CONTENTS
Page_
Introduction
Unit Conversions: Exercise: Fill in the missing information
PART 1: Exercises: Calculate an Intermittent Dose
Calculate an Intermittent Dose of a Solid Formulation
Calculate an Intermittent Dose of a Liquid Formulation
Calculate an Intermittent Dose Adjusted to the Patient’s Body Weight
PART 2: Exercises: Calculate a Continuous Dose (administered by intravenous infusion)
Calculate the Corresponding Infusion Rate for a Prescribed Dose
2
3
4
4
5
8
9
9
Solutions to the Exercises
Unit Conversions Exercise: Fill in the missing information
PART 1 Exercises: 1 … 18
PART 2 Exercises: 1… 8
11
11
11
24
Appendix: Medication Errors
31
1
INTRODUCTION
You are being offered this Medication Calculation Module because clinical instructors are
concerned that students are struggling to translate the amount of drug prescribed, into the
corresponding amount of an available formulation of that drug that should be administered to the
patient.
A medication error is perhaps the most frequent, swift and subtle act of negligence by which
nurses pose harm to patients. Medication errors are widely recognized as a big complicated
patient safety problem that can’t be solved with a calculator alone (read some of the background
material included as an appendix if you’re interested). Only a fraction of medication errors stem
directly from mathematical errors.
Giving the wrong drug has nothing to do with math, but giving the wrong dose might. A drug
dose calculation is a principled procedure. Proficiency in mathematics does not ensure
proficiency in calculating a drug dose, but there is a link. When you become familiar with the
concepts that link a mathematical calculation with giving a correct dose, your patients and career
will be better for it.
There are two kinds of dose calculations, depending on whether a drug is delivered in
intermittent doses or administered continuously:
1. Most drugs are administered in discrete doses at intermittent times (i.e., once-daily,
twice-daily, every six hours…). The time between each dose is called a dose interval.
Most drugs come in solid or liquid forms. Sometimes a drug that will be given in
liquid form is supplied as a solid, and thus needs to be reconstituted (ie, dissolved or
suspended in a diluent). Directions for reconstitution will always be found in the
package insert. We will begin with exercises on how to deliver a correct intermittent
dose of a solid or liquid formulation.
2. Some drugs are administered continuously, often by intravenous infusion of a drug in
solution. Accordingly, there will be a second set of exercises on how to initiate and
adjust a continuously administered drug.
2
UNIT CONVERSIONS
WARNING!!! Analogies help some to relate a new concept with familiar concepts, but for others, analogies
conversely add confusion. The same is true for background trivia: for some it inspires interest, for others it’s too
much information! Don’t read the green stuff if it will only confuse you.
Concept: Money is a currency we’re familiar with. Money is expressed in units such as dollars {$(Canadian, US, Australian)}, Pounds {£}, Yen
{¥}, or Euros {€}. Money can be issued as bank notes or coins of various denominations (i.e., a fifty dollar bill or a hundred dollar bill). A $50
bank note is about the same size and weight as a $100 bank note.
“Dose” is a currency. It is almost always expressed as “mass units” (e.g., grams {g}, milligrams {mg}, micrograms {μg}). A few older drugs
such as penicillin, heparin and insulin are still prescribed in “conventional units”. Both kinds of units represent an amount of drug. The
recommended dose range ties an amount of drug to its expected biological effects. Instead of bank notes or coins, drugs are issued in solid or
liquid formulations such as tablets, capsules or vials. Instead of denominations, solid drug formulations are issued in various strengths such as a
50 mg tablet or a 100 mg tablet. Liquid drug formulations may be issued or reconstituted in various concentrations such as 50 mg per mL or 100
mg per mL. Whereas solid formulations are issued as “units per capsule” or “units per tablet”, liquid formulation units have a volume of liquid as
a denominator that defines concentration. The math is simply to ‘purchase’ the prescribed dose using available formulations as currency, but first
ensure that the prescription and the formulation on hand are converted to the same units.
You wouldn’t want to pay $50 for something that costs 50 cents, because that’s a hundred times too
much! You shouldn’t give 50 milligrams of drug to a patient that was prescribed 50 micrograms; that’s a
thousand times too much! Try filling in the “?”s in the tables below. If you are having trouble with
metric conversions and symbols, you ought to make yourself a pocket card and carry it with you for
reference until you’ve caught on to the system.
1000
0.1
0.01
0.001
0.000001
1000/1
1/10
1/100
1/1000
1/1000000
103
a thousand
kilo
10-1
one tenth
deci
10-2 one hundredth centi
10-3 one thousandth milli
10-6
one millionth micro
Fill in the missing information:
kilogram (kg) =
____?___grams
gram (g) = 1000 ___?
milligram (mg) = 0.001 ____?
microgram (μg) = 0.000001____?
1000000 _____?
______?____ kg
1000_____?
0.001_____?
10-9___ ?
106____?
10-6___?
10-6___?
Fill in the missing information:
one litre (L) = ____?____ mL 1000000 ____?
75 milliliters (mL) = ____?____ L
75000 ____?
500 microlitres (μL) = 5 × 10-4_____? _____?____ mL
The "insulin unit" dates back to when preparations of the hormone extracted from porcine or bovine pancreas were impure and it was necessary to
standardize batches so that one unit of insulin was the amount required to reduce blood glucose in a fasting rabbit to 45 mg/dL (2.5 mmol/L). In
most countries, human insulin is supplied in solution or suspension of 100 U/mL, which is about 3.6 mg/mL, which is between 25 and 30 U/mg.
The biological activity of heparin varies slightly between commercial preparations, but is around 150 USP units/mg. One USP unit of heparin is
the amount that prevents 1.0 mL of citrated sheep plasma from clotting for 1 hour after the addition of 0.2 mL of 1% calcium chloride.
3
Part 1: How to deliver a correct intermittent dose of a solid or liquid formulation:
Try these exercises on how to deliver a correct intermittent dose of a solid or liquid formulation,
starting with solid formulations that have been prescribed in the same units as the strengths of the
formulation on hand:
1. Warfarin tablets are scored so they can be split in half. Supplies of both 4 mg tablets and
5 mg tablets have been issued to treat your patient who has chronic atrial fibrillation. He
is initially prescribed warfarin 10 mg p.o. once-daily. How will you administer that
dose? [HINT: an item priced at $10 can be purchased with two $5 bills, but drug calculations require exact change, meaning that
you can’t give the patient three 4’s and expect him to spit out 2 mg.]
•
His target INR is 2.5, but after 48 hrs on 10 mg/day his INR is actually 4.5. In
response, the prescription is to skip the next dose, then resume warfarin at 7 mg p.o.
once-daily. From a supply of 4 mg and 5 mg tablets, how will you administer a 7 mg
oral dose?
•
Within 36 hours of adjusting the dose, his INR is now 1.8, so his dose is increased to
9 mg daily. From a supply of 4 mg and 5 mg tablets, how will you administer a 9 mg
oral dose?
[Warfarin is the principal oral anticoagulant prescribed for most patients at substantial risk for arterial and venous thromboembolic complications, but it has a narrow therapeutic index: a little too much warfarin will put the patient at excess risk of non
compressible hæmorrhage (e.g., intracranial or GI bleed), but not enough warfarin leaves the patient at risk of a thromboembolic
catastrophe such as an ischemic stroke. Warfarin is inconvenient because it interacts with numerous foods and drugs, thus
requires dose adjustments in relation to close laboratory monitoring of fluctuations in a patient’s prothrombin times (PT, now
most often standardized as international normalized ratio {INR}).]
2. Digoxin 0.125 mg p.o. is prescribed to a patient with a fast ventricular response to atrial
flutter. You have digoxin 0.25 mg tablets on hand.
How many tablet(s) should you give to the patient?
3. Diazepam 25 mg p.o. is prescribed. You have diazepam 10 mg tablets on hand. How
many tablet(s) should you give to the patient?
[If you don’t know why diazepam is being prescribed (e.g., manage anxiety, pre-anaesthetic, raise convulsive threshold, skeletal
muscle relaxant, and mitigate ethanol withdrawal symptoms) you won’t know how to assess the response. It will likely make the
patient drowsy, and sometimes that’s the desired effect. If not, it is an expected side-effect.]
Be careful with this next question. The units in which the drug is prescribed are not the same
units as the formulation on hand is labeled.
4. An woman with bacterial otitis media is prescribed sulfisoxazole 1 g p.o. You have 500
mg tablets on hand.
How many tablet(s) should you give to the patient?
4
Now try calculating a liquid dose:
5. A fellow with intractable hiccups is prescribed chlorpromazine 25 mg IM. You have an
unopened 10 mL vial of solution for injection labeled 25 mg/mL.
What amount of chlorpromazine solution should you prepare to inject?
6. An ampoule of “Drug A” is labeled, 100 mg/10 mL. The patient is to receive a 15 mg
dose. What volume should you administer?
7. “Drug B” is supplied in 2 mL ampoules labeled 100 mg/mL IM STAT. If your patient is
to receive a 200 mg dose, what volume should you inject?
8. A casualty officer orders “Gravol 30 mg IM STAT” for an 8 year old that is puking in the
ER. The department doesn’t stock that brand. On hand are Novo-Dimenate®
(dimenhydrinate) 50 mg/2mL and PMS-Diphenhydramine (diphenhydramine) 50 mg/mL.
