A Five-Step Problem Solution with Commentary


Page 224, problem #1 seems to cover most of the areas of difficulty you mentioned.  Let's do it with some commentary on the side.


1.  Order:  Lidocaine 30 mcg/kg/min IV.  Dilute 300 mg lidocaine in 250 mL D5W.

    Label:  Lidocaine 1 g per 25 mL

    Weight:  32.6 kg


Before we start answering questions, let's classify the information we've been given.  The "Med-Math Hangman" diagram that I use on the whiteboards is a little difficult to draw in this medium, so let's try this kind of organization:


Concentrate in a Vial


1 g / 25 mL (from vial label)



IV Bag


300 mg of lidocaine from vial

250 mL of D5W





flow rate into the patient:  30 mcg/kg/min

weight:  32.6 lb




a.  How many mL of lidocaine should be added to the 250 mL D5W to obtain the ordered dilution? 

This is pretty much one of the injection problems that we did in Chapter 8, except that we're injecting the bag of D5W instead of the patient.  When we were injecting patients with 300 mg of a drug, we looked at the label on the vial to get the concentration (strength) of the medication in mg / mL  We have that data here except that it's in g / mL, but we can fix that.  Let's start with the 300 mg of lidocaine we need to get into the D5W bag and use the concentration information to convert the 300 mg to a number of mL.


300 mg   x   25 mL / 1 g    (oops! we need to convert the grams  to mg to make this work, so ...)


300 mg   x    1 g  / 1000 mg    x    25 mL / 1 g  


The surviving units are mL. Separating the numeric and units information we have


    300 x 1 x 25    mL

=  ------------------



=   7.5   mL



b.  How many mcg of lidocaine should the child receive per min?  (How fast should we give the lidocaine in mcg/min?)


Since the problem gives us the drug infusion rate in mcg / kg / min, we should be able to get this by multiplying the patient weight in kg times the drug infusion rate in mcg / kg / min, as follows:


32.6 kg   x   30 mcg


                   kg x min



=  978 mcg / min .


c.  How many mg of lidocaine should the child receive per hour?  Since we calculated the number of  mcg / min  in part b), it shouldn't be too difficult to transform the mcg to mg and the min to hr to get the required mg / hr.  Let's see the time part is easy:


60 min      978 mcg           

----------- x  --------------  .

1 hr             1 min


That gets us to mcg / hr, which is closer to the required answer units, but we need the mcg converted to mg, so


60 min      978 mcg          1 mg 

----------- x  --------------  x. --------------

1 hr             1 min         1000 mcg


will give us the required answer units.  Separating numeric items from the surviving units of mg / hr, we have


60 x 978 x 1    mg

------------------    ----  .

1 x 1 x 1000     hr


Since 978 / 1000  is nearly  1000 / 1000, we can correctly deduce that the answer is a little less than 60 mg / hr and a bit of calculation shows that


= 58.68 mg / hr .   The text answer is rounded to 3 SDs, or 58.7 mg/hr, and that's quite acceptable.



d.  What should the flow rate be in mL / hr to infuse the calculated dose?


From the answer to part c), we know that the flow rate is 58.7 mg / hr, so let's transform that into mL / hr.  But how do we convert mg to mL?  Once again, we need a strength or concentration in mg / mL.  But WHICH concentration are we talking about?  The concentration of the medication in the vial?  No, we used that to inject the required 300 mg into the IV bag.  The concentration we need is the concentration of lidocaine in the IV bag, and we'll have to calculate that ourselves.  Let's see, from the order there are 300 mg of lidocaine in 250 mL of D5W, so the required concentration is 300 mg / 250 mL.  Okay, lets start with the flow rate from part c)  ('when they ask for a flow rate, start with a flow rate") and transform it with the concentration we just calculated.



58.7 mg        250 mL

------------  x  -------------  =  48.9  mL / hr ~= 49 mL / hr

    1 hr          300 mg


We knew that this would be a little less than 58.7, since we multiplied 58.7 by  250 / 300, a fraction a bit less than 300 / 300.


e.  At the calculated rate, how many hours should it take for the total IV to infuse?


Remember the example that went, "It's 240 miles to Amarillo, how long does it take to get there if we average 60 mi / hr?"  In dimensional analysis form that one looks like


                  1 hr

240 mi  x  -----------  =  4 hr .

                 60 mi

We need to do the same kind of calculation here, except that what's being consumed is milliliters, instead of miles.

In part d) we found that the rate of infusion ("consumption") was 49 mL / hr.  In the order, we notice that there are 250 mL of D5W to infuse ("consume"), so


                     1 hr

250 mL   x  ----------   =   5.1 hr .   

                    49 mL


That's nice, but it would be better to state the time in hours and minutes.  The hours part isn't hard, just "5 hours."  The minutes part can be calculated from the tenth(s) of an hour this way:


              60 min 

0.1 hr  x  ----------  =  6 min.

                1 hr


The infusion, then requires 5 hour and 6 minutes.


That concludes the first installment of Module 4 by Mail [cue schmaltzy theme music].  Look it over, see if you can follow the calculations, then look away.  See if you can perform the calculations on your own.