Biomedical Calculations: Principles and Practice

Biomedical Calculations......Page 3
Contents......Page 7
Preface......Page 13
This book, and how to use it......Page 17
Part I......Page 19
1.1 Calculating with units......Page 21
1.3 How unit analysis can guide thinking and help solve problems......Page 23
1.4 When to specify substances along with units......Page 24
1.5 The need to use appropriate and compatible units in formulae......Page 25
1.6 Checking and deriving formulae......Page 26
1.8 Dimensional analysis......Page 28
Part II......Page 31
2.1 The Syst` eme International and unit prefixes......Page 33
2.2 Length and distance......Page 34
2.5 Mass......Page 35
2.6 Moles......Page 36
2.7 Equivalents......Page 37
2.8 Conversion between units......Page 38
Problems......Page 40
3 Percentages......Page 41
3.1 When percentages mislead: human body fat and fat in milk......Page 42
3.2 Heat loss from the body: further questionable percentages......Page 45
Problems......Page 46
4 Composite units I – density......Page 47
4.2 Specific volume......Page 48
4.3 Two definitions of body density......Page 49
Problems......Page 51
5 Composite units II – concentration......Page 53
5.1 Concentrations: kilograms of water vs litres of solution......Page 54
5.2 Simple protein-free salt solutions......Page 55
5.3 Millimolar and millimolal concentrations in blood plasma......Page 56
5.4 Some quite different uses for Eq. (5.1)......Page 57
Problems......Page 58
6.1 Letting unit analysis solve the problem......Page 59
6.2 ‘Let x be the unknown’......Page 62
Problems......Page 67
7.1 Preparing 250 mL of 150 mM NaCl from the dry salt......Page 69
7.2 Preparing dilutions from stock solutions......Page 71
Problems......Page 74
8 Calculating drug doses......Page 75
Problems......Page 77
9.1 The principle of electroneutrality......Page 79
9.3 Anion gap......Page 82
9.4 Osmoles and osmolality......Page 84
9.5 Osmolar gap......Page 86
9.7 Cell contents......Page 88
9.8 Effective osmolality, effective osmotic pressure......Page 90
9.9 Osmotic shifts of water between cells and extracellular fluid......Page 91
9.10 Free and bound concentrations, activities......Page 94
Part III......Page 97
10.1 Graphs: some terminology......Page 99
10.3 The equation of a straight line......Page 100
10.4 Finding the equation of a line that passes through two specified points......Page 101
10.5 Drawing a line that is defined by a specified equation......Page 103
10.7 Finding the line that best fits a number of points when these lie only roughly in a straight line......Page 104
10.10 A note on units......Page 105
10.11 On the different kinds of formulae and equations......Page 106
Problems......Page 108
11.1 Areas and volumes of simple shapes......Page 111
11.2 Erythrocytes, cylinders and spheres......Page 112
11.3 The swelling of erythrocytes in hypo-osmotic solutions......Page 114
11.4 Distortion of erythrocytes in passing along narrow blood vessels......Page 115
11.5 An exercise in rearranging equations to eliminate an unwanted term......Page 116
11.6 Easy and general ways to check algebraic working......Page 118
11.8 Why do we not have naturally spherical erythrocytes?......Page 119
11.9 General properties of simple geometrical shapes......Page 120
11.11 A digression on graphs......Page 123
11.12 Calculating surface area from volume and height: another exercise in re-arranging equations and eliminating unwanted......Page 124
11.13 Another digression to check algebraic working......Page 125
11.14 Generalizing the formula to include the human body......Page 126
11.15 Surface/volume and surface/mass ratios......Page 128
11.16 The surface area of the human body......Page 130
11.17 Standard formulae for body surface area......Page 131
11.18 An exercise in comparing formulae containing exponents......Page 134
Problems......Page 136