Which drug should you give, and what volume of that drug should you inject?
Regarding the use of brand names in general: The names of drugs are a problem. Each and every drug has a single
generic name that is common to USA, Canada, the EU and Japan. Generic drug nomenclature is somewhat systematic
in relation to drug class: (e.g., -statins, -glitazones, -triptans, -prils, -olols…). But most drugs eventually acquire
multiple brand names that vary internationally, and are catchy sounding but sometimes confusingly similar sounding.
Solution: educational material should emphasize generic names and de-emphasize brand names. Examples: Generic
Name: amoxacillin Brand Names: CANADA: Amoxil, Apo-Amoxi, Gen-Amoxicillin, Novamoxin, Nu-Amoxi, plus
combinations; ELSEWHERE: Agram, Alfamox, Almodan, Amodex, Amoxidal, Amoxidin, Amoxillat, Amoxypen,
Ardine, AX250, Clamoxyl, Cuxacillin, Dura AX, Flemoxin, Hiconcil, Ibiamox, Larocin, Larotid, Moxal, Moxaline,
Neamoxyl, Polymox, Raylina, Robamox, Sigamopen, Silamox, Trimox, Uro-Clamoxyl, Ultimox, Zamocillin; Generic
Name: metoprolol Brand Names: CANADA: Lopressor, Betaloc, Dom-Metoprolol, Apo-Metoprolol, NovoMetoprolol, Nu-metop, PMS-metoprolol, Gen-metoprolol… Health professionals should avoid behaviours that reflect
or might be construed to reflect conflicts of interest. Reference to brand names raises suspicion that treatment
decisions may be unduly influenced by marketing forces rather than unbiased clinical scientific evidence and sound
clinical judgment.
9. Morphine and atropine are compatible in the same syringe and may be given together as a
single injection. A physician orders morphine 4 mg IV and atropine 0.6 mg IV to be
given together to a man with symptomatic bradycardia. In stock, morphine sulphate is
available in ampoules containing 5 mg/mL, 10 mg/mL and 15 mg/mL. Atropine sulfate
is available in ampoules of 0.4 mg/mL or 0.6 mg/mL. Select the most appropriate size
syringe: 1 mL, 3 mL or 5 mL.
Which stock concentration of morphine do you choose?
What volume of that concentration yields a 4 mg dose?
Which stock concentration of atropine do you choose?
What volume of that concentration yields a 4 mg dose?
What is the total volume (i.e., both drugs) for injection?
What size of syringe would be appropriate for that volume?
5
10. A preoperative medication order reads: Give morphine 12 mg IM, atropine 0.4 mg IM
and prochlorperazine 7.5 mg IM one hour prior to induction. In stock, morphine sulphate
is available in ampoules containing 5 mg/mL, 10 mg/mL and 15 mg/mL. Atropine
sulfate is available in ampoules of 0.4 mg/mL or 0.6 mg/mL. Prochlorperazine is
available in 10 mg/2 mL ampoules. Select the most appropriate size syringe: 1 mL, 3 mL
or 5 mL.
Which stock concentration of morphine do you choose?
What volume of that concentration yields a 4 mg dose?
Which stock concentration of atropine do you choose?
What volume of that concentration yields a 4 mg dose?
What volume of prochlorperazine 10 mg/2 mL yields a 4 mg dose?
What is the total volume (i.e., both drugs) for injection?
What size of syringe would be appropriate for that volume?
It may be of interest that the American Society of Anesthesiologists Task Force Practice Guidelines for Preoperative
Fasting and the Use of Pharmacologic Agents to Reduce the Risk of Pulmonary Aspiration: Application to Healthy
Patients Undergoing Elective Procedures do not recommend routine use of gastric acid reducing agents, antiemetics or
antimuscarinic drugs intended to minimize the risk of pulmonary aspiration, because there is insufficient evidence that
these medications actually have any effect on the incidence or severity of pulmonary aspiration.
11. You are caring for a woman with threatened premature delivery at 31 weeks gestation.
An order is given to administer “betamethasone 12 mg IM STAT, and repeat in 24
hours”. Betamethasone is available in 1 mL vials containing 4 mg/mL.
How many vials will you need to open to administer the prescribed dose?
What volume of that solution will you prepare to inject?
12. The physician orders 5 International Units (IU) of oxytocin administered with the
delivery of the anterior shoulder. The vial contains 1 mL of solution containing 10 IU of
oxytocin.
What volume of oxytocin solution will you ‘draw up’?
13. Following birth, the physician orders “Vitamin K 1 mg I.M.” for the infant. Vitamin K is
supplied in 1 mL vials containing 10 mg/mL.
What volume of that solution will you prepare to administer by intramuscular injection?
What size of syringe (0.5 mL, 1 mL, 3 mL) would be least appropriate for this injection?
6
14. A woman in early labor is prescribed Demerol 150 mg with Gravol 25 mg IM.
You have the following concentrations of these drugs available to you:
Demerol® 50 mg/mL in a 1 mL vial
Demerol® 75 mg/mL in a 1 mL vial
Demerol® 100 mg/mL in a 1 mL vial
Gravol® 50 mg/mL in a 1 mL vial
Which stock concentration of Demerol® do you choose? Explain.
What volume of that concentration yields a 150 mg dose?
What volume of the Gravol® concentration yields a 25 mg dose?
What is the total volume (i.e., both drugs) for injection?
Is that an appropriate volume for IM injection?
Regarding the use of meperidine (aka, pethidine) [Demerol®] as an example: Although it is still used frequently on many
labor units, there may be better alternatives. The choice is controversial. The American Society for Gastrointestinal Endoscopy
suggested that meperidine might be preferred over morphine, on the basis of evidence that morphine crosses the fetal blood-brain
barrier more rapidly. However, both drugs readily enter the fetal brain and there is no evidence cited in the guideline that a
differential rate of fetal CNS penetration after maternal administration of either meperidine or morphine is of any clinical importance.
Other jurisdictions continue to describe meperidine as a choice for early labor analgesia.
ƒ
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Mander R. Analgesia and anaesthesia in childbirth: obscurantism and obfuscation. J Advanced Nursing 1998;28:86-93.
Faucher MA and Brucker MC. Intrapartum Pain: Pharmacologic Management. JOGNN 2000;29:169-80.
ISMP Canada Safety Bulletin. Meperidine (Demerol) Medication Safety Issues. Spring 2005. accessed online 17DEC05
@ http://www.ismp-canada.org/download/CACCN-Spring05.pdf
Hale TW. Drug therapy and breastfeeding: antibiotics, analgesics, and other medications.
NeoReviews. 2005;6(6):e233-e240.
NSW-TAG. Use of pethidien for pain management in the emergency department. August 2004
ASGE. Guidelines for endoscopy in pregnant and lactating women. 2005;61(3):357-362.
Nova Scotia Perinatal Program: http://www.rcp.gov.bc.ca/guidelines/Master[1].OB4.PainManage.May2000.pdf
7
What if the dose is to be adjusted to the size of the patient?
To get the most benefit with the least side effects, it may be useful to normalize (i.e., tailor) the
dose of a drug to the volume of the body compartment into which the drug distributes, which
often corresponds well enough with the patient’s total body weight (or perhaps lean body weight, estimated
bone mass or body surface area). The general idea is to give bigger people bigger doses, and smaller
people proportionally smaller doses, so they all achieve the same tissue levels following a dose
that is the right size for them. It is especially common to adjust pædiatric doses according to a
child’s weight. In that case, the prescription might read, “Drug-C syrup 2 mg/kg p.o. q4h”. It
means, first determine how much the child weighs, then give 2 milligrams of Drug-C for every
kilogram of body weight. If the child weighs 14 kg, the dose would be 14 × 2 mg = 28 mg.
Try to determine the correct volume of a drug formulation that you should prepare to give to a
patient who has been prescribed these weight-adjusted doses:
15. A 5 year old asthma patient is prescribed theophylline elixir 3 mg per kg body weight p.o.
q6h. She weighs 15 kg.
What dose of theophylline elixir does that work out to?
How much theophylline would she get per day?
Theophylline elixir comes in a 480 mL bottle containing 80 mg/15 mL.
What volume of elixir will provide the prescribed dose?
16. A 4 year old child has “oxacillin 50 mg/kg/day in divided doses infuse IV at 6 hour
intervals; not to exceed 1.5 g/day”. Oxacillin comes pre-mixed in vials of two different
sizes containing either 1 g or 2 g of oxacillin in 50 mL of iso-osmotic dextrose solution.
This child weighs 12.5 kg.
How much oxacillin should this child receive on a daily basis?
Does that exceed the prescribed daily limit?
Dividing the total daily dose into equal doses, how many milligrams should be given every 6
hours?
If you choose to draw a dose from the 1g/50 mL concentration, what is the smallest syringe you
could use to draw up the dose: will you need a 1 mL, 3 mL, 5 mL, or a 10 mL syringe?
17. A 4 month old child is prescribed cefpodoxime oral suspension 4 mg/kg p.o. q12h. The
child weighs 25 kg. The bottle is reconstituted to a 50 mg/mL concentration of lemon
crème flavored cefpodoxime suspension.
How much of that suspension should you give for each dose?
