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The Optical Fractionator

The Optical Fractionator is the most commonly used stereological method in the biological sciences. It is used to estimate the number of objects. It can be used for cells, synapses, glomeruli, and other small objects within tissue. The Optical Fractionator requires that the tissue sections are thick – typically at least 20um thick for neurons. The tissue can be sectioned in any orientation (also known as preferential sectioning). The cell counts carried out with the Optical Fractionator are unbiased in that they are not influenced by the size, shape, spatial orientation, and spatial distribution of the cells under study.

The Optical Fractionator starts by using the fractionator principle to select a series of systematically random sampled (SRS) sections. Then, each of the sections is sampled in XY, again using the fractionator principle. Finally, each section is also sampled in z. We will use an example from an actual research study to demonstrate the process.

Selecting the sections

The first step in the Optical Fractionator is to choose the section fraction by examining how many slices are available to the study. Suppose there are 60 sections containing the structure of interest. A reasonable approach to the Optical Fractionator is to use 10 to 15 of the sections. In this case, a fraction of 1/5 will serve us well, i.e. we will use one out of every 5 sections since 1/5 of our 60 sections is 12 sections. This is called the section sampling fraction or ssf.

Figure 1. Here we see an SRS series of 50 µm thick, Nissl-stained coronal cryostat sections encompassing the entire right cerebellar half of a 9-month old rat, with a distance of 250 µm between the upper surfaces of the sections (i.e., every fifth section was selected [systematic aspect of sampling], and section no. 1 was randomly selected from the first 5 sections of the cerebellar half [random aspect of sampling]).

Selecting the XY fraction of the section

The process of selecting the XY fraction of the section to sample involves two steps. First, a counting frame size needs to be determined, then the spacing of the counting frames needs to be determined. The ratio of the counting frame area to the area formed by the distance between counting frames is known as the area sampling fraction, or asf.

Selecting the counting frame size

To determine the size of the counting frame for use with the Optical Fractionator use a high magnification objective lens with a high numerical aperture (NA) is required. Typically a 60x oil or a 100x oil with 1.4 NA is used. A high NA objective provides a thin depth-of-field. The thinner the depth-of-field, the more accurate is the z position information.

A good choice is to use a counting frame that is large enough to get a count 1 to 3 cells on average. Make sure that the counting frame is not so large that the edge effect comes into play. More information on the counting frame and the edge effect can be found in the sections on the counting frame.

Figure 2 shows a high-magnification image of the microscopic field indicated in section 7, showing details of the cerebellar molecular layer (ML), Purkinje cell layer (PL) and granule cell layer (GL). Five Purkinje cells are found in this microscopic field. The microscopic field is superimposed with a counting frame with dimensions 125×75 um,

Selecting the SRS grid of counting frames

In this study, it was determined that it was appropriate to count aprroximately 600 cell to achieve the desired level of accuracy of the populuation estimate. See the section on CE and study design for more information. Since 12 sections have been chosen for this study, it will require approximately counting approximately 50 cells per section (12×50 = 600) to achieve this target. Now take into consideration that the counting frame is sized to count an average of 2 cells per counting frame, and will take approximately 25 counting frames per section (2×25 =50). Notice that the sections vary significantly in their profile areas. Section 1, 2, ans 12 have relatively small areas compared with the other sections in the series. To take all this into consideration a sampling grid of 300×300 um was selected.

Figure 3 shows section number 7 from the series, shown at medium magnification, superimposed with a rectangular lattice with uniform distances between the lines in directions X and Y. The position of the lattice on the section was randomly selected. This lattice defines the positions of a SRS set of microscopic fields (indicated as gray rectangles) with uniform distances between the fields in directions X and Y of 300x 300 um at which the section is then inspected at higher magnification. The gray rectangles represent high magnification fields-of-view, similar to Figure 2. In this example the asf = 9375 (the counting frame is 125 x 75 um) / 9000 (the sampling grid is 300 x 300 um).

Selecting the height sampling fraction of the section

The final issue is to decide the is size of the guard zones and the Optical Disector height. Typically, guard zones are used to avoid cutting artifacts that occur at the upper and lower surfaces of the sections. Guard zones reduce the available section thickness that can be used for counting. The height of the Optical Disector divided by the mean tissue thickness is the height sampling fraction or hsf.

Figure 4 shows an Optical Disector from section 7 in Figure 1.

The figure shows the selected microscopic field at the top surface of the section, at six consecutive focal planes below the top surface with a distance of 3 µm between the focal planes, and at the bottom surface of the section that was found 20 µm below the top surface. Between -3 µm and -18 µm the microscopic field is superimposed by a counting frame; explained in detail in the section Optical Disector. As shown, three nucleoli of Purkinje cells (marked with arrows at -6 µm and -9 µm) fulfilled the counting criteria and were therefore counted. Two other nucleoli of Purkinje cells came into focus at -3 µm and -12 µm, respectively (also marked with arrows), i.e., within the range of the section thickness covered by the height of the Optical Disector. However, both nucleoli were not found entirely within the counting frame or at least hitting one of its inclusion lines and were therefore not counted. Provided the nuclei or the perikarya of the Purkinje cells would have been selected as objects of interest in this example, also, the cells found at -6 µm and -9 µm would have been counted.

Putting it all together

At this point all of the sampling parameters have been established. None of these settings should be changed while processing this set of slices.

1. Slice interval
2. Counting frame width and height
3. Sampling grid size width and height
4. Optical Disector height

Next, the counting occurs. Here, a computer controlled stereology system would typically be used to count all of the cells from each sampled section that occur in the Optical Disectors. The total population of cells would then be calculated as follows:

Total population = total cells counted x 1/ssf x 1/asf x 1/hsf.

In our example, we wanted to estimate the total number of Purkinje cells in the right cerebellar half of the rat brain shown in Figure 1. To this end, we counted Purkinje cells in the SRS series of sections shown in Figure 1 with Optical Disectors. The base area of the unbiased counting frames (B) was 9,375 µm² (125 µm x 75 µm), the height of the Optical Disectors (H) was 7 µm, and the top of the Optical Disectors were placed 3 µm below the upper surface of the sections that had an average thickness (t) of 25.3 µm after histological processing. The distance between the counting frames in directions X and Y (D) was 300 µm. This sampling scheme resulted in a total number of 1,670 unbiased virtual counting spaces hitting the cerebellar half, and a number of 898 Purkinje cells that were counted. Accordingly, fractions were calculated as follows:

ssf = 1/5 = 0.2
asf = B/D2 = 9,375 µm2 / (300 µm × 300 µm) = 0.104
hsf = H / t = 7 µm / 25.3 µm =0.277

Accordingly, the estimated total number of Purkinje cells in the right cerebellar half of the rat brain shown in Figure 1 was 155,803.

In summary, the steps for the Optical Fractionator are:

1. Prepare a set of SRS sections.
2. Select a counting frame size.
3. Select a sampling grid size.
4. Select the size of the guard zones and the Disector.
5. Randomly place the sampling grid onto each slide.
6. Use the counting rules at each sampling site to obtain a cell count.
7. Process all of the sections.
9. Calculate the number of cells and the CE.

For more information, see Glaser, J, Green, G, and Hendricks, S. (2007) _Stereology for Biological Research with a Focus on Neuroscience_ (2nd ed.) Williston, VT: MBF Press.,