True or false: Setting a patient- controlled analgesia (PCA) infusion pump at a higher concentration than the actual drug results in an overdose and setting it at a lower concentration than the drug results in an underdose.

False. Counterintuitive as it may seem, drug concentration and volume have an inverse relationship. The more concentrated the drug, the less volume is needed to deliver a specific dose. Conversely, less concentrated drugs need more volume to deliver the dose. Most facilities use standard drug concentrations for PCA pumps, but patients who are opioid-tolerant may need customized concentrations of drugs such as morphine, hydromorphone, or fentanyl.

A PCA pump is programmed with the actual dose, so you also need to input the drug concentration so the pump can calculate the volume needed to deliver the dose. The programmed concentration should match what's in the bag or syringe. For example: Your patient is supposed to receive 1 mg of morphine with each demand dose from the PCA pump. If the concentration is programmed as 0.1 mg/mL, the pump must deliver 10 mL of solution to achieve the 1 mg dose. However, if the actual concentration of the morphine in the bag is 1 mg/mL and the concentration is inadvertently programmed as 0.1 mg/mL, the pump will still deliver 10 mL. So the patient would receive 10 mg (10 mL) of morphine-an overdose, even though the concentration programmed into the pump was less than the concentration of the drug in the infusion bag.

If your facility uses pumps that alert you to low concentration errors, remember that "low concentration" on a PCA pump isn't the same as a "low dose" alert on other infusion pumps.

For more on this math mind bender, see http://www.ismp.org/d/SpecialFollowUp.pdf.