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reviewed paper: Schmitz, C. and P.R. Hof (2005) Design-Based Stereology in Neuroscience. Neuroscience 130, 813-831.

This review (Schmitz and Hof, 2005) reflects a crystallization of vision in the field of unbiased stereology; made possible by the advent of probes to be used in thick sections. The goal of unbiased or design-based stereology is to sample and probe characteristics of tissues and organs under the microscope without systematic mistakes, largely for estimating number, length, and the surface and volume of regions and particles. Thick sections allow for isotropic probes when estimating surface and length and when combined with an embrace of probes that have long been in existence offer a complete and now well established array of tools to estimate first and second order properties of biological tissue. “Design-based stereology can nowadays be viewed as a well-established methodology to reveal certain features of development, repair, natural aging, and normal anatomy of the brain which could not be detected otherwise” (Schmitz and Hof, fourth paragraph, first sentence).

The authors start off by differentiating between qualitative and quantitative comparisons and tell in what case quantitative comparisons need to be used; “to test for statistically significant changes in appearance resulting from a disease or an experimental treatment, particularly if differences between pathologic and physiologic conditions are discrete” (Schmitz and Hof, first paragraph). A corollary is “Beware of seeking some form of quantification even though the biological effect is clear from simple observation of the material” (Evans, et al., 2004, Chapter 1, third paragraph, second sentence).

Thick sections that allow room for isotropic probes so that the tissue can be sectioned arbitrarily (also called preferentially) are stressed; it is pointed out that the original definition of stereology, to obtain three-dimensional information from lower dimensional data is evolving since “in the current use of design-based stereology many methods (so-called probes) make use of three-dimensional sections” (Schmitz and Hof, second paragraph, second sentence).

The characteristics deemed most important for Neuroscience research that can be estimated with either global or local probes are listed; “volume, number, connectivity, spatial distribution, and length of linear biological structures” (Schmitz and Hof, third paragraph).

Important considerations that must be planned before sectioning and histology are covered; “design-based stereologic analyses cannot be initiated right away on existing sections, if they have not been prepared adequately for design-based stereology” (Schmitz and Hof, Section 2: Considerations for specimen preparation for design-based stereologic analysis). This affects the selection of, thickness, and orientation of sectioning of the tissue sections. Several important points about requirements are made:

-access to the complete region of interest

-sections and microscope fields that are representative of the whole region

-all parts of the brain region have an equal chance of being sampled

-all structures can be recognized

-the size, shape, orientation and distribution in space can’t affect the estimate

Systematic random sampling is recommended throughout the entire region to ensure representative and equal selection of sections and microscope fields because “alterations in neuron densities may considerably differ from alterations in the corresponding total numbers of neurons, and results obtained from systematically and randomly sampled sections may considerably differ from corresponding results obtained using single “representative” sections” (Schmitz and Hof, section 2, third paragraph). A reference is given to a study showing different results for systematic random sampling verses only looking at representative samples based on size (Schmitz et al., 2004).

“Independence of design-based stereologic estimates from the size, shape, spatial orientation, and spatial distribution of the neurons or linear biological structures under study is achieved by the three-dimensional design of almost all probes described” and “the application of these new 3-dimensional (3D) stereologic probes requires the use of thick (i.e. 3D) sections instead of thin (2-D) sections” (Schmitz and Hof, Section 2, second paragraph). The requirement that no three dimensional arrangement of lengths and surfaces is favored when sampling is efficiently and easily met by using thick section probes that are themselves isotropic. The Cavalieri/point-counting probe to estimate volume can be carried out on thin optical sections of thick physical sections. When estimating number it is also easier and more efficient to use the thick-section optical fractionator probe. When thick sections can’t be obtained thin sections can be used, but extra steps (isotropic or vertical sectioning), that cause decreases in efficiency and facility, must be taken to ensure isotropy of interaction with the probe and surfaces or lengths and to ensure a three-dimensional probing situation for number. Model based stereology, such as the use of the Abercrombie correction for estimating number of cells (Abercrombie, 1946) could be used, but “it is rarely possible to figure out how well the application of such correction methods really adjusted for bias in quantitative analyses based on the size, shape, spatial orientation, and spatial distribution of the neurons to be investigated” and “With the correct use of design-based stereology this is not any longer an issue” (Schmitz and Hof, section 2, third paragraph).

The modern array of unbiased stereological probes can be carried out on a system that includes specialized hardware and software. A camera for live imaging or software that will load image stacks, an automatic X,Y,Z stage, a modern microscope and a z-encoder and software to control the systematic sampling and super-position of probes on images of the biological structures is standard. The thick section probes require that the z-position is accurately encoded (Schmitz and Hof, Section 3, Laboratory equipment for design based stereologic analyses).

Following the rules of unbiased stereology will give estimates without having to take into consideration the size, shape spatial orientation and spatial distribution of the structures. To further minimize bias these other steps should be taken (Schmitz and Hof, Section 4, Potential bias in results of design-based stereologic analyses):

-comparisons between groups should be restricted to tissue processed in the same way, although number estimates are not affected by differential tissue shrinkage during histology

-the entire brain region should be available, recognizable and all parts must have an equal chance of being sampled; each study should provide a description of the method selected to identify the region of interest

-the estimate cannot be affected by artifact where the knife has sectioned or due to incomplete staining

-shrinkage in the z-dimension during histology must be measured for thick section probes using an oil lens and taken into account, when, for instance, estimating in-situ volume

Section 5: Parameters that can be assessed by design-based stereology (Schmitz and Hof)

Volume of a brain region. (Schmitz and Hof, section 5.2)

Use Cavalieri with either point-counting or tracing. To avoid over-projection, use thin sections.