18. Remember the woman that was prescribed Demerol®150 mg during early labor in
question #14? Following birth three hours later, her 3500 g infant has respiratory
8
depression. The resuscitation team calls for naloxone hydrochloride [Narcan®] 0.1
mg/kg IV. Naloxone hydrochloride comes in 1 mL vials that contain 0.4 mg/mL.
What is the correct dose in mg?
How many millilitres of the 0.4 mg/mL solution corresponds to that dose?
Part 2: exercises on how to initiate and adjust a continuously administered drug:
1. Your patient is receiving a continuous heparin infusion. The intravenous solution
contains 10000 units of heparin in 500 mL of 5% dextrose (D5W). The patient is to
receive 1800 units of heparin per hour.
What volume of the heparin solution must infuse to provide that dose of heparin in one hour?
The infusion pump rate has to be programmed in mL/hr, so what rate will you select?
At that rate, how long will a 500 mL bag of heparin in D5W last?
2. A patient’s daily fluid balance is being supplemented by constant intravenous infusion of
1500 mL/24 hours of 5% dextrose in 0.9% sodium chloride solution (D5S), using a 60
drops = 1 mL infusion set.
At how many drops per minute should you regulate the iv to deliver 1500 mL/24 hrs?
3. The patient you are caring for is a type 1 diabetic in active labor. She has a continuous
insulin infusion prescribed according to a sliding scale (i.e., you adjust the infusion rate,
and thus titrate her insulin dose according to her capillary blood glucose response). The
intravenous solution contains Humulin R 50 units/500 mL of 0.9% sodium chloride
(normal saline):
Blood glucose (mmol/L) Humulin R (units/hour)
< 4 mmol/L
Hold insulin
< 6 mmol/L
1 unit/hr
< 8 mmol/L
2 units/hr
3 units/hr
≥ 8 mmol/L
You obtain a capillary blood glucose reading of 6.9 mmol/L.
What rate in mL/hr will you program the pump to deliver the corresponding insulin dose
rate?
[Insulin is a critical dose hormone that has been associated with a high rate of serious adverse events worldwide. Several patient
safety advocates recommend that institutions institute policy to establish 1 unit/mL as the standard concentration of insulin for
continuous infusion, and exceptions should be clearly flagged. Thus, an exception is represented in the above example: 0.1 unit/mL
rather than 1 unit/mL However, 1 unit/mL is a rather high concentration, and safe delivery implies use of infusion equipment
designed to accurately deliver small hourly volumes. If an empty bag of the more dilute 0.1 unit/mL concentration was replaced with
a new bag of 1 unit/mL and proceeded to run at the same rate, the woman would receive 20 units per hour rather than 2 units per hour.
Her mental and physical status would deteriorate and she might seizure.]
This next question will challenge your skill with very potent drugs that are administered in doses
measured in uncommonly small units.
4. You are caring for a woman who will undergo an attempt to induce labor with IV
oxytocin. You initiate a primary IV line of normal saline, and are now preparing the
9
oxytocin solution to run as a secondary “piggyback” infusion. Oxytocin is supplied in
vials containing 10 international units (IU)/mL. One mL of oxytocin 10 IU/mL is added
to a 500 mL bag of normal saline (assume a final concentration of 10 IU/500mL [rather
than 10 IU/501 mL]). What is the resulting oxytocin concentration expressed in
milliunits/mL? If that concentration of oxytocin is infused at a rate of 1 mL/hour, how many
milliunits/minute would be infused? If the infusion is to be initiated at 0.66 milliunits/minute, at
what rate in mL/hour should you program the infusion pump? If the induction protocol is to
increase the oxytocin infusion rate by 3 milliunits every 30 minutes, what will be the incremental
change in mL/hour pump rate will you make every 30 minutes?
5. Imagine that you begin a shift on a hospital inpatient unit. One of the patients has an
insulin drip that according to the last capillary blood glucose reading should be running
at 5.5 insulin units per hour. The reservoir is labeled, “Humulin R 10 units in 100 mL of
0.9% saline”. The infusion pump is set at 45 mL/hr. Assuming that the labeled
concentration is correct, what rate should the infusion pump be set at to infuse 5.5 units per
hour?
[If you patient appears stable, the very next thing you’ll probably want to do is another capillary blood glucose reading, right?]
6. If you are to infuse ranitidine 50 mg in 10 mL IV over 15 minutes, at what rate should the
ranitidine solution be infused if the infusion pump must be programmed in milliliters per hour?
7. A patient with acute coronary syndrome weighs 67 kg. Following a 180 μg bolus, she is
receiving eptifibatide [Integrilin®] by continuous infusion of 2 μg/kg/min. If the
eptifibatide concentration for infusion is 75 mg in 100 mL of 0.9% sodium chloride
solution, what rate should the drug solution be infused if the infusion pump must be
programmed in milliliters per hour?
8. You are to start an intravenous infusion of 0.9% sodium chloride containing potassium
chloride 20 mEq/L, and maintain the infusion at 125 mL/hr.
If you use a macrodrip infusion set (15 gtts/mL), at how many drops per minute should
this infusion be maintained?
If you use a microdrip infusion set (60 gtts/mL), at how many drops per minute should
this infusion be maintained?
What dose of KCl will the patient be getting: each hour? each day?
10
Solutions to the problems:
Unit Conversion Exercise
Fill in the missing information:
kilogram (kg) =
_1000_grams
gram (g) = 1000 mg
milligram (mg) = 0.001 g
microgram (μg) = 0.000001 g
Fill in the missing information:
one litre (L) = 1000 mL
75 milliliters (mL) = 0.075 L
500 microlitres (μL) = 5 × 10-4 L
1000000 mg
0.001 kg
1000 μg
0.001mg
10-9 μg
106 μg
10-6 kg
10-6 g
1000000 μL
75000 μL
0.5 mL
Part 1: Exercises on how to deliver a correct intermittent dose of a solid or liquid formulation.
Important math skill set up and rearrange a ‘cross-multiply’ equation:
1. Warfarin tablets are scored so they can be split in half. Supplies of both 4 mg tablets and
5 mg tablets have been issued to treat your patient who has chronic atrial fibrillation. He
is initially prescribed warfarin 10 mg p.o. once-daily. How will you administer that
dose? The “prescribed dose” is 10 mg.
Here’s the math:
(1) 10 mg dose = 4 mg formulation or (2) 10 mg dose = 5 mg formulation
? tablets
1 tablet
? tablets
1 tablet
{this is where you rearrange the equation by cross-multipication:
the top number (numerator) on one side of the ‘equal sign’
times the bottom number (denominator) on the other}
4 × ? = 10 × 1
5 × ? = 10 × 1
{rearrange according to another rule: if a number is multiplied on one side of the ‘equal sign’,
it is the same as dividing the other side of the ‘equal sign’ by that number}
? = _10_
4
? = 2.5 of the 4 mg tablets
? = _10_
5
? = 2 of the 5 mg tablets
So, there are two reasonable answers:
(1) 10 mg dose divided by 4 mg tablets (i.e., 10/4) equals 2.5 tablets.
(2) 10 mg dose divided by 5 mg tablets (i.e., 10/5) equals 2 tablets
The solution that avoids splitting tablets and represents the lowest pill burden
administer two of the 5 mg tablets.
is to
11
(Part 1, question #1 – continued):
•
His target INR is 2.5x, but after 48 hrs on 10 mg/day his INR is actually 4.5x. In
response, the prescription is to skip the next dose, then resume warfarin at 7 mg p.o.
once-daily. From a supply of 4 mg and 5 mg tablets, how will you administer a 7 mg
oral dose? The “prescribed dose” is 7 mg.
Let’s solve this one like a building set (e.g., tinker toy) in which you have 4 types of
pieces, and you can use as many of each as you need to build a dose.
Desired Dose Combinations of Tablets
2 mg
2.5 mg
4 mg
4.5 mg
5 mg
5.5 mg
6 mg
6.5 mg
7 mg
7.5 mg
8 mg
8.5 mg
9 mg
9.5 mg
10 mg
10.5 mg
11 mg
11.5 mg
12 mg
12.5 mg
14 mg
15 mg
Half of a 4 mg tablet
Half of a 5 mg tablet
One 4 mg tablet
Half of a 4 mg tablet + Half of a 5 mg tablet
One 5 mg tablet
One 4 mg tablet + Half of a 5 mg tablet
One 4 mg tablet + Half of a 4 mg tablet
One 4 mg tablet + Half of a 5 mg tablet
One 5 mg tablet + Half of a 4 mg tablet
One 5 mg tablet + Half of a 5 mg tablet
Two 4 mg tablets
One 4 mg tablet + Half of a 5 mg tablet + Half of a 4 mg tablet
One 5 mg tablet + One 4 mg tablet
One 5 mg tablet + Half of a 5 mg tablet + Half of a 4 mg tablet
Two 5 mg tablets
Two 4 mg tablets + Half of a 5 mg tablet
One 5 mg tablet + One 4 mg tablet + Half of a 4 mg tablet
One 5 mg tablet + One 4 mg tablet + Half of a 5 mg tablet
Three 4 mg tablets or Two 5 mg tablets + Half of a 4 mg tablet
Two 5 mg tablets + Half of a 5 mg tablet
Two 5 mg tablets + One 4 mg tablet
Three 5 mg tablets
The only reasonable way to build a 7 mg dose from the formulations on hand, is to
give one 5 mg tablet plus half of a 4 mg tablet (i.e., 5 mg + 2 mg = 7 mg).
