There are, as is often noted, more than one technique for doing med-math problems. If the one you are using works for you, then don't read any further. If, however, med-math is still a bit of a struggle, consider using the technique preferred by chemists, physicists, and engineers for decades called, somewhat intimidatingly, "dimensional analysis" hereafter referred to as "DA."

##### Advantages include:

• One technique, not several

• Works with all problems

• No formulas to know, look up, or apply

• Problems are not solved piecemeal, but in one step

• You get to the right answer quicker—less error prone

• All calculations done at one time; no rounding errors

• You focus only on units of measure, not numbers, so math phobics can rejoice

• Stepwise approach makes solving almost all problems a virtual no-brainer

To illustrate I'll do the sample problems we were given using DA. I'll do the first one the long way, with explanations, then the rest as I would normally set them up.

Example 1:

*The patient weighs 73 kg. The MD orders dopamine at 3 mcg/kg/min. The dopamine is mixed as 400 mg in 250 mL of solution. What is the infusion rate in mL/hr?*

First you focus on what units of measure you want in the answer. In this problem we are kindly given "mL/hr." We are also given that there are 400 mg dopamine in 250 mL (or 400 mg/250 mL), but also that in 250 mL there are 400 mg dopamine (or 250 mL/ 400 mg). It is important to realize that factors can be turned over or inverted as needed.

The other important bit to realize in order to do DA is that 3 mcg/kg/min can also be written as 3 mcg/(kg x min). This may seem a little weird, but if asked to divide 1/4 by 2 you have 1/4/2. But dividing is the same as inverting and multiplying, so inverting 2 to get 1/2 and multiplying you have 1/4 x 1/2, or 1/(4 x 2), or 1/8. Another example is acceleration, which is measured in ft/sec/sec. This can be written as ft/(sec x sec) or, more familiarly, as ft/sec^{2}.

Since you want "mL" on top in your answer you won't go wrong starting with 250 mL/400 mg as a logical starting factor.

__250 mL__

400 mg

You are now ready to play a game called "plug in other factors to cancel out the units you don't want until you end up with the units you do want." Here goes:

The horizontal bar means "divide," as usual, and the vertical bars mean "multiply." If the units cancel out properly, then your set up is correct and you can be quite sure the answer will be correct if you just manage to punch the right keys on your calculator. The most twisted of med-math problems devised by the most fiendish minds can be solved, bing-bang-boom, in this manner.

If this introduction to DA is too brief, visit the following nursing math website for more:

http://www.alysion.org/dimensional/analysis.htm

Example 2:

*The patient is receiving nitroprusside at 23 mL/hr. The bag has 50 mg of nitroprusside in 250 mL of solution. The patient weighs 67 kg. What dosage of nitroprusside in mcg/kg/min is the patient receiving?*

Example 3:

*Your patient receives an order for procainamide at 3 mg/min. She weighs 58 kg. The pharmacy has mixed 2 g of procainamide in 500 mL of solution. What is the infusion rate in mL/hr?*

Note that weight is not used, extra details are often included in problems.

Example 4:

*The patient weighs 117 pounds. Dopamine is running at 30 mL/hr. There is 400 mg of dopamine in 500 mL of solution. How much dopamine is the patient receiving in mcg/kg/min?*

Since you want kg, a unit of weight (mass) on the bottom, starting with pounds on the bottom makes sense.

Example 5:

*You need to start a continuous drip of amiodarone at 1 mg per minute (by pump). The standard IV mixture is 450 mg in 250 mL. *

Pumps like to be programmed in mL/hr, so mL/hr are your answer units.

Example 6:

*Milrinone Lactate (Primacor) has been ordered for a patient at 0.4 mcg/kg/min. The patient weighs 100 kg. If the pharmacy mixes 20 mg of Milrinone in 100 mL of total solution, what would be the rate of the infusion?*

First, think what units will be in the answer. Since you're using a pump, it's mL/hr.

Example 7:

*A patient has a confirmed pulmonary embolus and the physician has ordered a heparin drip. The initial rate is ordered at 1000 units per hour. Premixed heparin infusions are 25,000 units of heparin in 250 mL of D5W. What is the rate of the infusion?*

You want mL/hr again, so start with mL on top.

Example 8:

*An IV solution containing 2 grams of Lidocaine in 500 mL of D5W is infusing at 15 mL per hour. What should the ordered dose be in milligrams per minute?*

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### External Links

- Fun with Dimensional Analysis
- For everyone else.

- Math Skills Review
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### Top 10 Poems from Alysion's

### Bucket List of Poems

to Read Before You Die

- 1. The Rainy Day by Henry W. Longfellow
- 2. Fire and Ice by Robert Frost
- 3. A Dream within a Dream by Edgar Allan Poe
- 4. The Purple Cow by Gelett Burgess
- 5. If by Rudyard Kipling
- 6. To See a World by William Blake
- 7. Ten Little Limericks
- 8. First Fig by Edna St. Vincent Millay
- 9. Alone by Edgar Allan Poe
- 10. I'm nobody! Who are you? Emily Dickinson

One of many How-to videos on YouTube.