This was a lecture presented to the Davie campus of Florida A&M University College of Pharmacy P4 students. The lecture was presented during their final semester, at a course geared towards NAPLEX preparation. During the lecture, students wer asked to participate. We worked through each problem together and questions were encouraged.

1. Joy A. Awoniyi, PharmD.
PGY1 Pharmacy Practice Resident
Miami VA Healthcare System
For The FAMU COPPS Class of 2013

2. Objectives
• To emphasize the importance of calculations
• To review important calculation concepts related to
• Patient Parameters
• Measurements
• Concentrations
• Electrolyte Solutions
• Clinical Laboratory Tests
• IV infusions flow rates
• Parenteral Nutrition
• To practice using the reviewed calculation concepts
• To review important pharmacokinetic concepts
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3. WHY SHOULD YOU CARE?
• You can’t escape it
• You need it to pass the NAPLEX
• It can be applied to any
pharmacy-related specialty
• It may save your patient’s money
• It may save your patient’s life
(and your license)
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4. PATIENT
PARAMETERS
Important Calculation Concepts
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5. BSA and IBW
• Body Surface Area (BSA), m2
• BSA = Weight (kg)0.425 x Height (cm)0.725 x 0.007184
• BSA = cm ´ kg
3600
• Ideal Body Weight, kg
• Males: 50 +( 2.3 x inches greater 60)
• Females: 45.5 + (2.3 x inches greater than 60)
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6. BODY MASS INDEX (BMI)
• Measure of body fat to help categorize patients and
assess risk of morbidity for certain diseases
• BMI = weight(kg) ÷ [height (m)2]
BMI Classification
< 18.5 Underweight
18.5 to <25 Normal
25 to <30 Overweight
>30 Obese
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7. Creatinine Clearance (CrCl)
• Formula used to estimate renal function
• Not useful when renal function is fluctuating rapidly
• Used in the dosing of several medications
• Tamiflu, Antibiotics, Low-molecular weight heparins
CrCl (mL/min) Interpretation
(140 - Age) ´ IBW 60 to 90
30 to < 60
Mild renal impairment
Moderate Renal impairment
72´ SCr 15 to <30 Severe Renal impairment
Multiply by 0.85 if female < 15 Kidney failure
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8. EXAMPLE
Mack “Big Mack” Donald
is a 55 year old man
recently admitted to your
service after choking on a
Zebra Cake. He is 6’2”
and 980 pounds.
Calculate his BSA and
BMI.
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9. EXAMPLE
Body Surface Area Body Mass Index
• Height in centimeters: 6’2” = 74 • Height in meters = 1.88 m
inches
• 74 inches x 2.54 cm/inch = • Answer: 126
187.96 cm
• How do we classify Big Mack’s
• Weight in kilograms: 980 lbs BMI?
• 980 lbs x 1 kg/2.2lbs = 445.45 kg • Underweight
• Normal
• Answer: 4.82 • Overweight
• Obese
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10. EXAMPLE
Mack had a DVT during
admission. The doctors
wish to start him on
Enoxaparin (Lovenox), a
renally dosed medication.
His SCr is 2.3.
Calculate his IBW and
Creatinine Clearance
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11. EXAMPLE
Ideal Body Weight Creatinine Clearance
• Inches over 60 • Use IBW of 82.2kg
• 74 – 60 = 14 inches
• Answer: 42.19 mL/min
• IBW = 50kg + 2.3 (14) • Dose of Lovenox is
50% if CrCl is less
• Answer: 82.2 kg than 30 mL/min
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12. MEASUREMENTS
Important Calculation Concepts
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13. The Basics Of
Measurement
• Irrelevant information is often given
• Fundamental information is often left
out
• How many grams are in a kilogram?
• How many milliliters are in a fluid ounce?
• Start each problem by assessing
what you know and what you want to
know
• Double check!
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14. EXAMPLE
A cough syrup contains 10mg of dextromethorphan per 5
mL. Your pharmacy has 6 bottles left in stock. Each bottle
contains 120mL of the syrup. How many grams of the
drug are in one bottle?
• What information is irrelevant?
• What fundamental information do you need to know to
complete this problem?
• What do you know?
• What do you want to know?
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15. EXAMPLE
A cough syrup contains 10mg of dextromethorphan per 5
mL. Your pharmacy has 6 bottles left in stock. Each bottle
contains 120mL of the syrup. How many grams of the
drug are in one bottle?
120mL/ 1 1 0.24 grams/ 1
10mg/5mL
bottle gram/1000mg bottle
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16. Specific Gravity
Definition Equations
• A ratio of the weight of any • Grams = mL x SG
substance in relation to the
weight of an equal volume of • mL = Grams ÷ SG
water
• SG = Grams ÷ mL
• Water is used because 1g of • Do not confuse with density or
water is equal to 1mL concentration
• If SG > 1 the substance is
heavier than water
• If SG < 1 the substance is
lighter
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17. EXAMPLE
There is 10 grams of glycerin in a 500mL solution.
