PPT Presentation

1. Pharmaceutics Lecture
2002 - Date
Computing
and
pharmaceutical numeracy

2. Review of Mathematical Concepts
for Pharmaceutics
1. Proper, Improper Fractions and Mixed Numbers
Proper fraction: numerator is less than denominator; value is less than 1.
Example: 1/2
Improper fraction: numerator is greater than denominator; value is greater than 1.
Example: 4/3.
Or numerator denominator; value 1.
Example: 5/5
Mixed number: whole number a fraction; value is greater than 1.
Example: 1(1/2)
Complex fraction: numerator and/or denominator are composed of a fraction, decimal,
or mixed number; value is less than, greater than, or = 1.
Example: (1/2) / (1/50)
Any nonzero number divided by itself 1.
Example: (3/3) = 1
To reduce a fraction to lowest terms, divide both terms by the largest nonzero whole
number that will divide both the numerator and denominator evenly. Value remains the
same.
Example: 1/6 = (6/2) / (10/2) = 3/5

3. To enlarge a fraction, multiply both terms by the same nonzero number. Value remains
the same.
Example: 1/12 = (1x2) / (12x2) = 2/24
To convert a mixed number to an improper fraction, multiply the whole number by the
denominator and add the numerator; use original denominator in the fractional part.
Example: 1(1/3) = 4/3
To convert an improper fraction to a mixed number, divide the numerator by the
denominator.
Express any remainder as a proper fraction reduced to lowest terms.
Example: 21/9 = 2(3/9) = 2(1/3)
When numerators are equal, the fraction with the smaller denominator is greater.
Example: 1/2 is greater than 1/3
When denominators are equal, the fraction with the larger numerator is greater.
Example: 2/3 is greater than 1/3
2. To add or subtract fractions:
 Convert to equivalent fractions with least common denominators.
 Add or subtract the numerators; place that value in the numerator.
Use the least common denominator as the denominator.
 Convert the answer to a mixed number and/or reduce to lowest terms.

4. 3. Multiplication of Fractions
When multiplying a fraction by a nonzero whole number, the same rule applies as for
multiplying fractions.
First convert the whole number to a fraction with a denominator of 1; the value of the
number remains the same.
Example (2/3) x (4/1)
To multiply mixed numbers, first convert them to improper fractions, and then multiply.
Example 31/2 x 41/3 = 7/2 x 13/3
To divide mixed numbers, first convert them to improper fractions.
Example[1(1/2)] / (3/4) = (3/2) / (3/4) = (3/2) x (4/3) = (1/1) x (2/1) = 2
To multiply fractions, cancel terms, multiply numerators, and multiply denominators.
 To divide fractions, invert the divisor, cancel terms, and multiply.
 Convert results to a mixed number and/or reduce to lowest terms.

5. 4. DECIMALS
In a decimal number, whole number values are to the left of the decimal point, and
fractional values are to the right.
Zeros added to a decimal fraction before the decimal point of a decimal number less
than 1 or at the end of the decimal fraction do not change the value.
Example: .5 = 0.5 = 0.50. However, using the leading zero is the only
acceptable notation (such as, 0.5).
In a decimal number, zeros added before or after the decimal point may change the
value.
Example: 1.5 ≠ 1.05 and 1.5 ≠ 10.5.
To avoid overlooking the decimal point in a decimal fraction, always place a zero to the
left of the decimal point.
Example: .5 ← Avoid writing a decimal fraction this way; it could be mistaken
for the whole number 5.
Example: 0.5 ←. This is the required method of writing a decimal fraction with a
value less than 1
The number of places in a decimal fraction indicates the power of 10.
Examples:
0.5 = five tenths
0.05 = five hundredths
0.005 = five thousandths

6. Compare decimals by aligning decimal points and adding zeros.
Example:
Compare 0.5, 0.05, and 0.005.
0.500 = five hundred thousandths (greatest)
0.050 = fifty thousandths
0.005 = five thousandths (least)
To convert a fraction to a decimal, divide the numerator by the denominator.
To convert a decimal to a fraction, express the decimal number as a whole number in
the numerator and the denominator as the correct power of 10. Reduce the fraction to
lowest terms.
Example:
0.04 = 4 (numerator is a whole number)
100 (denominator is 1 followed by two zeros)
= 4/100
= 1/25

