Transcript ect 4183 Module 9Bx

SELF STUDY GUIDE
DOSAGE CALCULATIONS
USED IN INTRAVENOUS
THERAPY
Dosage Calculations used in IV Therapy
TASK: Be able to accurately calculate medication dosages.
CONTEXT: A shocking number of patients die every year in United States hospitals as the result of medication
errors, and many more are harmed. One widely cited, if questionable, estimate (Institute of Medicine, 2000)
places the toll at 44,000 to 98,000 deaths, making death by medication "misadventure" greater than all
highway accidents, breast cancer, or AIDS. If this estimate is in the ballpark, then nurses (and patients) beware:
Medication errors are the fourth to sixth leading cause of death in America.
How many medication errors are miscalculation errors? No one really knows since by some estimates as little
as one in ten errors are reported (Pepper, 2002). Of reported errors one FDA study (Thomas, et. al., 2001)
found that 7% were due to "miscalculation of dosage or infusion rate." Combining this estimate with the
estimate for total deaths, as many as 3,000 to 6,800 deaths are caused annually by medication math errors.
This would mean that in the average hospital one patient dies every year or two because someone makes a
miscalculation, and one or two patients are sub-lethally harmed each month. As future nurses, then, there is a
distinct possibility that we will harm, or even cause the death of, a patient over the course of our career.
The time to build confidence is while you are students. I suggest that as a conscientious students you should
aim for 95% or better. You should, then, carefully study, learn from, and thereby avoid repeating what mistakes
you do make, so that by the time you are working in the real world you can be confident that, if you are vigilant
enough, you can approach 100% proficiency. Since "to err is human," you will always be at risk of not achieving
a goal of 100% proficiency, but you cannot aim for less, and knowing that you are always at risk will make you
extremely careful.
To demonstrate that you have mastered this Self Study you must be
able to:
1. Accurately calculate medication dosages.
2. Show your work.
Mastery Tests Required:
1. Complete all of the assignments in the self study guide.
2. Complete and hand in final assignment.
3. All of the above are graded on a “Pass/Fail” basis.
IV Dosage Calculations
They are easier than you think!
IV dosage calculations are of the upmost
importance if you are planning on working in the
medical field.
IV DOSEAGE CALCULATIONS
• There are 3 different ways to do dosage calculations.
1. Ratio and Proportion format.
2. Formula format.
3. Dimensional Analysis format.
No one way is correct, they all are. So find the format that works for
you and stick with it.
1. RATIO AND PROPORTION
• A ratio is composed of two numbers that are related to each other. In
health care,
• medications are often expressed as a ratio. For example:
• • 125 mg/ 1 tablet or 125 mg : 1 tablet, read as 125 mg per 1 tablet
• • 350 mg / 5 tablets or 350 mg : 5 tablets, read as 350 mg per five
tablets
• • 250 mg / 10 mL or 250 mg : 10 mL, read as 250 mg per 10 mL
• A proportion shows two ratios that are equal, like this:
• Sample Problem Proportion is often used to calculate a dosage.
Suppose a drug comes in tablets of 150mg. The dosage ordered is
375mg. How many tablets are needed? Here is the problem:
RATIO & PROPORTION
To solve for X, we have to cross-multiply:
X = 2.5 tablets
NOW YOU TRY SOME…….
RATIO/PROPORTION PROBLEMS
1. The order is for 80 mg Amoxicillin IM. The vial of the
medication is labeled 100 mg/mL. How many mL will you
give?
2. You are ordered to give a patient 250 mg Keflin. The bottle
says to add 9.5cc of sterile water to the vial to yield 0.5 g/cc.
How many cc's will you give?
3. The order is for 100,000 Units penicillin. The penicillin on
hand is labeled 250,000 Units/mL. How much of the drug will
you administer?
4. Order: Demerol 75 mg IM q 3-4 hours prn. Available is Demerol 50
mg/mL. What is the maximum mL's of Demerol the patient might
receive during your 12 hour shift?
5. The doctor ordered Ampicillin 300mg/kg/day for your patient and
has ordered the medication TID. How many mg per dose would you
administer to a 59 lb. patient?
6. How much would you draw up if a 70 mEq dosage is to be added to
an IV from the stock solution of 200mEq/10cc?
