Hi, this is Cathy with Level Up RN. In this video, I'll be going over a variety of dosage calculation problems that involve weight-based IV infusions. I will be working through these problems on my whiteboard using three different methods including dimensional analysis, ratio and proportion, and the formula method. You can find all the information that I'll be covering in this video in our Level Up RN dosage calculation workbook. If you are in nursing school, then you know how important it is to master dosage calculations, and our workbook will help you do just that. For more information about our workbook, you can click here. But in a nutshell, our workbook contains all different types of dosage calculation problems that you are likely to encounter in nursing school. And we demonstrate how to solve each problem using multiple methods so you can pick the way that makes the most sense to you.
In this first problem, we have an order for ganciclovir 5 milligrams per kilogram IV infusion to be given over 1 hour every 12 hours for seven days, and our patient weighs 154 pounds. What we have available to us is ganciclovir 10 milligrams per ml concentration. And we need to round all our answers to the nearest whole number. And we have three different questions we need to answer. The first question is, how many milligrams should the patient receive per dose? Okay. So per dose, they should be getting 5 milligrams per kilogram. So we know we're going to first have to convert our patient's weight from pounds to kilograms. So if we take their weight in pounds and divide by 2.2-- again, the conversion factor here that's important to know is 1 kilogram equals 2.2 pounds. If we multiply this out, we end up with 70 kilograms, so that's the patient's weight. So then we can take the ordered dose, which is 5 milligrams per kilogram, and then multiply that by the patient's weight in kilograms. And that will give us the milligrams that the patient should get per dose, so that is 350 milligrams. So that is the answer to part A.
Part B asks us, what is the IV pump rate in milliliters per hour? So we can solve part B using dimensional analysis, ratio and proportion, or the formula method. So I'm going to first solve part B using dimensional analysis. So like we figured out in part A, we need to give 350 milligrams with each dose, and we need to give it over one hour per the order. So we know we want to give 350 milligrams per hour, but we want to know the pump rate in milliliters per hour. So I can take this and multiply it by our available concentration. And I'm going to make sure I put my milliliters on top and my milligrams on bottom such that my milligrams will cross off, and I'll be left with milliliters per hour. So if we do this multiplication, we end up with 35 milliliters per hour. Okay. We can solve part B with ratio and proportion as well. So let me erase my work here so I have a little more room. All right.
So we're still on Part B, and now we're going to solve this with ratio and proportion. So again, we know from part A when we solved that that the patient should get 350 milligrams over an hour. But we need to find out how many milliliters will it take to give this 350 milligrams, so we're going to set up our ratios. On one side of the equation, we're going to put our known ratio, which is our drug concentration, which is 10 mgs in 1 ml. And then on the other side of the equation, we're going to put our dose that we figured out in part A, and we're going to put an X for the mls, because that's what we're trying to figure out. So if we do our cross multiplication here, we have 10X equals 1 times 350. X equals 350 divided by 10, that equals 35 milliliters. And again, since we need to give this over an hour, the rate would be 35 milliliters per hour. And that's how we would solve part B with ratio and proportion.
We can also solve that part with the formula method. So the formula method is desired over half times a vehicle. And again, we know we need to give 350 milligrams over an hour, but we need to know how many milliliters it will take to give that 350 milligrams. So our desired is 350 milligrams, and what we have is 10 milligrams in 1 ml of solution. That's our vehicle. So if we multiply this out, again, we end up with 35 milliliters. And since we need to give this over an hour, this becomes 35 milliliters per hour. And that's how we would solve part B with the formula method. And then finally, we have Part C. Part C is asking us, how many milligrams is the patient receiving per day? Well, per the order, they are getting this medication every 12 hours, which is twice a day. And each time they get it, they're getting 350 milligrams. So for part C, if we take the amount per dose and multiply it times two because they're getting it twice a day, they're going to be getting - I'm sorry - 700 milligrams per day. So that is the answer to part C.
Let's work through our next weight-based dose calculation problem. In this problem, we have an order for dopamine 3 micrograms per kilogram per minute IV infusion. Our patient weighs 118 pounds. Dopamine 400 milligrams in 250 mls of D5W is available. We should round all our answers to the nearest whole number. And we're being asked two questions. With A, how many micrograms per minute should the patient receive? So our ordered rate is 3 micrograms per kilogram per minute. So 3 micrograms per kilogram per minute. And if we multiply times the patient's weight in kilograms, then we'll be able to figure out the micrograms per minute. However, we have the patient's weight in pounds, so we're going to need to multiply times a conversion factor. So one kilogram equals 2.2 pounds, and then we can multiply times the patient's weight. So I just set this up with dimensional analysis. You could easily do it in two steps, like figure out the patient's weight in kilograms and then multiply it times this ordered rate. But like this, I can say, "Okay. My kilograms cross off here and my pounds cross off here, and I'm left with micrograms per minute," which is what I'm looking for. So that ends up being 161 micrograms per minute. And this is rounded because we were instructed to round our answers to the nearest whole number, so that is a rounded number. So that is part A. So this is A.
