Use of Dimensional Analysis to Reduce Medication Errors in EMS

By Daryl Boucher, MS, RN, CCEMT-P, Allied Health Coordinator, Northern Maine Community College

Dimensional Analysis, an old method of mathematical computation used in chemistry applications, has recently been developed for pharmacological calculations. It is extremely useful in teaching how to do medication dosage calculations to students with little experience with algebra or for those with weak math skills. Northern Maine Community College has been using this method in its Nursing and Allied Health programs, including EMS, for several years. One of the major advantages to this method is that students can use the same mathematical set-up for every calculation, and there is no need to memorize formulas. Once they learn the system, healthcare professionals can perform anything from simple metric conversions to complex drip rate calculations.

Greenfield, et al. (2005) completed a pilot study that evaluated whether using Dimensional Analysis as a method of math calculation could reduce calculation errors. Students’ scores using the Dimensional Analysis method were compared with the traditional teaching approach of formula memorization; the results revealed that the Dimensional Analysis group scored with greater accuracy and made fewer calculation errors than did the traditional math group. Students in the DA group excelled at converting units for oral, parenteral, intravenous, and body weight-based medication calculations. Though this study measured the ability to come up with correct answers on a written exam with simulated scenarios, the results are easily transferable to real patient situations.

The implications of this study are important. The national agenda continues to focus on preventable medication errors. In fact, a recent commentary written by Zachary Meisel identified ambulances as “one of the most dangerous places for patients to be.” Meisel’s work cites various calculation errors by paramedics that have led to patient injury or death in the pre-hospital arena. As educators and professionals, we know that it is important to assure that pre-hospital providers are able to perform to established standards, and those standards include safe medication administration. As a method for dosage calculation, Dimensional Analysis is emerging as a safer, easier, and more reliable approach, an approach which hopefully will lead to fewer errors and better patient outcomes than traditional methods.

Though it is impossible to present the intricacies of the entire system in a short article, I will attempt to present a few key points. First, the process can be learned using a programmed study text by Curren, called Dimensional Analysis for Meds. If you have struggled to do or teach pharmacological calculations, I would encourage you to attempt using this text. The process allows medical personnel to convert measurement weights (i.e. milligrams to grams), convert from one system to another (i.e. apothecary to household to metric (i.e. pounds to kilograms), or to do complex mathematical computations using only one equation (i.e. such as would be required for a lidocaine drip). Once you have learned a few basic rules, you will have established the foundation to complete even more complex problems. (Students of this system must still commit measurement units to memory.)

In traditional ratio and proportion conversions and calculations, students were required to divide or move decimal points before beginning the actual calculation. Additionally, they had to learn multiple formulas depending on the situations (i.e. conversions, IV drips, medication drips, etc.) For example, if the student is required to administer 30 mg of a medication, and the medication is available as 2 grams in 10 ml, in the traditional formula-based approach he would follow these steps:

Dose ordered

x vehicle = amount to give

Drug on hand

1. Convert mg to grams, either by moving the decimal point (which has a high risk of error), or by calculating: if 1g = 1000mg, then 2 g= 2000mg

2. Next, he would place the numbers into the formula (D/H x V) = amount to give:

30 mg

x 10 mL = 0.15 mL

2000 mg

Or, he could choose to cross-multiply (which requires some level of algebraic knowledge) to be able to solve for “x.” However, regardless of the approach he uses, for every additional step in the calculation process, he increases the risk of error. With the above system, needing two to three equations is not uncommon. The more complex the problem, the more calculations are required and therefore the greater the risk of error.

In Dimensional Analysis, the same calculation is done in one combined equation:

? mL

10 mL

1 gm

30 mg

300 ml

= 0.15 mL

2 gms

1000 mg

2000

To calculate the result, you multiply all the numerators (top), and multiply all the denominators (bottom). Then you divide the top by the bottom of the resulting fraction to yield the answer. There are a couple of safety checks to the system to assure there are no errors:

1. Note in the original equation how the labels from the denominator match up with the subsequent numerator (i.e. grams matches grams). This allows you to cancel the labels, and you are left with the desired measurement unit, in this case, mL, that is not cancelled.

2. The known conversion factor is part of the equation (1g = 1000mg). This helps assure there are no errors in the calculation.

Here are a couple of dimensional analysis problems. I would encourage you to solve them using your current method, and then look at the example for DA that I provide. Then, determine for yourself which method is easier to perform, is easier to teach, and most importantly has less chance for error.

a. 12 microgram per minute drip of a medication is ordered. The medication is available in an 8 mg/250 mL solution. Calculate the drip rate using a microdrip set (60 gtts/ml).

DA set up:

? gtts

60 gtts

250 mL

1 mg

12 mcg

= 22.5 gtts

min

1 mL

8 mg

1000 mcg

1 min

b. An IV mediation with a volume of 60 milliliters is to infuse at 45 drops per minute. Using a microdrip set, calculate the infusion time.

DA set up:

? min =

1 min

60 gtts

60 mL

= 80 min

45 gtts

1 mL

c. A pill contains 6 milligrams. How many micrograms is this?

DA set up:

? mcg=

1000 mcg

1 mg

x 6 mg

= 6,000 mcg

d. How many kilograms does a 21 pound child weigh?

DA set up:

? kg=	1 kg	x 21 lbs	= 9.5 kg
	2.2 lbs

Notice that the setup of all of these problems is the same—there no need to learn a new formula as the situation changes, as long as you know the standard equivalents. Also note that by canceling labels (i.e. pounds on top and bottom), you are left with the measurement you looking for.

One of the neat things with the Dimensional Analysis process is that it is relatively easy for those already experienced with calculations to relearn. But for students who have little math experience, it is also easy to teach and easy to learn. Additionally, once learned, even if you have not done a calculation for a while, it is easy to remember. Though this method clearly will not eliminate all calculation errors, it certainly has been shown to help.

If you would like more information about the Dimensional Analysis method for drug calculation or would like to schedule a training session for your staff, please contact Daryl Boucher via e-mail at dboucher@nmcc.edu.

Resources:

Curren, Anna M. (2006). Dimensional Analysis for Meds, 3/e. New York: Delmar Thomas, 1998. On line link: www.delmarlearning.com/

Meisel, Zachary. (2005). “Ding-a-Ling-a-Ling; Ambulances Can Be Dangerous Places.” Slate 8 November 2005. 20 March, 2007

www.slate.com/toolbar.aspx?action=print&id=2129684

Greenfield, S. Whelen, B. & Cohn, E.. “Use of Dimensional Analysis to Reduce Medication Errors.” Journal of Nursing Education 45.2 (2006): 91-94.