7. The label reads 250mcg/mL and the order is for 0.6 mg. How many
mL’s will be administered?
8. You are asked to prepare a 300 mcg dose. The medication is labeled
0.4mg/ ml How many ml will you need for the prescribed dose?
9. The patient is receiving an antibiotic IV at the rate of 50mL/hr. The IV
solution contains 1.5g of the antibiotic in 1000 mL. Calculate the mg/hr given
10. The order is: 25 mcg/kg/min. The patient weighs 44 kg. How many mg of
medication will the patient receive in one hour? Per day?
11. An IV medication of 235 mL is to infuse at the rate of 60 mL/hr. What is
the total infusion time?
12. An IV of 550 mL infused in 638 minutes. The IV infused at ______ mL/hr.
RATIO/PROPORTION PROBLEM SET - ANSWERS
1. 0.8 ml
2. 0.5 cc
3. 0.4 ml
4. 6 mL (range 4.5-6 mL)
5. 2700 mg per dose
6. 3.5 cc
7. 10. 2.4 ml
8. 0.75 mL
9. 75 mg/hr
10. 66 mg/hr, 1584 mg/day
11. 3 hr 55 min
12. 51.7 mL/hr
If you answer 2 or more incorrect, go back and re-read the previous section
and re-take the test. Otherwise, proceed on to the next section.
Formula Format
• ABOUT IV FLOW RATE
You may see flow rates expressed in different ways, using different
names for the basic factors, but remember this ONE basic formula!
Here are some of the other factor names you
might see.
RULES FOR CALCULATIONS USING THE FLOW RATE FORMULA
1. Identify the values of the three factors in the given data.
You may need to use intermediate steps to determine these.
2. Plug them into the appropriate spots in the formula
3. DO THE MATH!
4. Generally for IV drips, the flow rate should be rounded to a
whole number. There are no partial drops (gtts)! Some critical
care IV pumps can drip at a tenth (0.1) of a drip and syringe
dosages can be rounded to a tenth (usually a tenth of a mL).
However, when solving flow rate problems, round to a whole
number unless you are specifically told otherwise.
Sample Problem #1: Solve for Flow Rate
The order is to infuse 250 mL of NS in 100 minutes. The set is 15
gtts/mL. What is the flow rate?
Sample Problem #2: Solve for Volume
• The order is for an IV of D5W to infuse at 35 gtts/min for 4 hours. If
the set is 20 gtts/mL, what volume will infuse?
Sample Problem #3: Solving for Time
• A doctor orders 2 liters of 0.9% NS to infuse at 75 mcgtts/min. How
long will it take to infuse the whole 2 liters? Remember: if the flow
rate is in mcgtts/minute, use a microdrop set of 60 gtt/mL.
75 x = 2000 * 60
75 x = 120,000
x = 1600 minutes
1600 minutes = 26.67 hours, or 26 hrs. 40 min
MATH IV FLOW RATE PROBLEM SET
1. The patient is to receive heparin at 1500 Units per hour. The IV contains 25,000 Units in 250 mL of
D5W. Find the rate in mL/hr.
2. The order is for 125 mg Aldomet given q 6hr IVPB. The medication is diluted in 100cc of 5% dextrose.
Using 60 μgtts/mL set, find the flow rate to deliver the volume in two hours.
3. Order is for Keflex 500 mg IVPB q 6 hrs for a 19 kg child. The pharmacy sends you Keflex 500 mg in 50
mL NS. What would the flow rate be if it is delivered over 30 minutes with a microdrip set? The safe
child dosage is 80-160 mg/kg/da. Is the dosage you have calculated a safe dosage ?
4. If an IV ran for 7 hours and 30 minutes, how much volume was given if there was a 15 gtts/mL set
and the flow rate was 80mL/hr?
5. You are to set the IV pump to deliver 300 cc over 6.5 hours. What cc/hr rate would you set?
6. The order is for Penicillin G 775,000 Units q 4 hrs for a child. The Penicillin on shelf is 250,000
Units/ml. The recommended time to infuse is 30 minutes. What mL/hr will you set the IV pump at?
7. The order is for Dobutamine 250mg/250cc. The doctor wants the medication delivered at
3.5mcg/kg/min. The patient weighs 154 lbs. Using an IV pump, determine the flow rate in mL/hr.