•
Within 36 hours of adjusting the dose, his INR is now 1.8x, so his dose is increased to
9 mg daily. From a supply of 4 mg and 5 mg tablets, how will you administer a 9 mg
oral dose? Give one 5 mg tablet + one 4 mg tablet
(5 mg + 4 mg = 9 mg).
[Some will recognize that this is a permutation problem. If you have calculus, you don’t need to
construct the table, and probably don’t need this module.]
[Warfarin is the principal oral anticoagulant prescribed for most patients at substantial risk for arterial and venous thromboembolic complications, but it has a narrow therapeutic index: a little too much warfarin will put the patient at excess risk of non
compressible hæmorrhage (e.g., intracranial or GI bleed), but not enough warfarin leaves the patient at risk of a thromboembolic
catastrophe such as an ischemic stroke. Warfarin is inconvenient because it interacts with numerous foods and drugs, thus
requires dose adjustments in relation to close laboratory monitoring of fluctuations in a patient’s prothrombin times (PT, now
most often standardized as international normalized ratio {INR}).]
12
2. Digoxin 0.125 mg p.o. is prescribed to a patient with a fast ventricular response to atrial
flutter. You have digoxin 0.25 mg tablets on hand.
How many tablet(s) should you give to the patient? Prescribed dose is 0.125 mg, and we
know there’s 0.25 mg of digoxin in one tablet.
This is where you set up and rearrange a ‘cross-multiply’ equation:
0.25 mg
=
1 tablet(s)
0.125 mg
? tablet(s)
then rearrange,
0.25 × ? = 0.125 × 1
then rearrange again,
? = 0.125 = 0.5 tablet(s)
0.25
So a 0.125 mg dose will be half of a 0.25 mg tablet
3. Diazepam 25 mg p.o. is prescribed. You have diazepam 10 mg tablets on hand. How
many tablet(s) should you give to the patient? The “prescribed dose” is 25 mg, and we
know there’s 10 mg of diazepam in one tablet.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10 mg
=
1 tablet(s)
25 mg
? tablet(s)
then rearrange,
10 × ? = 25 × 1
then rearrange again,
? = 25 = 2.5 tablet(s)
10
So a 25 mg dose will be administered as two and a half 10 mg tablets
[If you don’t know why diazepam is being prescribed (e.g., manage anxiety, pre-anaesthetic, raise convulsive threshold, skeletal
muscle relaxant, and mitigate ethanol withdrawal symptoms) you won’t know how to assess the response. It will likely make the
patient drowsy, and sometimes that’s the desired effect. If not, it is an expected side-effect.]
13
Be careful with this next question. The units in which the drug is prescribed are not the same
units as the formulation on hand is labeled.
4. An woman with bacterial otitis media is prescribed sulfisoxazole 1 g p.o. You have 500
mg tablets on hand.
How many tablet(s) should you give to the patient? The “prescribed dose” is 1 gram
(i.e., 1000 mg), and we know there’s 500 mg (i.e., 0.5 g) of sulfisoxazole in one tablet.
Decide which units you want to work with (both are used in the following example):
Here’s the math:
(1) 1000 mg dose = 500 mg or (2) 1 g dose = __0.5 g
? tablets
1 tablet
? tablets
1 tablet
{this is where you rearrange the equation by cross-multipication:
the top number (numerator) on one side of the ‘equal sign’
times the bottom number (denominator) on the other}
500 × ? = 1000 × 1
0.5 × ? = 1 × 1
{rearrange according to another rule: if a number is multiplied on one side of the ‘equal sign’,
it is the same as dividing the other side of the ‘equal sign’ by that number}
? = _1000_
500
? = 2 of the 500 mg tablets
? = _1_
0.5
? = 2 of the 0.5 g tablets
The supply is labeled 500 mg, so if you chose to work the equation in grams, you have to conclude that 0.5 g = 500 mg.
14
Now try calculating a liquid dose:
5. A fellow with intractable hiccups is prescribed chlorpromazine 25 mg IM. You have an
unopened 10 mL vial of solution for injection labeled 25 mg/mL.
What amount of chlorpromazine solution should you prepare to inject?
The “prescribed dose” is 25 mg, and we know there’s 25 mg of chlorpromazine in one
mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
25 mg
1 mL
=
25 mg
? mL
then rearrange,
25 × ? = 25 × 1
then rearrange again,
? = 25 = 1 mL
25
So a 25 mg dose will be administered as a 1 mL injection of a 25 mg/mL solution.
6. An ampoule of “Drug A” is labeled, 100 mg/10 mL. The patient is to receive a 15 mg
dose. What volume should you administer?
The “prescribed dose” is 15 mg, and we know there’s 100 mg of “Drug A” in 10 mL of
solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
100 mg
10 mL
=
15 mg
? mL
then rearrange,
100 × ? = 15 × 10
then rearrange again,
? = 150 = 1.5 mL
100
So a 15 mg dose will be administered as a 1.5 mL injection of a 100 mg/10 mL solution.
7. “Drug B” is supplied in 2 mL ampoules labeled 100 mg/mL IM STAT. If your patient is
to receive a 200 mg dose, what volume should you inject?
The “prescribed dose” is 200 mg, and we know there’s 100 mg of “Drug B” in 1 mL of
solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
100 mg
1 mL
=
200 mg
? mL
then rearrange,
100 × ? = 200 × 1
then rearrange again,
? = 200 = 2 mL
100
So a 200 mg dose will be administered as a 2 mL injection of a 100 mg/mL solution.
15
8. A casualty officer orders “Gravol 30 mg IM STAT” for an 8 year old that is puking in the
ER. The department doesn’t stock that brand. On hand are Novo-Dimenate®
(dimenhydrinate) 50 mg/2mL and PMS-Diphenhydramine (diphenhydramine) 50 mg/mL.
Which drug should you give, and what volume of that drug should you inject?
The “prescribed dose” is 30 mg, and we know there’s 50 mg of dimenhydrinate
[Gravol®] in 2 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
50 mg
2 mL
=
30 mg
? mL
then rearrange,
50 × ? = 30 × 2
then rearrange again,
? = 60 = 1.2 mL
50
So a 30 mg dose will be administered as a 1.2 mL injection of a 50 mg/2 mL solution.
Regarding the use of brand names in general: The names of drugs are a problem. Each and every drug has a single
generic name that is common to USA, Canada, the EU and Japan. Generic drug nomenclature is somewhat systematic
in relation to drug class: (e.g., -statins, -glitazones, -triptans, -prils, -olols…). But most drugs eventually acquire
multiple brand names that vary internationally, and are catchy sounding but sometimes confusingly similar sounding.
Solution: educational material should emphasize generic names and de-emphasize brand names. Examples: Generic
Name: amoxacillin Brand Names: CANADA: Amoxil, Apo-Amoxi, Gen-Amoxicillin, Novamoxin, Nu-Amoxi, plus
combinations; ELSEWHERE: Agram, Alfamox, Almodan, Amodex, Amoxidal, Amoxidin, Amoxillat, Amoxypen,
Ardine, AX250, Clamoxyl, Cuxacillin, Dura AX, Flemoxin, Hiconcil, Ibiamox, Larocin, Larotid, Moxal, Moxaline,
Neamoxyl, Polymox, Raylina, Robamox, Sigamopen, Silamox, Trimox, Uro-Clamoxyl, Ultimox, Zamocillin; Generic
Name: metoprolol Brand Names: CANADA: Lopressor, Betaloc, Dom-Metoprolol, Apo-Metoprolol, NovoMetoprolol, Nu-metop, PMS-metoprolol, Gen-metoprolol… Health professionals should avoid behaviours that reflect
or might be construed to reflect conflicts of interest. Reference to brand names raises suspicion that treatment
decisions may be unduly influenced by marketing forces rather than unbiased clinical scientific evidence and sound
clinical judgment.
16
9. Morphine and atropine are compatible in the same syringe and may be given together as a
single injection. A physician orders morphine 4 mg IV and atropine 0.6 mg IV to be
given together to a man with symptomatic bradycardia. In stock, morphine sulphate is
available in ampoules containing 5 mg/mL, 10 mg/mL and 15 mg/mL. Atropine sulfate
is available in ampoules of 0.4 mg/mL or 0.6 mg/mL. Select the most appropriate size
syringe: 1 mL, 3 mL or 5 mL.
Which stock concentration of morphine do you choose?
Should we try to minimize the volume for injection? The upper limit of acceptable volume that may be injected into
various tissue sites will be supported by opinions and policies at the least, but it would be interesting to review the quality
of evidence available to define clinically important limits. On a pharmacological basis, it stands to reason that the optimal
volume could vary with the nature of the solution as well as the physical size and health of the muscular injection site.
Let’s choose the middle one: morphine 10 mg/mL.
What volume of that concentration yields a 4 mg dose?
The “prescribed dose” is 4 mg, and we know there’s 10 mg of morphine in 1 mL
of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10 mg
1 mL
=
4 mg
? mL
then rearrange,
10 × ? = 4 × 1
then rearrange again,
? = _4_ = 0.4 mL
10
So a 4 mg dose of morphine will be administered as a 0.4 mL injection of a 10
mg/mL solution.
