## Medical Math Mistakes: Muddled Milliliters

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The article “In the Lab: Simple Math Errors Can Imperil Patients” by Nicholas Bakalar in the Health Section of the New York Times last month related an experiment in which difficulty with math computations led to doctors measuring incorrect dosages of medicine.

In response to a simulated emergency, doctors had to collect and inject 0.12 mg of epinephrine. Both speed and accuracy were measured.

Fourteen doctors drew the amount from a bottle labeled “1 milligram in 1 milliliter solution”. Since they needed 0.12 mg, the correct amount to draw was 0.12 milliliters. Eleven of these doctors calculated the amount correctly, with an average speed of 35.5 seconds from start to finish. The bad news: this 79% success rate for the correct dosage is the good news.

Fourteen other doctors drew the amount from a bottle labeled “1 milliliter of a 1:1000 solution”. According to this Pharmacology web page, “Some solutions such as adrenaline (epinephrine) may be expressed as 1:1000 or 1:10 000 or 1:100 000. This means that in a 1:1000 adrenaline ampoule there is one part adrenaline to 1000 parts solution.” So in the 1:1000 solution of epinephrine, there would be 1 mg of epinephrine in 1000 mg (in other words, 1 gram) of solution. But 1 gram of water is the same as 1 ml, so assuming the conversion stays the same for the solution this would lead to 1 mg of epinephrine per 1 ml of solution. In other words, this was exactly the same concentration as the bottles used by the other group of doctors, and the correct dosage was .12 ml. However, only two of the doctors (14%) drew the correct amount, and on average the doctors in this group took 91 seconds longer than first group of doctors. (That’s all?)

According to the published study in the Annals of Internal Medicine, the conclusion of the study was:

The use of ratios to express drug concentration may be a source of drug administration error. Patient safety might be improved by expressing drug concentrations exclusively as mass concentration.

They caution that in the real world “ampule labels provide both expressions of concentration”. I’m not convinced, however: a quick search revealed that at least this brand of epinephrine shows the 1:1000 measurement most prominently, with the other expression either buried or absent.

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