Skip to 0 minutes and 15 secondsThe answer of this exercise there it is 200 milligrams every 12 hours. Now let's take a look at why that is. If V increases K will decrease and the dosing interval will have to be lengthened or increased proportionately. Okay~ Again the change in V causes an opposite change oran inverse change in K and then we have to respond by changing the dosing interval. in this case, if K decreases, we're going to lengthen the dosing interval proportionately. If V increases the dose is going to have to increase proportionately to keep Cmax and Cmin from changing. So we need to change both the dose and the towel to keep Cmax and Cmin from changing when V increases. Here's the illustration V doubles.

Skip to 1 minute and 10 secondsSo we double the towel and we double the dose. We go from 100 milligrams q6 every 6 hours to 200 milligrams every 12 hours. There it doesn't change but K did change because of the volume change. K goes from 0.2 to 0.1. Volume goes from 25 liters to 50 liters. So you can see in the red curve. The fact that we doubled the dose compensated for the fact that the volume doubled and the concentration at x 0 did not change. But the elimination rate constant is decreased and therefore the serum concentration falls less rapidly.

Skip to 2 minutes and 1 secondSo by doubling the dosing interval we enable the minimum the Cmin to remain at 1.7 and by doubling the dose to compensate for the the doubling of the volume we keep C max the same at 5.7. C average steady state would also stay the same at 3.3 and the area under the curve because we doubled the dose. And the clearance did not change the area under the curve will double.

Skip to 2 minutes and 34 secondsNow if we respond to a doubling of the volume by simply doubling the dose and this was what would seem intuitively obvious. If volume doubles then simply double the dose and that should compensate for it. But that ignores the fact that the elimination rate constant drops in half. So the red curve illustrates what would happen if we compensated for a doubling of the volume of distribution simply by doubling the dose. In this case we go from 500 milligrams q12 to 1,000 milligrams g12. In this case Cmax will increase we've increased the dose again but we have not increased the dosing interval.

Skip to 3 minutes and 20 secondsSo Cmax will increase, Cmin will increase because we've not allowed more time for the serum concentration to fall despite the decrease in the elimination rate constant. Our C max minus C men will not change because we compensated for the change in volume by doubling the dose so dose over volume would not change it's still going to be 10 milligrams per liter C average steady state would double C our steady state is dose divided by tau we double the dose without changing tau and there's no change in clearance C average steady state will double and the area under the curve would also double again we've doubled the dose we've not changed the clearance so you can see that the C max will increase due to the effect of volume change on K now let's consider what happens when the clearance and also K drop in half and so we double the top so now we go from 500 milligrams every 12 hours to 500 milligrams every 24 hours with the clearance that is dropping in half when we do that we can see that the lengthening of the dosing interval compensates for the decrease in clearance the red curve and sees the drug being eliminated much less rapidly and therefore the longer dosing interval allows enough time for the Sarah concentration to fall to the original cement so when we compare the results there's no change in the C max there's no change in the C min we didn't change dose over volume and we allowed extra time in the dosing interval to compensate for the decrease in K and in clearance C max minus C men would not change because dose and volume did not change C average steady state would not change because dose over tau did not change nor did the clearance change so what we have here is an area under the curve that would double from 100 to 200 so the change in tau essentially neutralizes the change in clearance and in K we haven't changed the dose so the the average steady state concentration would remain the same because we haven't changed the dose and the tau and the clearance would cancel each other out see if you can answer this question why does area under the curve not change when volume changes first of all let's consider a in comparison to the equations that we have we know that area under the curve is equal to the concentration at time zero divided by K and also dose divided by clearance but now we're introducing volume into this equation it's not specifically listed as such but we know that a change in volume causes a change in K and K is part of our area under the curve equation but that's not the whole story because area under the curve is not going to change when V changes we also know that a change in volume will cause a change in the concentration at time zero so essentially what we have is a change in volume causing a change in both parameters concentration at time zero and K and they essentially cancel each other out so you can't just look at one aspect of the impact of volume when you put the answer to a and B together it essentially identifies why there's no change in area under the curve when volume changes C is a false statement a change in V does not cause a change in clearance clearance is not dependent on volume of distribution so the answer is D both a and B explain why area under the curve does not change when volume changes

# What happens when volume increases?

Prof. Brown explains the situation for an increase in volume (V).

If volume (V) doubles, we should double dosing interval (tau) and the dose at the same time, or simply double the dose? Both conditions are discussed in this section.

Finally, we need to know the reason why AUC keeps the same even if volume (V) changes. You can try to write down the relationship between AUC and k to figure out the answer.

Feel free to share any question you may have.

##### Educator:

Prof. Daniel L. Brown