Sometimes instead of ordering an IV in mL/hr, the physician may order the IV based on a dose of medication.  This is particularly true in the critical care enviroment.  Such orders will include a medication dose (such as milligrams, micrograms, units, etc.) and a time in hours or minutes. The order may also address the patient's weight in pounds or kilograms.   Examples:  1200 units/hr;  4 mg/min;  6 mcg/kg/min.

For dose rate problems, the left hand side of the ratio should always be the IV label---the amount of medication and the amount of fluid.  As usual, put units of measurement on right side to match left side, "plug in" numbers into appropriate location on right, cross multiply, and solve for X.  When you have put the numbers in on the right side of the ratio, you have to make sure the units of measurement are complete and what you have on the top you must have on the bottom on the right side of the equation.  Once you have solved for X, you need to see if that is what is needed, or if additional steps may be needed.


Example problem #1:  The physician orders Heparin 1500 units per hour.  You have an IV of 50,000 units in 500 cc D5W.  What is the mL per hour flow rate?

The basic ratio will be:

     50,000 units   =       units
         500 mL                 mL

When you put the 1500 units in the top on the right, remember that it is 1500 units/hour; therefore, the "per hour" needs to be added to the bottom.

     50.000 units   =   1500 units/hr
         500 mL              X mL/hr

        50,000 X   =   750,000
                  
        50,000 X   = 750,000
        50,000          50,000

              X  =  15 mL/hr

(HINT:  As in any arithmatic process, reduce when possible.  You cannot reduce across an equation.  However, you can reduce top to bottom.  In the above problem, you could have reduced the 50,000/500 to 100/1 which would make the arithmatic easier.  Or you could have left those numbers and reduced the 750,000/50,000 to 75/5 by crossing out an equal number of zeros.  Again, this will make the arithmatic easier, particularly when you are working without a calculator.)


Example problem #2:  Ordered is Lidocaine 2 mg/min.  You have an IV of Lidocaine 1 g in 250 cc D5W.  At what mL/hr rate should you set the IV pump?

You can work this problem using a ratio with information as it appears, or you can calculate an hourly dose and then set up the ratio.  Either option is OK and you will get the same answer.

Using the information as given but converting for matching units:

       1 g     =    0.002 g/min   {the per min on top needs to be added to bottom}
     250 mL         X mL/min

        X  =  250 times 0.002 = 0.5 mL/min

   60 minutes in an hour so 60 times 0.5 mL/min = 30 mL/hr


If you had calculated an hourly dose at the start:

   2 mg/min times 60 minutes = 120 mg/hr, converted to 0.12 mg/hr for matching labels.

      1 g    =   0.12 mg/hr    {per hour on top gets added to bottom}
     250 mL        X mL/hr

        X   =   0.12 times 250  = 30 mL/hr


Example problem #3:  The physician orders 4 mcg/kg/min of dopamine for a patient who weighs 156 pounds.  You have an IV of dopamine 800 mg in 250 cc D5W.  What is the mL/hr flow rate?


Again, you can set the problem with information as given after converting to get matching units.

The ratio would be:

     800 mg   =   0.004mg/kg/min
     250 mL             X mL/kg/min


If you set the problem up in this manner, you have to remember that when you solve for X, that is not mL/hr---it is mL/kg/min so you have additional steps.  

The answer to the above equation would be 0.00125 mL/kg/min.  You would need to multiply this number by the patient's weight in kilograms for a total mL per minute and then multiply by 60 to get to mL/hr.

    1 kg   =   X  kg
   2.2 lbs     156 lbs

    2.2 X   =  156

         X  =  70.9  = 71 kg  (PCC rule, weight over 100 pounds round to nearest whole number.)


0.00125 times 71 = 0.08875 mL/min

0.08875 times 60  =  5.325  = 5 mL/hr.


HINT:  I think it is much easier to calculate an hourly dose before setting up the ratio and recommend you do this. 

For this problem, order of 4 mcg/kg/min would equal 4 times 71 = 284 mcg/min; 284 times 60 = 17040 mcg/hr.  Then convert the mcg to mg to get hourly dose to plug into the ratio.  17040 mcg = 17.04 mg  (decimal move three places to left).  Do not round this number.


     800 mg    =   17.04 mg/hr
     250 mL           X  mL/hr

      800 X   =   4260

            X   =  5.325 = 5 mL/hr

Notice you got same answer either way.  I think it is easier to calculate the dose per hour; then when you have completed the calculation your answer will be in mL/hr.  Remember if you should be asked for drops per minute, do the calculation as noted by solving for mL/hr and then use the "magic number" to get to drops per minute.