Estimation of the section thickness and optical disector height with a simple calibration method

The distance between the upper and lower surfaces of a section (i.e. the section thickness) can be measured with a microcator or a shaft encoder. In the present report, an alternative simple method is described for estimating the section thickness where such equipment is not available. The basic principle of the method is based on a calibration method already described in the literature. The main difference is that it enables one to make more precise measurements. Provided that the calibration and measurements are made properly, this method can be used in estimating the section thickness, optical disector heights, and in particular in the determination of the thickness sampling fraction for the optical fractionator.     

The smooth fractionator

A modification of the general fractionator sampling technique called the smooth fractionator is presented. It may be used in almost every situation in which sampling is performed from distinct items that are uniquely defined, often they are physically separated items or clusters like pieces, blocks, slabs, sections, etc. To each item is associated a ‘guesstimate’ or an associated variable with a more‐or‐less close – and possibly biased ? relationship to the content of the item. The smooth fractionator is systematic sampling among the items arranged according to the guesstimates in a unique, symmetric sequence with one peak and minimal jumps. The smooth fractionator is both very simple to implement and so efficient that it should probably always be used unless the natural sequence of the sampling items is equally smooth. So far, there is no theory for the prediction of the efficiency of smooth fractionator designs in general, and their properties are therefore illustrated with a range of real and simulated examples. At the cost of a slightly more elaborate sampling scheme, it is, however, always possible to obtain an unbiased estimate of the real precision and of some of the variance components. The only real practical problem for always obtaining a high precision with the smooth fractionator is specimen inhomogeneity, but that is detectable at almost no extra cost. With careful designs and for sample sizes of about 10, the sampling variation for the primary, smooth fractionator sampling step may in practice often be small enough to be ignored.     

A simple and efficient alternative to implementing systematic random sampling in stereological designs without a motorized microscope stage

When properly applied, stereology is a very robust and efficient method to quantify a variety of parameters from biological material. A common sampling strategy in stereology is systematic random sampling, which involves choosing a random sampling relevant objects start point outside the structure of interest, and sampling at sites that are placed at pre‐determined, equidistant intervals. This has proven to be a very efficient sampling strategy, and is used widely in stereological designs. At the microscopic level, this is most often achieved through the use of a motorized stage that facilitates the systematic random stepping across the structure of interest. Here, we report a simple, precise and cost‐effective software‐based alternative to accomplishing systematic random sampling under the microscope. We believe that this approach will facilitate the use of stereological designs that employ systematic random sampling in laboratories that lack the resources to acquire costly, fully automated systems.     

A simple technique to measure the movements of the microscope stage along the x and y axes for stereological methods

Measurements of microscope stage movements in the x and y directions are of importance for some stereological methods such as the optical disector and optical fractionator. The length of stage movements can be measured with great precision and accuracy using a suitable motorized stage, which is generally a computer-assisted instrument. This type of equipment is generally too expensive for and not readily available in many laboratories. This paper describes a simple method to measure the movements of the microscope stage along the x and y directions, which can be used for purposes such as systematic uniform random sampling. It needs a microscope attachment consisting of two dial indicators; one of them is used to measure the amount of stage movement along the x -axis and the other measures the amount of movement along the y -axis. Movements of the stage on the micrometre-scale can be measured easily using this device.     

Simplified nerve cell counting in the rat brainstem with the physical disector using a drawing-microscope

A simple modification of the physical disector is presented, which is used to count the number of neurons in the hypoglossal nucleus of the rat in a series of paraffin sections. One disector consists of two adjacent sections (6 μm thick) that have been Nissl-stained with cresyl fast violet. In the first step of the procedure each of the two sections is investigated separately with a drawing-microscope. The boundary of the hypoglossal nucleus and the position of neurons devoid of, or containing a part of, the cell nucleus in the plane of the section are marked on transparent paper. In the second step, these two drawings are placed one upon another, aligned and the number of cell profiles that show a cell nucleus in one but not in both drawings counted. This modification of the disector method for cell counting needs no specialized equipment, simply a light microscope with drawing apparatus, and can be combined with histochemical studies of other sections from the same tissue block.     

The efficiency of systematic sampling in stereology and its prediction*

The superior efficiency of systematic sampling at all levels in stereological studies is emphasized and various commonly used ways of implementing it are briefly described. Summarizing recent theoretical and experimental studies a set of very simple estimators of efficiency are presented and illustrated with a variety of biological examples. In particular, a nomogram for predicting the necessary number of points when performing point counting is provided. The very efficient and simple unbiased estimator of the volume of an arbitrary object based on Cavalieri's principle is dealt with in some detail. The efficiency of the systematic fractionating of an object is also illustrated.     