Part B asks us, what is the IV pump rate in milliliters per hour? So I'll take down my rate here in micrograms per minute, and I need to get that to milliliters per hour. So first thing I know I need to do is change these minutes to hours. So 60 minutes equals one hour. My minutes cross off, and I have micrograms per hour. Now I need to get to milliliters per hour. So my drug concentration is 400 milligrams in 250 mls, so. And right now, I have micrograms, so I know I'm going to need to convert to milligrams. So 1 milligram equals 1,000 micrograms. So I'm going to cross that off. Now I have milligrams per hour, and I can get to milliliters per hour by multiplying times the available concentration, so that is 250 mls and 400 milligrams. And I purposely put my milliliters on top where I need it and my milligrams on bottom so that these milligrams will cross off. And if I multiply this whole thing out, I will end up with milliliters per hour, which is what's being asked. So if you multiply this out, we end up with 6 milliliters per hour. And that, again, is rounded to the nearest whole number, which is what we were instructed to do.
All right. I'm going to work through the steps on how to solve part B of the problem using ratio and proportion, which is going to take a lot more steps. This is definitely the most efficient way to do it. So if you're comfortable with dimensional analysis, you probably don't want to mess with the way I'm about to show now. But if you're into ratio and proportion or formula method, I'm going to show you how to do those methods next. So if we're doing ratio and proportion, we want to give 161 micrograms per minute, and we need to figure out how many milliliters per hour that is. The first thing we need to do is take this 161 micrograms and change it to milligrams. And the reason I'm doing that is I need to find out how many milliliters we have for 0.161 milligrams by comparing it to our known ratio. So I can do that now. So we have 400 milligrams in 250 ml. That's our known ratio. And we want to find out for 160 milligrams how many milliliters is that. So I would do my cross multiplication here, and then I would solve for X. X ends up being 0.1 milliliters, and that is rounded. So then I know I need 0.1 milliliters given per minute. So 0.1 milliliters per minute. But I need to know how much milliliters per hour I should set the pump at. So I need to multiply this times 60 minutes, which is an hour. And then I get 0.6 milliliters per hour.
So we end up with the same answer as we did here with dimensional analysis. But we had to do this conversion, then set up our ratio, and then multiply times 60 minutes, so it definitely took three different steps. For the formula method, I also need to do this conversion just like I did here. Then instead of the ratio, I can set up my formula, which is desired over half times vehicle. So I desire 0.161 milligrams. What I have is 400 milligrams, and my vehicle is 250 mls. And if I multiply this out, again, I end up with 0.1 mls. And then again, 0.1 mls per minute, I need to get to milliliters per hour, so I need to multiply times 60. So I'd end up with 0.6 milliliters per hour.
All right. Let's work through our last weight-based dosage calculation problem. This one's a little trickier. So not all nursing programs are going to throw stuff like this at you, but I want to make sure you're prepared in case yours does. So with this problem, we have a 60 kilogram patient who has dopamine with a concentration of 400 milligrams in 250 mls running at 25 milliliters per hour. How many micrograms per kilogram per minute is the patient receiving? Round your answer to the nearest whole number. So this has us kind of working backwards from the last example problem. So the last one, we were given the micrograms per kilogram per minute, and we need to calculate the IV rate, but here, we kind of have to work backwards. So we can solve this problem with dimensional analysis or ratio in proportion. So let's do it with dimensional analysis first. That's definitely the most efficient way to do it.
So if we take our current rate, which is 25 milliliters per hour, we can multiply by a number of conversion factors to get us to micrograms per minute. And then we can divide by the patient's weight in kilograms to get micrograms per kilogram per minute. So right now, we have 25 milliliters per hour. I know I need to get to minutes, so I'll go ahead and multiply times this conversion factor. One hour equals 60 minutes, and now I have milliliters per minute. Now I can multiply times the available concentration, so that's 400 milligrams in 250 ml. And now my mls cross off, and I'm left with milligrams per minute, but I need micrograms. So I'm going to, once again, multiply by another conversion factor, have my milligrams cross off. Now I have micrograms per minute. So if I multiply this out, I end up with 667 micrograms per minute, but I need micrograms per kilogram per minute. So if I divide by my patient's weight, 60 kilograms, I end up with 11 micrograms per kilogram per minute, and that is rounded per our instructions here. So that is the rate of the medication administration that's been being given to our patient, 11 micrograms per kilogram per minute.
Now I'm going to work through this same problem with ratio and proportion. Definitely more steps. So if this way makes sense to you, I would stick with that personally. It's a little more straightforward. But for those of you who like ratio and proportion, the first thing we need to figure out is how many milligrams are in 25 ml. Patients getting 25 milliliters per hour of the dopamine. So let's figure out how many milligrams are in that 25 ml. So if we set up our ratio, we have 400 milligrams in 250 ml, and we want to find out how many milligrams are in 25 ml. And so we cross multiply 250X. So cross-multiply here, cross multiply there, equals 400 times 25. And then if we solve for X, we end up with 40 milligrams. Okay? So we know we need to give 40 milligrams over an hour, but we really need micrograms over minutes. So we're just going to convert these units. So 40 milligrams equals 40,000 micrograms, and one hour equals 60 minutes. And if you do this math, we're going to end up with 667 micrograms per minute, just like we got up here. And again, if we divide that by the patient's weight, 60 kilograms, we get 11 micrograms per kilogram per minute. So you can see this took several more steps. We had to figure out the number of milligrams in 25 milliliters, and we had to do this conversion. Few more steps. But that is how you would solve the same problem with ratio and proportion.
