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  • Design-Based Stereology
  • Symbols Used in Stereology
• Optical Fractionator
  • Tissue Preparation for Stereology
  • Selecting the XY fraction of the section
  • Criteria for counting cells
• Sampling
  • Fractionator Principle
  • SRS Preferential Sections
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  • Disector
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  • Edge Effect
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• Coefficient of Error
  • CE and Biological Variability
  • CE and Study Design
  • Some CE Theory
  • CE Controversy
  • Deciding on Precision of Sampling
• Cavalieri Estimator
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  • Length & Surface
• Tissue for Stereology FAQ
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Estimating length of fibers

Design-based stereology offers several methods for determining the length density and total length of capillaries or cell processes, in any region of interest, such as Space Balls, Isotropic Virtual Planes, Petrimetrics, IUR Optical Fractionator, L-Cycloid Optical Fractionator, Cycloids for Lv, Merz, and Weibel amongst others.

One method of estimating the length of tubular objects such as capillaries or cell processes is with systematically spaced straight lines, or a series linked semicircles (Merz), provided thin isotropic uniform random sections through the region of interest are available (For details, see Calhoun and Mouton, J Chem Neuroanat 2000;20:61). With vertical sections, systematically spaced sine-weighted curves (cycloids) can be used.

A second method is to quantify tubular objects with isotropic virtual planes ( Larsen et al., J Microsc 191:238.) In this case, the tubular objects under study contained in thick (3D) sections are investigated with software-randomized isotropic virtual planes in volume probes in systematically sampled microscopic fields. A disadvantage of this technique is the fact that the analysis has to be carried out on virtual planes within the thick sections, the counting rules for which can be tedious and cumbersome.

Another solution is the Space Balls methods ( Calhoun and Mouton, J Chem Neuroanat 2000;20:61; Mouton et al., J Microsc 2002;206:54). First, an SRS set of sampling sites encompassing the 3D region of interest is generated. Then, virtual spheres (or hemispheres, which are better suited to thinner tissue and in situations with a very high density of fibers) are placed within the sections at all microscopic sampling sites, and the intersections between the spheres (or hemispheres) and the tubular objects under study are counted. Note that the mounted tissue thickness must be greater than the diameter (for spheres) or radius (for hemispheres) of the Space Balls. From this data, you can obtain both the length density of the linear biological structures as well as the total length of the tubular objects.