300 mL of glycerin weighs 165 grams. What is the
specific gravity of glycerin?
• Specific Gravity = grams / mL
• 10 g / 500mL ?
• 165 g/ 300mL ?
• Think of SG as a conversion factor
• 10 grams of glycerin does not EQUAL 500 mL of
glycerin
• 165 grams of Glycerin EQUALS 300 mL of glycerin
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18. EXAMPLE
There is 10 grams of glycerin in a 500mL solution.
300 mL of glycerin weighs 165 grams. What is the
specific gravity of glycerin?
165 300
0.55
grams mL
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19. EXAMPLE
What is the weight, in grams of a 2 fluid ounces of a
liquid with a specific gravity of 1.118?
• Grams = mL x SG
30mL/ 67.08
2 fl oz 1.118
1 fl oz grams
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20. DOUBLE CHECK
• DOES THE ANSWER MAKE
SENSE?
• If the SG is 1.118, the substance is
• Heavier than water?
• Lighter than water?
• 2 fluid ounces of water (60mL) = 60
grams
• The answer is 67.08 grams which is
> 60 grams
• Any answer below 60 would be
WRONG
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21. CONCENTRATIONS
Important Calculation Concepts
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22. PERCENTAGE
PREPARATIONS
Weight in volume
• Amount of grams in 100mL of solution
Volume in volume
• Amount of mL in 100mL of solution
Weight in weight
• Amount of grams in 100 grams of substance
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23. EXAMPLE
Weight in Volume
How many grams of dextrose are required to prepare
4000 mL of a 5% solution?
• 5% Dextrose by definition means 5 grams in 100mL
5
4000mL grams/ 200 grams
100mL
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24. ALLIGATION
• Alligation is a method of solving
problems that involves the mixing
of solutions or substances with
different percentage strengths
• Alligation alternate is a method
to calculate the number of parts
of two or more components of
different strengths mixed to
prepare a desired strength.
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25. EXAMPLE
ALLIGATION
What is the percentage of zinc oxide in an ointment
prepared by mixing 200 grams of a 10% ointment, 50
grams of a 20% ointment, and 100 grams of a 5%
ointment
0.10 x 200 g = 20 grams
0.20 x 50 g = 10 grams
0.05 x 100 g = 5 grams
350 g 35 grams
35 grams ÷ 350 grams = 0.10 x 100% = 10%
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26. EXAMPLE
ALLIGATION ALTERNATE
A pharmacist needs to prepare 50 mL of 3% hydrogen
peroxide solution. He has 30% and 1.5% solutions in
stock. How many mL of each should he use?
• A– C =Y
Percent Percent Proportions
Available Desired required • C–B=X
A X
• X and Y are
C proportions of A and
B (respectively)
B Y
needed for the
entire preparation
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27. EXAMPLE
ALLIGATION ALTERNATE
A pharmacist needs to prepare 50 mL of 3% hydrogen
peroxide solution. He has 30% and 1.5% solutions in
stock. How many mL of each should he use?
Percent Percent Proportions
Available Desired required • 1.5 parts of 30%
30% 1.5
• 27 parts of 1.5%
3%
• Total Parts: 28.5
1.5% 27
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28. EXAMPLE
ALLIGATION ALTERNATE
A pharmacist needs to prepare 50 mL of 3% hydrogen
peroxide solution. He has 30% and 1.5% solutions in
stock. How many mL of each should he use?
• We need 1.5 of all 28.5 parts to contain 30% Hydrogen
peroxide
• 1.5/28.5 = x/50mL
• X = 2.63mL of 30%
• We need 27 parts of all 28.5 parts to contain 3% Hydrogen
peroxide
• 27/28.5 = x/50mL
• X = 47.37mL of 1.5%
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29. ELECTROLYTE
SOLUTIONS
Important Calculation Concepts
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30. MILLIEQUIVALENTS
• Unit of measure related to the total number of ionic
charges in a solution
• Measures the chemical activity of an electrolyte
relative to 1mg of hydrogen
• 1 mEq represents the milligrams equal to its
equivalent weight, taking into account the valency
mg ´ valence mEq ´ Molecular.Weight
mEq = mg =
Molecular.Weight Valence
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31. MILLIEQUIVALENTS
Ion Abbr. Valence Atomic Milliequivalent
Weight weight
Aluminum Al3+ 3 27 9
Magnesium Mg2+ 2 24 12
Sodium Na+ 1 23 23
Bicarbonate HCO32- 2 60 ???
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32. EXAMPLE
What is the concentration, in milligrams per milliliter, of a
solution containing 2mEq of NaCl per mL?
