Calculating Drug Titration Dosages
Pharmacological agents used in critically ill patients are administered in a variety of doses:

To calculate drug doses you need to memorize the following formula:

Dose = Rate X Concentration

You will know two of the factors and will have to calculate the third.

Sometimes you will need to add conversion factors for minutes/hour and kilograms.

Dose

The drug you are administering determines the dose. If you are not certain what unit to use (mg/hr, mg/min, etc.) ask your preceptor. You will either know the dose (from the doctor’s order) or you will need to calculate it.

Rate

The rate will always be in ml/hr. IV pumps are used to administer all of these drugs because of their potential adverse reactions. You will either know the rate (by reading it off the IV pump) or you will need to calculate it. Some of the IV pumps will deliver rates to the tenth (0.1) of a milliliter. So after all of your calculations, round to the nearest tenth.

Concentration

You will always be given the concentration; however, it may not be in the unit you need. The concentration may be in mg/ml, units/ml or mcg/ml. The concentration can be found on the label on the bag.

Let’s calculate some problems:

Units/hr

You need to administer 800 U/hr of Heparin. The label states there are 25,000 U/500 ml of fluid. Calculate the rate you will set on the IV pump.

Dose = Rate X Concentration (D = R X C)

You want the answer in ml/hr.  Therefore, ml needs to be on top in the equation.  You set up each of the additional factors to cancel out any labels you do not want at the end.  So

 500 ml    X   800 U =  400000 ml =   16 ml/hr     (units cancel each other and
25,000 U        1 hr        25000  hr                           you are left with ml/hr)


Milligrams/hr (mg/hr)

At the beginning of your shift, you note that Theophylline 1gm/ 500ml is infusing at 20 ml/hr. You have an order to administer Theophylline at 40 mg/hr. Is the rate correct?

You want the answer in ml/hr.   

  500 ml    X  40 mg  =    20000  ml   =  20 ml/hr     (mg cancel each other)
1000 mg         1 hr            1000   hr
1 gm = 1000 mg

The Theophylline is infusing at the correct rate. It is important to calculate all IV drips to make sure they are infusing correctly at the beginning of your shift. You cannot assume that anyone else can do math as good as or better than you can.

Milligrams/minute (mg/min)

You have an order to increase the Lidocaine infusion to 3 mg/min. The label states there are 2 gm/500 ml. What rate will you infuse the Lidocaine?

Again, you want the answer in ml/hr.  You will set it up the same way, but need to put in a conversion factor for min to hr because IV pumps infuse in ml/hr.

 500 ml     X   3 mg   X   60 min   =     90000  ml = 45 ml/hr  (mg and min cancel out)
2000 mg          min           1 hr               2000  hr

Micrograms/minute (mcg/min)

Your patient has been having chest pain and is receiving 30 ml/hr of Nitroglycerine 50 mg / 250 ml of D5W. You are going to notify the physician that the Nitroglycerine is not controlling the chest pain. You need to calculate the dose (mcg/min) the patient is receiving. (Remember that you need to use the min/hr conversion factor).

50 mg = 50,000 mcg

50000 mcg  X  30 ml  X   1 hr   =  1500000 mcg = 100 mcg/min           (ml and hr
  250 ml              hr         60 min       15000 min                                    cancel out)

 

Micrograms/kilogram/minute (mcg/kg/min)

Your patient's blood pressure has been unacceptably low (70's/40's). He is receiving dopamine 800 mg/D5W 250 ml at a rate of 5 ml/hr. You have increased the dopamine to 12 ml/hr and need to talk to the physician. In order to discuss the dopamine, you need to know the dose the patient is receiving. (Note: weight is 70 kg. and you will need conversion from hours to minutes.)


    800,000 mcg  X  12 ml  X    1 hr    X     1       =  9600,000 mcg   =  9.14 mcg/kg/min
      250 ml                 hr         60 min      70 kg         1050000 min/kg

Lets try a problem calculating the rate:

The physician orders you to start dobutamine at 10 mcg/kg/min. You have a premixed bag with 1000 mg/500 ml D5W. What rate will you infuse the dobutamine?  Your client weighs 50 kg.

     500 ml     X  10 mcg  X  50 kg   X  60 min  =  15000000  ml  =  15 ml/hr
  1000000 mcg   kg.min          1             1 hr           1000000

Now it is time to try some problems on your own: Practice Problems

Sharon Kumm, University of Kansas School of Nursing, August 2007