OCCC APPM 1313
Problems for Pediatric Medications
(Chapter 12, a.k.a.: Module 4)
Below are a few solved problems from Module 4 to aid you with your homework.
The Worksheet 32 problems require that we do the calculations we've been doing twice: once for the lower limit of the range and once for the upper limit of the range. We'll also extend these problems to include the question, "Is a dose of ______ mg / day in four divided doses safe?" This is equivalent to asking, "Does the ordered dose fall between the upper and lower limits of the recommended dosage range?" A physician may choose to intentionally prescribe outside this range, but an order outside the rage may also be the result of an error somewhere along the way among physician, nursing staff, and pharmacy.
For Worksheet 32, problem 1, let's calculate the dosage range for the 40 lb. child in units of mg/day first and then in mg/dose.
Lower limit calculation:
40 lb x 1 kg / 2.2 lb x 25 mg / (kg x day)
40 x 25 mg
= ------------ ---- .
Using our now-permitted calculators (thank goodness!), we find that the lower limit of the recommended range is
= 454.54... mg /day (
~= 455 mg / day (to 3 SDs, since we know we'll have to use this in a calculation to get milliliters to be delivered.)
Since the upper limit is 50 mg/kg/day, exactly twice the lower limit, the upper limit will be
40 lb x 1 kg / 2.2 lb x 50 mg / (kg x day)
40 x 50 mg
= ------------ ----
= 909.09 mg / day (HIGH)
~= 909 mg / day, again to 3 SDs.
From this range of 455 to 909 mg/day, we can calculate that the amount per dose for four doses is
(HIGH:) 909 mg / day x 1 day / 4 doses = 227 mg / dose for each of 4 doses in a day.
Now we can answer the next logical question (not stated in the problem), "Is a dosage of '200 mg (per dose), every 6 hours' safe?"
Well, yes it is BECAUSE 200 mg / dose for each four doses in a day is with in the recommended range 114 to 227 mg/dose for each of four doses per day. A dosage of, say, 50 mg/dose for each of 4 doses per day would be too low and therefore "unsafe," as would a dosage of, say 500 mg/dose for each of 4 doses per day. Note that "unsafe" as used here simply means that the dosage is outside the recommended range. It is quite possible that a physician might properly and legally prescribe a dosage that is outside the recommended range. The dosage amount decision is his/hers to make, based on knowledge, experience, and the particular circumstances of a given patient.
For Worksheet 32 problem 4, we'll do a similar calculation, as follows.
Part a: 12 lb x 1 kg / 2.2 lb x 10 mg / (kg x day) x 1 day / 2 doses
12 x 10 mg
= ------------ -----
2.2 x 2 dose
= 27.2727... mg / dose
~= 27.3 mg / dose (to 3 SDs, since we're about to use this in part b).
Part b: 27.3 mg / 1 dose x 2 mL / 100 mg
27.3 x 2 mL
= ------------- ------
= 0.545 mL / dose
~= 0.55 mL / dose .
Notice that the calculated dose is less than 1 mL, so a child should be able to handle it IM.
Let's see, for Practice Test 5, problem 4, I believe this will do the trick:
62 lb x 6 mg / (lb x day) x 1 day / 4 doses x 5 mL / 75 mg
62 x 6 x 5 mL
4 x 75 dose
= 6.20 mL to 3 SDs
~= 6.2 mL to 2 SDs
That's a reasonable amount for an oral dosage (notice that it's to be given with an oral syringe).
Also, notice that we didn't have to convert the 62. lb. to kg, since the dosage was stated in mg / LB / day. That's a mixed-system specification, in that it uses both metric and US traditional units, but sometimes that's the way its done. Veterinarians tell me that their medications are frequently specified that way.