Biomedical Calculations


"It is said if you take care of the pennies, the pounds willtake care of themselves. Richard Burton's excellent book takes thisapproach to calculations applied to the biomedicalsciences…This is certainly interesting and engaging but itavoids being complicated." –Journal of BiologicalEducation, April 2009

Biomedical Calculations: Principles and Practice is anaccessible, student-friendly introduction to calculating, applyingformulae and solving quantitative problems within these ...

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"It is said if you take care of the pennies, the pounds willtake care of themselves. Richard Burton's excellent book takes thisapproach to calculations applied to the biomedicalsciences…This is certainly interesting and engaging but itavoids being complicated." –Journal of BiologicalEducation, April 2009

Biomedical Calculations: Principles and Practice is anaccessible, student-friendly introduction to calculating, applyingformulae and solving quantitative problems within these subjects.This book targets a problem area for many students and aims to givethem the confidence which they are so often lacking whenundertaking scientific calculations. It takes a unique approach tothe subject and uses unit analysis as a central theme throughoutthe book to enhance student understanding. 

Clearly structured throughout, little basic knowledge ofmathematics is assumed, but even the most numerate readers will beinterested in the sometimes-novel biological detail. Numerousworked examples, supplementary questions and practice problems areprovided and although the book is written to be read in sequence,it will also be a useful reference. 

The central theme of the book focuses on the value of unitanalysis in solving quantitative problems, with explanations on howto avoid errors in calculations and in checking, understanding andderiving formulae and equations.   As a background to this,there is extensive treatment of physical units, both individually(e.g. kg, m, mmol) and in combination (e.g. m s¯², mmolL¯¹), and also of other aspects of quantitativethinking.  A variety of topics (mostly from physiology,pharmacology and biochemistry) are used to demonstrate thesecalculations in practice. 

Key features: 

  • An accessible, student-friendly introduction for all thosehesitant in calculating, applying formulae and solving quantitativeproblems 
  • An innovative approach to scientific calculations and how towork with unfamiliar formulae for the biomedical and lifesciences
  • Includes modern, up to date definition of pH eliminating theneed for logarithms and a discussion of the importance of pH
  • Clear introduction on how to use the book, guidance on unitsand unit conversion, and an appendix on basic mathematics andnotation 
  • Use of unit analysis as a central theme 
  • Includes numerous worked examples and supplementary questionsthroughout the text to enhance student understanding
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Editorial Reviews

From the Publisher
'I really liked this book and the approach the author has taken. It will certainly be useful for biomedical scientists and for those teaching potential biomedical scientists, either at university or during training in the laboratory.? ( British J of Biomedical Science, 2008)

"It is said if you take care of the pennies, the pounds will take care of themselves. Richard Burton's excellent book takes this approach to calculations applied to the biomedical sciences-This is certainly interesting and engaging but it avoids being complicated." ?Journal of Biological Education, April 2009

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Product Details

  • ISBN-13: 9780470519110
  • Publisher: Wiley
  • Publication date: 10/27/2008
  • Edition number: 1
  • Pages: 310
  • Product dimensions: 6.60 (w) x 9.50 (h) x 0.80 (d)

Table of Contents



This book, and how to use it.


1. Unit analysis: the neglected key to confidence.

1.1 Calculating with units.

1.2 Ways of writing composite units.

1.3 How unit analysis can guide thinking and help solveproblems.

1.4 When to specify substances along with units.

1.5 The need to use appropriate and compatible units informulae.

1.6 Checking and deriving formulae.

1.7 When unit analysis raises questions about formulae.

1.8 Dimensional analysis.


2. Units: length, area, volume, mass, moles andequivalents.

2.1 The Système International and unit prefixes.

2.2 Length and distance.

2.3 Area.

2.4 Volume.

2.5 Mass.

2.6 Moles.

2.7 Equivalents.

2.8 Conversion between units.


3. Percentages.

3.1 When percentages mislead: human body fat and fat inmilk.

3.2 Heat loss from the body: further questionablepercentages.


4. Composite units I - density.

4.1 Specific gravity.

4.2 Specific volume.

4.3 Two definitions of body density.

4.4 Thinking about a formula.


5. Composite units II - concentration.

5.1 Concentrations: kilograms of water vs litres ofsolution.

5.2 Simple protein-free salt solutions.

5.3 Millimolar and millimolal concentrations in bloodplasma.

5.4 Some quite different uses for Eq. (5.1).


6. Aspects of problem solving.

6.1 Letting unit analysis solve the problem.

6.2 ‘Let x be the unknown’.


7. Making up and diluting solutions.

7.1 Preparing 250 mL of 150 mM NaCl from the dry salt.

7.2 Preparing dilutions from stock solutions.


8. Calculating drug doses.


9. More about solutions - electroneutrality, osmotic pressureand activity.

9.1 The principle of electroneutrality.

9.2 But what about membrane potentials and short-circuitcurrents?

9.3 Anion gap.

9.4 Osmoles and osmolality.

9.5 Osmolar gap.

9.6 Osmosity.

9.7 Cell contents.

9.8 Effective osmolality, effective osmotic pressure.

9.9 Osmotic shifts of water between cells and extracellularfluid.

9.10 Free and bound concentrations, activities.


10. Graphs, straight lines and equations.

10.1 Graphs: some terminology.

10.2 Advice on drawing graphs.

10.3 The equation of a straight line.

10.4 Finding the equation of a line that passes through twospecified points.

10.5 Drawing a line that is defined by a specified equation.

10.6 Finding the equation of a line from its gradient and thecoordinates of a single point on it.

10.7 Finding the line that best fits a number of points whenthese lie only roughly in a straight line.

10.8 ‘Proportional’ and ‘inverselyproportional’.

