Pharmaceutical Calculations

Retaining the successful previous editions' programmed instructional format, this book improves and updates an authoritative textbook to keep pace with compounding trends and calculations – addressing real-world calculations pharmacists perform and allowing students to learn at their own pace through examples.

• Connects well with the current emphasis on self-paced and active learning in pharmacy schools
• Adds a new chapter dedicated to practical calculations used in contemporary compounding, new appendices, and solutions and answers for all problems
• Maintains value for teaching pharmacy students the principles while also serving as a reference for review by students in preparation for licensure exams
• Rearranges chapters and rewrites topics of the previous edition, making its content ideal to be used as the primary textbook in a typical dosage calculations course for any health care professional
• Reviews of the prior edition: "...a well-structured approach to the topic..." (Drug Development and Industrial Pharmacy) and "...a perfectly organized manual that serves as a expert guide..." (Electric Review)

Maria Glaucia Teixeira, PhD, is Associate Professor Emeritus in the School of Pharmacy at the University of Wyoming, where she retired after 23 years on the faculty, following 10 years as Professor at the Federal University of Ceará in Fortaleza, Brazil. She has received numerous recognitions for her teaching, including the Top Prof and Excellence in Teaching awards at Wyoming. She received her PhD in Pharmacology at Paul Sabatier University, Toulouse, France.

Joel L. Zatz, PhD, is Professor Emeritus at Rutgers University, New Jersey.

