Preface to First Edition 1998

This book addresses a problem common to almost all scientists who use a microscope in their work.  Consider a `lump' of something of interest.  To the biologist it might be a kidney or piece of brain, for the materials scientist a piece of ceramic or steel and for the geologist a flake of rock.  In each case the investigators are interested in the internal microstructure of their respective lumps of material.  These microstructures are generally beyond the resolving power of the naked eye and are furthermore concealed within the object.  For these reasons the investigators must rely upon sectioning to reveal the inside of the object and microscopy to measure the interesting detail of the structure. 

To gain a qualitative feel for a particular microstructure it may be sufficient to take a few sections, choose some interesting looking regions and record a small number of micrographs. If the structure has not been observed before these micrographs may well be published with an interpretation of what has been observed.  This type of subjective analysis and interpretation of microscopic features has been the foundation of many new areas of scientific microscopy.  However, this is not the only way to employ microscopy in a scientific manner and in this book we focus on its use as a tool for objective analysis.  For example, the specimens being analysed may be part of an experimental series in which there are important but subtle changes between groups. If these changes are not qualitatively obvious it is then natural to turn to quantitative microscopy.

Qualitative microscopic studies, with expert interpretation and analysis, will continue to play a valid and useful role in the initial stages of many scientific problems.  However, it is the use of quantitative methods that is the hallmark of modern scientific research. Once the results of a study are to be used in a quantitative way then it must be planned and executed with a more rigorous approach than is employed in a qualitative analysis. If this is true for any macroscopic measurement then it is thrice so for a microscopic analysis, because of the following questions:

Q1.  Is the `lump' that is brought to the laboratory bench representative of the whole ?
Q2. Is my sub-sample representative of that particular `lump'?
Q3.  Are the measurements that are being made on the sub-sample sensible and useful with     respect to the underlying scientific question?

Most scientists are well trained in ensuring that Q1 is addressed properly.  For example, the biologist will try to reduce variability in his system by using an inbred strain of animals, all of the same age and possibly sex, with similar diets etc.  It is clearly and rightly beyond the scope of this book to try to describe  sampling regimes for the multitude of scientific disciplines that can successfully apply quantitative microscopy.  Therefore in this text it will always be assumed that the sample being `brought to the table' is representative of the greater whole, however that may be defined.  For life scientists the lump brought to the table will usually be the whole of an organ or identifiable organ component from within one animal or plant, i.e. the fundamental sampling unit in biology.  For materials science where the `greater whole' is often more difficult to define, the sample brought to the table may be several sub-samples from the output of a production process over a given time period etc.

It is our experience that many scientists are not trained to consider Q2 and in general tend to make arbitrary decisions about where to take their `within lump sample'. However, although arbitrarily chosen samples may suffice for qualitative analysis they are usually inadequate for objective quantitation.  We will devote a considerable part of this book to addressing ways of sampling specimens in 3D so that every part of the specimen has the same chance of being in the final sample, before sampling commences.  Clearly some element of randomness has to be introduced into this process and in general this is uniform randomness.  The process of randomising the sampling continues throughout the many hierarchical levels inherent in a quantitative microscopical analysis.  The golden rule at each stage is that the investigator should never choose things to measure (for example because they look interesting or they have high contrast).

Finally, with most of the sampling complete, slides are prepared, stained and viewed in the microscope and now Q3 looms into sight.  What to measure?  Most modern image analysers provide a plethora of things that can be measured - boundary lengths, profile numbers, Feret diameters, shape factors etc. etc. Unfortunately most of these parameters are rooted firmly in the 2D `flatland' of the microscope image and have remarkably little to do with the 3D real world we are interested in.  Fortunately all is not lost. If the sections have been obtained using the sampling methods we describe here then it takes no more effort (and often considerably less) to use the 2D slides to make the highly relevant and intuitively understandable 3D measurements that stereology has to offer.

As always in science the most important step is to formulate sound hypotheses and ask the right questions.  Given good scientific questions it is then possible to decide which measurements are required to answer them. With stereology we can ask very penetrating questions.  Does drug A cause a loss of cells in the development of this organ?  Does exercise cause an increase in the surface area of this absorptive membrane?  Does the continued heat treatment of this steel change the mean grain volume?  (It should be noted that in each case the form of the high-level scientific question will dictate which parameters should be measured not vice-versa).

In this book we describe practical methods for obtaining stereological estimates of feature volume, surface, length and number and mean particle size. We believe our audience will primarily be experimental scientists who want to apply stereology to their problems. For this reason we have largely hidden the underlying theory and have instead focused upon clear and unambiguous presentation of the practical essentials.  We see this book very much as an introduction to a fascinating and diverse field and hope that we have provided enough material to aid further reading.  With these thoughts in mind readers who are experienced in statistics and probability theory may find Chapters 1 and 2 a bit `slow'. We make absolutely no apology for this!  It is the statistical and probabilistic ideas underlying unbiased stereology which, in our experience, cause problems amongst new comers to stereology. We have therefore made efforts to illustrate the theory by using examples drawn from everyday experience. 

The presentation in the book is as near as we can get to the way we present these ideas in taught courses.  We have tried to make the narrative logically structured and it should be followed in the order presented. Important material that does not fit easily into the flow of the book is included in  `boxes'. In common with many other areas of microscopy there is no substitute for practical experience. The book therefore includes a considerable number of exercises either developed by ourselves or kindly donated by expert stereologists from around the world.

We hope you enjoy reading this book as much as we did writing it.

Vyvyan Howard & Matt Reed

Liverpool, UK. September 1997