u E L E V E N T H E D I T I O N Pharmaceutical Calculations Howard C. Ansel, Ph. D. Professor and Dean Emeritus College of Pharmacy The University of Georgia Athens, Georgia Mitchell J. Stoklosa, A.M., Sc.D. Professor of Pharmacy Emeritus Massachusetts College of Pharmacy and Health Sciences, Boston, Massachusetts LIPPINCOTT WILLIAMS & WILKINS A Wolters Kluwer Company Philadelphia Baltimore New York London Buenos Aires Hong Kong Sydney Tokyo
Contents Introduction xi 1. Some Fundamentals of Measurement and Calculation I Numbers and Numerals 1 Kinds of Numbers 1 Arabic Numerals 2 Roman Numerals 3 Common and Decimal Fractions 5 Exponential Notation 11 Fundamental Arithmetic Operations with Exponentials 11 Ratio, Proportion, and Variation 13 Dimensional Analysis 17 Significant Figures 20 Estimation 25 Percentage of Error 29 Measurement of Volume 31 Measurement of Weight 33 Aliquot Method of Weighing and Measuring 36 Least Weighable Quantity Method of Weighing 38 2. Interpretation of the Prescription or Medication Order 41 Medication Scheduling and Patient Compliance 47 3. The Metric System 51 Measure of Length 52 Measure of Volume 53 Measure of Weight 54 Fundamental Computations 55 Relation of Metric to Other Systems of Measurement 57 4. Calculation of Doses 63 Calibration of Droppers 61 Calculations in Miscellaneous Dosage Problems 67 Special Dosing Considerations for the Pediatric and Elderly Patient 71 Drug Dosage Based on Age 72 Drug Dosage Based on Body Weight 74 Drug Dosage Based on Body Surface Area 75 Special Dosing Considerations in Cancer Chemotherapy 79 Clinical Laboratory Test Values and Dosage 81 Heparin Dosing Calculations 82 vii
viii Contents 5. Reducing and Enlarging Formulas 92 Formulas that Specify Amounts of Ingredients 93 Formulas that Specify Proportional Parts 95 6. Density, Specific Gravity, and Specific Volume 101 Density 101 Specific Gravity 101 Density Versus Specific Gravity 103 Calculating the Specific Gravity of Liquids 103 Calculating the Specific Gravity of Solids 104 Calculating Specific Volume 106 Use of Specific Gravity in Calculations of Weight and Volume... 108 7. Percentage, Ratio Strength, and Other Expressions of Concentration 113 Percentage 113 Percentage Preparations 113 Percentage Weight-in-Volume 113 Percentage Volume-in-Volume 115 Percentage Weight-in-Weight 117 Use of Percent in Compendial Standards 119 Ratio Strength 120 Simple Conversions of Concentration to "mg/ml" 122 Milligrams Percent 123 Expressing Clinical Laboratory Test Values 123 Parts per Million (PPM) and Parts per Billion (PPB) 124 8. Dilution and Concentration 133 Relationship Between Strength and Total Quantity 133 Dilution and Concentration of Liquids 134 Stock Solutions 136 Dilution of Alcohol 141 Dilution of Acids 142 Dilution and Concentration of Solids 143 Triturations 144 Alligation 145 Specific Gravity of Mixtures 151 9. Isotonic Solutions 160 Preparation of Isotonic Solutions 160 10. Electrolyte Solutions: Milliequivalents, Millimoles, and Milliosmoles 172 Millimoles 178 Osmolarity 178 Clinical Considerations and Calculations 181 11. Some Calculations Involving "Units," " xg/mg," and Other Measures of Potency 188
Contents ix 12. Constituted Solutions, Intravenous Admixtures, and Rate of Flow Calculations 195 Constitution of Dry Powders 195 Intravenous Admixtures 200 Parenteral Nutrition 203 Rate of Flow of Intravenous Fluids 207 13. Some Calculations in Contemporary Compounding 218 Use of Prefabricated Dosage Forms in Compounding 218 Pharmaceutical Formulas 222 14. Body Mass Index and the Nutrition Label 226 Body Mass Index (BMI) ' 226 The Nutrition Label 228 15. Some Calculations Associated with Drug Availability and Pharmacokinetics 234 Drug Availability from Dosage Forms and Delivery Systems... 234 Some Introductory Concepts and Calculations Involved in Pharmacokinetics 238 Dosage Calculations Based on Creatinine Clearance 242 16. Some Calculations Involving Veterinary Pharmaceuticals 248 17. Calculation of Active Drug Moiety 253 Atomic and Molecular Weights 253 Chemically Equivalent Quantities 255 Active Drug Moiety Equivalence 255 18. Some Calculations Associated with Plant Extractives 260 Extracts, Fluidextracts, and Tinctures 260 Botanic Dietary Supplements 262 19. Some Calculations Involving Radiopharmaceuticals 265 Radioisotopes 265 Radioactivity 265 Units of Radioactivity 268 20. Some Pharmacoeconomic Calculations 274 Pharmacoeconomic Methods of Analysis 274 Cost Considerations of Drug and Drug Product Selection 275 Drug Acquisition Costs 278 Markup 279 Prescription Pricing 280 21. Miscellaneous Pharmaceutics Calculations 287 Solubility Ratios 287 Emulsion Nucleus 289 Hydrophile-Lipophile-Balance (HLB) System 291 Buffers and Buffer Solutions 294 Thermometry 299 Proof Strength 304
x Contents Appendices 308 A. The Common Systems of Measurement and Intersystem Conversion 308 Apothecaries' Fluid Measure 308 Apothecaries' Measure of Weight 308 Avoirdupois Measure of Weight 309 Fundamental Operations and Calculations 309 Relationship of Avoirdupois and Apothecaries'Weights. 312 Intersystem Conversion 313 Conversion of Linear Quantities 315 Conversion of Liquid Quantities 316 Conversion of Weights 317 B. Graphical Methods 321 Linear Relationships on Rectangular Graph Paper 321 Linear Relationships on Semilogarithmic Graph Paper... 324 Other Methods of Data Presentation: Tables and Charts. 325 C. Basic Statistical Concepts 331 The Array 331 The Frequency Distribution 331 Averages 332 Measures of Variation 333 Some Aspects of Probability 335 D. Glossary of Pharmaceutical Dosage Forms and Drug Delivery Systems 342 Review Problems 347 Answers to Practice and Review Problems 369 Index 385 Atomic Weights Inside front and back covers