Optical Fractionator
Overview
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The Optical Fractionator probe enables you to sample a 3D region of interest and estimate the total number of particles. The Optical Fractionator is available as a stand-alone probe, however, it is fairly complex to use. Use the Optical Fractionator workflow for step-by-step guidance.
The Optical Fractionator (West, et al., 1991) combines the Optical Disector and the Fractionator for counting. It is unaffected by tissue shrinkage and does not require rigorous definitions of structural boundaries.
Using the Optical Fractionator involves counting objects with optical disectors in a uniform systematic sample that constitutes a known fraction of the volume of the region being analyzed. In practice, this is accomplished by systematically sampling a known fraction of the section thickness, of a known fraction of sectional area, of a known fraction of the sections that contain the region of interest.
Use the Optical Fractionator to perform systematic sampling of populations distributed within a series of serial sections to estimate the population number in a volume. Properly designed systematic sampling yields unbiased estimates of population number.
The theory underlying this sampling methodology also makes it possible to estimate the precision of the population size estimate for a single subject; this estimate of precision is called the Coefficient of Error (CE).
The concept of the optical disector is an extension of the original disector (described in Physical Fractionator). But instead of observing two physical sections as in the disector, you observe 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. You can then count following the disector—also referred to as a counting frame—counting rules (see Counting rules for the counting frame).
The optical disector has one very important advantage over the physical disector: it eliminates the difficult, time consuming task of identifying corresponding parts of two physical sections (i.e., determining whether a particular object can be seen on one section and not on the other). With optical disectors, the sections are always optimally positioned for comparisons. This capability is extremely valuable, if not essential, when counting branching or highly irregular objects.
Before using the Optical Fractionator probe to estimate a population using a series of sections from a single animal, you need to set or specify the following parameters. Then, you implement the probe across this series of sections.
The size of the counting frame should be small enough to fit in a single field of view when using the objective lens to count cells. We recommend that you size the counting frame so that it includes only a few objects.
The thickness of the counting frame, added to the thickness of the upper and lower guard zones, must be less than or equal to the minimum physical section thickness.
Counting Frame Thickness + Guard Zones Thickness <= Min Physical Section Thickness
Thus, the maximum thickness of the counting frame is constrained by the section thickness (and guard zone thickness), while the minimum counting frame thickness is determined by the cell distribution and the depth of field of the objective lens that will be used to count the cells. This latter factor is important since only cells that come into focus while focusing down through the counting frame will be counted. This means that the depth of field of the objective lens should be significantly less than the thickness of the counting frame.
The guard zones should normally be thick enough to ensure that the tissue sampled by the 3D counting frame is not disturbed by the process of preparing the sections.
The minimum guard zone thickness required depends on how the tissue was sectioned, and on how it was processed before and after sectioning (e.g., guard zones may be unnecessary for plastic-embedded sections).
See Guard Zones for more information.
The height of the optical disector needs to be viewed in light of several considerations:
- The thickness of the optical disector must be less than the thinnest portion of any section.
- It must be thick enough to provide a representative volume.
- It must be significantly thicker than the depth of field for the objective lens that is used when counting cells.
If sections were cut at 40 microns and the final section thickness varies between 18 and 20 microns, the optical disector height could be 12 microns, allowing the top and bottom guard zones to be 3 microns.
There are several methods of determining an appropriate section increment (see See "Determining sampling precision"). This value is constrained by the total number of sections in the series that contain some portion of the volume of interest. Sample enough sections so that what you see is a representative cross-sectional volume of the region of interest.
Normally, you should neither sample every section, nor only one or two sections.
It is important to know the minimum actual section thickness (mounted thickness) in order to properly determine the thickness of the counting frames and their guard zones. Most histological processes result in shrinkage along the Z-axis of a section (due to greater exposed surface area). Some cutting procedures result in inconsistent section thickness. Even if a section starts out with a consistent section thickness, different areas within the section can shrink differently, depending on the characteristics of the tissue.
To measure the section thickness:
- Click the Z Meter icon to display the Z Meter.
- Focus to the top of a section using a lens that has a depth of field significantly smaller than the section thickness.
- If you can't focus on the top of the section, try to focus on the first object below the top of the section.
- If there is no object at the top of the section, focus on the extracellular matrix at the top of the section. This can be difficult to execute, but it is essential for an accurate determination of section thickness.
- Press ALT+S to set the Z position to 0.
- Focus to the bottom of the section.
If you cannot identify the bottom of the section, try to adjust the stage height such that the bottom of the lowest object in the field of view is just leaving focus as you are focusing down through the section.
- Look at the Z (focal) depth value (third of the three coordinate numbers displayed in the parentheses) in the lower-left of the status pane. This value is the distance (in microns) between the top and the bottom focal planes you have chosen. If you focused at the top and bottom of the section, it is the section thickness at this particular location.
Alternatively, you can measure the section thickness in step 5 of the Optical Fractionator Workflow.
The optimal mounted thickness is 20–30 microns; this allows for an optical disector with four to five distinct optical planes. Determining the optimal thickness is important and must be done at the pilot study stage to obtain the best results.