10.9 Gradients of curves.

10.10 A note on units.

10.11 On the different kinds of formulae and equations.


11. On shapes and sizes.

11.1 Areas and volumes of simple shapes.

11.2 Erythrocytes, cylinders and spheres.

11.3 The swelling of erythrocytes in hypo-osmotic solutions.

11.4 Distortion of erythrocytes in passing along narrow bloodvessels.

11.5 An exercise in rearranging equations to eliminate anunwanted term.

11.6 Easy and general ways to check algebraic working.

11.7 Solving the equation by trial and error in aspreadsheet.

11.8 Why do we not have naturally spherical erythrocytes?

11.9 General properties of simple geometrical shapes.

11.10 Replacing volumes with masses in these equations.

11.11 A digression on graphs.

11.12 Calculating surface area from volume and height: anotherexercise in re-arranging equations and eliminating unwantedterms.

11.13 Another digression to check algebraic working.

11.14 Generalizing the formula to include the human body.

11.15 Surface/volume and surface/mass ratios.

11.16 The surface area of the human body.

11.17 Standard formulae for body surface area.

11.18 An exercise in comparing formulae containingexponents.


12. Body size, body build, fatness and muscularity: unitanalysis as an aid to discovery.

12.1 Variations in fat-free mass with height and age.

12.2 The Rohrer index, or ‘height-weight index ofbuild’.

12.3 The body mass index; estimating body fat from body mass andheight.

12.4 Upper arm muscle: how its cross-sectional area varies withbody height.

12.5 Weightlifting - and the cross-sectional area of muscle.

12.6 Estimating body fat from skinfold thicknessmeasurements.

12.7 Postscript.


13. Introducing time.

13.1 Frequency.

13.2 Speed and velocity.

13.3 Acceleration.

13.4 Rates of flow of substances carried in fluids.

13.5 Thinking about a formula.

13.6 The concept of renal clearance.

13.7 Relating the clearance formula for renal plasma flow to theFick Principle.

13.8 Creatinine clearance as a measure of GFR, and a convenientformula for estimating it.



14. Force, pressure, energy, work and power.

14.1 Force and weight.

14.2 Pressure.

14.3 Columns of water, columns of blood.

14.4 Osmotic pressure and colloid osmotic pressure (oncoticpressure).

14.5 Energy and work.

14.6 Power.

14.7 An overview of units - from mass to pressure and power.


15. Lessons from another formula.

15.1 Poiseuille’s equation and viscosity.

15.2 Peripheral resistance.


16. Heat and temperature.

16.1 Temperature scales.

16.2 The temperature coefficient, Q10.

16.3 Heat capacity and specific heat.


17. Gases: dry and wet gas mixtures, partial pressures, gasesin solution.

17.1 A reminder of units.

17.2 Natural variations in atmospheric pressure.

17.3 The gas laws.

17.4 A closer look at Eq. (17.1) and the universal gas constant,with attention to units.

17.5 Treatment of gas mixtures - percentages.

17.6 Treatment of gas mixtures - partial pressures,tensions.

17.7 Water vapour pressure.

17.8 ‘Standard temperature and pressure, dry’.

17.9 Dissolved O2 and CO2 in blood plasma and other fluids.



18. Introduction to logarithms.

18.1 Definitions.

18.2 Rules for working with logarithms.

18.3 The usefulness of remembering log102.

18.4 Logarithmic scales on graphs.

18.5 What about units?

18.6 Natural logarithms.


19. Exponential time courses.

19.1 Use of semi-logarithmic plots.

19.2 Common complications.


20. Nernst equations in physiology and biochemistry:logarithms and ‘RT/zF’.

20.1 More on RT/zF.


21. pH - two definitions and a possible dilemma forteachers.

21.1 pH as -log[H+].

21.2 The true definition of pH: pH as a number on a conventionalscale.

21.3 The meaning of 10-pH.

21.4 Final comments.


22. Equilibrium constants, the Henderson-Hasselbalchequation, dose-response curves.

22.1 Equilibrium constants.

22.2 Concentrations or activities?

22.3 The Henderson-Hasselbalch equation.

22.4 Application of the Henderson-Hasselbalch equation todrugs.

22.5 The dependence of [AB] on [A] when ([B] + [AB]) isconstant.

22.6 Concentration-response curves, dose-response curves.


23. Buffering and acid-base balance.

23.1 Non-bicarbonate buffering.

23.2 A link with dose-response curves.

23.3 Bicarbonate buffering.

23.4 CO2/HCO3- and non-bicarbonate bufferstogether.

23.5 The whole body: diet and the titratable acidity ofurine.

23.6 Other aspects of acid-base balance.



Appendix A. Basic mathematics and mathematicallanguage.

Appendix B. Some non-metric units.

Appendix C. Notes.

Appendix D. Solutions to problems.


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