Preface xiii

Chapter 1 Review of Basic Mathematical Principles1

1.1. Significant Figures 2

1.2. Rounding Off 4

1.3. Fractions 5

1.4. Exponents and Powers 8

1.5. Estimation 10

1.6. Units 12

1.7. Ratio 15

1.8. Proportion 15

1.9. Dimensional Analysis 18

Practice Problems 21

Chapter 2 Systems of Measurement 31

2.1. Metrology 31

2.2. The Metric System 32

2.3. The English Systems 33

2.3.1. The Avoirdupois System 33

2.3.2. The Apothecary or Troy System 33

2.4. Measurement of Weight 33

2.4.1. Metric Weight 33

2.4.2. English Weight 35

2.4.2.1. Avoirdupois Weight 35

2.4.2.2. Apothecary Weight 36

2.4.3. Practical Weight Equivalents 36

2.5. Measurement of Volume 38

2.5.1. Metric Volume 38

2.5.2. English Volume 39

2.5.3. Practical Volume Equivalents 39

2.6. Measurement of Length 41

2.7. Intersystem Relationships 43

2.8. Household Equivalents and Metric Estimation 44

Practice Problems 49

Chapter 3 Prescriptions and Medication Orders 54

3.1. Prescribing Authority 55

3.2. Components 57

3.3. Practices to Prevent Medication Errors 58

3.4. Common Abbreviations 60

3.5. Outpatient Prescription Drug Orders 69

3.5.1. Prescriptions for Manufactured Drug Products 69

3.5.2. Prescriptions for Compounded Drug Products 69

3.5.2.1. Types of Compounded Orders 70

3.5.2.2.1. Formulation Based on Total Quantity 70

3.5.2.3.2. Formulation Based on Single Dosage Unit 71

3.6. Inpatient Medication Orders 72

3.7. Interpretation 77

3.8. Calculations to Check “DEA” Numbers 77

3.9. Reducing and Enlarging Formulas 80

3.10. Parts Formulas 87

Practice Problems 90

Chapter 4 Weighing and Measuring in Pharmacy Practice 103

4.1. Measurement Errors 103

4.2. Indication of Error 104

4.2.1. Absolute Error: Indication of Error Based on Maximum Deviation and Significant Figures 104

4.2.2. Relative Error: Indication of Error Based on Percentage of Estimated Value 107

4.3. Tolerance in Prescription Compounding and Pharmaceutical Manufacturing 108

4.4. Weighing and Measuring 109

4.4.1. Electronic Balances 109

4.4.2. Prescription Balances: Class A, Torsion 110

4.4.2.1. Sensitivity Requirement (SR) 110

4.4.2.2. Minimum Weighable Quantity (MWQ) or Least Weighable Quantity (LWQ) 110

4.4.2.3. Percent Error 111

4.4.3. Volumetric Devices for Pharmaceutical Measurements 114

4.4.3.1. The Meniscus and Effect of Viscosity 114

4.4.3.2. Graduates 114

4.4.3.3. Pipets (Pipettes) 115

4.4.3.4. Syringes 115

4.4.3.5. Droppers 116

4.5. Aliquot Method and Triturations 119

4.5.1. Solid–Solid Aliquot Method 119

4.5.2. Solid–Solid Triturations 122

4.5.3. Liquid–Liquid Aliquots and Triturations 131

4.5.4. Solid–Liquid Aliquots 136

4.5.5. Serial Dilutions 140

4.6. Density 142

4.7. Specific Gravity 144

Practice Problems 145

Chapter 5 Dosage Calculations 160

5.1. Calculations Involving Dose, Size, Number of Doses, Amount Dispensed, and Quanity of a Specific Ingredient in a Dose 161