Which stock concentration of atropine do you choose?
Let’s use the 0.6 mg/mL solution.
What volume of that concentration yields a 4 mg dose?
The “prescribed dose” is 0.6 mg, and we know there’s 0.6 mg of atropine in 1 mL
of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
0.6 mg
1 mL
=
0.6 mg
? mL
then rearrange,
0.6 × ? = 0.6 × 1
then rearrange again,
? = _0.6_ = 1 mL
0.6
So a 0.6 mg dose of atropine will be administered as a 1 mL injection of a 0.6
mg/mL solution.
What is the total volume (i.e., both drugs) for injection?
0.4 mL + 1 mL = 1.4 mL
What size of syringe would be appropriate for that volume?
A 3 mL syringe would work.
17
10. A preoperative medication order reads: Give morphine 12 mg IM, atropine 0.4 mg IM
and prochlorperazine 7.5 mg IM one hour prior to induction. In stock, morphine sulphate
is available in ampoules containing 5 mg/mL, 10 mg/mL and 15 mg/mL. Atropine
sulfate is available in ampoules of 0.4 mg/mL or 0.6 mg/mL. Prochlorperazine is
available in 10 mg/2 mL ampoules. Select the most appropriate size syringe: 1 mL, 3 mL
or 5 mL.
Which stock concentration of morphine do you choose?
Let’s work out what the dose would be for both the 10 and 15 mg/mL solutions.
What volume of that concentration yields a 12 mg dose?
(1) 15 mg = 12 mg or (2) 10 mg = __12 mg
1 mL
? mL
1 mL
? mL
{this is where you rearrange the equation by cross-multipication:
the top number (numerator) on one side of the ‘equal sign’
times the bottom number (denominator) on the other}
15 × ? = 12 × 1
10 × ? = 12 × 1
{rearrange according to another rule: if a number is multiplied on one side of the ‘equal sign’,
it is the same as dividing the other side of the ‘equal sign’ by that number}
? = _12_
? = _12_
15
10
? = 0.8 mL of the 15 mg/mL sol’n or ? = 1.2 mL of the 10 mg/mL sol’n.
Which stock concentration of atropine do you choose?
Let’s work out what the dose would be for both the 0.4 and 0.6 mg/mL solutions.
What volume of that concentration yields a 4 mg dose?
(1) 0.4 mg = 0.4 mg or (2) 0.6 mg = _0.4 mg
1 mL
? mL
1 mL
? mL
{this is where you rearrange the equation by cross-multipication:
the top number (numerator) on one side of the ‘equal sign’
times the bottom number (denominator) on the other}
0.4 × ? = 0.4 × 1
0.6 × ? = 0.4 × 1
{rearrange according to another rule: if a number is multiplied on one side of the ‘equal sign’,
it is the same as dividing the other side of the ‘equal sign’ by that number}
? = _0.4_
? = _0.4_
0.4
0.6
? = 1 mL of the 0.4 mg/mL sol’n or ? = 0.66 mL of the 0.6 mg/mL sol’n.
What volume of prochlorperazine 10 mg/2 mL yields a 7.5 mg dose?
The “prescribed dose” is 7.5 mg, and we know there’s 10 mg of prochlorperazine in 2 mL of
solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10 mg
= 7.5 mg
2 mL
? mL
then rearrange,
10 × ? = 7.5 × 2
then rearrange again,
? = _14_ = 1.4 mL
10
So a 7.5 mg dose of prochlorperazine will be administered as a 1.4 mL injection of a 10 mg/2 mL
solution.
18
What is the total volume (i.e., all 3 drugs) for injection?
(1.4 mL of prochlorperazine) + (0.8 mL or 1.2 mL of morphine) + (0.66 or 1 mL of atropine) = from 2.86 to 3.6 mL,
depending on which concentration of each drug you selected.
What size of syringe would be appropriate for that volume?
A 3 mL syringe would work if you chose the highest concentrations of morphine and
atropine, otherwise you will need a 5 mL syringe. Some institutions might have policies
against injecting more than 3 mL at a single IM site, others won’t.
It may be of interest that the American Society of Anesthesiologists Task Force Practice Guidelines for Preoperative
Fasting and the Use of Pharmacologic Agents to Reduce the Risk of Pulmonary Aspiration: Application to Healthy
Patients Undergoing Elective Procedures do not recommend routine use of gastric acid reducing agents, antiemetics or
antimuscarinic drugs intended to minimize the risk of pulmonary aspiration, because there is insufficient evidence that
these medications actually have any effect on the incidence or severity of pulmonary aspiration.
11. You are caring for a woman with threatened premature delivery at 31 weeks gestation.
An order is given to administer “betamethasone 12 mg IM STAT, and repeat in 24
hours”. Betamethasone is available in 1 mL vials containing 4 mg/mL.
What volume of that solution will you prepare to inject?
The “prescribed dose” is 12 mg, and we know there’s 4 mg of betamethasone in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
4 mg
= 12 mg
1 mL
? mL
then rearrange,
4 × ? = 12 × 1
then rearrange again,
? = _12_ = 3 mL
4
So a 12 mg dose of betamethasone will be administered as a 3 mL injection of a 4 mg/mL
solution.
How many vials will you need to open to administer the prescribed dose?
In other words: How many 1 mL vials will it take to make 3 mL?
The math: ? × 1 mL vials = 3 mL;
rearrange to: ? = 3/1 = 3
The 3 mL injection will be drawn from 3 × 1 mL vials.
19
12. The obstetrician orders 5 International Units (IU) of oxytocin administered with the
delivery of the anterior shoulder. The vial contains 1 mL of solution containing 10 IU of
oxytocin.
What volume of oxytocin solution will you ‘draw up’?
The “prescribed dose” is 5 IU, and we know there’s 10 IU of oxytocin in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10 IU
= 5 IU
1 mL
? mL
then rearrange,
10 × ? = 5 × 1
then rearrange again,
? = _5_ = 0.5 mL
10
So a 5 IU dose of oxytocin will be administered as a 0.5 mL injection of a 10 IU/mL solution.
13. Following birth, the physician orders “Vitamin K 1 mg I.M.” for the infant. Vitamin K is
supplied in 1 mL vials containing 10 mg/mL.
What volume of that solution will you prepare to administer by intramuscular injection?
The “prescribed dose” is 1 mg, and we know there’s 10 mg of vitamin K in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10 mg
= 1 mg
1 mL
? mL
then rearrange,
10 × ? = 1 × 1
then rearrange again,
? = _1_ = 0.1 mL
10
So a 1 mg dose of vitamin K will be administered as a 0.1 mL injection of a 10 mg/mL solution.
What size of syringe (0.5 mL, 1 mL, 3 mL) would be least appropriate for this injection?
You need higher precision syringes to administer small volumes of potent drugs acurately. If the
0.5 mL and 1 mL syringes have the same precision, either will do.
20
14. A woman in early labor is prescribed Demerol 150 mg with Gravol 25 mg IM.
You have the following concentrations of these drugs available to you:
Demerol® 50 mg/mL in a 1 mL vial
Demerol® 75 mg/mL in a 1 mL vial
Demerol® 100 mg/mL in a 1 mL vial
Gravol® 50 mg/mL in a 1 mL vial
Which stock concentration of Demerol® do you choose? Explain.
Choosing the highest concentration will allow the lowest volume for injection. The highest concentration
of Demerol® available in this case is the 100 mg/mL concentration.
What volume of that concentration yields a 150 mg dose?
The “prescribed dose” is 150 mg, and we know there’s 100 mg of Demerol® in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
100 mg
= 150 mg
1 mL
? mL
then rearrange,
100 × ? = 150 × 1
then rearrange again,
? = _150_ = 1.5 mL
100
So a 150 mg dose of Demerol® will be administered as a 1.5 mL injection of a 100 mg/mL
solution.
What volume of the Gravol® concentration yields a 25 mg dose?
The “prescribed dose” is 25 mg, and we know there’s 50 mg of Gravol® in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
50 mg
= 25 mg
1 mL
? mL
then rearrange,
50 × ? = 25 × 1
then rearrange again,
? = _25_ = 0.5 mL
50
So a 25 mg dose of Gravol® will be administered as a 0.5 mL injection of a 50 mg/mL solution.
What is the total volume (i.e., both drugs) for injection?
1.5 mL of Demerol® + 0.5 mL of Gravol® = 2 mL for injection
Is that an appropriate volume for IM injection?
Usually?
Regarding the use of meperidine (aka, pethidine) [Demerol®] as an example: Although it is still used frequently on many labor units,
there may be better alternatives. The choice is controversial. The American Society for Gastrointestinal Endoscopy suggested that meperidine
might be preferred over morphine, on the basis of evidence that morphine crosses the fetal blood-brain barrier more rapidly. However, both
drugs readily enter the fetal brain and there is no evidence cited in the guideline that a differential rate of fetal CNS penetration after maternal
administration of either meperidine or morphine is of any clinical importance. Other jurisdictions continue to describe meperidine as a choice for
early labor analgesia.
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
ƒ
Mander R. Analgesia and anaesthesia in childbirth: obscurantism and obfuscation. J Advanced Nursing 1998;28:86-93.
