CA is a 43 yo M presenting to your emergency department with no pulse. Using ACLS measures, the team was able to achieve return of spontaneous circulation (ROSC) and a norepinephrine drip was initiated after initial resuscitation fluids. The drip was titrated up to 40 mcg/min, and CA’s BP 5 minutes later was 90/54 mm Hg with a mean arterial pressure (MAP) of 66. The team decides to continue this rate to achieve a MAP goal > 65. Assuming a 16 mg/250 mL bag of norepinephrine is used and a steady administration rate of 40 mcg/min is infused, how long will the bag last? Provide answer in hours and minutes. 

Answer with rationale:

Two important competency statements for the NAPLEX are 4.3 (rates of administration) and 4.5 (drug concentrations, ratio strengths, osmolarity, osmolality, or extent of ionization) as these are areas in which pharmacists perform calculations in some practice areas on a daily basis.

We can set this problem up using a ratio since we know the drip rate of the norepinephrine and how much drug is contained in the bag. In this scenario, knowledge of the amount of volume is not necessary to solve the problem.  Since the rate is in mcg/min, we first need to convert this to mg/min since the bag is in mg to have consistent units. So 40 mcg/min = 0.04 mg/min. Now that we have the drip rate as the same units as the bag, we can find out how long it will last by using the following equation as there is 16mg in one 250mL bag:

0.04 mg/ 1 min = 16mg / X minutes

We can then cross multiply to get 400 minutes which is 6 hours and 40 minutes.