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1 BASIC STEREOLOGY FOR BIOLOGISTS AND NEUROSCIENTISTS

2 ALSO FROM COLD SPRING HARBOR LABORATORY PRESS RELATED LABORATORY MANUALS Basic Methods in Microscopy Imaging: A Laboratory Manual Imaging in Developmental Biology: A Laboratory Manual Imaging in Neuroscience: A Laboratory Manual Live Cell Imaging: A Laboratory Manual, Second Edition RELATED COLD SPRING HARBOR PERSPECTIVES IN BIOLOGY TITLE Neuronal Guidance The Nucleus HANDBOOKS At the Bench: A Laboratory Navigator, Updated Edition Lab Math: A Handbook of Measurements, Calculations, and Other Quantitative Skills for Use at the Bench Statistics at the Bench: A Step-by-Step Handbook for Biologists

3 BASIC STEREOLOGY FOR BIOLOGISTS AND NEUROSCIENTISTS MARK J. WEST Aarhus University COLD SPRING HARBOR LABORATORY PRESS Cold Spring Harbor, New York

4 BASIC STEREOLOGY FOR BIOLOGISTS AND NEUROSCIENTISTS All rights reserved # 2012 by Cold Spring Harbor Laboratory Press, Cold Spring Harbor, New York Printed in the United States of America Publisher Acquisition Editor Director of Development, Marketing, & Sales Project Manager Permissions Coordinator Production Manager Production Editor Compositor Cover Designer John Inglis David Crotty Jan Argentine Maryliz Dickerson Carol Brown Denise Weiss Rena Steuer Techset Composition Ltd. Michael Albano Front Cover: Series of unbiased sampling frames, superimposed on a Golgi-Cox stained section of neocortex, that can be used to perform stereological analyses of various threedimensional structural features of the tissue. (Image courtesy of Mark J. West.) Library of Congress Cataloging-in-Publication Data West, Mark J., Basic stereology for biologists and neuroscientists / Mark J. West. p. cm. Includes bibliographical references and index. ISBN (hard cover : alk. paper) 1. Stereology. I. Title. Q175.W dc All World Wide Web addresses are accurate to the best of our knowledge at the time of printing. Authorization to photocopy items for internal or personal use, or the internal or personal use of specific clients, is granted by Cold Spring Harbor Laboratory Press, provided that the appropriate fee is paid directly to the Copyright Clearance Center (CCC). Write or call CCC at 222 Rosewood Drive, Danvers, MA ( ) for information about fees and regulations. Prior to photocopying items for educational classroom use, contact CCC at the above address. Additional information on CCC can be obtained at CCC Online at For a complete catalog of all Cold Spring Harbor Laboratory Press Publications, visit our website at

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6 Contents Preface, ix 1 Introduction to Stereology, 1 2 Estimating Volume, 15 3 Estimating Object Number, 31 4 Isotropy, isectors, and Vertical Sections, 59 5 Estimating Length, 71 6 Estimating Surface Area, 83 7 The Precision of an Estimate, 91 8 Systematic versus Random Sampling, Getting Started, Optimizing the Sampling Scheme: Amount of Individuals, Sections, and Probes, Shrinkage, Local Estimators of Size, Counting and Measuring Ultrastructural Features, What to Report: Information to Be Included in Publication, 189 Index, 197 vii

7 Preface MORPHOLOGY (HISTOLOGY) HAS HISTORICALLY BEEN a qualitative descriptive discipline. It has provided us with a wealth of names and definitions of a multitude of structural features that have provided valuable insight into numerous cell and tissue functions. Attempts to quantify morphological features, in order to make fourdimensional comparative statements about cell and tissue function, have been mired in controversy, however, due to lack of concordance in the data, disagreement about quantitative methodology, and a general lack of appreciation of rational practical approaches to the quantitation of histological features. During the past two decades, a large number of scientific papers have been published that collectively represent a paradigm shift in thinking about how to derive meaningful quantitative data about structural features in biological tissues; these are design-based, unbiased stereological methods. The unique aspect of the new design-based stereology is that, unlike previously available methods, these methods involve no prerequisite information about the structural features being quantified. These new methods have a strong foundation in stochastic geometry and sampling theory and result in meaningful reproducible data. This book is an attempt to present a number of the concepts and principles of the new stereology in one coherent discussion of what these methods involve in terms of their application, with the goal of providing the reader with the knowledge necessary to design, supervise, and critically evaluate design-based stereological studies. Although sufficient detail regarding the theoretical basis of these methods is provided, along with numerous references to the original papers, the primary emphasis of the book is on the application of design-based stereology to the structure of the nervous system and how this would be extended to other tissues. The nervous system provides a wealth of structural features that can be used to exemplify modern stereological methods for estimating number, length, number, surface, and volume. The book does not exhaustively cover the full range of stereological methods, but it does, however, present detailed descriptions of methods for obtaining data regarding the fundamental structural organization of organs, tissues, cells, and subcellular structures. ix

8 x PREFACE This book is based on a series of lectures held at the NeuroStereology Workshops, together with Lutz Slomianka, between 2000 and Readers who are new to design-based stereology are advised to proceed to read the chapters in sequence, because there are numerous references to concepts and terms presented in earlier chapters and because some of the practical exercises build upon the results of earlier exercises. In addition to describing stereological methods (Chapters 2 5), practical issues that must be dealt with when applying these methods are presented and discussed in detail. These include descriptions about how to get started (Chapter 9), designing pilot studies (Chapter 10), and getting to know your tissue, tissue preparation, and tissue shrinkage (Chapter 11). Numerous examples of applications of the methods are based on the author s own work in the central nervous system, although the book is written in general terms for those interested in applying modern, designbased stereology to other tissues, as mentioned above. I thank my colleague and coauthor on many stereology papers, Lutz Slomianka, for his helpful assistance in the preparation of this book; Hans Jørgen Gundersen, Luis Cruz-Orive, Adrian Baddeley, and Eva Bjørn Jensen for enriching my view of the structure of the world; and Albert Meier for his expert assistance with many of the illustrations and figures in this book and in the earlier papers upon which this book is based. MARK J. WEST Aarhus, October 1, 2011