Unbiased Stereology: Three-dimensional Measurement In Microscopy

, by Howard, C. V.; Reed, M. G.; Howard, Vyvyan

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ISBN: 9781859960899 | 1859960898
Cover: Paperback
Copyright: 1/7/2005

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The Advanced Methods series is intented for advanced undergraduates, postgraduates and established research scientists. Titles in the series are designed to cover current important areas of research in life sciences, and include both theoretical background and detailed protocols. The aim is to give researchers sufficient theory, supported by references, to take the given protocols and adapt them to their particular experimental systems. Unbiased Stereology, Second Edition expands the comprehensive practical first edition guide to 3-D measurements in microscopy using stereological methods by adding a section on 2-D stereology, or "Petri-metrics". There is also an additional chapter on single-object stereology, which permits the measurement of total volume, surface and feature length of single arbitrary objects. The book is intended to lead the reader logically through a self-teaching course, with illustrative exercises at each stage. The techniques described have become benchmark methods intoxicology and neuroscience; the use of inferior methods often leading to missed or spurious results.

Abbreviations

Preface to the first edition

Preface to the second edition

xiii

Acknowledgments

xiv

Dedication

Safety

xvi

Foreword

xvii

L. Wolpert

Concepts

(16)

Sampling and bias

(1)

Why unbiasedness is desirable

(1)

Sources of bias in microscopy

(2)

Sampling bias

(1)

Systematic bias

(1)

The hierarchical nature of microscopical investigations

(1)

Stereology -- geometrical quantification in 3D

(1)

Think in three dimensions -- a macroscopic analogy by thought experiment

(2)

Points probe volume

(1)

Lines probe surface

(1)

Planes probe length

(1)

Volumes probe number

(1)

Dimensions and sectioning

(2)

Geometrical probes

(1)

Ratios and densities

(1)

The reference space

(5)

Random sampling and random geometry

(18)

Stereology and randomness

(1)

Two simple experiments

(1)

Take a sweet, any sweet

(1)

A uniform random (UR) sample

(1)

A single UR point in 1D, 2D and 3D

(2)

Repeat the process ...

(3)

A systematic random sample in 2D and 3D

(1)

Random geometry

(4)

Randomizing directions -- isotropy in the plane

(5)

Estimation of reference volume using the Cavalieri method

(18)

Exercise 3.1

(1)

Exercise 3.2

(1)

Exercise 3.3

(2)

Exercise 3.4

(3)

Exercise 3.5

(3)

Estimation of component volume and volume fraction

(12)

Estimation of volume fraction

(2)

Estimation of total volume of a defined component

(10)

Exercise 4.1

(1)

Exercise 4.2

(1)

Exercise 4.3

(1)

Number estimation

(38)

Some useful `definitions'

(1)

Some `non-definitions'

(1)

A cautionary tale

(2)

On the right road

(1)

Continuous scanning of a plane

(1)

The disector principle

(2)

From theory to practise

(3)

Implementation of the physical disector

(3)

Typical sampling regime for the physical disector

(1)

Optical section `scanning' methods -- the unbiased brick and optical disector

(4)

The unbiased brick-counting rule

(1)

Application of the optical disector counting rule

(1)

Typical sampling regime for the optical disector

(2)

Direct estimation of number -- the fractionator

(1)

A 2D example of the fractionator principle

(2)

The multi-stage fractionator

(1)

The optical fractionator

(2)

Some special designs for counting in 3D

(14)

The single section or `cheating' disector!

(1)

The double disector

(1)

The `molecular' or `golden' disector

(1)

Counting closed space curves -- Terminal bronchial ducts in lung

(1)

Counting complex shaped objects in 3D and connectivity estimation

(1)

Exercise 5.1

(2)

Exercise 5.2

(2)

Exercise 5.3

(1)

Exercise 5.4

(4)

Estimation of total surface area and surface density

103

(16)

Estimation of surface density

104

(1)

Random directions and orientations in 3D space

105

(3)

Generating isotropic line probes -- 1 Vertical sections

108

(2)

Generating isotropic line probes -- 2 Isotropic sections

110

(1)

Estimation procedure

110

(1)

Examples of vertical sectioning protocols

111

(8)

Exercise 6.1

113

(4)

Exercise 6.2

117

(2)

Length estimation

119

(8)

Generation of IUR sections -- the orientator and isector

122

(5)

Exercise 7.1

125

(2)

Stereological analysis of layered structures

127

(6)

Stereological ratios

127

(1)

Vertical sections of layered structures

127

(2)

Practical example

129

(1)

Application areas

130

(1)

Worked example of application

130

(3)

Particle sizing

133

(10)

Step 1 -- selecting particles

133

(1)

Step 2 -- measuring the size of the selected particles

134

(1)

The difference between the number-and volume-weighted distributions of size

134

(2)

Direct estimators of mean particle volume

136

(5)

The `point-sampled intercept' (PSI) method

136

(1)

The `selector'

137

(1)

The `nucleator'

138

(3)

Indirect estimation of mean particle size from stereological ratios

141

(1)

Distributions of particle volume

141

(2)

Indirect estimation of the second moment of the number-weighted particle volume distribution

141

(1)

Direct estimation of particle volume distributions

142

(1)

Statistics for stereologists

143

(22)

`Quantifying is a committing task' (Cruz-Orive, 1994)

143

(1)

Preliminary concepts

144

(1)

Population

144

(1)

Parameter

144

(1)

Sampling unit

144

(1)

Sample

144

(1)

Estimate

145

(1)

Estimator

145

(1)

Uniform random sample

145

(1)

Unbiased estimates

145

(1)

Elements of good statistical practice

146

(2)

Quantities of interest

148

(4)

Application to a single object

152

(1)

Addition of variances

152

(2)

Two-stage estimation

154

(1)

Calculation of CE for the Cavalieri method

154

(3)

Calculation of the CE of a ratio estimator

157

(2)

Prediction of CE for two-stage estimation

159

(1)

Precision of Cavalieri estimation for single objects

160

(5)

Exercise 10.1

162

(1)

Exercise 10.2

163

(2)

Single-object stereology

165

(18)

Introduction

165

(1)

Volume of single objects -- arbitrary orientation designs

166

(1)

Surface of single objects -- isotropic or vertical orientation designs

167

(8)

The isotropic `spatial grid'

167

(8)

The vertical spatial grid

175

(1)

Length estimation in vertical orientation designs

175

(8)

Length density

175

(2)

Total feature length

177

(3)

Exercise 11.1

180

(3)

`Petri-metrics'

183

(12)

Introduction

183

(1)

Counting methods

183

(4)

The 2D fractionator

183

(2)

Practical application at the microscope

185

(2)

Length estimation in 2D

187

(2)

Combined length and number estimation

189

(6)

Exercise 12.1

191

(2)

Exercise 12.2

193

(2)

Second-order stereology

195

(16)

Introduction

195

(1)

Second-order methods for point patterns

195

(3)

Second-order methods for volumetric features

198

(1)

The covariance estimator

199

(4)

Linear dipole probes

203

(2)

Making sense of covariance

205

(2)

Example of the application of linear dipole probes

207

(1)

Using isotropic rulers to get `one-stop stereology'

208

(3)

Appendix A: Practical gadgets for stereology

211

(6)

Appendix B: Set of stereological grids

217

(22)

Appendix C: Worked answers to exercises

239

(20)

Appendix D: Useful addresses

259

(2)

References

261

(10)

Index

271

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Unbiased Stereology: Three-dimensional Measurement In Microscopy

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