Intermittent infusion dosing & AMG serum level analysis

Intermittent infusion dosing, we can morph two dosing equations that you should already be familiar with to determine that the calculations that should be used in minimum glycoside dosing. The infusion calculation that you are familiar with the rate of infusion times 1 minus e to the minus KT where T is the time of infusion divided by the clearance that determines the concentration that exists at any point in time T prior to steady state. When we administer vancomycin and aminoglycosides considering aminoglycosides in this case the drug is administered by infusion. So this part of the equation will tell us the concentration that will will exist after the infusion is complete.

However that infusion is given as a multiple dosing intermittent regimen and the Cmax for an intermittent regimen is dose over volume times 1 minus e to the minus K tau or T is now the dosing interval. So if we morph these two equations together for multiple dosing of aminoglycosides when the drug is going to be administered by infusion, what we see is that the C peak at steady state would be equal to the rate of infusion times 1 minus e to the minus K T where T is the time of infusion over the volume of distribution times the elimination rate constant times 1 minus e to the minus K tau.

What we see is that V times K essentially replaces the clearance, that’s in the continuous infusion equation. And if we multiply that portion of the morphed equation by e to the minus K T Prime that provides for the percent of drug that’s remaining after that time interval from the end of the infusion to the measurement of the peak level. So what you see is is a very complicated appearing equation. That’s really not very complicated when you stop and consider how it it really combines two equations that you’re already quite familiar with.

Step one, in analyzing Aminioglycoside serum levels is simply to take the measured serum concentrations to determine the patient’s elimination rate constant and volume based on the current dosing regimen. The elimination rate constant as we’ve already discussed in a previous lesson, you simply take the natural log of the measured peak over the measured trough and divide that by the time interval between those two to determine the elimination rate constant.

And volume is simply a rearrangement of the equations shown in the previous slide where volume is equal to the rate of infusion times 1 minus e to the minus KT where T is the time of infusion divided by the C peak times the elimination rate constant time it’s 1 minus e to the minus K tau or T is the dosing interval times e to the minus KT Prime. Keep in mind, when you’re calculating the volume of distribution of an aminoglycoside patient that it’s not the dose that’s in this equation. It’s the rate of infusion.

So if a patient is receiving 80 milligrams as a dose, that’s administered over 30 minutes or 0.5 hours the rate of infusion would actually be 160 milligrams per hour, not the 80 milligram dose that’s given. It’s important to keep track of what the three different time intervals represent in this equation.

Step two in the aminoglycosides serum level analysis process is to determine the new dosing regimen the rate of infusion and the tau the dosing interval based on the desired serum levels and the patient’s elimination rate constant and volume that were just determined. So to do this you would the Tau would be equal to the natural log of the desired peak over the desired trough divided by the patient’s elimination rate constant that was just determined. The rate of infusion would be equal to the C peak and again this is an algebraic rearrangement of the equation on the previous slide.

The C peak times the patient’s volume times the elimination rate constant times 1 minus e to the minus K tau or tau is the dosing interval divided by 1 minus e to the minus K T where T is the time of infusion. Generally either 0.5 hours that puts a 30-minute infusion or 1 it’s a 1 hour infusion, times e to the minus KT prime where T prime is the time interval from the end of the infusion to the measurement of the peak level.

Now oftentimes this is done automatically using a computer or an online program, but I think it’s important for pharmacists even if you’re using a program to crank these calculations, it’s important for pharmacists to understand the processes that are taking place as these equations are being calculated. Another important consideration is when to start the new dosing regimen? In other words, how long will it take for the peak level on the old dosing regimen the last peak that was measured to drop down to what the new trough level would be.

In order to do this, that this time to the next dose would be the natural log of the C peak that was measured on the old dosing regimen, divided by the C trough that were shooting for with the new regimen. And all of that divided by the patient’s elimination rate constant. Okay the first dose of the new regimen is due when the concentration drops to what the new trough is expected to be. I learned this the hard way when I was a resident.

I had a case in which I was paged in the middle of the night patient was receiving 80 milligrams every eight hours of an aminoglycoside and I calculated based on the patient’s serum concentrations that the dose needed to be changed to a hundred milligrams to twelve hours. Problem was when I relayed that information to the physician, I didn’t specify when the new dosing regimen should be started.

Physician wrote in order to discontinue the 80 milligrams every eight hours and start 100 milligrams every 12 hours didn’t specify a time and the pharmacists the process the order just put it into the computer as is and what ended up happening was the patient received an 80 milligram dose in just a couple hourse of late couple hours later received the first 100 milligram dose in the new regimen.

And I learned a very valuable lesson at that point it’s give some thought when you’re going to change a dosing regimen; give some thought to when the new dose should be given in relation to when the last former dose had been administered and make sure that’s clearly communicated to the prescribed what I should have said is discontinue the 80 milligrams every eight hours start 100 milligrams every 12 hours at nine o’clock this morning provided a specific time and in order to do that you have to calculate the optimal time to begin it’s using this equation shown on the slide.