Faucher MA and Brucker MC. Intrapartum Pain: Pharmacologic Management. JOGNN 2000;29:169-80.
ISMP Canada Safety Bulletin. Meperidine (Demerol) Medication Safety Issues. Spring 2005. accessed online 17DEC05
@ http://www.ismp-canada.org/download/CACCN-Spring05.pdf
Hale TW. Drug therapy and breastfeeding: antibiotics, analgesics, and other medications.
NeoReviews. 2005;6(6):e233-e240.
NSW-TAG. Use of pethidien for pain management in the emergency department. August 2004
ASGE. Guidelines for endoscopy in pregnant and lactating women. 2005;61(3):357-362.
Nova Scotia Perinatal Program: http://www.rcp.gov.bc.ca/guidelines/Master[1].OB4.PainManage.May2000.pdf
21
What if the dose is to be adjusted to the size of the patient?
To get the most benefit with the least side effects, it may be useful to normalize (i.e., tailor) the
dose of a drug to the volume of the body compartment into which the drug distributes, which
often corresponds well enough with the patient’s total body weight (or perhaps lean body weight, estimated
bone mass or body surface area). The general idea is to give bigger people bigger doses, and smaller
people proportionally smaller doses, so they all achieve the same tissue levels following a dose
that is the right size for them. It is especially common to adjust pædiatric doses according to a
child’s weight. In that case, the prescription might read, “Drug-C syrup 2 mg/kg p.o. q4h”. It
means, first determine how much the child weighs, then give 2 milligrams of Drug-C for every
kilogram of body weight. If the child weighs 14 kg, the dose would be 14 × 2 mg = 28 mg.
Try to determine the correct volume of a drug formulation that you should prepare to give to a
patient who has been prescribed these weight-adjusted doses:
15. A 5 year old asthma patient is prescribed theophylline elixir 3 mg per kg body weight p.o.
q6h. She weighs 15 kg.
What dose of theophylline elixir does that work out to?
Dose = 3 mg/kg × 15 kg = 45 mg of theophylline every 6 hours.
How much theophylline would she get per day?
24 hours/day divided into 6 hour intervals = 24/6 = 4 doses.
4 doses/day × 45 mg/dose = 180 mg/day
Theophylline elixir comes in a 480 mL bottle containing 80 mg/15 mL.
What volume of elixir will provide the prescribed dose?
The “prescribed dose” is 45 mg, and we know there’s 80 mg of theophylline in 15 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
80 mg
= 45 mg
15 mL
? mL
then rearrange,
80 × ? = 45 × 15
then rearrange again,
? = _675_ = 8.44 mL
80
So a 45 mg dose of theophylline will be administered as 8.44 mL of a 80 mg/ 15mL solution.
22
16. A 4 year old child has “oxacillin 50 mg/kg/day in divided doses infuse IV at 6 hour
intervals; not to exceed 1.5 g/day”. Oxacillin comes pre-mixed in vials of two different
sizes containing either 1 g or 2 g of oxacillin in 50 mL of iso-osmotic dextrose solution.
This child weighs 12.5 kg.
How much oxacillin should this child receive on a daily basis?
Dose/day = 50 mg/kg × 12.5 kg = 625 mg/day.
Does that exceed the prescribed daily limit?
No. 625 mg/day < 1500 mg/day limit
Dividing the total daily dose into equal doses, how many milligrams should be given every 6
hours? 24 hours/day divided into 6 hour intervals = 24/6 = 4 doses.
625 mg/day divided into 4 doses/day = 625/4 = 156.25 mg/dose
If you choose to draw a dose from the 1g/50 mL concentration, what is the smallest syringe you
could use to draw up the dose: will you need a 1 mL, 3 mL, 5 mL, or a 10 mL syringe?
The “prescribed dose” is 156 mg, and we know there’s 1000 mg of oxacillin in 50 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
1000 mg
= 156 mg
50 mL
? mL
then rearrange,
1000 × ? = 156 × 50
then rearrange again,
? = _7812.5_ = 7.8 mL
1000
So a 156 mg dose of oxacillin will be administered as 7.8 mL of a 1 g/ 50 mL solution.
You’ll need a 10 mL syringe.
17. A 4 month old child is prescribed cefpodoxime oral suspension 4 mg/kg p.o. q12h. The
child weighs 25 kg. The bottle is reconstituted to a 50 mg/mL concentration of lemon
crème flavored cefpodoxime suspension.
How much of that suspension should you give for each dose?
The “prescribed dose” is 4 mg/kg × 25 kg = 100 mg, and we know there’s 50 mg of cefpodoxime in 1 mL
of suspension.
This is where you set up and rearrange a ‘cross-multiply’ equation:
50 mg
= 100 mg
1 mL
? mL
then rearrange,
50 × ? = 100 × 1
then rearrange again,
? = _100_ = 2 mL
50
So a 100 mg dose of cefpodoxime will be administered as 2 mL of a 50 mg/mL oral suspension. .
23
18. Remember the woman that was prescribed Demerol®150 mg during early labor in
question #14? Following birth three hours later, her 3500 g infant has respiratory
depression. The resuscitation team calls for naloxone hydrochloride [Narcan®] 0.1
mg/kg IV. Naloxone hydrochloride comes in 1 mL vials that contain 0.4 mg/mL.
What is the correct dose in mg?
The dose is 0.1 mg/kg × 3.5 kg = 0.35 mg
How many millilitres of the 0.4 mg/mL solution corresponds to that dose?
The “prescribed dose” is 0.35 mg, and we know there’s 0.4 mg of naloxone in 1 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
0.4 mg
= 0.35 mg
1 mL
? mL
then rearrange,
0.4 × ? = 0.35 × 1
then rearrange again,
? = _0.35_ = 0.875 mL
0.4
So a 0.35 mg dose of naloxone will be administered as 0.875 mL of a 0.4 mg/mL solution. You’ll need a 1
mL syringe.
Part 2: exercises on how to initiate and adjust a continuously administered drug:
1. Your patient is receiving a continuous heparin infusion. The intravenous solution
contains 10000 units of heparin in 500 mL of 5% dextrose (D5W). The patient is to
receive 1800 units of heparin per hour.
What volume of the heparin solution must infuse to provide that dose of heparin in one hour? The
“prescribed dose” is 1800 units/hr, and we know there’s 10000 units of heparin in 500 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
10000 = 1800
500 mL
? mL
then rearrange,
10000 × ? = 1800 × 500
then rearrange again,
? = _900000_ = 90 mL
10000
So a 1800 unit/hr dose of heparin will be administered by infusing 90 mL of a 10000 unit/500 mL solution.
The infusion pump rate has to be programmed in mL/hr, so what rate will you select?
To run at 90 mL/hour, program the pump to infuse 90 mL/hour.
At that rate, how long will a 500 mL bag of heparin in D5W last?
500 mL = 5.56 hours; i.e., not quite 6 hours.
90 mL
24
2. A patient’s daily fluid balance is being supplemented by constant intravenous infusion of
1500 mL/24 hours of 5% dextrose in 0.9% sodium chloride solution (D5S), using a 60
drops = 1 mL infusion set.
At how many drops per minute should you regulate the iv to deliver 1500 mL/24 hrs?
Let’s work this out in mL/minute, then multiply mL/min × 60 gtts/mL. There are 24hrs/day × 60
min/hrs = 1440 minutes/day.
Set up and rearrange a ‘cross-multiply’ equation:
1500 mL = ? mL
1440 min
1 min
then rearrange,
1440 × ? = 1500 × 1
then rearrange again,
? = _1500 = about 1 mL/min,
1440
and using a 60 drops = 1 mL infusion set, we should run 1 mL/min × 60 gtts/mL = 60 gtts/min
(about 1 drop/second).
3. The patient you are caring for is a type 1 diabetic in active labor. She has a continuous
insulin infusion prescribed according to a sliding scale (i.e., you adjust the infusion rate,
and thus titrate her insulin dose according to her capillary blood glucose response). The
intravenous solution contains Humulin R 50 units/500 mL of 0.9% sodium chloride
(normal saline):
Blood glucose (mmol/L) Humulin R (units/hour)
< 4 mmol/L
Hold insulin
< 6 mmol/L
1 unit/hr
8.9 is < 8 mmol/L
2 units/hr
3
units/hr
≥ 8 mmol/L
You obtain a capillary blood glucose reading of 6.9 mmol/L.
What rate in mL/hr will you program the pump to deliver the corresponding insulin dose
rate?
Set up and rearrange a ‘cross-multiply’ equation:
50 units = 2 units
500 mL
? mL
then rearrange,
50 × ? = 500 × 2
then rearrange again,
? = _1000 = 20 mL/hr,
50
[Insulin is a critical dose hormone that has been associated with a high rate of serious adverse events worldwide. Several patient
safety advocates recommend that institutions institute policy to establish 1 unit/mL as the standard concentration of insulin for
continuous infusion, and exceptions should be clearly flagged. Thus, an exception is represented in the above example: 0.1 unit/mL
rather than 1 unit/mL However, 1 unit/mL is a rather high concentration, and safe delivery implies use of infusion equipment
designed to accurately deliver small hourly volumes. If an empty bag of the more dilute 0.1 unit/mL concentration was replaced with
a new bag of 1 unit/mL and proceeded to run at the same rate, the woman would receive 20 units per hour rather than 2 units per hour.
