Making the counts count: the stereology revolution

Basic quantitative morphological methods applied to the central nervous system

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as design‐based stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are “good enough.” Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.

A concise review of optical, physical and isotropic fractionator techniques in neuroscience studies, including recent developments

Stereology is a collection of methods which makes it possible to produce interpretations about actual three-dimensional features of objects based on data obtained from their two-dimensional sections or images. Quantitative morphological studies of the central nervous system have undergone significant development. In particular, new approaches known as design-based methods have been successfully applied to neuromorphological research. The morphology of macroscopic and microscopic structures, numbers of cells in organs and structures, and geometrical features such as length, volume, surface area and volume components of the organ concerned can be estimated in an unbiased manner using stereological techniques. The most practical and simplest stereological method is the fractionator technique, one of the most widely used methods for total particle number estimation. This review summarizes fractionator methods in theory and in practice. The most important feature of the methods is the simplicity of its application and underlying reasoning. Although there are three different types of the fractionator method, physical, optical and isotropic (biochemical), the logic underlying its applications remains the same. The fractionator method is one of the strongest and best options among available methods for estimation of the total number of cells in a given structure or organ. The second part of this review focuses on recent developments in stereology, including how to deal with lost caps, with tissue section deformation and shrinkage, and discusses issues of calibration, particle identification, and the role of stereology in the era of a non-histological alternative to counting of cells, the isotropic fractionator (brain soup technique).

Myths and truths about the cellular composition of the human brain: A review of influential concepts

Over the last 50 years, quantitative methodology has made important contributions to our understanding of the cellular composition of the human brain. Not all of the concepts that emerged from quantitative studies have turned out to be true. Here, I examine the history and current status of some of the most influential notions. This includes claims of how many cells compose the human brain, and how different cell types contribute and in what ratios. Additional concepts entail whether we lose significant numbers of neurons with normal aging, whether chronic alcohol abuse contributes to cortical neuron loss, whether there are significant differences in the quantitative composition of cerebral cortex between male and female brains, whether superior intelligence in humans correlates with larger numbers of brain cells, and whether there are secular (generational) changes in neuron number. Do changes in cell number or changes in ratios of cell types accompany certain diseases, and should all counting methods, even the theoretically unbiased ones, be validated and calibrated? I here examine the origin and the current status of major influential concepts, and I review the evidence and arguments that have led to either confirmation or refutation of such concepts. I discuss the circumstances, assumptions and mindsets that perpetuated erroneous views, and the types of technological advances that have, in some cases, challenged longstanding ideas. I will acknowledge the roles of key proponents of influential concepts in the sometimes convoluted path towards recognition of the true cellular composition of the human brain.

The use of design-based stereology to evaluate volumes and numbers in the liver: a review with practical guidelines

Stereology offers a number of tools for the analysis of sections in microscopy (which usually provide only two-dimensional information) for the purpose of estimating geometric quantities, such as volume, surface area, length or number of particles (cells or other structures). The use of these tools enables recovery of the three-dimensional information that is inherent in biological tissues. This review uses the liver as a paradigm for summarizing the most commonly used state-of-the-art methods for quantitation in design-based stereology. Because it is often relevant to distinguish hyperplasia and hypertrophy in liver responses, we also focus on potential pitfalls in the sampling and processing of liver specimens for stereological purposes, and assess the existing methods for volume and number estimation. With respect to volume, we considered whole liver volume (V), volume density (V(V)) and so-called local volumes, including the number-weighted volume (V(N)) and the volume-weighted volume (V(V)). For number, we considered the total number (N) and the numerical density (N(V)). If correctly applied, current stereological methods guarantee that no bias is introduced in the estimates, which will be therefore accurate; additionally, methods can be tuned for obtaining precise quantitative estimates that can reveal subtle changes in the volume or number of selected hepatic cells. These methods have already detailed the effects of some substances and specific diets on the liver, and should be routinely included in the toolbox of liver research.

