The Disector and Optical Disector

The Disector

The disector is a 3D stereological probe that has one unique and very important attribute, it samples objects with a probability that is proportional to their number, not their size. Because of this, the disector can be used to count objects without having to make any assumptions about their size, shape, or orientation. In its simplest form, the disector involves the use of two sections, hence the name disector.

The counting rule used with the disector probe is simple. One counts the objects that are present on the second section of a pair of adjacent sections that are not present on the first, as one proceeds systematically through a series of sections that includes the region under consideration. An equally valid counting rule is to count objects that are observable in the first section and not in the second. Essentially what one is doing is determining whether or not a unique point on each object, the "top", or as in the second case, the "trailing edge", lies within the volume sampled by the disector.

In Stereo Investigator the disector is not a stand-alone probe, but is used as an integral part of other probes, such as the physical disector and the linear disector. Designing a disector involves defining its dimensions.

The Optical Disector

The concept of the optical disector is an extension of the original disector. Instead of observing two physical sections as in the disector, one observes optical sections. It is possible to optically section thick histological sections by using microscope objectives with high numerical apertures that produce images with relatively narrow depths of focus. The focal plane (or optical section) can be moved a known distance through the thickness of the section, producing in effect, a continuous series of superimposed sections within which counting could be carried out with disector counting rules.

In practice this consists of counting the number of new objects that come into focus (or alternatively, disappear) as one focuses through a known volume of the tissue. The motion through the focal plane axis is determined using a stepper motor or a position encoder(z-encoder) mounted on the microscope.

The optical disector has one very important advantage over the physical disector: it eliminates the difficult and time consuming task of identifying corresponding parts of two physical sections (i.e., determining whether particular object can be seen on one section and not the other). With optical disectors, the sections are always optimally positioned for comparisons. This means that it is easier to fulfill the first requirement for the application of the disector, i.e., the ability to identify the sectional profiles of the same object on the sections used in the analysis. One simply focuses up and down, prior to counting, to establish the relationship between profiles at different levels. This capability is extremely valuable, if not essential, when branching or highly irregular objects are being counted. With physical disectors, this process may require the preparation of additional sections between those used for counting.

The optical disector is primarily used in conjunction with other probes. For instance, the optical fractionator is a combination of the fractionator and the optical disector.

Although it is not used independently in Stereo Investigator, the optical disector is an important stereological probe in its own right and is described here as such.

Unbiased sampling of a Volume

The optical disector is a technique for counting particles in a small sample volume. It uses a 3D counting frame and a counting rule that defines when particles inside the counting frame are to be counted and when they are to be ignored.

Guard Zones

The counting frame must enclose a representative volume. Due to irregularities that occur at the surface of a tissue section (lost caps, warping, tearing, compression, etc.), the top plane of the counting frame should be located below the top surface of the section. The region between the top of the section and the top of the counting frame is called the guard zone.

Normally, it is desirable to have a guard zone both above and below the counting frame. The guard zones must exclude the artifact regions at the top and bottom of the section.

The thickness of the guard zones and the counting frame thickness are constrained by the actual section thickness and an evaluation of how much shrinkage the section has experienced along the Z-axis after processing.

You are prompted to enter the section thickness, the counting frame thickness and the top guard zone thickness when you preview or run a probe that utilizes the optical disector.

Reference

• West, M.J., L. Slomianka, and H.J.G. Gundersen (1991) Unbiased stereological estimation of the total number of neurons in the subdivisions of the rat hippocampus using the Optical Fractionator. The Anatomical Record 231: 482-497.

Counting Rules

The first counting rule is the unique point rule; the unique point rule requires that a unique and arbitrary point is associated with each particle being counted. The point can be thought of as a leading edge, it must come into focus and leave focus quickly. For instance, a unique point e.g., the top of the particle, or its nucleolus (if the particle is a cell and every cell has one point-like nucleolus) is used to determine if the particle is inside the counting frame. Every particle only has one unique point, so you can’t over count cells as you would be doing if you were counting cell pieces.

The second counting rule is to only count particles whose unique point comes into focus as you focus down from the top of the counting frame (assuming you are scanning down through the counting frame). Particles that are in focus above and at the top of the counting frame should not be counted. If a particle’s unique point comes into focus inside the counting frame, but extends down past its bottom face it can be counted.

The third counting rule defines three neighboring faces of the counting frame's six as forbidden. A particle is ignored if its unique point crosses these faces. Particles whose unique point crosses any of the other three faces are counted. Conventionally, the counting frame's forbidden faces are the left YZ face, the lower XZ face, and the top XY face. In addition, extensions of the left and right YZ faces (z projections of the counting frame tails) exclude the counting of particles that cross the permitted faces and then curve around to cross these extensions. The following illustrations may help explain the concept of the forbidden and allowed surfaces of the counting frame.

The following illustrations may help explain the concept of the forbidden and allowed surfaces of the counting frame.

A typical counting frame. This illustration shows a typical counting frame for sampling particles. Any particles whose unique point falls entirely inside the square are to be counted, but unique points touching or crossing the boundaries must follow the counting rules. The top and right surfaces of the square are the inclusion (allowed) lines, the left and bottom surfaces are the exclusion (forbidden) lines. In addition, the exclusion lines continue to infinity up and down from the right and left sides of the square.

 

The counting rules for this type of counting frame are as follows:

• All unique-points falling entirely within the square are to have their particles counted.
• Decide whether you will use touching or crossing when counting or not counting particles. Choose one, but not both. Be consistent in counting/excluding. For example, If you count particles whose unique points are crossing the inclusion line, you must not count particles whose unique points are only touching the exclusion line.

The following illustration shows an array of particles in and around a counting frame:

Notice the position of the unique points on the particles in relation to the counting frame elements. Particles with a check mark are to be counted—they touch the inclusion lines. Particles with an x are not to be counted—their unique points either fall entirely outside the counting frame, or touch the exclusion lines. If a particle touches both the inclusion and exclusion lines, it is not to be counted.

Visualizing Counting Frame Rules

One way that is helpful in remembering the counting frame rules is to remember that in stereological sampling, each particle or cell must have one and only one counting frame in which it can be counted, and it cannot be counted in any other location. Your counting frame has fallen in a particular location, but imagine that there is a grid of adjacent counting frames all around it. If the particle in question could be counted in any adjacent frame, it cannot be counted in the current frame. For example, the crescent shaped particle in the above illustration does cross the inclusion line, so why not count it? Imagine another counting frame directly beneath the one illustrated. In this counting frame, the crescent particle would cross the inclusion line and be counted. Therefore, it should not be counted in the current frame. If a particle could be counted anywhere else, do not count it.