Her mental and physical status would deteriorate and she might seizure.]
25
This next question will challenge your skill with very potent drugs that are administered in doses
measured in uncommonly small units.
4. You are caring for a woman who will undergo an attempt to induce labor with IV
oxytocin. You initiate a primary IV line of normal saline, and are now preparing the
oxytocin solution to run as a secondary “piggyback” infusion. Oxytocin is supplied in
vials containing 10 international units (IU)/mL. One mL of oxytocin 10 IU/mL is added
to a 500 mL bag of normal saline (assume a final concentration of 10 IU/500mL [rather
than 10 IU/501 mL]).
What is the resulting oxytocin concentration expressed in milliunits/mL?
10 units × 1000 = 10000 milliunits added to 500 mL of saline.
Set up and rearrange a ‘cross-multiply’ equation:
10000 milliunits = ? units
500 mL
1 mL
then rearrange,
500 × ? = 10000 × 1
then rearrange again,
? = _10000 = 20 milliunits/mL.
500
If that concentration of oxytocin is infused at a rate of 1 mL/hour, how many milliunits/minute
would be infused? 1 hr = 60 min.
Set up and rearrange a ‘cross-multiply’ equation:
20 milliunits = ? milliunits
60 min
1 min
then rearrange,
60 × ? = 20 × 1
then rearrange again,
? = _20 = 0.33 mU/min,
60
If the infusion is to be initiated at 0.66 milliunits/minute, at what rate in mL/hour should you
program the infusion pump?
Set up and rearrange a ‘cross-multiply’ equation:
0.33 milliunits/min
= 0.66 milliunits/min
1 mL/hr
? mL/hr
then rearrange,
0.33 × ? = 0.66 × 1
then rearrange again,
? = _0.66 = 2 mL/hr
0.33
26
If the induction protocol is to increase the oxytocin infusion rate by 3 milliunits [per what unit of
time?] every 30 minutes, what will be the incremental change in mL/hour pump rate you will
make every 30 minutes? This is an example of an improperly written order: to increase by 3
milliunits at 30 minutes intervals is not the same as to increase by 3 milliunits/30 min (i.e., 6
milliunits/hr). The order should read, “increase the oxytocin infusion rate by 3 milliunits/minute,
every 30 minutes, until desired contraction pattern is achieved.” You clarify the order to mean:
“start at 0.66 milliunits/minute, then 30 minutes later increase to 3.66 milliunits/minute, then 30
minutes after that increase to 6.66 milliunits/minute, then 9.66 milliunits/minute and so forth
We want to know what flow rate (in mL/hr) corresponds to a dose increase of 3 milliunits/minute
when infusing a 20 milliunit/mL oxytocin solution, because that is the incremental rate (how
much) you will speed up the pump rate, every 30 minutes:
Set up and rearrange a ‘cross-multiply’ equation:
20 milliunits = 3 milliunits/minute
1 mL
? mL/minute
then rearrange,
20 × ? = 3 × 1
then rearrange again,
? = __3__ = 0.15 mL/minute.
20
The pump has to be programmed in mL/h, so 0.15 mL/minute × 60 minutes/hr = 9 mL/hr
The protocol goes like this: start at 2 mL/hr (0.66 milliunits/minute), then at every 30 minute
interval thereafter, increase the rate by 9 mL/hr (3 milliunits/minute) until the desired contraction patern is
achieved.
5. Imagine that you begin a shift on a hospital inpatient unit. One of the patients has an
insulin drip that according to the last capillary blood glucose reading on a sliding scale,
should be running at 5.5 insulin units per hour. The reservoir is labeled, “Humulin R 10
units in 100 mL of 0.9% saline”. The infusion pump is set at 45 mL/hr. Assuming that
the labeled concentration is correct, what rate should the infusion pump be set at to infuse 5.5
units per hour?
Set up and rearrange a ‘cross-multiply’ equation:
10 units = 5.5 units/hr
100 mL
? mL/hr
then rearrange,
10 × ? = 5.5 × 100
then rearrange again,
? = _550_ = 55 mL/hr
10
(i.e., the patient is getting 1 unit/hr less insulin than was prescribed, but don’t be too hasty to
increase the rate from 45 mL/min to 55 mL/min…[If your patient appears stable, the very next thing you’ll
probably want to do is another capillary blood glucose reading, right? Once you’ve got a new blood glucose baseline,
adjust the insulin infusion according to the sliding scale, and document your brilliant discovery of a medication error so all
can learn from it.])
27
6. If you are to infuse ranitidine 50 mg in 10 mL IV over 15 minutes, at what rate should the
ranitidine solution be infused if the infusion pump must be programmed in milliliters per hour?
10 mL in 15 minutes corresponds to how many mL in 60 minutes?
Set up and rearrange a ‘cross-multiply’ equation:
= ? mL
10 mL_
15 min
60 min
then rearrange,
15 × ? = 60 × 10
then rearrange again,
? = _600_ = 40 mL/hr
15
7. A patient with acute coronary syndrome weighs 67 kg. Following a 180 μg bolus, she is
receiving eptifibatide [Integrilin®] by continuous infusion of 2 μg/kg/min. If the
eptifibatide concentration for infusion is 75 mg in 100 mL of 0.9% sodium chloride
solution, what rate should the drug solution be infused if the infusion pump must be
programmed in milliliters per hour?
The “prescribed dose” is 2 μg/kg/min × 67 kg = 2 × 67 = 134 μg/min. In 60 minutes, she should get 60
min × 134 μg/min = 8040 μg/hr = 8.04 mg/hr. She should receive 8.04 mg/hr, and we know there’s 75 mg
of eptifibatide in 100 mL of solution.
This is where you set up and rearrange a ‘cross-multiply’ equation:
75 mg
= 8.04 mg/hr
100 mL
? mL/hr
then rearrange,
75 × ? = 8.04 × 100
then rearrange again,
? = _804_ = 10.72 mL/hr
75
So a 2 μg/kg/min dose of eptifibatide for a 67 kg patient will be administered by infusing a 75 mg/100 mL
solution at a rate of 11 mL/hour.
8. You are to start an intravenous infusion of 0.9% sodium chloride containing potassium
chloride 20 mEq/L, and maintain the infusion at 125 mL/hr.
If you use a macrodrip infusion set (15 gtts/mL), at how many drops per minute should
this infusion be maintained?
125 mL
60 min
= ? mL
1 min
then rearrange,
60 × ? = 125 × 1
then rearrange again,
? = _125_ = 2.083 mL/min. 2.083 mL/min × 15 gtts/mL = 31.25 gtts/min
60
or
(125 mL × 15 gtts/mL) /60 minutes = 1875 gtts/60 minutes = 31.25 gtts/min
If you use a microdrip infusion set (60 gtts/mL), at how many drops per minute should
this infusion be maintained? 2.083 mL/min × 60 gtts/mL = 125 gtts/min
28
What dose of KCl will the patient be getting: each hour? each day?
20 mEq/L = 20 mEq/1000 mL infusing at 125 mL/hr
(which also means 24 hr/day × 125 mL/hr = 3000 mL/day)
This is where you set up and rearrange a ‘cross-multiply’ equation:
20 mEq
=
? mEq/hr
1000 mL
125 mL/hr
then rearrange,
1000 × ? = 20 × 125
then rearrange again,
? = _2500_ = 2.5 mEq/hr
1000
2.5 mEq/hr × 24 hr/day = 60 mEq/day
So the iv is running at 125 mL/hr = 3 L/day. Every litre contains 20 mEq of KCl; so the patient will be
getting 3 L/day × 20 mEq/L = 60 mEq of KCl/day
29
APPENDIX: Medication Errors background information
BBC News: Dangers of drug errors exposed
Thousands of drug injection errors are probably made every day in NHS hospitals, say
researchers.
When nurses give drugs intravenously, they are making mistakes in almost half of the injections
because they are poorly trained, the study says.
Some of these are putting patients at risk. At least one patient each day in every major NHS
hospital may experience a "potentially serious error".
Researchers carried out their study in just two hospitals, but say their findings are likely to be
reproduced across the health service.
They recommend nurses are given better training and technology to help them give intravenous
(IV) drugs properly. They add that the amount of preparation of the drug needed on the ward
should be reduced to cut the risk of errors.
The team observed the preparation and administration by nurses of IV drugs, which are injected
into the vein, over six to 10 consecutive days on 10 wards in the hospitals.
Just over 100 patients were given 430 doses of intravenous drugs during the period.
Errors were seen in 212 doses. In around a third, they were potentially harmful, and in three
cases, the error was potentially severe, and could have led to long-term hospitalisation or even
death.
However, the observer in the study who was a trained pharmacist intercepted to ensure the
patient was not harmed.
Nurses identified fear of reactions by managers and peers as the main reason for not reporting
drug errors, according to a survey of 983 nurses. Yet about 46% believed that all drug errors are
reported. They cited illegible physician handwriting and being distracted or tired as the primary
causes for drug errors.
Crucial drugs
Mistakes in the administration of drugs occurred in a third of cases, preparation errors, where
there could be several steps preparing the drugs, occurred in 7%.
