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Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_5576_Библиотеки_им_академика_М_И_Перельмана
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CONTENTS
Preface
Acknowledgments
Contents
Introduction
1 Fundamentals of Pharmaceutical Calculations
2 International System of Units
3 Pharmaceutical Measurement
4 Interpretation of Prescriptions and Medication
Orders
5 Density and Specific Gravity
6 Percent Strength, Ratio Strength, and Other
Expressions of Concentration
7 Calculation of Doses: General Considerations
8 Calculation of Doses: Patient Parameters
9 Calculations Involving Units of Activity and Other
Measures of Potency
10 Selected Clinical Calculations
11 Isotonic and Buffer Solutions
12 Electrolyte Solutions: Milliequivalents, Millimoles,
and Milliosmoles
13 Intravenous Infusions, Parenteral Admixtures, Rateof-Flow Calculations
14 Assessment of Nutritional Status, Enteral and
Parenteral Nutrition, and the Food Nutrition Label
15 Altering Product Strength, Use of Stock Solutions,
and Problem Solving by Alligation
16 Reducing and Enlarging Formulas
17 Selected Calculations in Contemporary
Compounding
18 Selected Calculations Involving Veterinary
Pharmaceuticals
19 Selected Calculations Associated with Plant
Extractives
20 Calculation of Active Drug Moiety
21 Selected Calculations Involving
Radiopharmaceuticals
22 Basic Pharmacokinetics
23 Cost Differential Calculations in Drug Therapy
Appendix A Common Systems of Measurement and
Intersystem Conversion
Appendix B Glossary of Pharmaceutical Dosage Forms
and Drug Delivery Systems
Appendix C Table of Atomic Weights
Comprehensive Review Problems
Index
INTRODUCTION
Scope of Pharmaceutical Calculations
The use of calculations in pharmacy is varied and broad-based.
It encompasses calculations performed by pharmacists in
traditional as well as in specialized practice settings and within
operational and research areas in industry, academia, and
government. In the broad context, the scope of pharmaceutical
calculations includes computations related to:
Prescriptions and medication orders including drug
dosage, dosage regimens, and patient adherence to
medication treatment plans
Pharmaceutical product development and formulation
Chemical and physical properties of drug substances and
pharmaceutical ingredients
Biological activity and rates of drug absorption, bodily
distribution, metabolism, and excretion
(pharmacokinetics)
Statistical data from basic research and clinical drug
studies
Pharmacoeconomics and other areas
For each of these areas, there is a unique body of
knowledge. Some areas are foundational, whereas others are
more specialized, constituting a distinct field of study. This
textbook is foundational, providing the basic underpinnings of
calculations applicable to pharmacy practice in community,
health system, and industrial settings.
In community pharmacies, pharmacists receive, fill, and
dispense prescriptions and provide relevant drug information
to ensure their safe and effective use. Prescriptions may call
for prefabricated pharmaceutical products manufactured in
industry, or, they may call for individual components to be
weighed or measured by the pharmacist and compounded into
a finished preparation. In hospitals and other institutional
settings, medication orders are entered into a patient’s medical
chart, becoming part of the electronic medical record.
In the preparation of pharmaceuticals, both medicinal and
nonmedicinal materials are used. The medicinal components
(active pharmaceutical ingredients or APIs) provide the benefit
desired. The nonmedicinal ingredients (pharmaceutical
excipients) are included in a formulation to produce the
desired pharmaceutical qualities, as physical form, chemical
and physical stability, rate of drug release, appearance, and
taste, when desired.
Whether a pharmaceutical product is produced in the
industrial setting or prepared in a community or institutional
pharmacy, pharmacists engage in calculations to achieve
standards of quality. The difference is one of scale. In
pharmacies, relatively small quantities of medications are
prepared and dispensed for specific patients. In industry, largescale production is designed to meet the requirements of
pharmacies and their patients on a national and even
international basis. The latter may involve the production of
hundreds of thousands of dosage units of a specific drug
product during a single production cycle. The preparation of
the various dosage forms and drug delivery systems (defined
in Appendix B), containing carefully calculated, measured,
verified, and labeled quantities of ingredients, enables accurate
dosage administration.
A Stepwise Approach toward
Pharmaceutical Calculations
Success in performing pharmaceutical calculations is based
on:
An understanding of the purpose or goal of the problem
An assessment of the arithmetic process required to reach
the goal
An implementation of the correct arithmetic
manipulations
For many pharmacy students, particularly those without
pharmacy experience, difficulty arises when the purpose or
goal of a problem is not completely understood. The
background information provided in each chapter is intended
to assist the student in understanding the purpose of each area
of calculations. Additionally, the following steps are suggested
in addressing the calculation problems in this textbook as well
as those encountered in pharmacy practice.
Step 1. Take the time necessary to carefully read and
thoughtfully consider the problem prior to engaging in
computations. An understanding of the purpose or goal
of the problem and the types of calculations that are
required will provide the needed direction and
confidence.
Step 2. Estimate the dimension of the answer in both
quantity and units of measure (e.g., milligrams) to
satisfy the requirements of the problem. A section in
Chapter 1 provides techniques for estimation.
Step 3. Perform the necessary calculations using the
appropriate method both for efficiency and
understanding. For some, this might require a stepwise
approach, whereas others may be capable of combining
several arithmetic steps into one. Mathematical
equations should be used only after the underlying
principles of the equation are understood.
Step 4. Before assuming that an answer is correct, the
problem should be read again and all calculations
checked. In pharmacy practice, pharmacists are
encouraged to have a professional colleague check all
calculations prior to completing and dispensing a
prescription or medication order. Further, if the process
involves components to be weighed or measured, these
procedures should be double checked as well.