7. To multiply decimals, place the decimal point in the product to the left as many decimal
places as there are in the two decimals multiplied.
Example:
0.25 x 0.2 = 0.050 = 0.05 (Zeros at the end of the decimal are unnecessary).
To divide decimals, move the decimal point in the divisor and dividend the number of
decimal places that will make the divisor a whole number and align it in the quotient.
Example: 24 / 1.2
To multiply or divide decimals by a power of 10, move the decimal point to the right (to
multiply) or to the left (to divide) the number of decimal places as there are zeros in the
power of 10.
Examples:
5.06 x10 = 5.0.6 = 50.6
2.1 /100 = .02.1 = 0.021
When rounding decimals, add 1 to the place value considered if the next decimal place
is 5 or greater.
Examples:
Rounded to hundredths: 3.054 = 3.05; 0.566 = 0.57.
Rounded to tenths: 3.05 = 3.1; 0.54 = 0.5

16. Weights and Measures

54. Pharmaceutical Calculations
Reducing & Enlarging Formulas
Percentage Preparations
Ratio Strength
Dilution and Concentration

65. Dilution and Concentration

106. MEDICAL DOSE
CALCULATION

107. OUTLINE
• Dosage units
• Oral medication doses
• Parenteral medication doses
• Special precautions:
Pediatric
Renal dysfunction
Hepatic dysfunction
107

108. DOSAGE UNITS
108
• Units of volume
• Units of mass
Unit Equivalent to
1 kilogram 1000 g
1 gram 1000 mg
1 miligram 1000 micrograms
1 microgram 1000 nanograms

109. UNDERSTANDING CONCENTRATIONS
109
1. How would a dose of 125 micrograms of digoxin
be given to a patient from an ampoule of digoxin
injection containing 500 micrograms in 2 ml?
2. How would a dose of 2.5 mg of midazolam be
given to a patient from an ampoule of midazolam
injection containing 10 mg in 2 ml?

110. Step by step no.1
110
• Step 1: calculate the amount of digoxin in 1 ml
of solution. Solution contains 500 micrograms
in 2 ml. Therefore, it contains 500 micrograms
÷ 2 = 250 micrograms in 1 ml
• Step 2: the volume of solution that would
contain 125 micrograms is:
125
------ X 1 ml = 0,5 ml
250
Dose required
------------- x vol. = vol. required
Strength available

111. Step by step no.2
111
• Step 1: calculate the amount of midazolam in 1 ml of
solution. Solution contains 10 mg in 2 ml. Therefore, it
contains 10 mg ÷ 2 = 5 mg in 1 ml.
• Step 2: calculate the volume of solution that contains
2.5 mg midazolam. Solution contains 5 mg in 1 ml.
Therefore, for a dose of 2 mg, we would need:
• 2.5
----- x 1 ml = 0.5 ml
5

112. ORAL DOSE CALCULATION
112

113. Determine how you would administer
this dose
The order is Ryzolt 300 mg po daily.
113

114. Calculation
114
Dosage on hand Dosage desired
------------------- = --------------------
Amount on hand X amount desired

115. Give?
Order: Ceclor 100 mg p.o q.i.d
115
125 mg 100 mg
---------- = -----------
5 ml X ml

116. Give?
Order: Lanoxin 0.125 mg p.o daily
116

117. 3 Step Approach
117
Convert Think Calculate

118. PARENTERAL DOSE
CALCULATION
118

119. Parenteral Medication Package
119
AMPULES VIALS

120. How many grams of dextrose contained in 30 ml
of this solution?
120

121. SUBCUTAN
121
• The maximum dosage volume per subcutan
injection:
– Infant : 0,1 ml
– Child : 0,5 ml
– Adult : 0,5-1 ml

122. INTRAMUSCULAR
122
• The maximum dosage volume per
intramuscular injection:
– Adult : 3 ml
– Children age 6-12 years : 2 ml
– Children birth to age 5 years : 1 ml

123. Example 1.
• Order: Quinidine
gluconate 600 mg IM
and 400 mg IM q4h prn
• Give?
123

124. Step by step
124
• 400 mg = ? ml
• Label : 80 mg per ml
• So: 400 mg 1 ml
x ------ = 5 ml
80 mg

125. 125

126. RECONSTITUTION
126

127. 127

128. Calculating Dosage by body weight
128
• Mg/kg
• Patient receive 15 miligrams of the drug for
each kilogram of body weight
• 15 mg (of drug) = 1 kg (of body weight)

129. EXAMPLE
129
• The order for an adult who has adrenal
insufficiency is dexamethasone sodium
phospate 5 mg IM q12h. Patient weighs 100
kg. Strength in the vial is 4mg/ml
• If the recommended daily dosage is 0.03-0.15
mg/kg, is the prescribed dosage safe?

