## 02.06 Complex Calculations (dosage calculations/med math)

### Overview

- Multi-step, multi-variable
- Weight-based
- Key Points
- Know what you’re looking for
- Careful

- Highly recommend using dimensional analysis
- Prevents skipping steps or missing conversions

- Multiple parts?
- Plan ahead – may require multiple steps

- Take your time
- SAFETY!

- Triple Check
- Plug your answer back in
- Does it make sense?
- Is it appropriate?

- Know what you’re looking for

### Nursing Points

#### Examples

- Order: Dopamine 7.5 mcg/kg/min IV infusion. Available: Dopamine 800 mg in 250 mL D5W. Patient weighs 207 lbs. How should you set the IV pump?
- Order: Heparin 12 units/kg/hr IV infusion. Available: 20,000 units Heparin in 500 mL NS. Patient weighs 184 lbs. How should you set the IV pump?
- A patient has Heparin infusing at 22.1 mL/hr. The bag contains 20,000 units Heparin in 500 mL NS. The patient weighs 162 lbs. The patient’s PTT returned at 42 seconds. Based on the orders below, what should the NEW IV pump rate be?
- Less than 30 seconds: increase rate by 2 unit/kg/hr
- 31-54 seconds: increase rate by 1 unit/kg/hr
- 55-75 seconds: leave rate the same
- 76 – 90 seconds: decrease rate by 2 unit/kg/hr
- Greater than 90 seconds: pause infusion for 1 hour, restart at half previous rate.

##### Study Tools

#### Video Transcript

### Video Transcript

Hi guys. We’re going to look at some more complex calculations to kind of work through a few of these together.

So as with every calculation, you always want to make sure that you know what we’re looking for. Focus in on what the question is actually asking. There’s going to be a lot of information, and you kind of need to narrow it down. For problems like this, the really complex ones, I highly recommend dimensional analysis, it keeps everything in one place, it prevents you from missing steps. Now some of these problems may have multiple parts so plan ahead, think about what different steps do I need to take. And we’re going to look at an example of that. Whatever it is, take your time. Don’t rush, make sure that you’re being safe in this calculation and getting the right answer at the end of it. Always triple check. Plug your answer back in, does it make sense? All right? Let’s work through a couple of these together.

So example number one. The order is for Dopamine 7.5 mcg per kg per minute IV infusion. What we have available is Dopamine 800 mg in 250 mL of D5W. The patient weighs 207 pounds. How should you set the IV pump?

Well, IV pump is always what? mL per hour. So dimensional analysis, start with what you are looking for, mL per hour. Transfer your units over, mL. What do we know, what are we given about mL? Right here, we know that for every 250 mL, there are 800 mg of Dopamine. Okay? Transfer our units up. What do we know about mg? Well, we don’t have anything else do we? We’ve already used this one so we’re going to have to do a conversion.

One mg is 1,000 mcg. Okay, transfer your units up. Remember, these can cancel. Now, what do we know about mcg? Well, we know that we have 7.5 mcg per kg per minute. Anytime you have a double ‘per’, put them both on the bottom. All right, cancel mcg. Do we have what we need yet? Well, we’ve got mL because we started there. We need to get to hours. Well, we’ve got minutes so let’s do that conversion, 60 minutes in one hour. So we can cancel minutes, we have hours. We have mL per hour but we still have this kg just hanging out on the bottom.

Remember, your goal with dimensional analysis is to cancel everything until you’re left with only what you need. So we’ve got to get rid of those kg. Let’s transfer those units to the top and let’s do a conversion. One kg, 2.2 pounds, cancel kg. What do we know about pounds? We know the patient weighs 207 pounds. Cancel, cancel. Now we’ve canceled everything, we’re left with just mL per hour. We know we can move forward.

You’re going to multiply across the top, divide across the bottom. 250 times 1 times 7.5 times 60 times 1 times 207. Divided by 800, divided by 1,000, divided by 1 – these are your hypothetical ones – divided by 1, divided by 2.2. The number that you end up with in your calculator should be 13.231 et cetera. Round to the nearest 10ths because this is mL per hour. You’re going to end up with 13.2 mL per hour. Do your final verify, does it make sense? You can always plug it back in but 13.2 seems like a reasonable number so we know this is correct.

All right, let’s look at another one. Heparin, 12 units per kilo per hour IV infusion. What we have available, 20,000 units of Heparin in 500 mL of normal saline. The patient weighs 184 pounds. How should you set the IV pump?

Again, mL per hour, always know what you’re looking for. So with dimensional analysis, we start with what we’re looking for, mL per hour. We transfer our units over. Insert what we know, convert if we don’t. What do we know about mL? For every 500 mL, there’s 20,000 units. 500, 20,000 units of Heparin. All right, transfer your units up. What else do we know about units? Well, right here we know that we want 12 units per kilo per hour. Again, if you have two ‘pers’, put them both on the bottom. Kilo per hour.

All right, so we cancel units. We’ve got our mL, we’ve got our hours. But again, we’ve got this random kilos just hanging out down here that we’ve got to get rid of. So do we know anything about kilos? Nope, but we can convert. One kg is 2.2 pounds. Cancel kilos, bring the pounds up. What do we know? Patient’s 184 pounds, cancel, cancel. So again, with dimensional analysis the goal here is to cancel everything until we end up with only what we want. We’ve canceled everything except mL per hour. So we know we’re good to solve.