8. The patient's IV has Dopamine 200 mg in 250 mL D5W. The drip must run at 8 mcg/kg/min and your
patient weighs 66 kg. What will the rate of mL/hr be?
ANSWER KEY
• IV FLOW RATE PROBLEMS
1. 15 mL/hr
2. 50 μgtts/min
3. 100 gtts/min. Dose is safe.
4. 600 mL
5. 46 cc/hr
6. 6.2 mL/hr
7. 14.7 mL/hr, or 15 mL/hr if necessary to round
8. 31.6 mL/hr, or 32 mL/hr if necessary to round
COMPLETE SOLUTIONS FOR THE TWO IV FLOW RATE PROBLEMS IN SET
3. Order is for Keflex 500 mg IVPB q 6 hrs for a 19 kg child. The pharmacy sends you Keflin
500 mg in 50 mL NS. What would the flow rate be if it is delivered over 30 minutes with a
microdrip set? The safe child dosage is 80-160 mg/kg/day.
• Flow rate solution:
Is this a safe dosage?
• The safe dosage is 80-160 mg/kg/day.
• For this patient's weight of 19 kg, the safe dose would be 1520-3040 mg/day.
• The order is for 500 mg q 6 hr, which equals 2000 mg/day.
• The dose is safe.
COMPLETE SOLUTIONS FOR THE TWO IV FLOW RATE PROBLEMS IN SET
8. The order is for Dobutamine 250mg/250cc. The doctor wants the
medication delivered at 3.5 mcg/kg/min. The patient weighs 154 lbs.
Using an IV pump, determine the flow rate in mL/hr.
• If the IV pump cannot be calibrated to .1 mL, the answer should be
rounded to 15 mL/hr
If you answer 2 or more incorrect, go back and re-read the previous section and re-take the test.
Otherwise, proceed on to the next section.
DIMENSIONAL ANALYSIS FORMAT
• So what someone figured out is that you don't need formulas at all.
For every problem you can just take the factors associated with it and
arrange them so all the units you don't want cancel out. You're then
left with only the units you do want (the ones in your answer). This
process is fairly trivial, and with only slight attention to detail, you
always get the right answer, bing-bang-boom, every time.
DIMENTIONAL ANALYSIS
• The technique has been taught to students for
longer than anyone has been able to determine
and for the sole reason that students using it
make fewer mistakes. You pay attention to the
units of measure and if they're not canceling out
right, you know that you're doing something
wrong and that your answer is guaranteed to be
wrong.
DIMENTIONAL ANALYSIS
• While mistakes can still be made using any
technique, dimensional analysis does the best
job of minimizing them. The only fault lies in the
name. Perhaps the Math-Weenie-No-Brainer
technique would be more appropriate. At any
rate, give dimensional analysis a try.
DIMENSIONAL ANALYSIS
There are, as is often noted, more than one technique for doing med-math problems. If the one you
are using works for you, then don't read any further. If, however, med-math is still a bit of a struggle,
consider using the technique preferred by chemists, physicists, and engineers for decades called,
somewhat intimidatingly, "dimensional analysis" hereafter referred to as "DA."
Advantages include:
•
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•
•
•
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•
• One technique, not several
• Works with all problems
• No formulas to know, look up, or apply
• Problems are not solved piecemeal, but in one step
• You get to the right answer quicker—less error prone
• All calculations done at one time; no rounding errors
• You focus only on units of measure, not numbers, so math phobics can rejoice
• Stepwise approach makes solving almost all problems a virtual no-brainer
DIMENTIONAL ANALYSIS
• IV DRIP RATE USING DIMENTIONAL ANALYSIS
You are to administer lidocaine at a rate of 2 mg/min to a patient with an
arrhythmia. You have a vial of Lidocaine that contains 1 g in 5 mL. You also
carry a 250 mLbag of Normal Saline. Your administration set is a microdrip
with a rate of 60 gtts/mL. How many drops/min will you set your IV set to
drip?
• Step 1:Organize the information.
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Order:2 mg lidocaine/min IV
On Hand:1 g lidocaine/5 mL
Bag:250 mLNS
Admset:60 gtt/mL
• Looking for:gtt/min
DIMENSIONAL ANALYSIS
DIMENSIONAL ANALYSIS
Here is another step-by-step example of DA
The patient weighs 73 kg. The MD orders dopamine at 3 mcg/kg/min. The dopamine is mixed as 400 mg in 250 mL of solution. What
is the infusion rate in mL/hr?