Step 5. Finally, consider the reasonableness of the answer in
terms of the numerical value, including the proper
position of a decimal point, and the units of measure.
1
Fundamentals of Pharmaceutical
Calculations
OBJECTIVES
Upon successful completion of this chapter, the student will be able to:
Apply the method of ratio and proportion in problem solving.
Apply the method of dimensional analysis in problem solving.
Demonstrate the use of percent in pharmaceutical calculations.
Apply and validate the method of estimation in pharmaceutical
calculations.
Introduction
Pharmaceutical calculations is the area of study that applies the basic
principles of mathematics to the preparation and efficacious use of
pharmaceutical preparations. It includes calculations from initial product
formulation through clinical administration and outcomes assessment.
Mathematically, pharmacy students beginning use of this textbook are
well prepared. The basic units of measurement and problem-solving
methods have been previously learned and are familiar. The newness lies
in the terminology used and in the understanding of the
pharmaceutical/clinical purpose and goal of each computation. Of vital
importance is an appreciation of the need for accuracy, as each
calculation must be understood to be directly applicable to the health
outcomes and safety of patients. Therefore, the student must communicate
information clearly and accurately. According to the Institute for Safe
Medication Practices, a trailing zero should never be used following a
decimal point to show accuracy (e.g., 1.0 mL) because it can result in a 10fold error if the decimal point is not seen (i.e., 10 mL). Similarly, a zero
should always precede the decimal point in decimal fractions less than one
(e.g., 0.2 mg) to avoid missing the decimal point and also creating a 10-
fold error.1 Rounding of numbers within a calculation should be avoided,
and no rounding should be done until the final answer has been calculated
to determine the most accurate answer. In most instances rounding the
final answer to two or three decimal places is acceptable.
This initial chapter introduces some basic aspects and methods of
pharmaceutical calculations.
Units of Measurement
Pharmacy and all other health professions utilize the International System
of Units (SI), commonly referred to as the metric system. This familiar
system, with its base units (meter, liter, kilogram) and corresponding
subdivisions, is presented in detail in Chapter 2. Pharmaceutical
calculations often require the accurate conversion of quantities from a
given or calculated unit to another (e.g., milligrams to micrograms).
Proficiency in operating within this system is fundamental to the practice
of pharmacy.
Two other systems of measurement are presented in Appendix A. The
avoirdupois system is the common system of commerce, which has not
fully been replaced in the United States by the International System of
Units. Many product designations are dual scale: that is, equivalent SI and
common system measures. It is in the common system that goods are
packaged and sold by the ounce, pound, pint, quart, and gallon or linearly
measured by the inch, foot, yard, and mile. The apothecaries’ system of
measurement is the traditional system of pharmaceutical measurement,
which is now largely of historic significance. Intersystem conversion
remains an exercise in pharmaceutical calculations and is a component of
Appendix A.
Ratio and Proportion
Ratio
The relative amount of two quantities (one to the other), is called their
ratio. A ratio resembles a common fraction except in the manner in which
it is presented. For example, the fraction ½ may be expressed as the ratio
1:2, which is not read as “one half,” but rather as “one is to two.” Rules
governing common fractions apply to ratios. For example, if the two terms
of a ratio are either multiplied or divided by the same number, the value
remains unchanged. The value is the quotient of the first term divided by
the second term. For instance, the value of the ratio 20:4 is 5. If the ratio is
multiplied by 4, becoming 80:16, or divided by 4, becoming 5:1, the value
remains 5. When two ratios have the same value, they are termed
equivalent ratios, as is the case with the ratios 20:4, 80:16, and 5:1.
As described next, equivalent ratios provide the basis for problem
solving by the ratio-and-proportion method.
Proportion
A proportion is the expression of the equality of two ratios. It may be
written in any one of three standard forms:
Each of these expressions is read: a is to b as c is to d, and a and d are
called the extremes (meaning “outer members”) and b and c the means
(“middle members”).
In any proportion, the product of the extremes is equal to the product
of the means. This principle allows us to find the missing term of any
proportion when the other three terms are known. If the missing term is a
mean, it will be the product of the extremes divided by the given mean, and
if it is an extreme, it will be the product of the means divided by the given
extreme. Using this information, we may derive the following fractional
equations:
In a proportion that is properly set up, the position of the unknown term
does not matter. However, some persons prefer to place the unknown term
in the fourth position—that is, in the denominator of the second ratio. It
important to label the units in each position (e.g., mL, mg) to ensure the
proper relationship between the ratios of a proportion.
The application of ratio and proportion enables the solution of many of
the pharmaceutical calculation problems in this text and in pharmacy
practice.
1. If 3 tablets contain 975 milligrams of aspirin, how many milligrams
should be contained in 12 tablets?
2. If 3 tablets contain 975 milligrams of aspirin, how many tablets should
contain 3900 milligrams?
3. If 12 tablets contain 3900 milligrams of aspirin, how many milligrams
should 3 tablets contain?
4. If 12 tablets contain 3900 milligrams of aspirin, how many tablets
should contain 975 milligrams?
Proportions need not contain whole numbers. If common or decimal
fractions are supplied in the data, they may be included in the proportion
without changing the method. For ease of calculation, it is recommended
that common fractions be converted to decimal fractions prior to setting up
the proportion.
5. If one dose of a cough syrup is 1¼ milliliters (mL) for a small child,
how many milliliters will be needed for 12 doses of the syrup?
CALCULATIONS CAPSULE
Ratio and Proportion
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