Who would have predicted that the SARS-CoV2 pandemic could increase the risk of medication error by forcing us to use math? Despite drug shortages, our pharmacy supply administrators buy what they can, when they can, to keep patient care going. However, buying different concentrations and different brands of local anesthetics, with and without epinephrine, forces us to use clinical calculations to mix what we need using what we have. Any time human beings use math, the risk of medication error rises because:

• Different brands often come in different size and color vials – providers may give the wrong medication if they rely on vial color and don’t read the label.
• Different concentrations mean that providers may inadvertently give the wrong dose. Providers must sometimes mix the concentrations they need from the ingredients they have, an additional risk.

Local anesthetic supply has been particularly affected by drug shortages. Just last week I came to work and saw this written on our message board. All our ORs were filled with orthopedic cases needing nerve blocks that day.

We frequently must mix the local anesthetic concentrations we have to get the ones that we need. We must dilute stronger doses to get less concentrated ones. We must add epinephrine to plain solutions. And we rely on math to do this. These clinical calculations are easy to perform, however getting the math wrong can produce serious complications. Since many of us have not had to do this sort of math since our school days, let’s review some basics.

How to Read Local Anesthetic Concentrations

To mix different concentrations of medications, we first have to know how much drug is in each ml of solution. Rather than labeled with a straight forward mg/ml, epinephrine comes labeled as ratios such as 1:1000 or 1:100,000. Local anesthetics are labeled as a percentage, such as 0.5%. How do you translate these into mg/ml?

Epinephrine Concentrations

Let’s start with Epinephrine (epi). Why do we use epi in surgery? It’s a potent vasoconstrictor that:

• constricts blood vessels and decreases bleeding during the procedure.
• slows absorption, allowing a larger dose of local to be given with less risk of toxicity
• prolongs the duration of numbness.

A vial of epinephrine is labeled 1:1000.

1:1000 epi has 1g/1000 ml = 1000mg/1000 ml = 1 mg/ml = 1000 mcg/ml

Local anesthetics commonly contain either 1:100,000 or 1:200,000 epinephrine. What does this mean in terms of mg/ml?

The concentration 1:100,000 means 1 g of epinephrine is dissolved in 100,000 mL solvent

1g/100,000 ml = 1,000 mg/100,000 mL = 1 mg/100 mL = 1,000 mcg/100 ml = 10 mcg/ml

Therefore, 1:100,000 = 0.01 mg /ml = 10 mcg /mL of epinephrine solution

Memorize this number because you can use it to easily calculate the other common epinephrine concentrations. For example, 1:200,000 is half as much epi as 1:100,000. So that means 1:200,000 has 5 mcg/ml epinephrine

Local Anesthetic Concentrations

Regardless of local anesthetic, the calculation is the same for lidocaine, bupivacaine (Marcaine), mepivacaine, and ropivacaine.

• A 1% solution of lidocaine has 1g/100 ml = 1,000 mg/100 ml = 10 mg/ml
• 0.5% solution of bupivacaine has 0.5 g/100 ml = 500 mg/100 ml = 5 mg/ml
• 0.25% solution of bupivacaine has 250 mg/100 ml = 2.5 mg/ml
• 0.2% solution of ropivacaine has 200 mg/100 ml = 2 mg/ml

Clinical Calculations: Combining Different Mixtures

Epinephrine Clinical Calculations: Adding Epi to Local Anesthetics

Let’s say our surgeon asks us to prepare 30 ml of a 0.25% bupivacaine solution containing 1:200,000 epinephrine and all we have is a 30 ml bottle of plain bupivacaine and a 1:1000 vial of epinephrine. How many ml of 1:1000 epinephrine should you add to the 30 ml bottle of bupivacaine?

Step #1 — How much epi, in mg/ml, is in the starting ingredients?

1:1000 epi has 1g/1000 ml = 1000mg/1000 ml = 1 mg/ml = 1000 mcg/ml

Step #2 — How much epi do you need in the final volume of bupivacaine?

Our surgeon wants 1:200,000 epi in her bupivacaine

1:200,000 epi means 1g/200,000 ml = 1000mg/200,000 ml = 100,000mcg/200,000 ml = 5 mcg/ml

30ml x 5mcg/ml = 150mcg of epi

Step #3 —How much of the 1:1,000 epi solution contains 150mcg of epi? We’ll call this volume “V”

V x 1000 mcg/ml = 150 mcg

V  = 150 mcg ÷ 1000 mcg/ml = 0.15 ml

Therefore, you would need to draw up 0.15 ml of the epi to add to the 30 ml of bupivacaine to make 1:200,000 epi

Local Anesthetic Clinical Calculations

It’s easy to calculate that when we start with 0.5% bupivacaine and we want 0.25% bupivacaine that we need to add an equal volume of saline to halve the concentration. So if I want 30 ml of 0.25% then I need to dilute 15 ml of 0.5% bupivacaine with 15 ml of saline. To prove that this is correct let’s check the math.

15 ml of 0.5% bupivacaine contains 15ml x 5mg/ml = 75 mg

30 ml of 0.25% bupivacaine contains 30 ml x 2.5 mg/ml = 75 mg

Now a more complicated example. Our surgeon asks me for 30 ml of 0.2% ropivacaine. We only have a 30 ml bottle of 0.5% ropivacaine. How many ml of 0.5% ropivacaine do we need to mix with saline to get 30 ml of 0.2%. Break it down.

Step #1: How much ropivacaine mg/ml is in the starting ingredients?

0.5% ropivacaine contains 0.5 g / 100ml = 500 mg/100 ml = 5 mg/ml

Step #2: How many mg of ropivacaine are in the final 30 ml volume of 0.2%?

0.2% ropivacaine contains 0.2 g / 100ml = 200 mg/100 ml = 2 mg/ml

30 ml x 2 mg/ml = 60 mg

Step #3: How many mls of 0.5% ropivacaine contains 60 mg? We will call this volume “R”

R x 5mg/ml = 60 mg

R = 60 mg ÷ 5mg/ml

R = 12 ml

So I need to combine 12 ml of 0.5% ropivacaine with 18 ml of saline to get 30 ml of 0.2% ropivacaine. To check to make sure this is the right value, work the equation backwards.

30 ml x 2 mg/ml = 60 mg

V x 5 mg/ml = 60 mg where V = the volume of 0.5% ropivacaine needed for that amount of drug

V = 60 mg ÷ 5 mg/ml = 12 ml

Patient Safety Always Comes First

You don’t have to do these clinical calculations in your head. Write them down. Use your smart phone calculator. Don’t let your ego get in the way — ask your coworkers check your math. It will make them feel safe to ask you to check theirs. Between the pandemic and increasing numbers of weather and other natural disasters, drug shortages are here to stay for the foreseeable future. Our need to work with what we have to get what we need will not go away any time soon. Practice math to keep your patients safe.

To review other common medication errors related to pediatric clinical calculations and dosing see:

• Avoiding Pediatric Drug Errors

May The Force BeWith You!
Christine E Whitten MD, author
anyone Can Intubate: A Step by Step Guide
and
Pediatric Airway Management: a Step by Step Guide

Note: both books are available at cost on amazon.com during the pandemic to promote education on airway management