Intravenous Infusions with Weight Based Dosing
Infusions of drugs used in critical care such as dopamine, dobutamine, nitroglycerin and lidocaine are based on body weight. The order may read μg/kg/min or mg/kg/hr. When the patient’s weight, the dose of the drug and the drug concentration in the infusion are given, the infusion rate can be calculated by the following equation:
$$ Infustion \ rate \ (ml/h) = {Patient's \ weight \ (kg) \times Dose \ (mcg, \ mg, \ or \ units \ /kg/min ) \times 60 \over Drug \ concentration, \ infusion \ (mcg, \ mg, \ or \ units \ /ml ) } $$
In using this equation, the units for the dose and the drug concentration must be the same (e.g, mcg, mg or units). Also, if the dosage rate is stated in hours (e.g mcg/kg/hr), the 60 is not needed in the equation to arrive at the flow rate per hour.
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Solved Problem: A physician wishes to infuse dopamine into a patient weighing 200 lb. at the rate of 20 μg/kg/min. Your pharmacy stocks a dopamine drip that contains 320 mg of dopamine in 100 ml of D5W.What is the infusion rate in ml/hr? Approach -1: Convert weight into kg and dosage rate into mg. Use the equation provided above to calculate infusion rate in ml/hr.
$$ Patient's \ weight = {200 \over 2.2 } = 90.9 \ kg $$ $$ 20 \ μg = 0.02 \ mg$$ $$ Durg \ concentration, \ infusion = {320 \ mg \over 100 \ ml} = {3.2 \ mg / ml}$$ $$ Infustion \ rate \ (ml/h) = {90.9 \ kg (Patient's \ weight) \times 0.02 \ mg/kg/min \ (Dose) \times 60 \over 3.2 \ mg/ml (Drug \ concentration, \ infusion) } $$ Answer: 34 ml/hr Approach -2: set up a dimensional analysis to calculate the infusion rate in ml/hr. Convert pounds to kg, minutes to hour. $$ x {ml \over h} = {20 μg \over kg / min} {\times} {kg \over 2.2 \ lb} {\times} {200 \ lb} {\times} {1 mg \over 1000 μg} {\times} {100 ml \over 320 mg } {\times} {60 min \over 1 \ h} $$ Answer: 34 ml/hr |
Some medications are made at standard concentration and stored in the pharmacy. A standard concentration is a set volume and concentration of a medication. Standard concentration is predetermined by the nursing and pharmacy, and all the bags of the medication are prepared using a specified recipe. So for example, if a physician orders dopamine 5 mcg/kg/minute, the pharmacy will automatically place 400mg of dopamine in a 250ml bag of D5W.
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Solved Problem: A medication order calls for 5 mcg/kg/minute for a 180-lb patient. You already calculated and mixed your pharmacy’s “standard” dopamine drip (400mg in 250ml of D5W). Calculate the drip rate per minute when using the administration set delivering 20 drops/ml. Approach: set up a dimensional analysis to calculate the infusion rate in ml/min. Convert pounds to kg.
$$ x {ml \over h} = {5 μg \over kg / min} {\times} {kg \over 2.2 \ lb} {\times} {180 \ lb} {\times} {1 mg \over 1000 μg} {\times} {250 ml \over 400 mg } $$ $$ Infusion \ r ate = 0.25 \ ml/min $$ Convert infusion rate from ml/min to drops/min. $$ Drip \ rate = {20 \ gtt \over ml} {\times} {0.25 \ ml \over min} = 5 \ drops/min$$ Answer: 5 drops/min |