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.     

Two distinct events, section compression and loss of particles ("lost caps"), contribute to z-axis distortion and bias in optical disector counting

Deformation of tissue sections in the z-axis can bias optical disector counting. When samples of particle densities are not representative for the entire tissue section, significant bias of estimated numbers can result. To assess the occurrence, prevalence, extent, sequence of events, and causes of z-axis distortion, the distribution of neuronal nucleoli in thick paraffin and vibratome sections was determined in chicken, rodent, and human brain tissues. When positions of neuronal nucleoli were measured in the z-axis, nucleoli were more frequent at the surfaces (bottom and top) of tissue sections than in the core. This nonlinear z-axis distribution was not lab-, equipment-, or investigator-specific, and was independent of age, fixation quality, coverslipping medium, or paraffin melting temperature, but in paraffin sections, was highly correlated with the tilt of the knife (cutting) angle. Manipulation of subsequent tissue processing steps revealed that two events contribute to z-axis distortion. Initially, a higher density of particles results at surfaces after sectioning, apparently due to section compression. Subsequently, particles can be lost to varying degrees from surfaces during floating or staining and dehydration, resulting in "lost caps." These results may explain different degrees of z-axis distortion between different types of sections and different labs, and reinforce the importance of checking z-axis distributions as a "quality control" prior to selection of guard zones in optical disector counting. Indirect approaches to assess section quality, such as resectioning in a perpendicular plane, yield additional artifacts, and should be replaced by a direct quantitative measurement of z-axis distribution of particles.     

Estimating volumes from common carp hepatocytes using design‐based stereology and examining correlations with profile areas: Revisiting a nutritional assay and unveiling guidelines to microscopists

Assessing fish liver status is common in aquaculture nutrition assays. This often implies determining hepatocytes profile areas in routine thin (5–7 μm) histological sections. However, there are theoretical problems using planar morphometry in thin sections: inherent sampling cells biases, too small numbers of sampled cells, under/overestimation of size, measuring size as areas when cells are three‐dimensional (3D) entities. The gold standard for assessing/validate cell size is stereology using thick sections (20–40 μm). Here, we estimated the volume of hepatocytes and their nuclei by the nucleator and optical disector stereological probes (in thick sections), and, innovatively, in thin sections too (using single‐section disectors). The liver of common carp eating feed containing either low or high level of lipids was targeted. Results were compared with prior profile areas from planar morphometry using thin sections, and with profile areas estimated here with the two‐dimensional (2D) nucleator. Ratios between nucleus and cell/cytoplasm (N/C) areas and volumes were calculated and compared. There was high positive correlation between volumes in thin and thick sections (r = .85 to .89; p < .001), empirically validating the single‐section disector. Strong correlations existed between profile‐derived versus 2D‐nucleator areas (r = .74 to .83; p < .001). There was systematic underestimation of cells and nucleus size using planar morphometry. The N/C ratios derived from the 2D‐nucleator data were higher than those from planar morphometry. Despite theoretical premises for using simple planar morphometry in thin sections are flawed, our results support that such morphometry on carp/fish hepatocytes may offer some valid biological conclusions. Anyway, we advanced guidelines for implementing proper methods.     

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.     

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%.     

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.     

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.     

Methodological principles for fractal analysis of trabecular bone

A standardized methodology for the fractal analysis of histological sections of trabecular bone has been established.
A modified box counting method has been developed for use on a PC-based image analyser. The effect of image analyser settings, magnification, image orientation and threshold levels was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to calculate objectively more than one fractal dimension from the modified Richardson plot.
The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ < 25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0.
It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than one fractal dimension, describing spatial structural entities. Fractal analysis is a model-independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and complements conventional histomorphometric and stereological techniques.     

An improved method for preparing thick sections for immuno/histochemistry and confocal microscopy and its use to identify rare events

Detection of rare events within solid tissues by immunocytochemistry is aided by imaging thick sections. Sections of 40–100 µm thickness of paraformaldehyde‐fixed solid tissue can be prepared by use of a vibrating microtome and when immunolabelled these sections can be imaged in a confocal microscope. This approach provides excellent preservation of the structure of the sample and imposes minimal antigenic damage. In studies of the invasion of the bovine intestinal epithelium by Salmonella , this method has allowed detection of individual invading bacteria within large samples. The thick vibrating microtome sections were also used for the detection of rare apoptotic cell nuclei identified by TUNEL staining.     

