Sampling in stereology determines which specimens, tissue blocks, sections and microscopic fields contribute to an estimate. The aim is not to find a few images that look representative. It is to use a selection procedure that gives the target structure a known chance of entering the sample, then apply an estimator that matches that procedure.
A useful sampling plan answers three questions before measurements begin: what population or reference region does the result describe, how will locations and orientations be selected, and where should the available counting effort go? These decisions belong in the study design, not at the microscope after the interesting features appear.
Define What the Sample Must Represent
Start by naming the quantity you want to estimate and the reference space containing it. “Total neuron number in the left hippocampus” is a different target from “neuronal density within selected hippocampal biopsies.” A sample can support the second question without supporting the first. Whole structure estimates require a sampling route that reaches throughout the defined structure; carefully measuring a chosen fragment does not establish what lies outside it.
Write down anatomical boundaries, eligible specimens and exclusions before selecting measurement fields. In materials work, the equivalent might be a defined production batch, a component or a region within that component. Avoid descriptions such as “typical tissue” unless the selection procedure gives that phrase an operational meaning.
Sampling bias cannot be repaired simply by collecting more measurements from the same biased selection. This distinction between accuracy and precision is central to the ATS/ERS standards for quantitative assessment of lung structure. More images can make the wrong answer look reassuringly consistent.
Build a Sampling Hierarchy
A practical plan works from the largest unit to the smallest. For a proposed cell counting study, write the sequence explicitly: experimental units, organs or regions, blocks if needed, sections, fields and counting probes. Beside each level, record how selection will occur and what information must be retained.
| Sampling level | Planning question | Useful record |
|---|---|---|
| Experimental units | What units provide independent replication? | Eligibility, allocation and unit identifiers |
| Regions or blocks | How will the defined reference space be covered? | Boundary map and block selection procedure |
| Sections | Which positions will be examined? | Random start, interval and section identifiers |
| Microscopic fields | How will locations within sections be selected? | Grid origin, spacing and sampled coordinates |
| Measurement probes | What makes an event eligible for measurement? | Probe dimensions and inclusion rules |
Do not confuse these levels with independent replication. If treatment is assigned independently to each animal, measuring 40 fields in each of six animals does not create 240 independent experimental units. Fields are observations within animals. Other designs may assign treatment at the cage or litter level, changing the experimental unit. The distinction is developed in the research paper What exactly is “N” in cell culture and animal experiments?
Use Random Starts and Systematic Coverage
Systematic uniform random sampling, usually shortened to SURS, combines a random starting position with a fixed sampling interval. Randomness determines the start; the interval spreads observations across the structure. The selected positions are therefore not independent random draws, but they still arise from a randomized design.
As an illustrative section schedule, suppose a complete series contains 120 sections and the plan selects every tenth section. Draw one integer uniformly from 1 to 10. If the result is 7, select sections 7, 17, 27 and so on through 117. Starting at section 1 because it is convenient would remove the required randomization.
Systematic sampling can provide better precision than independent random sampling for a given effort by distributing observations across an organized structure. Its efficiency and precision estimation are examined in Gundersen and Jensen’s research on systematic sampling in stereology. It is not a promise that every possible interval will perform well in every specimen.
At the microscope, the same principle applies to field locations: choose a random grid origin within one grid spacing, then follow the predetermined grid. Do not move a scheduled field to include a more attractive cluster, a clearer boundary or more positive staining.
For the example above, a workable worksheet would contain the full section sequence, the draw of 7, the interval of 10 and the resulting selected identifiers. Keep damaged sections in that record rather than renumbering the surviving slides. Implementation details belong in the guide to systematic uniform random sampling.
Separate Sampling Position from Section Orientation
Choosing where to sample and choosing how to orient a section are different decisions. A spatially well distributed sample does not automatically have suitable orientations for every estimator. Conversely, randomizing block orientation cannot rescue a selection restricted to convenient parts of the specimen.
Isotropic Uniform Random Sections
Isotropic uniform random sections combine uniform spatial sampling with isotropic section orientation. Isotropic means that orientation is distributed uniformly over spatial directions, not that every angle in an arbitrary rotation recipe is chosen uniformly. These are not interchangeable procedures.
For surface and length measurements in directionally organized structures, validated orientation procedures allow suitable estimators to avoid assumptions that the tissue itself has random orientation. The original orientator study describes generating isotropic section planes for such measurements.
The practical decision should come before embedding. Write “isotropic orientation required” into the preparation plan rather than expecting an operator to improvise it later. The companion guide to isotropic uniform random sections covers this branch of sampling in more detail.