130. ANSWER
130
• Calculate minimum and maximum number
Minimum
Maximum
• Determine how many mililiters of liquid in the
vial contain the prescribed quantity of the
medication

131. PEDIATRIC DOSE HANDLING
131

132. Pediatric
The dose of most pediatrics drugs is based on
 Age
 mg/kg body weight
 Body Surface Area
132

133. Dosage Calculation Based on Age
133

134. 134

135. Dosage calculations
based on body weight
135
1 pounds= 0,45 kg
1 kg=2.2 lb

136. Example
• Physician ordered EES
10mg/kg PO q8h for a
child who weighs 50
kg.
136

137. Dosage calculation based on BSA
 Calculation
Surface Area:
m2 = [ Height(cm) 0.3964x Weight(kg) 0.5378 ] 0.024265
OR
 Nomogram
137

138. 138

139. 139

140. 140

141. Dose Calculations for Paediatrics
Tabel 2. Percentage method for calculating doses
50237 year
33.3153 year
25101 year
206.54 months
154.52 months
12.53.5Neonate
Percentage of adult
dose
Mean weight of age
(kg)
Age
141

142. 10068Adult
905816 year
805014 year
753912 year
603010 year
142

143. Safe Medication Dose for Pediatric
 Calculate daily dose ordered (Physician orders)
 Identify the patient
 Calculate the low and high parameters of safe
range (from references)
 Compare the patient’s daily dose to the safe
range to see if it falls within the safe zone.
143

144. Cases
144
1. Zithromax 10 mg/kg PO, then give 5
mg/kg/day. The child weighs 18 kg.

145. 145

146. Cases (con’t)
146
2. A child who has BSA 0.76 m2 received
Dactinomycin 2.5 mg/m2 daily for 5 days.
Calculate the dose of this antineoplastic drug in
miligrams.
3. The recommended dose for neonates
receiving Amikacin sulfate is 7.5 mg/kg IM q12h.
Infant weighs 2.600 grams. How many mg of

147. Renal Dysfunction-Dosage adjustment
147
Avoid excessive accumulation of the drug and/or
its active metabolite(s) which could result in
serious adverse reactions

148. Cockroft Gault Equation
• LBW → Pria: 50 + 2,3/inch (TB>150 cm)
• Wanita: 45,5 + 2,3/inch (TB>150 cm)
148

149. MDRD Equation
149

150. MDRD equation
• Estimation of glomerular filtration rate (GFR)
• Best overall index of renal function in health and
disease
• Can be directly measured
• Estimated based on substances that are freely filtered
in the glomerulus
• The most accurate method of estimating renal function
• More accurate in severe renal impairment, accounts
for ethnicity
• Doesn’t address height or weight
150

151. Cockroft Gault Equation
• Estimates creatinine clearance (CrCl)
• Most commonly used
• Basis for most renal dosing recommendations
provided in the package insert
• Easy to calculate, produces consistent results in
adult patients of average size and build with
stable renal function and a SCr <3 mg/dL
• Not a true marker of renal impairment, may
overestimate renal function (especially in the
elderly), and validity in obese patients is
questionable
151

152. Dosage adjustment
• Calculate CrCl using Cockcroft-Gault equation
• Use a reference to identify renal dosing
parameters
• Identify suggested dosage adjustment
• Determine if the dosage adjustment is logical and
appropriate for your patient
• Factors to consider:
CrCl is a starting point (as it is only an estimation)
Toxicities of agents
Clinical condition of the patient
SCr trends, stability of patient, severity of disease 152

153. Progressive Model of Hepatic Dysfunction
153

154. Child Pugh Classification
Clinical Indicator 1 point 2 points 3 points
Serum bilirubin (mg/dL) <2 2-3 >3
Serum albumin (g/dL) > 3,5 2,8-3,5 <2,8
Prothrombin time
(s>control)
<4 4-6 >6
Encephalopathy (grade) None 1 or 2 3 or 4
Ascites Absent Slight Moderate
154

155. Child Pugh Score
5-6 points → A (mild)
7-9 points → B (moderate)
10-15 points → C (severe)
155

156. REFERENCES
156
• Courtenay M, Griffths M. Medication Safety: An Essential Guide. 2010.
Cambridge University Press
• Olsen JL, Giangrasso AP, Shrimpton DM. Medical Dosage Calculations: A
Dimensional Analysis Approach. 2012. Pearson
• Pickar GD. Dosage Calculation A Ratio-Proportion Approach. 2nd
edition. 2007. Thomson
• Eur J Clin Pharmacol (2009) 65:757–773
• Eur J Clin Pharmacol (2008) 64:1147–1161
• Hospital Pharmacy Volume 44, Number 7, pp 577–583, 603. 2009
Wolters Kluwer Health, Inc

157. 157

158. Reference:
1. Dosage Calculations: A Ratio-Proportion Approach, Gloria D. Pickar, EdD, RN 2007, 2nd Edition
2. Pharmaceutical and Clinical Calculations, Mansoor A.Khan. and Indra K. Reddy, 2000, 2nd Ed.