The revolution of counting "tops": two decades of the disector principle in morphological research

Twenty years have passed since the publication of the seminal paper enunciating the disector principle by an author using the pseudonym D.C. Sterio. During this time, methods based on the revolutionary principle of counting "tops" have become progressively better known and have been included in several commercially available systems for quantitative morphology. Analysis of the number of published studies citing Sterio's paper on the ISI Web of Knowledge database showed that its scientific "impact factor" has almost continuously risen since its publication, indicating the growing knowledge about disector-based methods in the various scientific fields where morphological quantification is required. This report briefly reviews the first two decades of disector use, pointing to its advantages as well as to shortcomings that have recently been addressed in critical papers and have given rise to a lively debate on the role of counting tops in quantitative morphology today.     

Efficient estimation of number density in opaque material microstructures: the large-area disector

Unbiased and efficient estimation of number density of features in opaque material microstructures has been quite difficult. In this contribution a montage-based efficient serial sectioning technique is presented as a practical solution for efficient estimation of number density in such microstructures. The new technique utilizes a combination of digital image analysis and unbiased disector sampling procedures.     

Tissue shrinkage and unbiased stereological estimation of particle number and size*

This paper is a review of the stereological problems related to the unbiased estimation of particle number and size when tissue deformation is present. The deformation may occur during the histological processing of the tissue. It is especially noted that the widely used optical disector may be biased by dimensional changes in the z‐axis, i.e. the direction perpendicular to the section plane. This is often the case when frozen sections or vibratome sections are used for the stereological measurements. The present paper introduces new estimators to be used in optical fractionator and optical disector designs; the first is, as usual, the simplest and most robust. Finally, it is stated that when tissue deformation only occurs in the z‐direction, unbiased estimation of particle size with several estimators is possible.     

Pronounced loss of cell nuclei and anisotropic deformation of thick sections

The local deformation and variations in section thickness are studied in 100-μm thick vibratome sections of well-fixed human brain tissue. During processing, including drying on glass slides, the section thickness is reduced to less than half, but close to the edges there is less shrinkage of the section thickness. Close to both surfaces there is a pronounced reduction in the number of neuronal nucleoli. At the scale of the original section, the upper 15 μm and the lower 10 μm are depleted. The loss is most pronounced at the upper surface, which is unprotected during processing. In the central 70% of the section height, where one would ordinarily use an optical disector for sampling, there is no indication of non-uniform shrinkage. The simplest explanation for the observed loss of nucleoli is that all cells opened by the knife may lose their nuclei across an unprotected section surface. The observations do not generalize to other tissues and other preparation techniques, but illustrate the magnitude of some of the problems for uniform sampling and unbiased estimation in very thick sections. The uniform optical disector sampling of nucleoli in thick sections, as opposed to that of cell nuclei, raises a special problem, which is discussed briefly.     

Assessment of particle retention and clearance in the intrapulmonary conducting airways of hamster lungs with the fractionator1

A modified version of the fractionator was used to estimate the total number of polystyrene microspheres retained in the airways of hamster lungs at two different time points after inhalation. A systematic three-stage subsampling procedure with known sampling fractions was adopted. First, each lung was cut into slices, from which primary disectors were sampled systematically with a known sampling fraction. From each primary disector, smaller sub-disectors were subsampled, and the corresponding sampling fraction was estimated by point counting. Finally, a few particles were counted at the microscopic level in the sub-disectors, and the final estimate of total particle number (which is unbiased irrespective of any tissue deformations) was easily computed as a product of the counted number times the reciprocal of the successive sampling fractions. The error variance of each estimate was assessed from the data using a new estimator. An average of 6% of the deposited particles were retained on the epithelial surface of the intrapulmonary conducting airways shortly after the inhalation, from which at least one-third was already phagocytosed by macrophages. After 24 h, an average of 87% of the particles retained shortly after the inhalation had been cleared. The proportion of particles ingested by macrophages had increased to at least 87%, in three out of four animals studied.     

The estimation of the Euler-Poincare characteristic from observations on parallel sections

An unbiased estimator of the Euler-Poincaré characteristic (Euler number) of an arbitrary object or a random structure, respectively, is given. The estimator is based on joint observations of pairs of parallel section profiles. Thus the present paper extends the use of Sterio's disector from counting particles to determining the Euler number for a wide class of probes. The correctness of the given formulae is proved with mathematical strictness. Furthermore, the feasibility of the method is illustrated by an example from materials sciences.     