5.2. Dosage Measured By Drops 169

5.3. Dosage Based on Body Weight 171

5.4. Dosage Based on Body Surface Area (BSA) 174

5.5. Pediatric and Geriatric Dose Calculations 181

5.6. Chemotherapy Dose Calculations 184

Practice Problems 187

Chapter 6 Drug Concentration Expressions 203

6.1. Concentration 204

6.2. Percentage Strength Expressions 204

6.2.1. Percent Volume-in-Volume 204

6.2.2. Percent Weight-in-Weight 205

6.2.3. Percent Weight-in-Volume 206

6.2.4. Default Rules for Percentage Expressions 208

6.2.5. Prescriptions and Formulations with Ingredients Listed as Percentage 210

6.2.6. Using Specific Gravity to Calculate the Exact Amount of Solvent in a Solution 215

6.2.7. Converting % w/w into %w/v Using Specific Gravity 217

6.3. Stock Solutions, Concentrates, and Triturations 218

6.4. Saturated Solutions 222

6.5. Ratio Strength Expressions 224

6.5.1. Ratio Volume-in-Volume 224

6.5.2. Ratio Weight-in-Volume 225

6.5.3. Ratio Weight-in-Weight 226

6.6. Other Pharmaceutical Expressions of Drug Concentration 230

6.6.1. Milligrams Per Milliliter (mg/mL) 230

6.6.2. Milligrams Percent (mg%) and Miligrams Per Deciliter (mg/dL) 231

6.6.3. Parts Per Million (ppm) and Parts Per Billion (ppb) 232

6.6.4. Millimols, Milliequivalents, and Milliosmols Per Unit of Volume 234

Practice Problems 235

Chapter 7 Dilution and Concentration 257

7.1. Problem-Solving Methodologies 258

7.1.1. Concentration Principle 258

7.1.2. Mass Balance Equation 260

7.1.2.1. Dilution of Powders or Solid Mixtures 261

7.1.2.2. Mixing Different Strengths 265

7.1.2.3. Modifying the Drug Concentration of a Prepared Product: Increasing Drug Concentration 267

7.1.3. The CQ Equation: Concentration X Quantity 268

7.1.3.1. Expanded CQ Equation 272

7.1.4. Algebraic Calculations Using the Concentration Equation and the CQ Equation 275

7.1.5. Alligation Alternate 283

7.1.5.1. Use of Alligation When Combining More Than Two Products 287

7.2. So, Which Method Should I Use? 291

7.2.1. Stock Solutions Diluted by the Patient 293

Practice Problems 296

Chapter 8 Isotonicity 310

8.1. Principles 310

8.2. Sodium Chloride Equivalent Values 312

8.3. Isotonicity by the Sodium Chloride Equivalent Method 315

8.3.1. Sodium Chloride Equivalent: Method 1 315

8.3.2. Sodium Chloride Equivalent: Method 2 318

8.4. Other Tonicity Agents 319

8.5. Isotonicity When One Ingredient is Already Isotonic 321

8.6. Isotonic Buffered Solutions 323

8.6.1. Using the White–Vincent Method to Adjust Tonicity 323

8.7. Other Methods 326

8.8. Determination of the Tonicity of a Solution (Hypotonic, Isotonic, or Hypertonic) 329

Practice Problems 330

Chapter 9 Dosage Calculations of Electrolytes 340

9.1. Molarity and Molality 341

9.1.1. Mols and Millimols 341

9.1.2. mmol/mL, mmol/L 344

9.2. Electrolyte Dissociation, Valence, Equivalent, and Equivalent Weight 344

9.3. Milliequivalents, mEq/mL, mEq/L 347

9.3.1. Problem-Solving Methods for Milliequivalents 348

9.4. Osmolarity (Osmolar Strength) 354

9.4.1. Milliosmoles and mOsm/L 355

Practice Problems 366

Chapter 10 Calculations for Injectable Medications And Sterile Fluids 378

10.1. Reconstitution of Dry Powders 378

10.1.1. Reconstituting with Volumes Other Than Those on Manufacturer’s Label 380

10.1.2. Considering Powder Volume 383

10.1.3. Powders as Compounding Sources of Drugs 385

10.2. Calculations Related to Units/ml (Insulin, Heparin) and Other Units of Potency 386

10.2.1. Calculations of Insulin Single Dose and Combinations 387

10.2.2. Calculations of Heparin Doses 391

10.3. Intravenous Admixtures 392

10.4. Extemporaneous IV Fluids 395

10.5. Flow Rates in Intravenous Sets 397

Practice Problems 399

Chapter 11 Enteral and Parenteral Nutrition 413

11.1. Screening and Assessment of Nutritional Needs 414

11.1.1. Body Mass Index (BMI), Waist Circumference, and Associated Disease Risks 414

11.1.2. Assessment of Malnutrition 416

11.2. Enteral Nutrition 416

11.3. Parenteral Nutrition (PN): 2-in-1 and 3-in-1 Formulations 418

11.4. Calculation of Nutritional Requirements 420

11.4.1. Caloric Requirement Equations 420

11.4.2. Fluid Requirement 425

11.4.3. Protein Requirement (Nitrogen) 425

11.4.4. Carbohydrate and Fat Requirements 428

11.4.5. Micronutrient Requirements (Electrolytes, Vitamins, and Trace Elements) 428

11.5. Calculations for Compounding Parenteral Nutrition 429

11.5.1. Calculation of Electrolytes 430

11.5.2. Calculation of Carbohydrate and Fat 433

11.5.3. Calculation of Protein 435

11.5.4. Calculation of Other Additives 438

11.6. Calculations Related to the Design of a PN 444

Practice Problems 446

Chapter 12 Miscellaneous Practical Calculations in Contemporary Compounding 458

12.1. Compounding with Manufactured Dosage Forms 459

12.1.1. Nonsterile Products 460

12.1.2. Sterile Products 463

12.2. Suppository Calculations 465

12.2.1. Calibration of Molds 465

12.3. Determination of Amount of Base/powder Occupied by the Drug(s): Solid Dosage Forms 466

12.3.1. Density Factor Method 467

12.3.2. Quantity/Volume of Base Occupied by Drug (or Density Ratio Method) 474

12.3.3. Dosage Replacement Factor Method 475

12.4. Lozenges and Lollipops 479

12.4.1. Lozenge/Lollipop Mold Calibration 479

12.5. Selecting a Capsule Size 480

12.5.1. The Rule of Sixes 480

12.5.2. The Rule of Seven 482

12.5.3. Volume Occupied by Active Ingredient in a Capsule 484

12.6. Primary Emulsion Calculations (4:2:1 Ratio) 485

12.7. A Little Touch of Veterinary Compounding 487

Practice Problems 489

Appendices 499

Appendix 1 Systems of Measurement 500

Appendix 2 Chemical Elements and Atomic Weights 502

Appendix 3 Calibration of Medicinal Dropper 503

Appendix 4 Solutions Used to Compound PN 504

Appendix 5 Conversions: Temperature, Time, Proof Strength 507

Appendix 6 HLB System 511

Appendix 7 Drug as a Base Versus Salt or Ester 514

Appendix 8 pH, Buffers, and Buffer Capacity 517

Appendix 9 Normal Concentration 525

Appendix 10 Biologics for Immunization 527

Literature Consulted 529

Index 531

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