You’re going to enter this into your calculator, multiplying across the top, dividing across the bottom. 500 times 12 times 1 times 184. Divided by 20,000, divided by 1, divided by 2.2. What you’re going to end up with is 25.0909 mL per hour. Round to the nearest 10ths place and you’re answer is 25.1 mL per hour. You’ve rounded, you’ve got the right units. Does it makes sense? Does it seem appropriate? Yes it does.

All right, let’s do one more. Now, this is a problem that we find in nursing school that honestly are some of the hardest ones in my opinion. This is going to require multiple parts because not only do you have to figure out what’s currently going on, but you have to interpret an order, implement it, and then find the new rate.

So our first … Or let me read you the question. A patient has Heparin infusing at 22.1 mL per hour. The bag contains 20,000 units of Heparin in 500 mL of normal saline. The patient weighs 162 pounds. The patient’s PTT returned at 42 seconds when we tested it. Based on the orders below, what should the new IV pump rate be?

So what we’re having to do is determine where we’re at, determine where we need to go based on the order and this lab result. And then determine the new rate. So there’s actually going to be three steps. One is, what is it currently running at? What is the current dose? Now the reason we need the current dose is because this order is based on units per kilo per hour, not based on mL per hour. So again, this is where you have to take your time, look closely. What does it give you? What do you need? What units are you working with?

So the first thing we need to do is determine the current dose in units per kilo per hour. Second thing is, we’re going to use our orders to determine what the new dose needs to be. Where are we going with it? You can see if it’s less than 30 seconds, we’re going to increase by two units per kilo per hour. If it was between these, we were going to decrease by two units per kilo hour. So the order tells you what you need to do. And the third step is then going to be, now that we know the new dose, find out the new rate. So we’ve planned ahead. We know what our three little steps are. So let’s go ahead and do them.

So part one is what is the current dose. So patient has Heparin infusing at 22.1 mL per hour. The bag contains 20,000 units of Heparin in 500 mL of NS. The patient weighs 162 pounds. The information about the PTT and the new dose, you don’t need that yet. We’re starting with part one. What is the current dose in units per kilo per hour. So start with what you’re looking for. Units per, double ‘per’, kilo per hour. Transfer your top units across. What do we know about units? 20,000. So 20,000 units is in 500 mL. Transfer your units across. What do we know about mL? 22.1 mL in 1 hour.

Cancel mL. We’ve got units, we’ve got hours, we’re missing kg. So let’s say one kg down here because that’s where we need it, right? And then we’re going to do a conversion because we don’t know anything about kg. So 1 kg is 2.2 pounds and the patient weighs 162 pounds. Cancel pounds, now we’ve got what we need. Units per kg per hour. When you do this math, you are going to end up with 12.00493 units per kilo per hour.

Now I happen to know from doing the math that if you were to round this to 12, you’d get the same final answer. But for the sake of safety, we’re actually going to use this number as we move forward and we’ll kind of go from there.

So part two is now to determine what the new dose need to be. We’ve already determined that our current dose is 12.00493 units per kg per hour. So we know this information, now we know that the patients PTT returned at 42 seconds. Based on the orders below, what should the new dose be in units per kilo per hour?

So 42 seconds falls right in here between 31 and 54. So we need to increase the rate by one unit per kg per hour. So now the new dose, instead of 12.00493, is going to be 13.00493 units per kg per hour. That’s it, that’s your second step. This is where we’re headed. So let’s go to part three.

Let’s remember our new dose needs to be 13.00493 units per kg per hour. So same information. Based on the new dose you decided, what should the new IV pump rate be? IV pump rate is always mL per hour. So start with what you’re looking for, mL per hour. Transfer your units over, mL. What do we know? Well, you know a couple of things. Since we know we’re looking for a new rate, putting in the current rates not really going to help us is it? So let’s start over here. We know that 500 mL is 20,000 units. Okay? What else do we know about units? Well, didn’t we just figure out what new units we want? Yup. So 13.00493 units, double per, kg per hour. Cancel units. We have our mL. We have our ours. We have the kg hanging out.

So do we know anything about kg? Nope but we can convert. One kg, 2.2 pounds. Cancel your kg’s. Now we need to cancel our pounds. The patient weighs 162 pounds. All right, we’ve canceled kg’s. Canceled pounds, canceled units. We’re left with mL per hour. You put this directly into your calculator, multiply across the top, divide across the bottom. 500 times 13.00493 times 162. Divided by 20,000, divided by 1, divided by 2.2. The answer that you are going to get is 23.94089. Okay? Round to the nearest 10th. You’re going to get 23.9 mL per hour.

Now if you had rounded this and used just 13 as opposed to 13.00493, you would’ve ended up with 23.9318. Again, rounding to the nearest 10ths, you still would’ve ended up with 23.9. However, you can see how those simple things, if this had ended up 95 something, something and this ended up 94, this one would’ve rounded up and this one would’ve rounded down. So that is why we always say to round at the end if at all possible. Okay? So there’s your answer, 23.9 mL per hour.

So part of the issue with this type of problem, let’s go back to the whole one. With these multiple parts is there’s a lot of information here, right? And so by planning ahead, by determining what information you need at each step, you can kind of start to pick and choose which information’s the most important. Keep yourself from being distracted by things that aren’t important yet.

So I hope that made sense to you. I know that it’s a complex problem. Please feel free to repeat this video again. Watch this multiple times. Use some of the example problems that we’ve given you and try your luck. Practice, practice, practice. The more you do these, the more sense they’re going to make to you. I hope that was helpful guys. We love you, we just want to see you be successful. Now go out and be your best selves today guys. And as always, happy nursing.