Unbiased and efficient estimation of the total number of terminal bronchiolar duct endings in lung: a modified physical disector

A novel modification of the physical disector is described which was used to estimate the total number of terminal bronchiolar duct endings (TBDEs) in human infant lung. TBDEs are closed three-dimensional space curves of complex shape that are inherently difficult to count from histological sections. However, careful consideration of the microanatomy of the terminal duct endings provides us with the opportunity to define a very simple and unbiased counting rule. To apply the rule in practice we also need to determine a suitable disector height. Owing to the complex shape of the TBDE we had no prior knowledge of what disector height would be suitable for counting the TBDE structures. Exhaustive serial sectioning of complete TBDE structures was carried out and showed that any disector height under 90 μm would give unbiased counts. A further empirical study was then undertaken to determine the most efficient disector height. This was found to be 50 μm.
The total number of TBDEs in the upper lobe of the right lung of six human infants aged between 13 and 25 weeks was also estimated. The estimates of numerical density obtained with our modification of the physical disector were multiplied by estimates of lung lobe volume obtained using Cavalieri's Principle. The total number of TBDEs in the lobes ranged from 15 323 to 57 768, with a mean of 40 306. The average coefficient of error of the number estimates was 19%, which was deemed precise enough given the biological coefficient of variation between TBDE number of 36%.     

Is there section deformation resulting in differential change of nuclear numerical densities along the z axis of thick methacrylate or paraffin sections?

The optical disector, a three‐dimensional counting frame or probe in stereology, is often positioned in the middle (depth) of a thick section for unbiased nuclear counting. Using 30–40 μm thick methacrylate or paraffin sections for nuclear counting of neurons with the optical disector, however, some studies showed markedly higher nuclear densities at 10% of the section thickness near the top or bottom surface of the section, suggestive of deformation of section along its z axis and thus affecting the number estimation. To verify the findings, this study obtained two sets of 12–14 methacrylate sections (average thicknesses 21.7 and 29.4 μm) and two sets of 12 paraffin sections (average thicknesses 13.8 and 29.2 μm) from mature rat testes. Each section was used to count round spermatid nuclei in the seminiferous epithelium densely packed with the cells, using 3–4 consecutive disectors placed vertically (along the z axis of the section) from the top surface of the section, through the whole section thickness (two sets of methacrylate and paraffin sections) or in 80–83% of the thickness (other sections). The results demonstrated that, overall, there were no considerable nonuniform changes of the nuclear densities along the z axis of the sections.     

Global spatial sampling with isotropic virtual planes: estimators of length density and total length in thick, arbitrarily orientated sections

Existing design-based direct length estimators require random rotation around at least one axis of the tissue specimen prior to sectioning to ensure isotropy of test probes. In some tissue it is, however, difficult or even impossible to define the region of interest, unless the tissue is sectioned in a specific, nonrandom orientation. Spatial uniform sampling with isotropic virtual planes circumvents the use of physically isotropic or vertical sections. The structure that is contained in a thick physical section is investigated with software-randomized isotropic virtual planes in volume probes in systematically sampled microscope fields using computer-assisted stereological analysis. A fixed volume of 3D space in each uniformly sampled field is probed with systematic random, isotropic virtual planes by a line that moves across the computer screen showing live video images of the microscope field when the test volume is scanned with a focal plane. The intersections between the linear structure and the virtual probes are counted with columns of two dimensional disectors.
Global spatial sampling with sets of isotropic uniform random virtual planes provides a basis for length density estimates from a set of parallel physical sections of any orientation preferred by the investigator, i.e. the simplest sampling scheme in stereology. Additional virtues include optimal conditions for reducing the estimator variance, the possibility to estimate total length directly using a fractionator design and the potential to estimate efficiently the distribution of directions from a set of parallel physical sections with arbitrary orientation.
Other implementations of the basic idea, systematic uniform sampling using probes that have total 3D × 4π freedom inside the section, and therefore independent of the position and the orientation of the physical section, are briefly discussed.     

Unbiased stereological estimation of the rat fetal pituitary volume and of the total number and volume of TSH cells after maternal dexamethasone application

Glucocorticoids have an inhibitory influence on proliferation activity of the pituitary cells while stimulating apoptosis. Therefore, it was hypothesized that the synthetic glucocorticoid, dexamethasone (DX), has an inhibitory influence on the number of thyroid‐stimulating hormone (TSH) cells during fetal development. The effects of maternal administration of DX on stereological parameters of TSH cells, and TSH serum concentration were investigated in 21‐day‐old rat fetuses. On day 16 of pregnancy, the experimental dams received 1.0 mg DX/kg b.w. subcutaneously, followed by 0.5 mg DX/kg b.w./day on days 17 and 18 of gestation. The control gravid females received the same volume of saline vehicle. TSH cells were stained immunocytochemically by the peroxidase–antiperoxidase (PAP) method. The fetal pituitary volumes were estimated using Cavalieri's principle. A physical disector counting technique in combination with the fractionator sampling method was used for estimation of pituitary TSH cell number. Cell and nuclear volumes were measured with a planar rotator. Maternal DX application was found to cause a significant decrease of pituitary volume and number of TSH cells per pituitary in 21‐day‐old fetuses in comparison with the control fetuses. TSH cell number expressed per body weight unit declined significantly after maternal DX administration. These results indicate an inhibitory DX influence on proliferative activity of precursors and likely differentiated TSH cells and increased apoptotic prevalence. The histological appearance, volume of TSH cells and TSH serum concentration suggest intensive synthetic activity in TSH cells of DX exposed fetuses. Microsc. Res. Tech. 73:1077–1085, 2010. © 2010 Wiley‐Liss, Inc.     