A review of recent methods for efficiently quantifying immunogold and other nanoparticles using TEM sections through cells, tissues and organs

Detecting, localising and counting ultrasmall particles and nanoparticles in sub- and supra-cellular compartments are of considerable current interest in basic and applied research in biomedicine, bioscience and environmental science. For particles with sufficient contrast (e.g. colloidal gold, ferritin, heavy metal-based nanoparticles), visualization requires the high resolutions achievable by transmission electron microscopy (TEM). Moreover, if particles can be counted, their spatial distributions can be subjected to statistical evaluation. Whatever the level of structural organisation, particle distributions can be compared between different compartments within a given structure (cell, tissue and organ) or between different sets of structures (in, say, control and experimental groups). Here, a portfolio of stereology-based methods for drawing such comparisons is presented. We recognise two main scenarios: (1) section surface localisation, in which particles, exemplified by antibody-conjugated colloidal gold particles or quantum dots, are distributed at the section surface during post-embedding immunolabelling, and (2) section volume localisation (or full section penetration), in which particles are contained within the cell or tissue prior to TEM fixation and embedding procedures. Whatever the study aim or hypothesis, the methods for quantifying particles rely on the same basic principles: (i) unbiased selection of specimens by multistage random sampling, (ii) unbiased estimation of particle number and compartment size using stereological test probes (points, lines, areas and volumes), and (iii) statistical testing of an appropriate null hypothesis. To compare different groups of cells or organs, a simple and efficient approach is to compare the observed distributions of raw particle counts by a combined contingency table and chi-squared analysis. Compartmental chi-squared values making substantial contributions to total chi-squared values help identify where the main differences between distributions reside. Distributions between compartments in, say, a given cell type, can be compared using a relative labelling index (RLI) or relative deposition index (RDI) combined with a chi-squared analysis to test whether or not particles preferentially locate in certain compartments. This approach is ideally suited to analysing particles located in volume-occupying compartments (organelles or tissue spaces) or surface-occupying compartments (membranes) and expected distributions can be generated by the stereological devices of point, intersection and particle counting. Labelling efficiencies (number of gold particles per antigen molecule) in immunocytochemical studies can be determined if suitable calibration methods (e.g. biochemical assays of golds per membrane surface or per cell) are available. In addition to relative quantification for between-group and between-compartment comparisons, stereological methods also permit absolute quantification, e.g. total volumes, surfaces and numbers of structures per cell. Here, the utility, limitations and recent applications of these methods are reviewed.

A brief update on lung stereology

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema-like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant-producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well-established classical stereological methods, these design-based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene-manipulated mice, at the light and electron microscopic level.

The number of alveoli in the human lung

The number of alveoli is a key structural determinant of lung architecture. A design-based stereologic approach was used for the direct and unbiased estimation of alveolar number in the human lung. The principle is based on two-dimensional topology in three-dimensional space and is free of assumptions on the shape, size, or spatial orientation of alveoli. Alveolar number is estimated by counting their openings at the level of the free septal edges, where they form a two-dimensional network. Mathematically, the Euler number of this network is estimated using physical disectors at a light microscopic level. In six adult human lungs, the mean alveolar number was 480 million (range: 274-790 million; coefficient of variation: 37%). Alveolar number was closely related to total lung volume, with larger lungs having considerably more alveoli. The mean size of a single alveolus was rather constant with 4.2 x 10(6) microm3 (range: 3.3-4.8 x 10(6) microm3; coefficient of variation: 10%), irrespective of the lung size. One cubic millimeter lung parenchyma would then contain around 170 alveoli. The method proved to be very efficient and easy to apply in practice. Future applications will show this approach to be an important addition to design-based stereologic methods for the quantitative analysis of lung structure.

Differential tissue shrinkage and compression in the z-axis: implications for optical disector counting in vibratome-, plastic- and cryosections

The optical disector is among the most efficient cell counting methods, but its accuracy depends on an undistorted particle distribution in the z-axis of tissue sections. Because the optical disector samples particle densities exclusively in the center of sections, it is essential for unbiased estimates of particle numbers that differential shrinkage or compression (and resulting differences in particle densities along the z-axis) are known and corrected. Here we examined, quantified, and compared differential shrinkage and compression of vibratome-, celloidin- and cryosections. Vibratome sections showed a significant z-axis distortion, while celloidin- and cryosections were minimally distorted. Results were directly compared with previous data obtained from paraffin and methacrylate sections. We conclude that z-axis distortion varies significantly between embedding and sectioning methods, and that vibratome-, methacrylate- and paraffin sections can result in grossly biased estimates. We describe a simple method for assessing differential z-axis shrinkage or compression, as well as simple strategies to minimize the bias of the optical disector. Minimal bias can be achieved by either adjusting the placement and extent of counting boxes and guard spaces for sampling, or by applying a correction factor in cases when guard spaces are deemed essential for particle recognition.