Revisiting the Selector

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Probes for unbiased stereology are powerful tools for biological research of microscopic structures when used on their own, but in certain situations combinations may be useful. The selector (Cruz-Orive, 1987) combines two probes to estimate numerical density without the need to know the percentage of sampling in the focal direction. In other words there is no requirement to keep track of z-positions with a z-encoder. The selector, however, has several drawbacks compared to using a z-encoder which were not as routine and easy to use at the time. It is worth revisiting, though, to understand our present tools through their history and possibly for use as a way to arrive at an unbiased estimate of number without being able to encode z-movements.

Any Stereologist familiar with unbiased techniques knows that counting cell pieces under the microscope at low magnification is not the same as counting cells at high magnification. Counting cells efficiently depends on unbiased stereological probes that have been developed for biology over the past several decades. Integral to these probes, the disector allows identification of a unique point of the particle during focusing. This is often a leading-edge such as the cell-top or nucleus-top, or the nucleolus if there is only one per cell.  By counting leading edges or singly-occurring nuclei, we are counting cells.

If it were possible to count all of the cells in a region or volume, making sure to count cells and not cell pieces would be enough, but most biological systems contain a prohibitive number. Systematic random sampling through the whole region should be used to get an estimate about the whole. That means sampling a sub-volume all the way through but using intervals started at positions selected by chance, both at the inter- and intra-section level.  By systematically skipping sections and microscope fields, it is possible to count a manageable number of cells. Making random starts ensures the same part of the anatomical region is not examined in each animal. There are  two ways to estimate the number in the whole volume of interest: the ‘fractionator method’ and the ‘numerical density-reference volume’ (NvVref) method.

The fractionator method uses extrapolation and the NvVref method involves the calculation of a density; in both cases the extent in the z-direction that was sampled must be known. For the fractionator method, the reciprocal of the percentage of the volume that was sampled (reciprocal of the volume fraction) is multiplied by the number of unique-points that were counted. The volume fraction is partially made up of the thickness sub fraction; that is the thickness of the disector divided by the thickness of the tissue section. For the NvVref method, a numerical density is multiplied by the volume of the whole region, and to get the numerical density the number of unique points counted is divided by the volume that was actually sampled.  To know the volume that was sampled the thickness of the disector has to be known.

The idea behind the selector is to use one probe to estimate the mean volume of the particles and another to estimate the percentage by volume occupied by the particles and then combine this information to come up with the number of particles per volume. If we know how big the cells are and how much of the tissue they take up, we know the number of cells per volume. As originally envisioned, the selector combines volume weighted sampling of particles for unbiased estimates of mean particle volume (vN) with point-counting (area fraction fractionator) for estimates of the percentage of volume occupied by the particles (VV). To calculate the estimate of the numerical density (Nv) of cells per volume of region of interest:

Nv = VV/vN

The selector can be performed on thin sections without any means of making measurements in z, but like any probe that involves estimating particle volume in an unbiased way, requires vertical or isotropic sections. When estimating particle volume, there is no way to make the probe completely isotropic. Therefore the tissue blocks must be randomized in two (vertical sections) or three (isotropic sections) planes. The difficulty and inconvenience entailed in these manipulations are one disadvantage of the selector.

The volume weighted sampling for the selector is done with point-sampled-intercepts; and the intercept is used to calculate the estimated volume of the particle. The sampling involves using equally spaced points to pick the particles resulting in a greater likelihood of choosing larger cells. Since we realize that bigger cells are being picked, this is still considered an unbiased estimator. There are cases where it is important to look at larger cells, but this has to be considered a drawback of the selector if you, like most people, want number-weighted estimates; estimates obtained with disectors in thick sections and therefore based on particles selected regardless of their size or orientation.

Because of these caveats and also the problem of resolving the tops and bottoms of cells when using point-counting during the area fraction fractionator to estimate their volume, the selector never really caught on. The disector was becoming the obvious way to obtain number weighted estimates of the number of cells on sections that don’t need to be vertical or isotropic, despite the disector’s requirement for thick sections or pairs of thin sections and for a way to measure the amount of focusing. Today, the selector could be used with a disector/nucleator combination in thick sections to pick the cells, thus getting rid of one of the problems; the estimates would be number- and not volume-weighted. It is preferable, however, to have a z-encoder so a disector can be used for an unbiased number-weighted estimate in sections that have no requirement to be vertical or isotropic.

EXAMPLES

 

Cruz-Orive, L.M. (1987) Particle Number can be Estimated Using a Disector of Unknown Thickness: the Selector. J. of Microscopy, 145, 121-142.