How do clearance and volume impact the serum concentration?

Now let’s consider what happens when the clearance doubles to ten liters per hour which means that the elimination rate constant will also double from point one to point two hours to the minus one. In this situation you can see in the red curve, because the clearance doubled the rate the slope of the elimination line is much steeper it falls much more rapidly. So that the Cmin drops and when we give a dose then when the Cmin is lower the Cmax is going to be lower. So in this situation we’re still giving 500 milligrams q12 in both circumstances. But the clearance is increased from five to ten and the K is increased from point one to point two.

Volume is still 50, the concentration at time zero is still ten because we have not changed the dose or the value. So let’s see what happens. The Cmax is going to decrease. Again because of the increased clearance Cmin will be lower than it would otherwise have been and therefore C max will be lower. C min as we said decreases so this is again from 4.3 to 1 just as the Cmax decreased from 14 excuse me from 4.3 to 1. The Cmax decreased from 14.3 to 11. Cmax minus Cmin does not change under these circumstances. Again the only two factors that determine Cmax minus Cmin for the dose and the volume, neither of those was changed.

We’re only talking about clearance and elimination rate constant changing in this example. Average steady state concentration would drop in half from 8.3 to about 4.2. This is because dose over tau divided by clearance is the C average steady state. We did not change the dose. We did not change the dosing interval. But the clearance doubled and since it’s in the denominator that will cause the C average steady state to drop in half. And lastly the area under the curve, that will up in half as well. Area under the curve is dose over clearance. And again we double the clearance therefore area under the curve will drop from one hundred milligram hours per liter to 50 milligram hours per liter.

Now let’s try an exercise. If the dosing regimen is 100 milligrams q6 hours and the clearance drops from 5 liters per hour to 2.5 liters per hour which dosing regimen would keep Cmax and Cmin from changing? Give that some thought. The answer to this exercise it’s very simple. The answer is B, one hundred milligrams to 12 hours. The change that took place was a decrease in the clearance. If we’re going to compensate for a decrease in clearance, it means the drug is going to be eliminated less rapidly. It’s going to take a longer dosing interval for the serum concentration to drop from the original, from the Cmax down to the C min without changing.

The dose and volume don’t, the does not need to be changed because the volume did not change. So the take-home points on this exercise are as follows. When the clearance changes k is going to change proportionately. So if K drops in half, the dosing interval needs to be lengthened in this case double. Secondly, because the volume did not change, the dose must not be changed, in order to keep the difference between Cmax and minus Cmin the same. So the 100 milligram dose has to remain the same, even though the dosing interval has to be increased from 6 hours to 12 hours. The illustration of this example is shown on the slide. Clearance drops in half.

So in response to the clearance dropping in half, we double the dosing interval. You can see in the the red curve the increased dosing regimen from 100 milligrams q 6 hours to 100 milligrams q12 hours. The Clearance dropped from 5 to 2.5, k dropped from 0.2 per hour to 0.1 per hour. Volume and distribution had not change the concentration at time 0 would not change because that depends on dose and volume. And what we see here is that the Cmax would hold steady at 5.7 the Cmin would hold steady at 1.7 and the C average steady state would hold steady at 3.3.

So what we did was essentially undo the change that took place, because the clearance dropped in half and the drug was eliminated much more slowly as shown in the red curve by allowing extra time for the serum concentration to fall to the original Cmin and then giving the dose, the same does. We essentially undid the change in clearance by changing the dosing interval. And the area under the curve would change because the clearance changed and the dose did not change. Now there’s a very unique impact of volume Cmax and Cmin. And this is something that we need to look at more closely. And the reason for this is that when the volume increases, K decreases.

Remember the relationship between volume, elimination rate constant and clearance. If K is equal to the clearance over the volume, and if clearance doesn’t change in the V increases, K must decrease. What we observe then if the volume increases and what you can see here, in the blue curve when the volume increases the same dose is going to give a smaller concentration at time 0 as illustrated by this blue curve. Now what happens because the volume has increased, we’re putting the same dose into a larger volume. And so this the value of Cmax minus Cmin is going to drop. We can see the lower Cmax on the blue curve, and we can see the Cmin however increasing on the blue curve.

Now this seems like a paradox. If Cmin decreases, why would Cmin increase? The reason for this is the fact that as volume increases the K decreases. You can see in the blue curve the fact that the elimination rate is so much less than in the red curve. Therefore because the some concentration is not falling as rapidly, even though the Cmax is lower, the Cmin rises due to the decrease in K. We can think of this as being analogous to vertical freight elevator doors. Essentially if we have Cmax and Cmin represented by my two hands here. Okay. with a freight elevator door when you close the door the two doors come together and they meet in the middle.

When you open freight elevator doors, they move apart. And if our upper door is Cmax, in the lower door is Cmin. If you think about what impact the volume is going to have on the Cmax, think about whether Cmax is going to go up or down and Cmin is going to behave in the opposite direction. So in this example, we increase the volume, when you increase the volume the serum concentration is going to fall. So by increasing the volume, Cmax is going to decrease. When Cmax decreases, Cmin is going to increase as they come together. Now by the same token if we decrease volume Cmax will increase. When Cmax increases Cmin decreases.

So if we decrease volume which would cause Cmax to increase by decreasing the volume we are now increasing K. And if we increase K, Cmin is going to drop further. So you have one of two situations either Cmax is increasing in Cmin is decreasing or Cmax is decreasing in Cmin is increasing. Simply because w hen V changes, the K changes inversely. Here’s an illustration of that if V doubles to 100 liters from 50 liters, K is also going to drop in half. So if we keep the dosing regimen the same 500 milligrams q12, clearance is the same 5 liters per hour. K, however has dropped from 0.1 to 0.05 and the volume is increased from 50 to 100.

You can see in the red curve where the volume has changed. The volume has increased, meaning the serum concentration at time 0 is much less. But you can see the decrease in k as well. So the result is that our Cmax decreases from 14.3 to 11.1, our Cmin increases from 4.3 to 6.1. Our Cmax minus Cmin drops in half from 10 to 5, because of the the doubling of the volume. The C average steady state does not change. C average steady state depends on the dose the dosing interval, and the clearance and not of those changed only the volume and K changed. The area under the curve there would also be no change because dose and clearance did not change.

So pay attention to how K changes when the volume changes and that explains the inverse relationship between how Cmax changes and Cmin changes do a change in volume. That seems confusing, you might need to go back and review these last couple of slides, make sure you understand the dynamics that take place. When volume changes, if clearance does not change, change in volume will cause a corresponding in verse change in the elimination rate constant. I’ll try another exercise. If the dosing regimen is 100 milligrams every 6 hours and the volume increases from 25 liters to 50 liters which dosing regimen would keep Cmax and Cmin from changing.