Without evidence of benefit, an intervention should not be presumed to be beneficial or safe.

- Rogue Medic

More on Drug Calculations

I am making a pun at my own expense. Not More on Drug Calculations, but Moron Drug Calculations.

And I am the moron.

In my last post, Current Drug Shortages, I was pointing out ridiculing concerns about the use of 1:1,000 epinephrine IV, since it should never be given through an IV to a live patient, except as a drip. This is true. It is not considered wrong by the FDA (Food and Drug Administration), but that is something the FDA should change.

The problem is with my calculation of the drip rate. I wrote, not just once, that putting 1 mg of epinephrine in 250 ml NS (Normal Saline) would produce a concentration of 4 mg/ml.

I hope that everybody reading this has noticed the mistake I made. You don’t need to be a math whiz to be able to figure out that when you dilute 1 mg/ml by adding 250 ml, you do not get a more concentrated solution. Dilution produces a less concentrated solution.

If the same mistake were being made by a student in an ACLS (Advanced Cardiac Life Support) class, and this mistake has been made plenty of times, I would ask the student some questions, because many of these mistakes cannot be made with the supplies that are in a crash cart or EMS drug bag.

For example, plenty of students have stated that they would give one gram of epinephrine. I have never seen a crash cart or EMS drug bag with even 100 mg of epinephrine. You have to do some restocking to get that much. In the hospital, that means somebody running to the pharmacy to get 1,000 mg. If they state 1:10,000, that means 10 liters, and it is unlikely that the pharmacy carries epinephrine in 1:10,000 concentration in liter containers. 1,000 preloaded syringes of 1:10,000 epinephrine may be more than is available in the pharmacy. Anyway, once I state, A coworker points out that we do not have enough epinephrine to give 1 gram of 1:10,000 epinephrine, the student usually realizes the mistake and corrects the mistake without any further need for hint or for explanation.

I have seen several instructors immediately state that the student killed the patient. I don’t know what kind of dream world these instructors live in, but it appears to be a sadistic one with no grasp on the reality. If the student does not have the capability to actually give 1 gram of epinephrine, then how can the student kill the patient with 1 gram of epinephrine?

I hear the excuse that the student has to learn somehow. This suggests that pointing out the drug calculation is not embarrassing enough to make it memorable. This suggests that a petty and unrealistic comment by an instructor is in some way an example of great teaching. It is not.

However, what I did was much worse than a student making a simple mistake in a stressful moment – a mistake that could not lead to the administration of the wrong dose to the patient. Well, JCAHO might try to make it possible, just so they can penalize people for this.

What I did was tell people that this impossible concentration is the correct concentration.

This is going to mislead and confuse people. It will get others to laugh at me. I should be decreasing confusion, not contributing to confusion. I do not have the same excuse as a student being tested in an ACLS class. I had plenty of time to check everything and in the unreality of the internet anything is possible, right up until it is tried in the real world.

There is one other problem with the drug concentration of 4 mg/ml.

The concentration of 1:10,000 epinephrine is 0.1 mg/ml. I cannot create a concentration of 4 mg/ml, unless I add even more concentrated epinephrine to this 0.1 mg/ml concentration. 4 mg/ml is 40 times more concentrated than 1:10,000 epinephrine.

If you do not understand this, assume that you add 1,000 mg epinephrine to 250 ml NS, you get 4 mg/ml. That works, but only as long as you do not consider the amount of solution that is already included with the epinephrine. For 1:10,000 that means 10 liters of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 10,250 ml or 97.6 mcg (MICROgrams)/ml. Ordinary 1:10,000 epinephrine is 100 mcg/ml (0.1 mg/ml or 100 mcg/ml – not significantly different from what we end up with).

The concentration of 1:1,000 epinephrine is 1 mg/ml. The same concentration problem exists, except that 4 mg/ml is only 4 times more concentrated than 1:1,000 epinephrine.

For 1:1,000, assume that you add 1,000 mg epinephrine to 250 ml NS and you get 4 mg/ml. For 1:1,000 that means 1 liter of solution with the 1,000 mg, so you do not end up with 4 grams/250 ml or 4 mg/ml. You end up with 1 gram in 1,250 ml or 800 mcg (MICROgrams)/ml. Ordinary 1:1,000 epinephrine is 1,000 mcg/ml (1 mg/ml or 1,000 mcg/ml – there is a more significant difference between 800 mcg/ml [0.8 mg/ml] and 1,000 mcg/ml [1 mg/ml]).

Either way, I was suggesting something that is impossible with standard concentrations of epinephrine. It was suggested to me that I was trying to engage in a bit of homeopathy, by pretending that dilution leads to greater strength. 🙁

Dilution does not lead to greater strength.

This is probably the reason that I made this mistake, other than just not thinking, and I wasn’t thinking. We learn the lidocaine clock for calculating concentrations of drips that we use in EMS. Lidocaine commonly comes in a package of 100 mg/10ml for IV push in cardiac arrest. It doesn’t improve outcomes, but that is a different discussion. If you add 100 mg/10ml lidocaine to 250 ml NS, you end up with 100 mg in 260 ml or 3.85 mg/ml. This should also be rounded off to 4 mg/ml, even though it is a much bigger difference from the 4 mg/ml. The reason is that both are not significant differences.

Mixing 1 in 250 will give you a 4/1,000 concentration. Since we can move the decimal (by changing the prefix) to give a 4/1 concentration we need to remember to make sure we are still dealing with the right amounts when we have completed our calculations. Any time we end up with numbers that seem as if they require a lot of drug, or very little drug, we need to consider the possibility, even the likelihood, that we made a decimal point (prefix) error.

Thank you to Matt J for pointing out my huge mistake. I will correct it on the original post, too.



  1. […] have also covered these drug shortages here, here, here, here, here, here, here, and […]

  2. […] 8/02/10 at 05:50 also see More on Drug Calculations for more details on problems with my drug calculation. Thank you to Matt J for pointing out my […]