Section Thickness and the Physical Disector.

Questions

My cells are about 40 um in diameter.
Are my 6 um sections ok to count these cells?
Is there a rule about how thick sections can be in relation to the size of the cell to count with the physical disector? The reason I ask this question is that I have seen in papers where people cut their tissue 3um thick for doing the physical disector. This would twice the number of sections that I have now. I want to be as efficient as possible by using as few sections as I can, but I don’t want to cut my sections too thick in order to be useful.

Discussion

The physical disector uses what a stereologists calls a section. A section is a very thin piece of tissue that approximates a plane. In mathematics a plane is infinitely thin. It isn’t possible to create such a section. What is important is that the tissue is cut thin enough to be considered a plane.

So just what is infinitely thin for all practical purposes? Imagine a plane passing through the tissue. Now imagine that the tissue disappears except where the plane touches the tissue. The result is a flat, infinitely thin image. The disector uses two such planes. The planes have to be parallel. The planes pass through the tissue and in a sense collect two images. The images have to be close enough so that all of the changes between the two images can be inferred from the images. This means that objects can be connected to each other if they are part of the same object. It also means that profiles that are not part of the same object can be understood to be separate particles. If it is possible to reconstruct the contents of the missing volume from the two images, then the two images can be thought of as representing a volume.

A 3D probe that is used to count must have at least 3 dimensions. That is what a disector provides if the conditions are met. The volume is the interval between the two planes. The volume’s contents are inferred from the information on the 2 planes.

The physical disector counts tops. To do this the planes must be close enough so that no particle being counted can fall between the planes. If particles could lie between the planes then the counts would be undercounts, since there are more particles there than would be sampled.

Another problem occurs when the planes are not infinitely thin. One particle might end and another particle might begin within the same tissue. These particles are stacked one above the other.

A reasonable rule of thumb is to use sections that are 1/3 the smallest dimension of the particles being counted (Gundersen 1986). This supposes that counting is done on a pair of sections of this thickness. For larger objects it is possible to use two thin sections that are not sequential sections.

In the situation that is described here it may be possible to use sections that are not sequential. The sections are thinner than 1/3 the height of the smallest objects being counted. The important issue is whether or not it is possible to understand the changes between the pair of sections used in the physical disector. Using sequential sections may not be optimal. It may turn out that the sections are so close that few tops are encountered. This means that few counts are generated and that means many section pairs must be used. This is not an efficient way to count.

A study that uses thicker sections is described in the Journal of Microscopy, Vol 197, January 2000, pp 36-45. This study uses 50 micron sections. The graph on page 41 illustrates the effects of various section thickness values on the number of counts that are generated. The graph clearly shows that 50 micron sections is the most efficient way to section material. As was asked before, so just what is infinitely thin for all practical purposes? In this article the answer is 50 microns.

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