Stereology Glossary - Stereology Society

Stereology uses sampled sections, images and geometric probes to estimate quantities such as volume, surface area, length and particle number. Its vocabulary separates what is visible in an image from what can be inferred about the specimen. A cell profile is not a whole cell, a density is not a total, and a precise estimate is not necessarily an accurate one.

This glossary groups terms alphabetically and explains their practical meaning. Use it alongside the stereology fundamentals guide when reading a methods paper, interpreting software output or preparing a study protocol. Definitions identify the purpose of each method without replacing its sampling and measurement requirements.

A–C: Accuracy, Bias and Counting Frames

Accuracy: Closeness of a measurement or estimate to the true value. Accuracy is not interchangeable with precision: repeated estimates can cluster tightly around the wrong value. In practice, accurate stereology requires suitable sampling, reliable object identification and control of preparation artifacts.
Anisotropy: Dependence on direction. Parallel fibers are an example of an anisotropic structure. Their appearance changes with section orientation, so surface and length estimation must account for the interaction between structural direction and probe orientation. Anisotropy does not mean that the structure cannot be measured.
Area fraction, A_A: The area occupied by a component divided by the reference area on a section. It describes a two dimensional observation. With appropriate spatial sampling, area fraction can estimate volume fraction; a deliberately selected field showing the most abundant component cannot stand in for the whole specimen.
Bias: A systematic tendency for an estimator to depart from the true quantity over repeated sampling. Selecting conspicuous cells or avoiding sparse regions can introduce bias. Taking more measurements does not remove that tendency. The distinction is developed in the guide to bias, precision and coefficients of error.
Cavalieri estimator: A volume estimator using parallel sections sampled at a known interval with a random start. Estimated volume equals the section interval multiplied by the sum of cross sectional areas. The relevant interval is the distance between sampled planes, not necessarily the thickness of each collected section.
Coefficient of error, CE: The sampling standard error of an estimate divided by its expected value, estimated in practice using the observed estimate and an appropriate variance formula. CE describes sampling precision within a specimen. Different designs require different calculations, as examined in this comparison of optical fractionator CE estimators.
Coefficient of variation, CV: Standard deviation divided by the mean for a stated set of values. Between specimen CV describes variation among specimen estimates, which may include both biological variation and stereological sampling error. It is not the same quantity as the CE of an individual specimen estimate.
Counting frame: A defined area with inclusion and exclusion boundaries used to decide which objects or counting events qualify. In a conventional unbiased frame, objects touching an exclusion line or its extension are rejected. The rule prevents boundary objects from receiving extra opportunities to be counted.

D–H: Disectors, Estimators and Guard Zones

Design-based stereology: An approach that obtains statistical validity through the sampling design and estimator rather than assumed particle shapes. It still requires recognizable targets, correct measurements and adherence to counting rules. The comparison of design-based and model-based stereology explains why freedom from geometric assumptions is not freedom from experimental requirements.
Disector: A three dimensional probe that samples particles through a defined counting event between two planes. It avoids treating every visible profile as a separate particle. Suitable particles can therefore be counted without assumptions about their size or shape. The name is spelled “disector,” not “dissector.”
Disector height, h: The separation between the planes defining the disector. Together with counting frame area, it defines the sampled volume. In an optical disector, this is the accepted depth interval through which the observer focuses, not the full mounted section thickness.
Disector count, Q⁻: The number of accepted particle counting events. In a physical disector, these are commonly particles present in the reference section but absent from the lookup section, subject to frame rules. The minus sign denotes disappearance; it is not subtraction from the total. This distinction comes from the original disector counting method.
Estimator and estimate: An estimator is the rule or formula used to infer a quantity from sampled observations. An estimate is the numerical result from applying that rule. “Total cell number” names the target; the fractionator formula is an estimator; 48,000 cells would be an estimate.
Fractionator: A sampling approach that tracks known fractions of a specimen. Counts from the sampled portion are expanded by the inverse sampling fraction to estimate the total. In a hypothetical design that samples each particle with probability 1/100, an accepted count of 240 estimates 24,000 particles.
Guard zone: A depth interval near a section surface excluded from optical counting. Guard zones address surface damage and related counting problems, but no single depth suits every preparation. Their placement must be considered alongside staining penetration, particle visibility and changes in particle distribution through the section.

I–N: Orientation, Density and Particle Volume

Isotropic uniform random, IUR: A sampling condition combining uniform spatial sampling with isotropic orientation: no direction is preferentially selected. “Uniform” concerns position, while “isotropic” concerns direction. Rotating an image within its existing plane does not make the original section isotropic in three dimensions.
Length density, L_V: Total length of the target linear structures per unit reference volume. Common units are mm/mm³, equivalent to mm⁻². It is not the number of fibers per image, nor the average length of an individual fiber. Those are different questions requiring different observations.
Lookup section: The comparison section in a physical disector pair. An observer checks whether particles identified in the reference section remain visible in the lookup section. Pair registration, separation and recognition criteria must allow the same particle to be followed between sections.
Model-based stereology: An approach in which inference depends on a model of the structure, such as assumptions about particle shape, size distribution or orientation. Its validity depends on how well those assumptions hold. A correction formula cannot compensate for a model that does not describe the specimen.
Nucleator: A local particle volume estimator using distances along appropriately sampled rays from an identifiable pivotal point. A nucleolus can provide that point for a cell. Ray orientation and boundary measurements must follow the chosen design; the research paper on nucleator precision distinguishes isotropic and vertical implementations.
Number-weighted mean volume: The arithmetic mean particle volume when each particle receives equal weight. For three hypothetical particles with volumes of 1, 2 and 9 units, it is 4 units. Selecting particles because they look large would change the sampling probabilities and no longer produce an ordinary particle average.
Numerical density, N_V: The number of particles per unit reference volume, commonly expressed as cells/mm³. It differs from profile density, which counts two dimensional appearances per area. Numerical density can change because particle number changes, reference volume changes, or both.