On the empirical variance of a fractionator estimate

The fractionator consists of several sampling stages with systematic sampling at each stage; data are collected only at the last stage. Therefore, predicting the error variance of a fractionator estimator is a non-trivial problem, because the observations are correlated in a complicated, unknown way. Gundersen proposed to split the material sampled at the first stage into two subsets, and to compute the variance of the pooled estimate empirically using the corresponding pair of observations made in these two subsets. The idea is very effective, but the estimator thus proposed needed some corrections. The purpose of this paper is to present an improved estimator of the coefficient of error of a fractionator estimator using Gundersen's design.     

The new stereological tools in metallography: estimation of pore size and number in aluminium

A number of simple, unbiased and efficient methods are now available in stereology for estimating the number and size of arbitrary particles or voids in a material, with the only assumption that particles must be identifiable on serial sections or confocal planes through the material. In recent years, these methods have been developed and applied mainly in a biomedical context: this paper reviews and illustrates them with the aid of a metallographic example, namely the pore population of a sand-cast aluminium alloy. Our goal is to convey the fact that stereology is sampling in three dimensions, and therefore its principles remain valid and applicable in no matter what context. The disector, the selector, and an indirect method to estimate the distance between two parallel planes of polish are thereby illustrated. It is also shown how to split the error variance of the estimator of the pore volume fraction (‘porosity’) into the three components due to blocks, sections within blocks and systematic point counting on sections.     

Using biased image analysis for improving unbiased stereological number estimation – a pilot simulation study of the smooth fractionator

The smooth fractionator was introduced in 2002. The combination of a smoothing protocol with a computer‐aided stereology tool provides better precision and a lighter workload. This study uses simulation to compare fractionator sampling based on the smooth design, the commonly used systematic uniformly random sampling design and the ordinary simple random sampling design. The smooth protocol is performed using biased information from crude (but fully automatic) image analysis of the fields of view. The different design paradigms are compared using simulation in three different cell distributions with reference to sample size, noise and counting frame position. Regardless of clustering, sample size or noise, the fractionator based on a smooth design is more efficient than the fractionator based on a systematic uniform random design, which is more efficient than a fractionator based on simple random design. The fractionator based on a smooth design is up to four times more efficient than a simple random design.     

Maternal dexamethasone treatment reduces ovarian follicle number in neonatal rat offspring

Elevated glucocorticoid levels in the gravid female circulation affect a number of endocrine functions in the fetuses and neonates. The aim of this study was to examine the effects of maternal dexamethasone (Dx) administration during late pregnancy on the ovaries of neonatal offspring. On the 16th day of pregnancy, experimental dams received subcutaneously 1.0 mg Dx/kg b.w., followed by 0.5 mg Dx/kg b.w./day on the 17th and 18th days of gestation. The control gravid females received the same volume of saline vehicle. Left ovaries from 5‐day‐old female pups were stereologically analyzed. The ovary volumes were estimated using Cavalieri's principle. The number of healthy and atretic primordial and primary follicles was estimated using a fractionator–physical disector method. The number of secondary follicles was determined by exact counts of every fourth section encompassing whole cross‐sections of the ovary. The ovary volume was significantly decreased (by 44.4%; P < 0.05) in the group of female pups from Dx‐treated mothers comparing to the controls. The numbers of healthy primordial and atretic follicles were 38.8% (P < 0.05) and 50.9% (P < 0.05), respectively, reduced in the ovaries of pups from the Dx‐treated mothers, when compared with the control values. There were 53.4% (P < 0.05) fewer healthy primary and 41.8% (P < 0.05) fewer healthy secondary follicles as well. The numbers of atretic primary and secondary follicles were reduced by 60.0% (P < 0.05) and 61.7% (P < 0.05), respectively. It can be concluded that fetal exposure to glucocorticoids decreased the pool of non‐growing follicles in the neonatal ovary, whereas the processes of folliculogenesis and atresia remained unaffected.