Stereology

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About

Stereology - "the spatial interpretation of sections" - is a technique for 3D interpretation of (2D) planar sections of materials or tissues. To achieve this, stereology uses a random sampling and systematic approach to provide unbiased quantitative data. Put another way, stereology exploits the fact that many 3D quantities can be determined without 3D reconstruction. The 3D volume of any object can be determined from the 2D areas of its planar sections.

In the fields of cell biology and electron microscopy, stereology allows scientists to estimate the volume, surface area, number and the size of cellular compartments by looking at a relatively small number of 2D slices and, unlike 3D reconstruction and segmentation (methods which are notoriously slow) it allows scientists to attain these estimates very very fast. As such, I believe all cell biologists should be familiar and experienced with this technique... and yet I've noticed that many are not! Due to its rapid nature (one day of counting is often enough to generate an entire table of results), and the fact that stereology can be done live on a microscope (no saving or storing of images required), or using existing 2D and/or 3D images of cells (images which have already been collected), I believe stereology is a brilliant compliment to slower methods of 3D analysis, such as the use of transmission electron tomography and scanning electron tomography to acquire 3D images. I've written this page to show just how quick and easy stereology can be.


Point Counting Stereology

There are many types of stereology, but on this page I highlight one of the most common and easy forms of stereology: "point counting stereology". In point counting stereology an image from your microscope is projected onto a computer screen and your microscope control program and/or special imaging software projects a uniform grid over this image. The image below (Figure 1) shows an example of this, where the grid is 9 x 6 lines - meaning a total of 54 intersection points (NOTE: lines and point on the edge of the screen are not counted). For each intersection point, the user then tallies how many points fall within each compartment. In this example I was interested in tallying the percent of non-nuclear volume occupied by mature granules (the round things) and mitochondria (the dark sausage things).

Figure 1 - an example of point counting stereology using a grid with 54 intersection points (9 colums x 6 rows). This image is a 2D micrograph of a region of beta cell imaged at 20k× magnification. Blue arrows show points inside a mature granule, green arrows show points inside a mitochondria, and the black arrow show a point that is almost inside a mitochondria, but isn't counted. Points are only counted inside if they are "on the line or in" - similar to tennis!

In this image I recorded that all 54 points fell inside non-nuclear volume in my desired cell type... 3 intersections points fell inside a mature granule (blue arrows) and 5 points fell inside a mitochondria. Note that any point on the membrane / on the line is counted as in. Results from this grid would indicate 5.5% of this area (5/54) is occupied by mature granules, but this clearly isn't a good sample size, hence this process must be repeated over many cells (i.e. many grids) to achieve a reliable statistical estimate. After tallying numbers, a new image is placed under the same grid. It is important this image is selected at random from within the large sample of tissue, so as not to be biased by any local differences between the density of organelles. Using a live image, this can be achieved by simply "spinning" the X-Y stage controls to a new area, and then progressing through the entire specimen without doubling back over the same area twice. An example of this is shown in Figure 2, where 30 different cells (and different grids) were counted on a single thin section. 30 grids x 54 points = 1620, which is already good numbers for an estimate, but since this tissue may not be represented, this was repeated on similar sections from three different animals.

Figure 2 - a low resolution micrograph of a 60 nm section cut from a mouse islet, imaged at 140× on the same instrument. Note that it is impossible to see sufficient detail, to distinguish between different types of cells at this resolution. However, this magnification provides a useful low resolution 'overview'. This image has been used to demonstrate how to randomly select regions within 30 different cells for point- counting stereology, by navigating in a snake-like pattern across the islet. Locations marked with dotted lines have been skipped because they do not contain a large area of non-nuclear beta cell. Note that the spacing between grid locations does not need to be perfect, as long as the distance between locations is large enough to ensure that the same cell does not get imaged/counted twice.

After counting a good number of grids (try to get over 2000 total intersection points), we then calculate the fraction of non-nuclear volume occupied by mature granules (fractMatureGrans) using:

fractMatureGrans = total points inside mature granules / total points inside non-nuclear area of cell

And likewise for the mitochondria. It's that easy! In this example, from my own project, it took about a day to collect a measurement of three sections (1620 points) - representing three mice with high blood sugar level, and the same again for three control mice, with normal blood sugar levels. In one day I was able to get preliminary results on the hypothesis: "the volume of mitochondria increases after glucose stimulation"... something I should have done BEFORE spending years reconstructing and segmentation data, but in my case I was VERY lucky in that the stereology nicely complemented results from my 3D models!


Performing Stereology

There are a number of ways to do stereology, but almost all modern technique require the use of computer software to generate a grid. Most microscope control software programs have stereology modules, which can be opened and used to display some type of stereology grid over the live image from the microscope. The user will then have to then count how many of these grid points or grid lines intersect particular types of organelles, and can tally these numbers either in a spreadsheet program or on a notepad to be transferred to the spreadsheet later (I actually prefer the latter). In cases where the image is already saved, the same principle applies: the image is opened and a software program puts a grid over the top. Using programs like the "IMOD SLASH stereology plugin" you can use shortcut keys and even painting tools to more rapidly classify points, and the program will tally the numbers for you. Better yet, if you get suspicious numbers, you can always go back to your same grid later and double-check, add extra classifications, or even refine the fidelity of your grid. Once you get proficient, you can count thousand of points per hour.

Classifying points with the number keys using the SLASH stereology plugin


Conclusion

In the field of microscopy, stereology represents a golden benchmark for unbiased and precise quantification. Certain things, like complex shape/morphology and proximity between organelles can only be obtained by complete 3D segmentation, however due to the slow nature of segmentation, stereology represents a wonderful complimentary technique. It also offers a great way to rapidly test hypothesis (eg: is there more mitochondria in this condition than this other condition) before a scientists commits the large amounts of time necessary to collect, reconstruct and segment on potentially huge datasets. It's my opinion that every cell biologist and electron microscopist should be familiar with stereology. Reading this simple little article is just the start, next I recommend you visit some of the links at the bottom to investigate more, or read a good little book like Unbiased Stereology to become fully versed on the subject - you won't regret it!


A Few Stereology Tools (Software)

There are many pieces of software for stereology, but here are just a few:

  • STEPanizer - an Java applet online tool where you can specify images on your computer and apply stereology. Great idea, although I found the interface very complex to use.
  • Stereo Investigator - a pretty advanced system by MBF Biosystem which can works like on their microscopes (see videos).
  • IMOD's SLASH Stereology Plugin - a stereology plugin I designed myself for working with TIF and 3D MRC images which have already been saved from the microscope.


Links

  • Wikipedia - Stereology
  • Stereology.info - a great website with information about stereology for the biological sciences.
  • Practical Stereology - if you're interested in learning more about stererology I suggest you read this book. Did a quick google and there seems to be a pdf here. The full reference is:
    • Russ, J.C., and R.T. DeHoff. 2000. Practical stereology. Kluwer Academic/Plenum, New York. 381.
  • Unbiased Stereology - another great book to get you started with stereology. The full reference is:
    • Howard, C.V., and M.G. Reed. 2005. Unbiased stereology. BIOS Scientific Publishers, New York. 246.