CLOates

OCCC APPM 1313

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

Patient

------------------------------

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

=
------------------

1000

=
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

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.