• Molecular weight of Sodium = 23
2mEq ´ 58.3
• Molecular weight of Chloride = 35.5
1
• Molecular weight of Sodium chloride = 58.5
• Valency = 1 (Na+, Cl+)
mEq´ Molecular.Weight 2mEq ´ 58.5
mg =
Valence 1
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33. MOLARITY
• Millimoles
• 1 mol = molecular weight in grams, therefore…
• mmol = molecular weight in milligrams
• Molarity is the number of mmols in a solution
How many milligrams would 3 mmol of monobasic
sodium phosphate (MW = 138) weigh?
138 mg/
3 mmol 414 mg
1 mmol
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34. OSMOLARITY
• mOsmoles represent the number of particles in a
solution when the substance dissociates
• NaCl = 2 mOsmol
• CaCl2 = 3 mOsmol
• Anhydrous dextrose = 1 mOsmol
• Osmolality is the milliosmoles of solute in a solution
1mmol
mOsmol = mg ´
Molecular.Weight(mg)
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35. CLINICAL
LABORATORY TESTS
Important Calculation Concepts
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36. CALCIUM-ALBUMIN
• Almost 50% of calcium is bound to plasma proteins
• If levels of proteins are low, then the serum calcium
may be inaccurate
• If albumin is low, calcium will appear to be low, when it
levels are actually within normal limits
• Correct levels when Albumin is less than 4 g/dL
• Corrected Ca2+ = Ca2+ + 0.8 [4 – albumin(g/dL)]
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37. SODIUM-GLUCOSE
• In patients with hyperglycemia, glucose does not enter
the cell, causing a shift of fluid from intracellular to
extracellular
• The shift of fluid dilutes the concentration of sodium in
the extracellular fluid
• This type of hyponatremia (translational) does not need
to be treated, instead control of glucose levels is
indicated
• Corrected Na+ = Na+ + 0.016(Serum Glucose – 100)
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38. INFUSION FLOW
RATES
Important Calculation Concepts
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39. EXAMPLE
A physician orders 2 liters of D5W to be administered
over 8 hours. The IV administration set in your pharmacy
delivers 10 drops/mL. How many drops per minute should
the patient be set to receive?
2 Liters/ 1000mL/ 1 hour/ 10 drops/ 42 drops/
8hours 1 Liter 60 min 1mL min
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40. TOTAL PARENTERAL
NUTRITION
Important Calculation Concepts
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41. TOTAL PARENTERAL
NUTRUTION
• Provides a patient with all
nutritional requirements
• Composition:
• Fluids
• Carbohydrates (Dextrose)
• Protein (Amino acids)
• Fats
• Vitamins, minerals, trace
elements
• Electrolytes
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42. TPN HIGHLIGHTS
• Fluid Requirements:
• Generally 30 – 40 mL/kg/day
• Calculated: 1500 mL + 20mL (kg over 20)
• Protein Requirements
• Ambulatory: 0.8 – 1 g/kg/day
• Hospitalized: 1.2 – 2 g/kg/day
• Non-Protein Requirements (Total Energy Expenditure)
• Male: 66.47 + 13.75(kg) + 5.0(cm) – 6.76 (yrs)
• Female: 655.1 + 9.6(kg) + 1.85(cm) – 4.68(yrs)
• Multiply by 1.2 if confined to a bed, and 1.3 if out of bed
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43. TPN HIGHLIGHTS
Component Units
• Each TPN
component Dextrose 3.4 kcal per gram
provides a defined Amino Acids 4 kcal per gram
amount of calories
Lipids 9 kcal per gram
• COMMIT THESE
10% lipid emulsion 1.1 kcal per mL
TO MEMORY!!
20% lipid emulsion 2 kcal per mL
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44. PHARMACOKINETICS
Important Calculation Concepts
43

45. PHARMACOKINETCS
• Pharmacokinetics describes what happens to a drug
or substance inside of the body
Absorption Distribution
Metabolism Excretion
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46. FIRST-ORDER KINETICS
• The amount of drug given is proportional to the change
in concentration
• The change in drug concentration with respect to time will
create a rate constant (k)
dC
-k =
dt
• C = C0e-kt
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47. HALF-LIFE
• The half-life (t1/2) is the time required for the
concentration of the drug to decrease by one-half
• t1/2 = 0.693/k (k is the rate constant)
A patient is receiving an antibiotic for the treatment of a
respiratory infection. The initial concentration of the drug
was 17.9mg/L. The drug has an elimination half-life of 2
hours. How much of the drug is present after 8 hours?
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48. EXAMPLE
A patient is receiving an antibiotic for the treatment of a
respiratory infection. The initial concentration of the drug
was 17.9mg/L. The drug has an elimination half-life of 2
hours. How much of the drug is present after 8 hours?
• C = C0e-kt SOLVE FOR “C”
• t1/2 = 0.693/k (k is the rate constant)
• 2h = 0.693/k
• k = 0.347h-1
• C = 17.90e-0.347(8) = 1.11mg/L
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49. QUESTIONS?
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50. THANK YOU!
• Joy A. Awoniyi
• Email your questions, comments or concerns to
Joy.awoniyi@va.gov
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