The most common errors made were giving concentrated doses too quickly and mistakes in
preparing drugs that required multiple steps, such as diluting or mixing them with a solvent.
The researchers said the rate of error they observed was high.
Nick Barber, professor of the practice of pharmacy at the University of London, told BBC News
Online: "This is something that concerns me, and I think it's something that needs acting on by
hospitals.
"For people who require IV drugs, it can be all that's keeping them alive. So errors which might
not matter with other patients could be very serious in these cases."
He said that a lot of problems occurred when people did not follow the rules.
"It's like when people break the speed limit. In a lot of cases, people can break the speed limit
and it's perfectly safe. But on some occasions, things go wrong."
He added: "Sometimes, the training given is not sufficient. We need to increase the amount of
training on the making up of drugs as well as information on dilution."
Professor Barber said he hoped the recently formed National Patient Safety Agency would be
able to make a difference.
Consequences
30
A spokesman for the Royal College of Nursing said: "This study only covered two hospitals and
a very short period of time."
But he added: "There are improvements which could be
made in the
training of nurses, and the role pharmacists play in the training of nurses."
He said nurses were not currently told about how to give IV drugs in their first few years of
training, and were only given instruction when they moved onto a ward where they were given.
A Department of Health spokeswoman said: "The NHS is committed to making drug treatment
as safe as possible.
"Standards of prescribing in this country are high and the vast majority of drug treatment is
provided safely.
"However mistakes do occur. They can arise in the prescribing, dispensing or administration of
medicines, and the consequences can be serious."
She said Chief Pharmaceutical Officer Dr Jim Smith, and the NPSA were preparing a
comprehensive report on medication errors which would provide guidance for health
professionals.
Story from BBC NEWS:
http://news.bbc.co.uk/go/pr/fr/-/1/hi/health/2891327.stm
Published: 2003/03/28 00:05:30 GMT
© BBC MMV
Preston RM. Drug errors and patient safety: the need for a change in practice. Br J. Nurs.
2004; 13(2): 72-8.
Concerns regarding drug errors and public safety have recently been raised in the British national newspapers and
professional nursing journals. This literature review considers why nurses may continue to make drug errors in their
practice. The findings suggest that drug errors are not caused by any one factor, but are multifaceted in nature.
Factors include calculation error, overdosing/underdosing of drug dosages, covert drug administration in food and
drink, and an increasingly relaxed attitude among professional nurses with regard to ensuring that drugs are
administered to the standard required by law. This article considers the notion that nurses may breach the legal "duty
of care" they owe patients by being complacent in their drug administration practice. Consideration of a system's
approach to minimize drug error through proactive action planning, risk identification, and implementation of an
anonymous incident-reporting framework is briefly explored.
J
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ournal of Child Health Care. Vol 7(4): 277–290,1367-4935.
NURSING MATTERS
Nursing Matters fact sheets provide quick reference information and international
perspectives from the nursing profession on current health and social issues.
Medication Errors
As emphasised in the ICN Position Statement on Patient Safety, patient safety is
fundamental to quality nursing and health care 1. Experts estimate medication errors are a
leading cause of death and disability 2 . More people die annually from medication errors
than from workplace injuries. Some studies suggest that physicians, administrators and
nurses perceive patient safety as primarily a nursing responsibility 3. Because nurses take a
central role in patient safety, there is a danger that errors can be attributed to nurses rather
than to system failures. However, evidence shows that nursing vigilance protects patients
against unsafe practices. For example, one study showed nurses were responsible for
intercepting 86% of all medication errors made by physicians, pharmacists and others before
the error occurred 4. A system - wide approach that involves all members of the health care
team as well as management, is a sound approach for patient safety.
Why do medication errors happen?
Every step in patient care involves a potential for error and some degree of risk to patient
safety. Today’s complex health care system can create some issues about patient safety. A
proper understanding of the factors that increase medication errors is the first step in
preventing them.
In a study of prescribing errors 5, the most common factors associated with errors included:
•
•
•
Using the wrong drug name, dosage form, or abbreviation;
Mistakes on calculating dosage;
Atypical or unusual and critical dosage.
As with other safety issues, medication errors arise from human errors and/or system
failures. Medications errors may, therefore, result from problems in practice, products,
procedures or systems. Other factors, such as training deficiencies, undue time pressure
and poor perception of risk can also contribute to medication errors.
Characteristics of Medication Errors
The three most frequently reported types of errors are:6
•
Omission errors (failure to administer a prescribed medication);
32
•
•
Improper dose (medication dose, strength, or quantity different from that
prescribed);
Unauthorised drug errors (the medication dispensed and/or administered was
not authorised by the prescriber).
An analysis of medication errors can help healthcare professionals and managers to identify
error-prone medications or categories of drugs, and make improvements to prevent or reduce
them.
Table 1: Types of Medication Errors
Types
extra dose
improper dose/quantity
omission error
Contributing Factors
distractions
workload increase
inexperienced staff
prescribing error
shift change
unauthorised drug
agency/temporary staff
wrong administration
no 24 hour pharmacy
technique
wrong dosage form
wrong drug preparation
wrong patient
wrong route
wrong time
insufficient staffing
emergency situation
cross coverage
code situation
no access to patient
information
Causes
performance deficit
procedure/protocol not followed
knowledge deficit
inaccurate or lack of
documentation
confusing communication
inaccurate or omitted
transcription
computer entry
drug distribution system
inadequate system safeguards
illegible or unclear handwriting
(Source: Ruth M. Kleinpell, Nursing Spectrum, February 2001. Vol. 2 No. 2. p.39)
Medication errors are preventable, although reducing the error rate significantly will require
multiple interventions and close collaboration between the health team and management.
Blame free health systems
In health care it is estimated that about 60–80 percent of adverse events involve human
error. For example, an analysis of anaesthesia found that human error was involved in 82
percent of preventable incidents; the remainder involved mainly equipment failure 7.
However, to say that accidents are due to human error should not lead to blaming and
shaming people. The common reaction when errors happen is to blame and shame and
punish individuals (e.g. firing or suing them), or other responses aimed at preventing
recurrence of the adverse event. Yet, proper analysis shows that it is unlikely that errors
happen due to a single act by a health care provider and blaming an individual does not
address the underlying risk factors. Although a punitive action may be appropriate in some
cases (e.g. deliberate negligence), it is not an effective way to prevent recurrence.
Humans commit errors for a variety of reasons often related to the practice environment.
Nurses and other health care professionals are among the most educated and dedicated of
workforces. The problem with patient safety is not bad professionals in health care, but bad
33
systems that need to be made safer. In its Position Statement on Patient Safety, ICN
strongly supports a system-wide approach, based on a philosophy of transparency and
reporting - not on blaming and shaming the individual care provider – and incorporating
measures that address human and system factors in adverse events 8.
Current thinking on patient safety places the prime responsibility for adverse events such as
medication errors, on deficiencies in system design, organization and operation rather than
on individual providers. Most adverse events are not the result of negligence or lack of
training, but rather occur because of faults within systems. Counter- measures based on
changes in the system are therefore more productive than those that target individual
practices or products 9.
Error reporting and learning
A good way to learn from medication errors is to establish a reporting system, as voluntary
reporting of adverse events provides data that leads to improved patient safety. However,
because of the “blame and shame” approach in health system, there is generally
underreporting and what is reported is often the tip of the iceberg.
Reporting errors is only the first step in the process of reducing errors and continuous quality
improvement. Sufficient attention must be given to analyzing and understanding the causes
of errors in order to create learning systems and improve patient safety. An approach that is
commonly used in human factor analysis is a critical incident analysis. This analysis
examines adverse events to understand where the system broke down, why the incident
occurred, and the circumstances surrounding the incident 10. Analyzing critical incidents,
whether or not the event actually leads to a bad outcome, provides an understanding of the
conditions that produced an actual error or the risk of error as well as the contributing factors.
Feedback and dissemination of information can create an awareness of errors that occur in
the system and improve system design to reduce or eliminate medication errors. Health care
organizations and health professionals should be encouraged to participate in voluntary
reporting systems as an important component of their commitment to patient
safety._________________________________
1.
International Council of Nurses. ICN Position Statement on Patient Safety.
Adopted 2002.
2. To Err is Human. Institute of Medicine.
http://books.nap.edu/books/0309090679/html/1.html#pagetop
3. Cook, F, A.; Guttmannova, K.; and Clare, (2004), An Error by any other name.
American Journal of Nursing. Vol.104, No.6. pp.32-43.
4. Leape, et.al (1995), systems analysis of adverse drug events. JAMA, 274 (1), 3543.
5. 56. Lesar, Timothy S.; Briceland, Laurie, and Stein, Daniel S. Factors Related to
Errors in Medication Prescribing. JAMA. 277(4):312–317, 1997
6. Kleinpell, R.M. (2001), Abstracted in Nursing Spectrum, Vol. 2 No. 2. p.39)
7. www.iom.edu/reports
8. ICN, Policy Statement on Patient Safety, adopted 2002.a
9. WHO, Quality of Care, patient safety. www.who.int
10. Cooper, Jeffrey B.; Newbower, Ronald; Long, Charlene, et al. Preventable
Anesthesia Mishaps: A Study of Human Factors. Anesthesiology. 49(6):399–
406, 1978.
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