Now why does fraction unbound only matter for highly protein bound drugs? Remember I mentioned earlier that unless the drug is 80% protein bound, changes in the fraction unbound really aren’t clinically significant. If we’re saying 80% of the drug is protein bound but we’re really saying is that the fraction of unbound drug is less than 0.2. So if you stop and think about it. If we’re talking about drugs that have a low fraction unbound to begin with, being clinically significant in terms of changes in fraction unbound, the reason is because of that low fraction unbound.
In other words, if we were going to change the fraction unbound to different drugs, one in which as a fraction unbound that starts at point one and increases by 0.1 up to point two that’s a 100 percent increase in the fraction unbound. However if the fraction unbound of a drug begins at point seven meaning that only 30 percent of the drug is protein bound, an increase of 0.1 is only a 14% increase. So, in the case on the Left we have a 100 percent increase, because of a point one increase in fraction unbound in the case on the right it’s only a 14% increase.
So it’s the proportionate change in fu that determines whether or not it’s going to be clinically significant and generally we say that’s significant if the protein binding of the drug is at least 80 percent. So let’s summarize the two factors that effect clearance, according to the fish tank model. The first involves renal or hepatic function changes which relate to the size of the net. So that the volume that the net passes through changes. If I have two different Nets. One that clears the amount of fluid that flows through this net as opposed to a larger net, this is obviously going to capture more fish because this net will pass through a larger volume.
It’s clear to see that difference between these two nets. Now keep in mind that in terms of dynamics the fishtank model assumes that the net is what’s movable and the the water in the tank is stationary. Now we know that when we’re talking about the kidney, filtering drugs, the nephrons of the kidney are stationary and blood flows through the kidney. But in terms of the dynamics of filtration of drug, whether we’re capturing fish in a net or we’re allowing drug to filter through the kidney, the dynamics are the same whether the net is stationary or movable.
The other factor that changes clearance is the fraction unbound and as we just described in the previous slide that relates to the proportion of fish or the portion of drug that is catchable that can be caught by the net because it’s not protected by those large protein molecules that prevent the net from capturing the fish. Either of these factors changing the the renal or hepatic function which in effect changes the size of the net or whether the fish or the drug molecule is protected by protein has a significant effect on the clearance and can cause a clearance change. Let’s try an exercise.
According to the fish tank model, which of the following would cause the rate of elimination to increase if nothing else changes? The answer to this exercise is that the increasing of the size of the net which causes the rate of elimination to increase or adding fish to the tank would also cause the rate of elimination to increase. If we increase the size of the net, we’re gonna catch more fish as we pull the net through the tank. And if we add fish to the tank, we’ll increase the concentration of fish in the tank. So as we pull the net through, we’ll catch more fish. Increasing the size of the tank would have the opposite effect.
And increasing the percent of unbound protected fish would also have the opposite effect. So let’s consider the take-home points from that exercise. Anything that increases clearance will increase the rate of elimination, increasing the size of the net or increasing the fraction unbound. anything that increases the concentration, like adding fish to the tank or giving a dose of drug to the patient will increase the rate of elimination. And increasing the size of the tank, increases the volume which decreases concentration and therefore decreases the rate of elimination. Let’s summarize what we’ve covered about the fish tank to see if this makes sense. First of all, volume is the size of the tank.
The net is the filter, in this case, the kidney that removes fish from the tank. The rate of elimination is the number of fish removed over time. Either a minute or an hour generally. The clearance is the volume of water that has fish removed from it over time. It has nothing to do with the number of fish that are contained in that volume.
It’s a very important point to remember: clearance is a factor of the volume that has drug cleared per time independent of the concentration of fish. K, the elimination rate constant is the fraction of the tanks volume that is cleared of fish over time. K changes proportionately when the clearance changes and K changes inversely when the volume changes. Remember that K can also be represented by the slope of the natural log of concentration versus time curve. So one last exercise, please pause the video and answer this question.
If K is 0.2 o to the minus 1 and after one dose the concentration at time zero is five milligrams per liter A tells us that the area under the curve is 25 milligram hours per liter that is true. Area under the curve is the concentration at time zero / K which is 5 divided by 0.2 which is 25 milligram hours per liter B is also true. If the volume is 50 liters the dose must have been 250 milligrams. In order to give us a concentration of 5 milligrams per liter. If we have 50 liters and we’re going to have 5 milligrams in each of those liters we must have given the patient 250 milligrams.
and C, 6 hours after the concentration at time 0 concentration would be 1 point 5 milligrams per liter that’s also true. C2 equals C1 times E to the minus KT. In this case e to the minus KT is 0.30. What this tells us is that after 6 hours no matter what the serum concentration was to begin with if we multiply it by 0.30 we’ll get the answer as to what the concentration would be at 6 hours. It will always be 30% of what it was 6 hours ago. So the answer is 1 point 5 milligrams per liter. So the answer of this question is E. A, B and C are all correct.
So to summarize then the key to solving the puzzle of pharmacokinetic dosing and monitoring is to remember the fish tank remember the relationships that define that first order elimination the significance of the net and how the net relates to whether the fish is bound or unbound protected by protein or not protected by protein and the fact that the net it relates to the clearance of water that the net pulls through and that the concentration of fish based on that volume that’s cleared is going to directly impact the rate of elimination of fish from the tank.
If you think of a human being as a tank filled with nothing but blood, the fish tank model gives us an exact indication of what takes place in terms of serum concentrations over time Remember our frame of reference, in this clinical pharmacokinetics course is serum or plasma. So I hope you’ll continue on with this online course, then continue with the second video which is going to zero in on drug dosing and how we apply these principles that have been covered in this first video to determining the best dose for a given patient.