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MCID Core Stereology Module

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Stereology

The stereology module is an optional addition for the MCID™ Core Image analyzer. It incorporates a set of tools, which are used to derive unbiased 3D geometric and topological parameters from measurements made on 2D sectional images. Measurements include number and density of targets, surface area and density, target volume and volume ratio. When used with an MCID™ system (equipped with the Tiled Field Mapping module and XYZ motor stage), the stereology module integrates microscope stage control and optical fractionator procedures.

Stereology Example

 

Introduction


Investigation of structure often requires that optical or physical sections be made. Sectioning can yield excellent views of two-dimensional structure, but the third dimension is lost (Figure 1). For example, we could measure the cross-sectional area, perimeter, and diameter of a target by counting the pixels within it. MCID™ Core contains extensive functions for this type of measurement, which we will refer to as standard morphometry.

Figure 1: Three sections through a target. Our measurement of cross-sectional area, and our view of the target's shape (cut in a different plane, this target might have a circular cross section), is entirely dependent upon the plane of section. We can use stereology or 3D reconstruction to estimate 3D properties of the target.

Slice image 1
A: the original target whole.


Slice 2
B: the target is studied in sections.


Slice 3
C: when presented as flat images, the sense of depth is lost.



Common techniques for regaining knowledge of the third dimension are to perform standard morphometry in each and every section (using every section is called exhaustive sampling), 3D reconstruction, and stereology. As a practical matter, however, exhaustive sampling with standard morphometry is very tedious. 3D reconstruction, while very useful if visualization is required, is also tedious and poorly suited to routine measurement tasks.

In some tasks, the easiest and fastest way to make 3D measurements will be stereology. Stereology offers a set of practical tools which can derive 3D geometric and topological parameters from measurements made on 2D sectional images. Some stereological tools require exhaustive sampling. Others can be applied to a random sample of sections.

Although potentially very useful, stereology has found limited application in routine image analysis. After all, the mathematical principles of stereology are somewhat abstruse, and manual stereological procedures can be both complex and very tedious. Despite these difficulties, interest in stereology is growing. There are two main reasons for this:

  • New tools (image analyzers) incorporate accepted procedures of stereological measurement. These tools remove the need for intimate familiarity with the mathematics of the procedures.
  • Image analysis systems can remove a great deal of the time and labor involved in manual stereology.



Stereological Principles

The basic principle of stereology is that we place test systems (grids, points, lines) over planes cut through our specimens (see cover illustration). The test systems have known properties. Therefore, we can derive information about unknown properties of our specimens by observing how the test systems interact with them.

Classic (model-based) stereological measurements are subject to bias arising from faulty assumptions of the models. In particular, it was assumed that targets were spherical or ellipsoid. Recently, "design-based" stereological methods have been developed, which permit unbiased measurements because they make no assumptions regarding object shape. Rather, the object is sampled with equal probability, regardless of its shape or position in 3D space. This is known as uniform random sampling, and uses probes known as dissectors.



Image Analysis and Stereology

Manual stereology systems require that a test system (e.g. a grid of points on celluloid) be placed over a photograph. The user then indicates each intersection of the test system with the targets in the photograph. A computer records the "hits", and provides data summaries.

An image analyzer makes measurements from digital images (as opposed to photographs). The advantages of using image analysis in stereology are summarized, below.

Test system generation
Any type of test system can be generated, digitally, and appears directly over the image of the specimen.

Automated target detection
The better image analyzers can automatically determine where intersections with targets occur, using a combination of density and spatial criteria set by the user.

Consistent sampling
The computer can apply the principles of sampling and measurement in consistent ways. The danger of biased sampling is reduced.

Flexible image acquisition
The imaging system can analyze photomicrographs, but it also allows us to form images without an intermediate photographic step. Acquire images, directly, from video cameras, cooled CCD cameras, phosphor plate imagers, or other devices that generate digital data.

Multiple images can be used to localize specific tissue components
We can use combinations of images (e.g. fluorescent and brightfield) to make stereological measurements on specific populations of labeled targets.





Stereological Tools in MCID™



                                   
Parameter Definition Method Name
Ns Number of targets sampled Unbiased sampling and counting frame
Na Numerical density (2D) Unbiased sampling and counting frame
N Number of 3D targets Disector
Nv Numerical density (3D) Disector
Aa Estimated area ratio Point-sampled-intercept
As Sampled 2D area Unbiased sampling and counting frame
Sv 3D surface density Test needles
Vv Volume Ratio Cavalieri's principle
Vm Mean target volume Point-sampled-intercept
Vs Volume sampled Disector
                                   

Fractionators (MCID™ Core only)

MCID™ implements optical fractionator methods, most commonly applied to cell counting. The MCID™ system must be equipped with a Tiled Field Mapping module and with a motorized XYZ microscope stage (preferably with a linear encoder on the Z-axis control).

 

                                   
Parameter Definition Method Name
NEst Estimated total number of targets Unbiased sampling and counting frame
NDet Number of targets counted Unbiased sampling and counting frame
                                   

To use fractionators, the user predefines the number of sections, section thickness, and the sampling frequency. A montage of each section is created at low power, and an area of interest is outlined on this montage. A higher power is selected, and the system uses random systematic sampling to move the microscope stage to locations within the region of interest. At each location, interactive sampling is performed.

To sample, the user focuses up and down and marks targets within the counting frame. An on screen indicator displays the current Z position and guard volume locations. The computer keeps track of the counts and calculates an estimate of the number of targets.

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