O–P: Optical Methods, Point Counting and Profiles

Optical disector: A disector implemented by focusing through a defined depth within a sufficiently thick section. Particles are counted when their designated feature first comes into focus within the accepted interval and satisfies the frame rules. Simply counting every cell visible in a thick section is not an optical disector.
Optical fractionator: A combination of optical disector counting and fractionator sampling used to estimate total particle number. It expands accepted counts using the relevant section, area and thickness sampling fractions. The original optical fractionator study established this combination for neuron number estimation.
Particle: A discrete object defined for counting or measurement, such as a nucleus, cell or inclusion. The operational definition matters. Counting nuclei does not automatically count cells if the relationship between nuclei and cells is not one to one.
Physical disector: A disector using two physically separate sections rather than optical focal planes. Corresponding fields are compared to identify accepted appearance or disappearance events. The section pair must be close enough to support reliable particle matching and the intended counting rule.
Point counting: A method that records which component lies beneath each test point. For volume fraction estimation, points hitting the target are divided by points hitting the reference space, with any grid weighting handled correctly. The point counting guide covers placement, boundaries and calculation.
Precision: The repeatability of estimates under repeated application of a sampling procedure. More efficient sampling can improve precision for a given workload. Precision describes scatter, not whether the estimate is centered on the true value; a consistently misplaced boundary may produce repeatable but wrong results.
Probe: A geometric sampling device, such as a point, line, plane or three dimensional counting volume. The probe need not be a physical instrument. A point grid displayed over an image and a virtual sphere viewed through a section stack are both probes.
Profile: The two dimensional appearance produced where a section intersects a three dimensional object. One particle can create profiles in several sections. Profile size also depends on where the section passes through the object, so a small profile does not necessarily represent a small particle.

R–S: Reference Space, Sampling and Surface Measurements

Reference space and reference trap: The reference space is the region to which an estimate applies. The reference trap is interpreting a density change as a total quantity change without checking that region’s volume. This distinction is formalized in the ATS/ERS standards for quantitative assessment of lung structure.
Region of interest, ROI: The delineated region selected for analysis. An ROI may represent the full reference space or only a sampled portion. Its boundaries should follow stated anatomical or material criteria, rather than being adjusted to include favorable fields or exclude inconvenient observations.
Sampling fractions: ssf, asf and tsf: The section sampling fraction, area sampling fraction and thickness sampling fraction. In a regular optical fractionator design, these describe the portions sampled at successive stages. Thickness sampling fraction is often written as h/t; variable section thickness requires appropriate local measurement and estimator treatment.
Section thickness: The distance between the upper and lower surfaces of a section. Nominal cutting thickness and measured mounted thickness are not interchangeable. Processing can alter dimensions, so optical counting requires attention to the section that is actually being observed.
Space balls: Virtual spherical or hemispherical surface probes used to estimate the length of linear structures from their intersections with the probe. Their geometry supplies the required orientation sampling without assuming randomly oriented fibers. The space balls methods paper discusses probe placement and application constraints.
Surface density, S_V: Surface area per unit reference volume, expressed in units such as mm²/mm³. It is not the perimeter visible on an image. Surface estimation connects boundary intersections with test probes to three dimensional surface area under the required orientation conditions.
Systematic uniform random sampling, SURS: Sampling at regular intervals after choosing a uniform random start. Selecting one of the first ten sections at random, then every tenth section, is a simple example. The foundational paper on systematic sampling efficiency and its prediction also develops Cavalieri volume estimation.

T–Z: Shrinkage, Unbiasedness and Volume Fractions

Tissue shrinkage: A reduction in dimensions during preparation. Shrinkage may differ between directions, tissue components and processing stages. It can affect densities and measured sizes, while optical fractionator estimates still require correct thickness sampling. The guide to section thickness, guard zones and tissue shrinkage treats these connected issues.
Unbiased estimator: An estimator whose expected value equals the target quantity under the stated sampling design. Unbiased does not mean every individual estimate is exact. It also does not certify the entire experiment: misclassification, missing tissue and incorrect measurements can compromise an otherwise valid estimator.
Vertical uniform random sections, VUR: Sections parallel to a chosen vertical axis, with uniform random rotation around that axis and appropriate spatial sampling. They are not fully isotropic sections. Suitable test systems, including correctly aligned cycloids, permit surface estimation without assuming isotropic tissue, as established in the original vertical sections method.
Volume fraction, V_V: The volume of a component divided by the volume of its reference space. It is dimensionless and may be expressed as a percentage. A hypothetical volume fraction of 0.20 means that the component occupies 20% of the defined region, not 20% of its cells.
Volume-weighted mean volume: A mean particle volume in which larger particles receive greater weight in proportion to their volume. It answers a different question from number-weighted mean volume. Always retain the weighting term when reporting results: “mean cell volume” alone can leave the measured quantity ambiguous.