12 Body size, body build, fatness and muscularity: unit analysis as an aid to discovery......Page 139
12.1 Variations in fat-free mass with height and age......Page 140
12.2 The Rohrer index, or ‘height–weight index of build’......Page 143
12.3 The body mass index; estimating body fat from body mass and height......Page 144
12.4 Upper arm muscle: how its cross-sectional area varies with body height......Page 149
12.5 Weightlifting – and the cross-sectional area of muscle......Page 151
12.6 Estimating body fat from skinfold thickness measurements......Page 154
12.7 Postscript......Page 156
Problems......Page 157
Part IV......Page 159
13.1 Frequency......Page 161
13.2 Speed and velocity......Page 162
13.4 Rates of flow of substances carried in fluids......Page 163
13.5 Thinking about a formula......Page 164
13.6 The concept of renal clearance......Page 169
13.8 Creatinine clearance as a measure of GFR, and a convenient formula for estimating it......Page 172
Problems......Page 174
Part V......Page 177
14.1 Force and weight......Page 179
14.2 Pressure......Page 181
14.3 Columns of water, columns of blood......Page 182
14.4 Osmotic pressure and colloid osmotic pressure (oncotic pressure)......Page 183
14.5 Energy and work......Page 185
14.6 Power......Page 187
14.7 An overview of units – from mass to pressure and power......Page 188
Problems......Page 189
15.1 Poiseuille’s equation and viscosity......Page 191
15.2 Peripheral resistance......Page 193
Problems......Page 194
16.1 Temperature scales......Page 195
16.3 Heat capacity and specific heat......Page 197
Problems......Page 198
17 Gases: dry and wet gas mixtures, partial pressures, gases in solution......Page 199
17.3 The gas laws......Page 200
17.4 A closer look at Eq. (17.1) and the universal gas constant, with attention to units......Page 201
17.5 Treatment of gas mixtures – percentages......Page 203
17.7 Water vapour pressure......Page 204
17.8 ‘Standard temperature and pressure, dry’......Page 205
Problems......Page 207
Part VI......Page 211
18 Introduction to logarithms......Page 213
18.3 The usefulness of remembering log10 2......Page 214
18.4 Logarithmic scales on graphs......Page 215
18.6 Natural logarithms......Page 219
Problems......Page 220
19 Exponential time courses......Page 221
19.1 Use of semi-logarithmic plots......Page 223
19.2 Common complications......Page 224
Problems......Page 225
20 Nernst equations in physiology and biochemistry: logarithms and ‘RT/zF ’......Page 227
20.1 More on R T/zF......Page 228
Problems......Page 230
21 pH – two definitions and a possible dilemma for teachers......Page 231
21.1 pH as -log [H ]......Page 232
21.2 The true definition of pH: pH as a number on a conventional scale......Page 233
21.3 The meaning of 10-pH......Page 234
21.4 Final comments......Page 235
Problems......Page 236
22 Equilibrium constants, the Henderson–Hasselbalch equation, dose–response curves......Page 237
22.1 Equilibrium constants......Page 238
22.3 The Henderson–Hasselbalch equation......Page 240
22.4 Application of the Henderson–Hasselbalch equation to drugs......Page 241
22.5 The dependence of [AB] on [A] when ([B] +[AB]) is constant......Page 242
22.6 Concentration–response curves and dose–response curves......Page 245
Problems......Page 247
23 Buffering and acid–base balance......Page 249
23.1 Non-bicarbonate buffering......Page 250
23.2 A link with dose–response curves......Page 253
23.3 Bicarbonate buffering......Page 254
23.4 CO2/HCO3 and non-bicarbonate buffers together......Page 257
23.5 The whole body: diet and the titratable acidity of urine......Page 259
23.6 Other aspects of acid–base balance......Page 260
Problems......Page 261
Appendix A. Basic mathematics and mathematical language......Page 263
Appendix B. Some non-metric units......Page 271
Appendix C. Notes......Page 273
Appendix D. Solutions to problems......Page 283
References......Page 305
Index......Page 309