If you have a very high numerical aperture (NA) 100X oil lens, you can expect to have distinct optical planes every 0.5–0.7 microns. At lower magnification or with lower NA lenses, the optical sections (depth of field) will be thicker.
If sections are too thin, there may not be enough room for adequate guard zones, or the objective lens to be used may not have an adequately thin depth of field for this protocol. If sections are too thick, it may be very hard to focus clearly to a given depth due to visibility constraints, working distances of objective lenses, etc. There may also be issues of consistent staining throughout the section thickness.
Once the section increment has been determined, the starting section index should be chosen at random. lets you do this easily when you define the first section of a series.
- Click Probes>Stereology results>Probe run list.
- Highlight the probe run(s) then click View Results
Stereo Investigator software provides multiple methods for calculating the Optical Fractionator Results for each type of marker used. The results vary based on the measurement used for the mounted (or post-processing) section thickness. The mounted section thickness value is divided into the counting frame thickness (or disector height) to calculate the height sampling fraction (hsf).
Select the results method to report the measurement that best reflects the histological properties of the region of interest.
All estimates calculated from measurements obtained while counting (i.e., all but Estimated population using user-defined section thickness) should return similar results if the measurements were taken correctly.
Calculated using a single value entered manually for the post-processed or “mounted” section thickness.
Because this estimate is generated with only one value for the section thickness, local variations in section thickness are not accounted for. As a result, this estimate should be considered the least accurate of the 4 available estimates. But if there is no section thickness variation (e.g., embedding protocols such as plastic embedding), reporting the Estimated population using user-defined section thickness is acceptable.
This value is typically entered manually, or calculated, in Step 5 of the Optical Fractionator workflow under the Manually enter the average mounted thickness method.
- If you don't enter a value for Manually enter the average mounted thickness, the estimate equals zero.
- To change the thickness value after the counting procedure, click the Edit Mounted Thickness button in the Sampling results window.
Calculated using the section thickness measurements recorded while counting.
These measurements are recorded in Step 5 of the Optical Fractionator workflow, after selecting Measure the mounted thickness while counting method.
The number of measurements used to calculate this estimate is based on the interval you entered (e.g., if you entered 2, you are prompted to set the top and bottom of the section at every other counting site). The measured thickness values from these sites are averaged to produce a mean measured thickness value used for the height sampling fraction calculation.
Because this estimate is generated from the mean of all obtained section thickness measurements, it is considered to be the most accurate estimate of the region of interest when measurements are not performed at every site.
You may also choose to use this value for low frequency events (e.g., BrdU+ neurons) with many counting sites containing zero objects when you want to generate an accurate average measured section thickness measurement for the hsf using a systematic interval for site measurement.
If you didn't measure the thickness of sections while counting, this estimate is not calculated.
This estimate is a variation of Estimated population using mean section thickness.
Calculated using only the section thickness measurements made at counting sites that contain marked objects (in other words, section thickness measurements from counting sites with NO counted objects aren't included in the calculated average).
These measurements are recorded in Step 5 of the Optical Fractionator workflow, after selecting Measure the mounted thickness while counting method.
In many cases, this estimate will be nearly identical to to that found using Estimated population using mean section thickness.
You may choose to use this value when :
- You chose to ignore measuring the section thickness where there were no objects.
- You made errors in section thickness measurement that were not corrected when there were no objects to be marked.
If you didn't measure the thickness of sections while counting, this estimate is not calculated.
Report this estimate when thickness was measured at every sampling site and when the section thickness varies dramatically across the sections that include the region of interest.
Calculated using only the section thickness measurements from counting sites that contain markers. These measured thickness values are then weighted by the number of objects associated with them to produce a weighted average.
The number weighted mean section thickness is reported in the Parameters section and is used to calculate the height sampling fraction.
Geiser, M., L.M.Cruz-Orive, and I.M. Hof (1990). Assessment of particle retention and clearance in the intrapulmonary conducting airways of hamster lungs with the fractionator. Journal of Microscopy 160 (Pt 1): 75-88.
Glaser, E.M. and P.D. Wilson (1998). The coefficient of error of optical fractionator population size estimates: a computer simulation comparing three probes. Journal of Microscopy. 192(Pt 2): 163-171.
Gundersen, H.J. et al. (1999). The efficiency of systematic sampling - reconsidered. Journal of Microscopy. 193(Pt3): 199-211.
Gundersen, H.J.G. and E.B.V. Jensen (1987). The efficiency of systematic sampling in stereology and its prediction. Journal of Microscopy. 147(Pt3): 229-263.
Schmitz, C. and P. Hof (2000). Recommendations for straightforward and rigorous methods of counting neurons based on a computer simulation approach. Journal of Clinical Neuroanatomy. 20:93-114.
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.
Watch this webinar for a practical demonstration of the Optical Fractionator workflow. If you are running Optical Fractionator on a FLUOVIEW system, see SRS Image Series and SRS Image Stack Series for instructions.