Section Thickness and Z-Resolution

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Some unbiased stereological probes are designed to be used with thick physical sections and require fine z-resolution; some are to be used with thin physical or optical sections. To be clear, these ranges refer to sections after they have been processed for histology; not before the sections have shrunken in size, but after.

THICK SECTIONS (about 15 to 30 microns)

In many cases, if the probe is designed to interact with the feature being probed so as not to favor any particular orientation of interaction, there will have to be thick sections to contain this isotropic probe.

Optical Fractionator: This probe requires a tissue thickness that can be broken up optically by the focal point of a high magnification (40x, 60x, 63x or 100x) and high numerical aperture (NA, 1.3 or 1.4) objective. The sections must be thick enough to allow many focal planes through the disector and to allow for guard zones. There must be multiple focal planes through the disector so that: one particle can be told apart from another; there will be a small leading edge that is detected; and there is room to focus up and down and make a good decision about whether the leading edge of the particle is contained in the disector or not.

Typically, tissue between 15-30 microns thick post-processing allows for upper and lower guard zones while still resulting in several optical Z-planes through the disector when using a high NA objective. Tissue sectioned between 30-60 microns may give useable results after staining and the shrinkage that results from dehydration. You should do some experimentation towards developing a staining protocol that does not result in excessive shrinkage in the Z axis.

Spaceballs: The tissue section must be thick enough to contain the virtual sphere plus upper and lower guard zones. Guard zones need to be big enough to cover up any artifact at the top and bottom of the section. There has to be many focal planes through the virtual sphere so you can focus up and down and decide if a string (e.g., blood vessel or nerve fiber) is piercing the sphere. The magnification and numerical aperture should be high enough to be able to see this event.

Tissue sections between 15-30 microns may meet these virtual sphere thickness requirements. Be aware that shrinkage-artifact will occur during histology, especially if immersion in ascending alchohol concentrations is involved.

Isotropic Fakir: This isotropic probe must be used in tissue sections thick enough to contain it plus guard zones. As with the optical fractionator and Spaceballs; sections between 15 and 30 microns, after shrinkage-artifact, may be large enough. The magnification and numerical aperture need to be high enough to observe every intersection of the line-segment probe with the surface being probed.

Optical Rotator: A probe used in thick sections on isotropic or vertical sections. It is used for volume or surface estimation of particles such as cells.

THIN SECTIONS (less than about three microns)

Most probes that are used for thin sections are not themselves isotropic; therefore the tissue must be made isotropic. The exceptions are:

Cavalieri/point-counting and Area Fraction Fractionator: Thin physical or optical sections are used to avoid over-projection. The sections need to be thin enough to catch changes in area. In practice, for most biological structures, sections that are a few microns thin (one to three microns) should work. The magnification should be high enough to not miss any bays, peninsula’s, or isthmuses in the cross-sectional areas.


Physical Fractionator

When estimating number, there must be a two dimensional situation. For the physical fractionator, a pair of contiguous thin sections is used. Thin means about one to three microns. A high power objective (40x, 60x, 63x or 100x) and high numerical aperture (NA, 1.3 or 1.4) must be used for the same reasons given above under ‘Optical Fractionator’.

These probes have the isotropy ‘built into the probe’.

All of the other thin section probes are either not isotropic themselves:

Length probed with the image plane


Orthogonal intercepts

Point Sampled Intercepts

Surface Weighted Star Volume

or have two planes that are randomized:

Cycloids for Sv


Two probes for the volume of a particle (such as a cell), the nucleator, and the planar rotator can be done on thin sections, but if like most people you would like a number weighted sample, a disector must be used in thick sections. The same is true for the surfactor, a probe that estimates the surface of particles.


By thin sections we mean about one to three microns thick. These probes must be conducted at a magnification high enough to see the event.

Discrete Vertical Rotator is designed for use on electron micrographs; ultra-thin sections are used that are appropriate for this technique.




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