s why I recommend 95 percent of the way to steady state which is four point three half-lives. We’ll also assume that absorption and distribution are immediate now I mentioned in one of the earlier sessions that what we’re going to assume when we measure CIRM concentrations. Is that absorption and distribution are complete. We do this in order to avoid the difficulties of estimating the rate of absorption or the rate of distribution of a drug. Now in the example shown at the bottom of this slide. You can see that if a serum concentration is drawn at the red X prior to the distribution of the drug being complete.

The sermon concentration falsely elevated because drug that is eventually going to distribute out of the blood. It’s still contained in the blood, giving a higher serum concentration than one would expect. Likewise if the serum concentration is drawn before a drug is completely absorbed then not all of the drug has gotten into the bloodstream and since our frame of reference in this case is serum. We may assume that the serum concentration is accurate when actually not all the drug is there, so it’s going to be falsely low. The way we avoid having to deal with issues pertaining to the rate of distribution or absorption is simply to wait long enough such that distribution and absorption are both complete.

At that point if we measure to serum levels and are able to calculate the slope of the line or the elimination rate constant K, it’s an easy task to back calculate to find out what the serum concentration would have been if distribution and absorption are immediate. So that’s a simple mathematical manipulation and it enables us to avoid having to deal with estimating rate constants for absorption or distribution. Let’s consider what effects C average steady state.

We know that our equation: the C average steady state equals dose over tau, the dosing rate the milligrams per hour divided by the clearance. What this tells us is that the elimination rate constant and value specifically do not matter when we’re considering C average steady state. It’s the clearance that matters because we’re looking at an average level. In terms of Cmax and Cmin, we know that C max is dose over volume divided by the accumulation factor 1 minus e to the minus K tau and we know that C min is equal to C max times e to the minus K tau.

Now it’s important to understand how the value of the elimination rate constant K times tau affects variables in an equation because what we’re dealing with is e to the minus K tau which means it’s a negative exponent. So as K increases meaning the slope of the line would be much steeper, the serum concentrations would fall much more rapidly or as tau increases beings meaning that the dosing interval is much longer allowing more time for the serum concentration to fall. If the value of K times tau increases, the fact that it’s a negative exponent means it’s actually going to be a smaller number. Such as 10 to the negative 5 is less than 10 to the negative three.

It’s a smaller decimal fraction. So if we have a larger K or a larger tau such as the product of K times tau increases. The percent remaining indicated by e to the minus K tau will be much smaller because of the rapid elimination or the longer length of time for the drug to be eliminated.

Now in the Cmax equation if e to the minus K tau is smaller that means the that total value of 1 minus e to the minus K tau is going to be closer to 1 so much of the drug is being eliminated and the Cmax at steady-state isn’t going to be much greater than the concentration at time 0 that we would get from dose divided by volume. The bottom line is that when we’re talking about Cmax and Cmin. Dose in volume both matter because they they will determine the concentration after one dose and the concentration after the concentration increase after every dose. The elimination rate constant in tau matters because that determines that percent that’s remaining after each dosing interval.

So we have to be concerned about the dose the volume the elimination rate constant and the dosing interval when we’re talking specifically about values of Cmax and Cmin. This is illustrated in these two serum level charts. When we increase K as shown by the red curve, you can see the the steeper slope the more rapid decline in serum concentration which right after the first dose causes Cmin to be lowered. And because Cmin is lower, when we give a dose the Cmax is going to be lower as well. When we increase tau as shown on the right set of curves, a much longer tau allows greater time for the serum concentration to fall.

So after the first dosing interval, Cmin is much less than it would be at the end of a shorter dosing interval. So this just illustrates that increasing either K or tau will lower the Cmin and also lower the Cmax. What affects area under the curve? As you recall, there’s two equations that we utilize routinely to determine area under the curve. One is the concentration at time 0 divided by the elimination rate constant and also we can use the dose divided by the clearance. With either of these equations we can see that the tau and volume of distribution don’t matter. So changes in tau volume are not going to affect the drugs area under the curve.

What effects the values of Cmax minus Cmin and also the concentration at time 0. Both of these values and these are equivalent or equal to dose over volume. Remember the C, the concentration at time 0 is simply the concentration results from a dose and a given volume when the initial concentration is 0. However, the same dynamic applies when we give a dose to a patient who’s standing at a Cmin. Whatever that level of Cmin is. The dose over volume determines how much that serum concentration will increase up to the Cmax. So Cmax minus Cmin and C at time 0 are identical that are equal to dose over volume.

So what we can we can gather from these relationships is that the elimination rate constant the clearance and the dosing interval tau do not matter when we’re talking about Cmax, -Cmin and the C at times 0. This is illustrated again as we increase the K. We can see that even though Cmin is lower and Cmax is lower. The difference between Cmax, -Cmin does not change. It depends on dose over volume. Likewise and the curves on the right, when we increase the dosing interval. Although Cmax and Cmin are both lower in red curves because of the longer dosing interval, the difference between Cmax and Cmin is the same. It does not change because it’s dependent only on dose and value.

It’s 10 milligrams per liter in both cases.