• First you focus on what units of measure you want in the answer. In this problem we are kindly given "mL/hr." We are also given
that there are 400 mg dopamine in 250 mL (or 400 mg/250 mL), but also that in 250 mL there are 400 mg dopamine (or 250 mL/
400 mg). It is important to realize that factors can be turned over or inverted as needed.
• The other important bit to realize in order to do DA is that 3 mcg/kg/min can also be written as 3 mcg/(kg x min). This may seem a
little weird, but if asked to divide 1/4 by 2 you have 1/4/2. But dividing is the same as inverting and multiplying, so inverting 2 to
get 1/2 and multiplying you have 1/4 x 1/2, or 1/(4 x 2), or 1/8. Another example is acceleration, which is measured in ft/sec/sec.
This can be written as ft/(sec x sec) or, more familiarly, as ft/sec2.
• Since you want "mL" on top in your answer you won't go wrong starting with 250 mL/400 mg as a logical starting factor.
250 Ml
400 mg
You are now ready to play a game called "plug in
other factors to cancel out the units you don't
want until you end up with the units you do want."
Here goes:
The horizontal bar means "divide," as usual, and the vertical bars mean "multiply." If the units cancel out
properly, then your set up is correct and you can be quite sure the answer will be correct if you just
manage to punch the right keys on your calculator. The most twisted of med-math problems devised by
the most fiendish minds can be solved, bing-bang-boom, in this manner.
DIMENSIONAL ANALYSIS QUESTIONS
1. The patient is receiving nitroprusside at 23 mL/hr. The bag has 50
mg of nitroprusside in 250 mL of solution. The patient weighs 67 kg.
What dosage of nitroprusside in mcg/kg/min is the patient
receiving?
2. Your patient receives an order for procainamide at 3 mg/min. She
weighs 58 kg. The pharmacy has mixed 2 g of procainamide in 500
mL of solution. What is the infusion rate in mL/hr?
3. The patient weighs 117 pounds. Dopamine is running at 30 mL/hr.
There is 400 mg of dopamine in 500 mL of solution. How much
dopamine is the patient receiving in mcg/kg/min?
4. You need to start a continuous drip of amiodarone at 1 mg per
minute (by pump). The standard IV mixture is 450 mg in 250 mL.
ANSWER KEY FOR DIMENSIONAL ANALYSIS QUESTIONS
1.
2.
3.
Since you want kg, a unit of weight (mass) on the bottom, starting with pounds on the
bottom makes sense.
4.
First, think what units will be in the answer. Since you're using a pump, it's mL/hr.
If you get any answers wrong, re-read the previous section and re-take the test. Otherwise,
continue on.
PEDIATRIC DOSEAGE CALCULATIONS
• Order: Ceclor (cefaclor) 100 mg p.o. q8h is ordered for a child weighing 32 lb. The
recommended dosage is 20 to 40 mg/kg/day divided q8h. (a.) What is the child's
weight in kilograms? _____ (b.) What is the safe 24-hour dosage range for this
child? _____ (c.) Is the dosage ordered safe? (Prove mathematically.)
_______________ Explain your action:
• Order: Ceclor (cefaclor) 100 mg p.o. q8h is ordered for a child weighing 32 lb. The
recommended dosage is 20 to 40 mg/kg/day divided q8h. (a.) What is the child's
weight in kilograms? _____ (b.) What is the safe 24-hour dosage range for this
child? _____ (c.) Is the dosage ordered safe? (Prove mathematically.)
_______________ Explain your action:
• step #1
• Determine child's weight in kg (if given in pounds)
32 lb/ 2.2 = 14.5 kg
ALWAYS ROUND KILOGRAM WEIGHT TO THE NEAREST TENTH, NOT WHOLE
NUMBER
PEDIATRIC DOSEAGE CALCULATIONS
• step #2
• Determine the safe 24-hour dosage range
As stated in the problem "The recommended dosage is 20 to 40 mg/kg/day
divided q8h."
multiply low range (stated in problem) by weight in kg:
Low range = 20 so 20 x 14.5= 290
multiply high range (stated in problem) by weight in kg:
High range = 40 so 40 x 14.5= 580
ThereforeThe safe doseage range for this child is 290-580 mg PER DAY
PEDIATRIC DOSEAGE CALCULATIONS
• Determine the safe 24-hour dosage range As stated in the problem "The recommended dosage is 20 to 40
mg/kg/day divided q8h." multiply low range (stated in problem) by weight in kg: Low range = 20 so 20 x
14.5= 290 multiply high range (stated in problem) by weight in kg: High range = 40 so 40 x 14.5= 580
Therefore- The safe doseage range for this child is 290-580 mg PER DAY
• step #3
• So, is the doseage ordered safe?
