Fentanyl CRI for a 26.4 lb dog
You need to start a fentanyl CRI at 5 µg/kg/hr in a 26.4 lb dog. Your fentanyl stock is 50 µg/mL. What pump rate (mL/hr) do you set?
Hint
The dose is per kg but the weight is in lb. That conversion is your first step. From there, the answer needs to be in mL/hr. Work backwards from there to figure out which units have to cancel.
Another hint
Three steps. (1) Convert lb to kg using 2.2 lb/kg. (2) Convert the dose to an hourly drug amount (µg/hr). (3) Divide by the stock concentration (µg/mL) so the µg cancel and you're left with mL/hr.
Show worked answer
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Convert the patient's weight from lb to kg using the standard clinical factor of 2.2 lb/kg.
$$\frac{26.4 \,\cancel{lb}}{2.2 \,\cancel{lb}/kg} = 12 \,kg$$ -
Now dose × weight to get the hourly drug requirement in µg/hr.
$$5 \,\tfrac{\mu g}{\cancel{kg}\cdot hr} \times 12\,\cancel{kg} = 60 \,\tfrac{\mu g}{hr}$$ -
Divide by the stock concentration to convert µg/hr to mL/hr. The µg in the numerator cancels the µg in the denominator of the concentration, leaving mL/hr.
$$\frac{60 \,\cancel{\mu g}/hr}{50 \,\cancel{\mu g}/mL} = 1.2 \,\tfrac{mL}{hr}$$
Pump rate: 1.2 mL/hr.