Complex Calculations: Advanced mcg/kg/min

Complex Calculations: Advanced mcg/kg/min Some medications are required to be given in mcg/kg/min. This means the amount of medication to be administered will be dependent on the patient s weight. Example John Smith weighs 80 Kg and is due for coronary bypass surgery. He has been ordered 250 mg of Dobutamine to be diluted in 50 ml of 0.9% Saline. If 5 mcg/kg/min is ordered how many ml/hr should be administered? Step 1 You can start by calculating the concentration of the solution by using the general formula: Concentration (mcg/ml) = Amount of medication (mcg) Volume (ml) The amount of medication is 250 mg and the volume is 50 ml. However, since the rate of administration has been given in mcg/kg/min we shall convert the 250 mg to mcg before putting it into the formula. To change 250 mg to mcg multiply it by 1000 mcg/mg: 250 mg x 1000 mcg/mg = 250000 mcg Substituting into the formula: Concentration = 250000 mcg 50 ml Concentration = 5000 mcg/ml

250000 50 = which gives an answer of 5000 mcg/ml. Step 2 Start by calculating the rate needed based on the patient s weight by using the following formula: Rate (mcg/min) = Rate ordered (mcg/kg/min) x Patient s weight (Kg) From the question the rate ordered is 5 mcg/kg/min and the patient s weight is 80 Kg. Rate (mcg/min) = 5 mcg/kg/min x 80 Kg = 400 mcg/min 5 x 80 = which gives an answer of 400 mcg/min. This means that based on John s weight of 80 Kg a rate of administration of 400 mcg/min is required. Step 3 At this point you should look at the final units required which are: ml/hr. This means that all references in time should be expressed in hours. You will therefore need to change the rate of administration of the medication from 400 mcg/min to a quantity in mcg/hr. This can be achieved by multiplying it by 60 min/hr as there are 60 minutes in an hour.

Rate (mcg/hr) = Rate (mcg/min) x 60 min/hr = 400 mcg/min x 60 min/hr = 24000 mcg/hr 400 x 60 = which gives an answer of 24000 mcg/hr. Step 4 Referring to the formula presented in the topic above called Rate of administration of the dilutant, to calculate the required rate of administration in ml/hr you need to divide the rate of administration in mcg/hr by the concentration in mcg/ml: Rate (ml/hr) = Rate (mcg/hr) Concentration (mcg/ml) Rate (ml/hr) = 24000 mcg/hr 5000 mcg/ml Rate = 4.8 ml/hr All ml/hr calculations should be rounded to the closest whole number and therefore the final answer is 5 ml/hr. 24000 5000 = which gives 4.8 ml/hr. Rounding to the closest whole number gives an answer of 5 ml/hr. Example

Paula weighs 65 Kg and is ordered Noradrenaline 4 mg in 100 ml of 5% Dextrose at 45 ml/hr. How many mcg/kg/min will she receive? Step 1 You can start by calculating the concentration of the solution by using the general formula: Concentration (mcg/ml) = Amount of medication (mcg) Volume (ml) It should be noted that the answer must be given in mcg/kg/min, which means that all quantities expressed in mg should be changed to mcg. The amount of medication is 4 mg which when multiplied by 1000 mcg/mg gives 4000 mcg. Putting this into the formula with the volume of 100 ml gives: Concentration = 4000 mcg 100 ml Concentration = 40 mcg/ml 4000 100 = which gives an answer of 40 mcg/ml. Step 2 The final answer must be given in mcg/kg/min. To calculate this, start by finding the required dosage in mcg/min. This can be achieved by using the formula shown earlier in the section called rate of administration of the medication:

Rate (mcg/hr) = Concentration (mcg/ml) " Rate (ml/hr) The concentration is 40 mcg/ml and the rate of administration of the fluid is 45 ml/hr: Rate (mcg/hr) = 40 mcg/ml " 45 ml/hr Rate = 1800 mcg/hr 40 x 45 = which gives an answer of 1800 mcg/hr. Step 3 From Step 2 you now know the required rate is 1800 mcg/hr. To find the rate in mcg/kg/hr you should divide this answer by the patient s weight in kilograms, which is 65 Kg. Rate (mcg/kg/hr) = Rate (mcg/hr) Patient s weight (Kg) Rate (mcg/kg/hr) = 1800 mcg/hr 65 Kg In addition, as the rate has been expressed in hours you should also divide this by 60 min/hr to change it to minutes as you are required to state your answer in minutes. Rate (mcg/kg/min) = 1800 mcg/hr 65 kg 60 min/hr Rate (mcg/kg/min) = 0.46153846 mcg/kg/min = 0.46 mcg/kg/min This answer should always be rounded to 2 decimal places.

1800 65 60 = which gives 0.461538461 mcg/kg/min. Rounding to 2 decimal places gives an answer of 0.46 mcg/kg/min. Example Mrs Harisson must receive Lignocaine 0.025 mg/kg/min. It is available as 2 g in 500 ml of 5% Glucose. If Jenny weighs 70 Kg: a) How many mg/min will she receive? b) How many mg/hr will she receive? c) What is the rate in ml/hr? a) To find the required dose in mg/min multiply the rate in mg/kg/min by the patient s weight in Kg: Rate (mg/min) = Rate (mg/kg/min) " Patient's weight (Kg) Rate (mg/min) = 0.025 mg/kg/min " 70 Kg Rate (mg/min) = 1.75 mg/min The rate of administration of the medication should always be rounded to 2 decimal places.

0.025 x 70 = which gives an answer of 1.75 mg/min. b) To calculate the rate in mg/hr simply multiply the rate in mg/min by 60 min/hr as there are 60 minutes in 1 hour: Rate (mg/hr) = Rate (mg/min) " 60 min/hr Rate (mg/hr) = 1.75 mg/min " 60 min/hr Rate (mg/hr) = 105 mg/hr 1.75 x 60 = which gives an answer of 105 mg/hr. c) To calculate the required rate in ml/hr start by calculating the concentration of the solution by using the general formula: Concentration (mg/ml) = Amount of medication (mg) Volume (ml) The amount of medication has been expressed in grams and we will need to change this to mg as all other quantities given to us in the question are expressed in mg. To change 2 g to mg multiply it by 1000 mg/g, which gives 2000 mg. Putting this into the concentration formula with the volume of 500 ml gives:

2000 mg Concentration = 500 ml Concentration = 4 mg/ml Now you know the concentration in mg/ml and also the rate of administration of the medication in mg/min. To calculate the rate of administration in ml/hr you must use the following formula: Rate (ml/hr) = Rate (mg/hr) Concentration (mg/ml) The formula asks for the rate in mg/hr and you currently have it expressed in mg/min. You must therefore change this so that it is expressed in mg/hr before putting it into the formula. To change a rate in mg/min to a rate in mg/hr you should multiply it by 60 min/hr, as there are 60 minutes in 1 hour. Rate (mg/hr) = Rate (mg/min) " 60 min/hr Rate (mg/hr) = 1.75 mg/min " 60 min/hr Rate (mg/hr) = 105 mg/hr 1.75 x 60 = which gives an answer of 105 mg/hr. Now using this value in the formula to calculate the rate in ml/hr: Rate (ml/hr) = Rate (ml/hr) = Rate (mg/hr) Concentration (mg/ml) 105 mg/hr 4 mg/ml Rate = 26.25 ml/hr This should always be rounded to the closest whole number and