Per the problem, the MD has ordered 100 mg q 8 hr = 300 mg per day
(q 8 hr= 3 times a day 100mg x 3 = 300mg PER DAY)
You determined the safe range to be 290-580 mg per day in the previous step
300 mg is within this range so,
YES, the ordered dose is safe for this child
• So, is the doseage ordered safe? Per the problem, the MD has ordered 100 mg q 8 hr = 300 mg per day (q 8
hr= 3 times a day 100mg x 3 = 300mg PER DAY) You determined the safe range to be 290-580 mg per day in
the previous step 300 mg is within this range so, YES, the ordered dose is safe for this child
• step #4
• Explain your action:
You would administer the dose as ordered because it has been determined to be safe
PEDIATRIC DOSEAGE QUESTIONS
1. A two year old toddler who weighs 30 pounds is diagnosed with otitis media (middle ear infection.) The
physician ordered the antibiotic amoxicillin 20 mg/kg PO q8h. The label reads 125 mg in 5 mL. How many
milliliters will you administer?
a. 20 mL
b. 5 mL
c. 1.75 mL
d. 10.9 mL
2. Claforan (cefotaxime) 50 mg/kg/d q8h via IVSS is ordered for a child who weighs 12 kg. The label reads 50
mg/mL. How many milliliters would you withdraw from the Claforan vial to add to the IVSS?
a. 1 mL
b. 4 mL
c. 6 mL
d. 12 mL
PEDIATRIC DOSEAGE QUESTIONS
3. Prescriber's order: Lanoxin (digoxin) 0.1 mg IM daily. The label reads 0.1 mg/mL injection. What is the dose in micrograms?
a. 0.1 mcg
b. 10 mcg
c. 0.001 mcg
d. 100 mcg
4. A child who weighs 100 pounds is admitted to the hospital for a repair of an inguinal hernia. The pre-op order is: Versed
(midazolam HCl) 0.08 mg/kg IM, 30 minutes before surgery. The label reads 5 mg/mL. How many milliliters will you administer?
a. 0.8 mL
b. 0.73 mL
c. 8 mL
d. 1.7 mL
ANSWER KEY
1.
2.
3.
4.
(d) 10.9 ml
(b) 4 ml
(d) 100 mcg
(b) 0.73 ml
If any answers were incorrect, go back and re-read the previous section
and re-take the test. Otherwise, proceed on to the next section.
Now perform these calculations using the format
that is easiest for you to follow
Show all work and submit to instructor for grading. This project will have a “Pass/Fail” grade. It is imperative
that you answer all questions correctly.
1.
A client is ordered 35 milligrams of Codeine phosphate by subcutaneous injection. 50 milligrams in 1 mL
of liquid for SC Injection is available. How many mL will you administer?_____
2.
A client is ordered 30 milligrams of Furosemide intravenously. 10 mg
available. How many mLs will you administer?______
3.
A client is ordered 50 mg of Aminophylline intravenously. 250 mg in 10 mL of liquid for IV Injection is
available. How many mLs will you administer?_____
4.
Calculate the drip rate for 100 mls of IV Fluids to be given over a half hour via an administration set which
delivers 10 drops/ml._____
5.
One litre of Normal Saline is ordered over 9 hours. The drop factor is 15. Calculate the number of drops
per minute._____
6.
Three litres of Lactated Ringer's is ordered over 12 hours. The drop factor is 15. The IV has been running
for 9 hours. 800 mls remain. How many drops per minute are needed so that the IV finishes in the
required time?______
in 1 mL of liquid for IV Injection is
Teacher Answer Key for Final Test.
1. 0.7 mls
2. 3 mls
3. 2 mls
4. 33 gtts/min
5. 28 gtts/min
6. 67 gtts/min