How to change dose or dosing interval in response to a change in volume, clearance , or k ?

Let’s consider the answer to this question. when measuring a drug serum concentration. A is false. Stating it will be higher than it should be if absorption is not complete. If absorption is not complete it means not all of the drug has gotten into the blood yet. So therefore it’s going to be lower if then it would be if absorption is not complete. B is a true statement. When measuring a drug serum concentration it will be higher than it should be if distribution is not complete.

If distribution is not complete, it means not all of the drug that is eventually going to distribute out of the blood has left the blood yet, so the serum concentration will be higher than it would otherwise B. And C is false. when measuring a drug serum concentration it will be higher than it should be if the patient is not yet it’s steady-state. That’s a false statement. But I should clarify, the answer to C is false based on the assumption that we started from a point a serum concentration of zero, and we began a dosing regimen or continuous infusion.

However if we had a certain situation that was higher than the steady-state concentration will eventually be and the patient was not yet at steady state. Under those specific circumstances, the serum level would be higher than it would be because the patient is not yet at steady state. But for most practical purposes if we are not yet at steady state the serum concentration will be lower than we it would eventually be at steady-state. So the answer is a B. Let’s consider a change in dose or tau in response to a change in volume or clearance. You see there are four variables here. Only two of the variables are under our control.

So generally when pharmacists are involved in adjusting dosing regimens what we’re trying to do is compensate for changes that have taken place in the volume of distribution of a drug or the clearance of a drug and we do that by changing either the dose or the dosing interval or both. In the case of a change in the patient’s volume of distribution we would correct that by changing the dose. The dose must change proportionately to a change in volume. If the volume increases, we have to increase the dose in order to keep the patient’s serum concentrations from changing. Likewise, if the clearance changes, it will be necessary to change the dosing interval but this would be an inverse change.

If the clearance increases, we would need to decrease the dosing interval to compensate for the increase in clearance or the increase in K. Likewise if the clearance decreases we would need to increase the dosing interval. It’s based on the relationship e to the minus K tau. We want to see to it in order to keep the Cmax and Cmin the same we need to see to it that the product of k times tau does not change. So if one increases the other would have to decrease and vice versa. So when we respond to a change in clearance or k we do so by changing the dosing interval.

So V and K or V and clearance will change based on patient parameters what’s going on between the patient and the drug and the pharmacist can respond by changing the dose or the dosing interval. Now I’m going to go through a series of examples to illustrate how changes in the volume of distribution or the clearance or K will affect serum levels and then how we can compensate for those changes by changing the dose or the tau. Our baseline example is a patient that’s receiving 500 milligrams every 12 hours. This patient has a clearance of 5 liters per hour, a K of 0.1 per hour and a volume of distribution of 50 liters.

So we can see that under these circumstances with a dose of 500 milligrams and a volume of 50 liters, The concentration at time 0 would be 10 milligramss per liter with a dose of 500 and a clearance of 5 liters per hour the area under the curve being dosed over clearance will be 100 milligram hours per liter. The Cmax will be 14.3, Cmin would be 4.3 and the C average at steady state would be 8.3. Now we can represent again the C at time 0 the concentration at time 0 is equal to dose over volume which is also equal to Cmax minus Cmin.

So we can see that the C at time 0 is 10 and the difference between 14.3 and 4.3 is also 10. This relationship is always holding true. We also know that area under the curve is equal to both the concentration at time zero divided by K and also dose over clearance. And that the concentration the average concentration at steady state is equal to dose over tau the dosing rate divided by the clearance. So in this case, the dosing rate of 500 milligrams every 12 hours is equal to 41 point 7 milligrams per hour divided by the clearance of 5 liters per hour gives us an average steady-state concentration of 8.3.

One thing I’d like to point out here when we’re talking about Cmax and Cmin and C average at steady state the arithmetic average of the Cmax and Cmin is not the average steady state concentration 14.3 and 4.3 and up to 18.6. The average of the two of them is 9.3 not 8.3. The average steady state concentration is based on the type of serum levels that actually yield a straight line which is the natural log of concentration. So if you convert the 14.3 the 4.3 and the 8.3 to natural logs what you find is that if you average the Cmax and Cmin natural log values 2.7 and 1.5.

They sum of those two is four point two which gives you an average of two point one. So only when we’re dealing with natural logs can we say that the arithmetic mean of the max and the min is the C average steady state concentration. Now let’s take a look at what happens when we double the dose from 500 milligrams q12 to a thousand milligrams q12. Everything else holds steady states. The clearance doesn’t change; the K doesn’t change; the volume doesn’t change. Because we’ve doubled the dose, we can see that the concentration at time 0 has doubled. Let’s take a look at what else happens here.

You can see in the red curve with a higher dose yielding the higher concentration at time 0. The Cmax is going to double because we’ve doubled the dose If Cmax is directly related to dose over volume the Cmin will also double. Because again we’re relating the dose over volume. The C average, excuse me, the Cmax- Cmin doubles from 10 to 20 because that is directly related to dose over volume. The C average steady state, because Cmax and Cmin both double, the C average steady state would also double and the area under the curve would double. So when the only thing we changes the dose, essentially everything will change proportionately to our change in dose.

It’s very straightforward and that should make sense because we’re giving twice as much drug with every administration of drug Now let’s take a look at doubling the dosing interval from 500 milligrams q12 to 500 milligrams every 24 hours. Again the clearance, K and volume all stay the same. You can see in the red curve allowing twice as long for the serum concentration to fall. So the Cmin drops down to a much lower level and the Cmax will also be much lower. But the Cmax - Cmin will have to take a look to see what happens with that. In this situation Cmax steady-state decreases because the Cmin lowered based on the longer dosing interval.

So every time we gave a dose, the serum concentration was lowered to begin with prior to the dose the C min fell from 4.3 to 1.0. Again note that the difference between Cmax - Cmin does not change. 14.3 - 4.3 is 10 and 11-1 is still 10. The Cmax - Cmin relates to the dose over volume which did not change. The only thing we changed was the dosing interval. The C average steady state is now going to drop in half. Because C average steady state is determined by the dose over tau. The dosing rate divided by clearance and since we doubled the dosing interval, we cut the dosing rate in milligrams per hour in half.

And the area under the curve will not change, dose over clearance will not change because we’ve changed the dosing interval. Now let’s take a look at doubling the dose and doubling the dosing interval. So we’re going from 500 milligrams q12 hours to 1000 milligrams every 24 hours. In this case, you can see in the red curve. We have a much higher concentration at time zero, but again we’re waiting twice as long for the drug to be eliminated before we give another dose 24 hours instead of 12 hours. In this case Cmax increases from 14.3 to 22 because we’ve doubled the dose. Cmin however decreases.

We’ve doubled the dose but we’ve also doubled these the dosing interval giving much more time for the serum concentration to fall. Cmax - Cmin will double from 10 to 20 because we’ve doubled the dose we haven’t changed the volume at all. And the C average steady-state is going to stay the same. See every steady state is dose over tau divided by clearance. If we double both the dose and the dosing interval we have not changed the dosing rate in milligrams per hour. Area under the curve will double because we’ve increased the dose and the clearance has not changed.