Counting neurons without bias: design-based stereology

Many questions in neuroscience come down to a number: how many neurons does a brain region contain, and does a disease or a gene change it? In Parkinson's disease, for example, the dopaminergic neurons of the substantia nigra die. With an unbiased stereological method, Pakkenberg et al. (1991) estimated an average of about 550,000 pigmented neurons in the substantia nigra of control subjects and a loss of about two thirds in patients. In mice, about 8,300 dopaminergic neurons were counted in the substantia nigra pars compacta (SNc) of both sides together in the C57BL/6J strain, by reconstructing every section (Baquet et al., 2009). These neurons are usually identified by staining for tyrosine hydroxylase (TH), the enzyme that makes the precursor of dopamine.

Counting cell profiles in single thin sections looks simple but is biased: a large cell is cut by more sections than a small one, so it appears more often, and a change in cell size can look like a change in cell number. This was recognised long ago (Abercrombie, 1946). Design-based stereology avoids the problem. A three-dimensional counting probe, the disector, counts each cell once, at a single point, whatever its size or shape (Sterio, 1984). The optical fractionator combines the optical disector, in which the observer focuses through a thick section, with systematic uniform random sampling of a known fraction of the region (West et al., 1991).

The total number is the number of cells counted multiplied by the inverse of each sampling fraction: the fraction of sections, the fraction of each section's area and the fraction of its thickness. Because only fractions are used, the result does not depend on how much the tissue shrinks in its plane; shrinkage across the thickness matters and must be measured (Dorph-Petersen et al., 2001). The precision of each estimate is given by its coefficient of error, which can be predicted from the counts in the sampled sections (Gundersen & Jensen, 1987; Gundersen et al., 1999); a clear worked form of the formula is given by Basler et al. (2017). A review written for neuroscientists is Schmitz and Hof (2005).

The region outlines come from real reference atlases: the Allen Mouse Brain Common Coordinate Framework (Wang et al., 2020; image credit: Allen Institute), the Waxholm Space atlas of the rat brain (Papp et al., 2014; Kleven et al., 2023), BigBrain (Amunts et al., 2013) and the Allen Reference Atlas of the mouse spinal cord (image credit: Allen Institute; drawings by Charles Watson and Gulgun Sengul). The shapes of the human nigra and of the spinal motor pools used for counting are schematic outlines, because these atlases do not label them.

Learning objectives

• Explain why counting cell profiles in single sections is biased by cell size, and why a disector counts each cell once
• Sample a region with systematic uniform random sampling: a random start and then every nth section
• Measure the mounted section thickness, explain shrinkage across the thickness, and set guard zones and the disector height
• Delineate a region with an atlas and a TH stain, and set up the counting frame, the sampling grid and the inclusion and exclusion lines
• Count cells by focusing through a section, calculate N = ΣQ⁻ × 1/ssf × 1/asf × 1/tsf, and judge its precision with the Gundersen coefficient of error
• Compare groups with the animal (or donor) as the unit, and interpret the result honestly

Ethics and safety

Work with animals needs approval by an Institutional Animal Ethics Committee (in India, the CCSEA under the Prevention of Cruelty to Animals Act 1960; elsewhere, frameworks such as EU Directive 2010/63/EU, the US Animal Welfare Act and PHS Policy, and the UK Animals (Scientific Procedures) Act 1986), trained staff and an ethical review that applies the 3Rs: replace animals where possible, reduce their number with a good design and a sample-size calculation, and refine procedures to minimise suffering, including humane end points in models of neurodegeneration. Brains are fixed by perfusion under deep terminal anaesthesia. Human brain tissue comes from brain banks, after consent given by the donor during life or by the next of kin, and is used under ethics committee approval and national rules (in India, the ICMR National Ethical Guidelines of 2017; in England, Wales and Northern Ireland, the Human Tissue Act 2004); donors are identified only by codes. Animal studies are reported following the ARRIVE guidelines, developed by the NC3Rs in the United Kingdom and endorsed by journals internationally (Percie du Sert et al., 2020).

Key terms

• Stereology: Methods for obtaining three-dimensional quantities, such as the number of cells or the volume of a region, from sections, by sampling the tissue in a known, random and systematic way.
• Profile: The cut surface of a cell seen in a section. One cell can give profiles in several sections, and large cells give more profiles than small ones.
• Disector: A three-dimensional counting probe: a counting frame of known area combined with a known depth. A cell is counted only where a single point of it, for example the top of its nucleus, comes into focus inside the probe.
• Optical fractionator: A design that counts cells with optical disectors in a known fraction of the sections, of the area of each section and of the thickness of each section, and multiplies the count by the inverse of these fractions.
• Systematic uniform random sampling (SURS): Sampling at regular intervals (every nth section, or grid positions a fixed distance apart) from a random starting point, so that every part of the region has the same chance of being sampled.
• Section sampling fraction (ssf): The fraction of sections that are examined, for example 1/6 when every sixth section is used.
• Area sampling fraction (asf): The area of the counting frame divided by the area of one step of the sampling grid.
• Thickness sampling fraction (tsf): The disector height divided by the measured thickness of the mounted section.
• Counting frame: A square drawn on the image with two inclusion lines and two (extended) exclusion lines, so that every cell in a tiled plane is counted exactly once.
• Guard zone: A layer at the top and bottom of the section that is not used for counting, because cut surfaces are uneven and cells there may be damaged or lost.
• Coefficient of error (CE): The expected relative error of one estimate caused by the sampling (its standard error divided by the estimate).
• Coefficient of variation (CV): The standard deviation between animals divided by the mean; it combines true biological differences and the error of each estimate.
• Post-mortem interval: The time between death and the start of tissue fixation; longer intervals can reduce tissue quality and antigen preservation.
• Neuromelanin: A dark brown pigment that builds up with age in the dopaminergic neurons of the human substantia nigra; it can be mistaken for a brown stain.