Number of neurons within a given tissue volume. (Schmitz and Hof, section 5.3)

Counting cell-pieces is not the same as counting cells (Schmitz and Hof, Fig. 3). Use the physical disector if you have thin sections or the optical disector with thick sections. A unique point on the cell, such as its leading edge, is identified to count cells as opposed to cell pieces. Guard zones should be used where sectioning has caused artifact.

Number of neurons within a given brain region. (Schmitz and Hof, section 5.4)

Unless the region is very small, systematic random sampling will be used to sample a fraction of the volume (Schmitz and Hof, figure 1). Then either the VrefXNv or the fractionator method can be used to arrive at an estimate. “Estimating the number of neurons within a given BROI with the Fractionator method is from an economical point of view more efficient than doing the same with the VrefXNv method. This is due to the fact that the Fractionator method does not require estimates of the global volume of the BROI.” (Schmitz and Hof, part 5, last paragraph).

Mean cellular/nuclear volume. (Schmitz and Hof, section 5.5)

Use the nucleator, or the rotator or the optical rotator probe, and for number weighted estimates, use these local probes in conjunction with a disector. For volume weighted estimates, point sampled intercepts can be used. Isotropic or vertical sections should be used to ensure that the shape and orientation of the particles does not influence the estimates. If it can be shown that the particles are themselves isotropic or arranged isotropically in space, then arbitrarily oriented sections can be used. “This problem has to be individually solved in each application” (Schmitz and Hof, section 5.5, last paragraph). For instance see Schmitz, et al., 1999.

Surface area. (Schmitz and Hof, section 5.6)

Use the isotropic fakir probe for both regional surface estimates and also for estimating surface of groups of particles. The surface area of individual particles can be estimated with the optical rotator.

Fiber length. (Schmitz and Hof, section 5.7)

Use the spaceballs probe. Remember that length estimates are of the length after histological shrinkage.

Three-dimensional cytoarchitecture. (Schmitz and Hof, section 5.7)

Use the nearest neighbor probe.

Section 6: Variability of estimates obtained with design-based stereology (Schmitz and Hof)

Unbiased stereology yields estimates and it is the mean of an infinite amount of unbiased estimates that will converge to the (unknown) true value. If an estimate is carried out many times it will vary; the coefficient of variation could be calculated, and the amount of variance will tell us something about the precision of the estimate. “It is one of the most desirable advantages of design-based stereology over other quantitative histologic techniques that predictions about this coefficient of variation (usually presented as “coefficient of error,” CE) are possible” (Schmitz and Hof, section 6, second paragraph, last sentence).

It is stated that as a ‘rule of thumb’ the reciprocal of the square root of the number of counted neurons for the optical fractionator can be used as a CE, with the goal of getting it to be low, around 0.1. In other words, in many cases the local term will swamp out the between sections term and the Gunderson CE reduces to the local or ‘noise’ term (Schmitz, 1998). “different scientific questions to be addressed by design-based stereology require different levels of precision in the estimates” therefore “It is always advisable to design an individual sampling scheme for each new study, taking into account all potential factors that will likely affect the precision of estimates such as potential biologic variability, the number of animals or brains to be investigated, the number of sections to be analyzed, the number of neurons to be counted, etc.” (Schmitz and Hof, section 6, last paragraph).

Suggestions are given about what parameters to report in the publication (Schmitz and Hof, Table 2), that match our guidelines for reporting.

This review has done a great job at laying out the bias that can compromise an experiment and talking about how unbiased stereology has answers to questions about bias: “In numerous published studies reporting quantitative data not obtained with design-based stereologic methods, these questions cannot be adequately answered. In some cases, such quantitative data can even be more misleading than purely qualitative statements, because they are based on inadequate methods and are prone to overinterpretation. The use of design-based stereologic methods permits one to answer all these questions positively.” (Schmitz and Hof, Concluding remarks).


Evans, S.M., A.M. Janson, J.R. Nyengaard (2004) Quantitative Methods in Neuroscience, Oxford University Press, Oxford, U.K.

Schmitz, C. (1998) Variation of Fractionator Estimates and its Prediction. Anat Embryol, 198(5):371-97.

Schmitz, C., Born, M., Dolezel P., Hof, P.R., and H. Korr (2004) Prenatal protracted gamma irradiation with extremely low does rate over several days induces massive neuronal loss in rat cerebellum and hippocampus. Neuroscience; 130 (4): 935-48.

Schmitz, C. and P.R. Hof (2005) Design-Based Stereology in Neuroscience. Neuroscience 130, 813-831.

Schmitz, C., Schuster, D., Niessen, P. and H. Korr (1999) No Difference between Estimated Mean Nuclear Volumes of Various Types of Neurons in the Mouse Brain Obtained on either Isotropic Uniform Random Sections or Conventional Frontal or Sagittal Sections, J. of Neuroscience Methods, 88, pp. 71 – 82.