Basic quantitative morphological methods applied to the central nervous system

Abstract

Generating numbers has become an almost inevitable task associated with studies of the morphology of the nervous system. Numbers serve a desire for clarity and objectivity in the presentation of results and are a prerequisite for the statistical evaluation of experimental outcomes. Clarity, objectivity, and statistics make demands on the quality of the numbers that are not met by many methods. This review provides a refresher of problems associated with generating numbers that describe the nervous system in terms of the volumes, surfaces, lengths, and numbers of its components. An important aim is to provide comprehensible descriptions of the methods that address these problems. Collectively known as designbased stereology, these methods share two features critical to their application. First, they are firmly based in mathematics and its proofs. Second and critically underemphasized, an understanding of their mathematical background is not necessary for their informed and productive application. Understanding and applying estimators of volume, surface, length or number does not require more of an organizational mastermind than an immunohistochemical protocol. And when it comes to calculations, square roots are the gravest challenges to overcome. Sampling strategies that are combined with stereological probes are efficient and allow a rational assessment if the numbers that have been generated are "good enough." Much may be unfamiliar, but very little is difficult. These methods can no longer be scapegoats for discrepant results but faithfully produce numbers on the material that is assessed. They also faithfully reflect problems that associated with the histological material and the anatomically informed decisions needed to generate numbers that are not only valid in theory. It is within reach to generate practically useful numbers that must integrate with qualitative knowledge to understand the function of neural systems.

Unbiased analysis of obesity related, fat depot specific changes of adipocyte volumes and numbers using light sheet fluorescence microscopy

“…The general principles and methodologies of quantitative stereological analyses and applicable sampling strategies have comprehensively been described in several textbooks [7,8,33,55], reviews and studies [9,[14][15][16][17]28,39,42,54] the interested reader is referred to. Early "modelbased" quantitative stereology methods use(d) (model-) assumptions about the shape, the shape-and size-distribution, the orientation, and the distribution of the examined tissue structures, to estimate their 3D volumes, numbers, surfaces, or lengths in histological sections.…”

“…The corresponding coefficients of error (CE) of the numerical volume density estimates, considering the variances originating from the sampling within sections, were calculated as described previously [39] and accounted for 0.1 ±0.01 on the average. The total number of adipocytes in an adipose tissue depot (N (AC,ATD) ) was calculated as the product of N V(AC/ATD) and V (ATD) .…”

“…adipose tissue depots of obese vs. lean minipigs were associated with significant increases of the mean adipocyte section profile areas and diameters, respectively, with significant decreases of the numbers of adipocyte section profiles per section area. However, 2D histomorphometric measurement data of cell section profiles are, offhand, neither equivalent to, nor can they be directly compared to 3D cell volumes and numbers, which represent inherently different parameters [8,39,54]. 2D histomorphometric measurements of cell section profiles in single histological sections can also not provide information about individual cell volumes, or the distribution of cell sizes in a defined tissue reference compartment.…”

“…A precise, accurate, and objective characterization and differentiation of obesity-related hyperplastic and hypertrophic adipocyte growth patterns requires, by definition, unbiased measures of quantitative morphological parameters, namely the mean adipocyte volume, and the total number of adipocytes. However, these quantitative morphological parameters can generally not be determined without bias by 2D histomorphometric measurements of cell section profiles in single arbitrarily sampled histological sections [7][8][9]14,39,54]. Here, unbiased quantitative stereological methods, based on stochastic geometry, are required, representing the "goldstandard" for quantitative morphological analyses of biological tissues in biomedical sciences [7][8][9]14,33].…”

Clinical significance of proliferation index and E-cadherin expression in colorectal adenocarcinoma

“…To test the density of Ki67+ cells per mm 2 , 10 "hot-spots" were counted successively. The absolute value of the density of positive cells in the "hot-spot" was determined stereometrically [8]. The means of the obtained values of the "hot-spots" represents the final number of Ki67+ cells in mm 2 per case.…”