Vertical Uniform Random Sections
Vertical sections retain a chosen axis while randomizing rotation around that axis and sampling section positions appropriately. The axis is a defined specimen direction; “vertical” does not mean upright relative to gravity. Surface estimation can then use cycloid test lines aligned with that known axis.
The required relationship between the retained axis, random rotation, section position and cycloid probes was demonstrated in research on surface density estimation in bone using vertical sections. A familiar longitudinal section is not automatically a valid vertical random section.
For a proposed study that must retain an anatomical direction, record that direction on the block map and preserve its identity through imaging. Use the vertical uniform random sections guide when planning the orientation and probe combination. Neither vertical nor isotropic sectioning is a universal requirement for all stereological quantities.
Keep Sampling Fractions Traceable
In fractionator sampling, the estimate depends on knowing what fraction of the target population was sampled. Several stages may contribute: section selection, area sampling within sections and, for an optical fractionator, sampling through section depth. The count must also follow the appropriate disector rules; multiplying ordinary profile counts by an expansion factor does not make them an estimate of cell number.
The combination of a counting probe with known sampling fractions is established in the original optical fractionator study. Equal, known fractions make the arithmetic straightforward, but the experimental work must justify those fractions.
Consider a deliberately simplified example. A study samples one tenth of the sections, one twentieth of their area and one half of the eligible section depth. Assume these fractions are constant and valid, with no additional sampling stages. The combined fraction is:
Sampling fraction = 1/10 × 1/20 × 1/2 = 1/400.
If the applicable counting procedure records 250 eligible events, the estimated total is 250 × 400 = 100,000. This is an arithmetic illustration, not a recommended sampling intensity. Variable section thickness, additional block selection or unequal probabilities require an estimator that accounts for them. The optical fractionator guide addresses the method beyond this sampling overview.
Plan Separately for Unequal Regions
When the research question distinguishes regions, consider defining them as separate strata before sampling. A proposed comparison of an outer shell and inner core, for example, should identify both boundaries and specify how each region will contribute to the final result. Keep regional estimates visible rather than pooling observations first and asking what they represent afterward.
A hypothetical volume fraction calculation shows why the combination rule matters. Suppose the shell occupies 20% of a specimen’s volume and has a target phase fraction of 40%. The core occupies 80% and has a target phase fraction of 10%. The whole specimen fraction is:
(0.20 × 0.40) + (0.80 × 0.10) = 0.16, or 16%.
A simple average of the two regional fractions would give 25%, answering a different question. This example assumes the regional volumes are known; estimated volumes bring their own uncertainty. If the intended output is regional rather than whole specimen, report the two regional results instead of forcing them into one number.
Allocate Effort with a Pilot Study
There is no universal number of sections, fields or counted particles that establishes an adequate study. A pilot should test the proposed allocation of effort, not just confirm that structures can be recognized. Record time spent at each stage and retain results by specimen, region and section so that uneven sampling performance can be investigated.
The useful distinction is between variation among experimental units and sampling variation within them. Once individual estimates are sufficiently precise for the research question, further counting within the same specimens may contribute less than adding independent units. This allocation principle is developed in Gundersen and Østerby’s research on optimizing stereological sampling efficiency.
For a proposed pilot, compare two feasible schedules rather than choosing an arbitrary counting target. One might spread effort over more sections with fewer fields per section; another might examine fewer sections more densely. Compare their precision and workload using calculations appropriate to the estimator and sampling design.
Set the main study’s adjustment rules before examining group differences. Avoid repeatedly adding fields only to specimens whose estimates look unexpected. The guide to sample size and pilot studies in stereology covers precision targets and allocation decisions without treating a single count threshold as a guarantee.
Write a Sampling Plan That Another Operator Can Follow
Finish the design with operational instructions. “Random fields were measured” is not enough to reconstruct the procedure. Prefer a record that states the reference boundaries, selection sequence, randomization method, intervals, grid settings and counting rules. Include both planned and achieved sampling, with an explanation for any difference.
Before collecting the main dataset, check four practical points:
- Every selected section and field can be traced back to its specimen and selection rule.
- Orientation requirements are specified before cutting or embedding.
- Damaged, missing or unreadable samples have a documented handling procedure.
- The calculation uses the sampling fractions actually applied, not settings copied from a previous study.
Keep the plan short enough to use at the bench, but precise enough that another operator would make the same selections. That is the practical test: the sample should follow the design, not the operator’s preference for what looks worth measuring.