Unbiased Stereology: Three-dimensional Measurement In Microscopy

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

• ISBN13: 9781859960899
• ISBN10: 1859960898
• Edition: 2nd
• Format: Paperback
• Copyright: 2005-01-07
• Publisher: Taylor & Franci

Summary

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.

Table of Contents

Abbreviations	ix
Preface to the first edition	xi
Preface to the second edition	xiii
Acknowledgments	xiv
Dedication	xv
Safety	xvi
Foreword	xvii
L. Wolpert
Concepts	1	(16)
Sampling and bias	2	(1)
Why unbiasedness is desirable	3	(1)
Sources of bias in microscopy	4	(2)
Sampling bias	5	(1)
Systematic bias	5	(1)
The hierarchical nature of microscopical investigations	6	(1)
Stereology -- geometrical quantification in 3D	7	(1)
Think in three dimensions -- a macroscopic analogy by thought experiment	7	(2)
Points probe volume	8	(1)
Lines probe surface	8	(1)
Planes probe length	8	(1)
Volumes probe number	9	(1)
Dimensions and sectioning	9	(2)
Geometrical probes	11	(1)
Ratios and densities	12	(1)
The reference space	12	(5)
Random sampling and random geometry	17	(18)
Stereology and randomness	17	(1)
Two simple experiments	18	(1)
Take a sweet, any sweet	19	(1)
A uniform random (UR) sample	20	(1)
A single UR point in 1D, 2D and 3D	21	(2)
Repeat the process ...	23	(3)
A systematic random sample in 2D and 3D	26	(1)
Random geometry	26	(4)
Randomizing directions -- isotropy in the plane	30	(5)
Estimation of reference volume using the Cavalieri method	35	(18)
Exercise 3.1	43	(1)
Exercise 3.2	44	(1)
Exercise 3.3	45	(2)
Exercise 3.4	47	(3)
Exercise 3.5	50	(3)
Estimation of component volume and volume fraction	53	(12)
Estimation of volume fraction	53	(2)
Estimation of total volume of a defined component	55	(10)
Exercise 4.1	62	(1)
Exercise 4.2	63	(1)
Exercise 4.3	64	(1)
Number estimation	65	(38)
Some useful `definitions'	66	(1)
Some `non-definitions'	66	(1)
A cautionary tale	66	(2)
On the right road	68	(1)
Continuous scanning of a plane	68	(1)
The disector principle	69	(2)
From theory to practise	71	(3)
Implementation of the physical disector	74	(3)
Typical sampling regime for the physical disector	77	(1)
Optical section `scanning' methods -- the unbiased brick and optical disector	78	(4)
The unbiased brick-counting rule	82	(1)
Application of the optical disector counting rule	82	(1)
Typical sampling regime for the optical disector	83	(2)
Direct estimation of number -- the fractionator	85	(1)
A 2D example of the fractionator principle	85	(2)
The multi-stage fractionator	87	(1)
The optical fractionator	87	(2)
Some special designs for counting in 3D	89	(14)
The single section or `cheating' disector!	89	(1)
The double disector	90	(1)
The `molecular' or `golden' disector	91	(1)
Counting closed space curves -- Terminal bronchial ducts in lung	92	(1)
Counting complex shaped objects in 3D and connectivity estimation	93	(1)
Exercise 5.1	94	(2)
Exercise 5.2	96	(2)
Exercise 5.3	98	(1)
Exercise 5.4	99	(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