Unbiased stereological estimation of the number and volume of nuclei and nuclear size variability in invasive ductal breast carcinomas

The application of design-based stereological methods for estimating nuclear features quantitatively in invasive ductal breast cancer is described. Nuclear number, size and size variability are explored in relation to the tumour grade and patient prognosis. The study includes an examination of the efficiency in estimating different nuclear volumes, and two different estimators of the nuclear size variability are contrasted. Forty-two invasive ductal breast carcinomas diagnosed and graded by two pathologists were used. Both 5-μm and 25-μm-thick sections were obtained from paraffin blocks for stereological study. More undifferentiated tumours show significantly larger nuclei than low-grade tumours. The estimates based on the disector method demonstrate a decrease in the number of tumour cell nuclei per unit volume of tissue from grades 1 to 2 and especially from grades 2 to 3. The univariate survival analysis shows a high prognostic value of the nuclear volume estimates. The study shows that an efficient sampling procedure was performed, particularly when estimating volume-weighted mean nuclear volume using the point-sampled intercepts method. This method is more efficient than estimation of the number-weighted mean nuclear volume using the selector method; however, the latter provides paired estimates of volume- and number-weighted mean nuclear volume, as well as an estimate of the coefficient of variation of nuclear volume in the number distribution of the same cells.     

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.     

En bloc optical sectioning of resin-embedded specimens using a confocal laser scanning microscope

Reconstruction of 3D structures of specimens embedded for light or electron microscopy is usually achieved by cutting serial sections through the tissues, then assembling the images from each section to reconstruct the original structure or feature. This is both time-consuming and destructive, and may lead to areas of particular interest being missed. This paper describes a method of examining specimens which have been fixed in glutaraldehyde and embedded in epoxy resin, by utilising the autofluorescence preserved or enhanced by aldehyde fixation, and by using a confocal laser scanning microscope to section optically such specimens in the block down to a depth of about 200 μm. In this way, the accurate estimation of the depth of particular features could be used to facilitate subsequent sectioning at the light microscope or electron microscope level for more detailed studies, and 3D images of tissues/structures within the block could be easily prepared if required.     

Celloidin–wax sandwich microtomy: a novel and rapid method for producing serial semithin sections

A method is described that allows rapid and reliable serial sectioning down to thicknesses of 1 μm. The tissue is first embedded in celloidin and then in wax and trimmed so that the block is sandwiched between two layers of wax. This combines the virtues of both media. The celloidin gives greater support to tissue than wax and enables the cutting of semithin sections. The wax allows ribbons of serial sections to be produced as in conventional wax microtomy. This makes it easy to produce serial semithin sections as a matter of routine.     

High-pressure freezing for immunocytochemistry

Ultrastructural immunocytochemistry requires that minimal damage to antigens is imposed by the processing methods. Immersion fixation in cross-linking fixatives with their potential to damage antigens is not an ideal approach and rapid freezing as an alternative sample-stabilization step has a number of advantages. Rapid freezing at ambient pressure restricts the thickness of well-frozen material obtainable to ≈ 15 μm or less. In contrast, high-pressure freezing has been demonstrated to provide ice-crystal-artefact-free freezing of samples up to 200 μm in thickness. There have been few reports of high-pressure freezing for immunocytochemical studies and there is no consensus on the choice of post-freezing sample preparation. A range of freeze-substitution time and temperature protocols were compared with improved tissue architecture as the primary goal, but also to compare ease of resin-embedding, polymerization and immunocytochemical labelling. Freeze-substitution in acetone containing 2% osmium tetroxide followed by epoxy-resin embedding at room temperature gave optimum morphology. Freeze-substitution in methanol was completed within 18 h and in tetrahydrofuran within 48 h but the cellular morphology of the Lowicryl-embedded samples was not as good as when samples were substituted in pure acetone. Acetone freeze-substitution was slow, taking at least 6 days to complete, and gave blocks which were difficult to embed in Lowicryl HM20. Careful handling of frozen samples avoiding rapid temperature changes reduced apparent ice-crystal damage in sections of embedded material. Thus a slow warm-up to freeze-substitution temperature and a long substitution time in acetone gave the best results in terms of freezing quality and cellular morphology. No clear differences emerged between the different freeze-substitution media from immunocytochemical labelling experiments.     

The saucor, a new stereological tool for analysing the spatial distributions of cells, exemplified by human neocortical neurons and glial cells

The 3D spatial arrangement of particles or cells, for example glial cells, with respect to other particles or cells, for example neurons, can be characterized by the radial number density function, which expresses the number density of so-called 'secondary' particles as a function of their distance to a 'primary' particle. The present paper introduces a new stereological method, the saucor, for estimating the radial number density using thick isotropic uniform random or vertical uniform random sections. In the first estimation step, primary particles are registered in a disector. Subsequently, smaller counting windows are drawn with random orientation around every primary particle, and the positions of all secondary particles within the windows are recorded. The shape of the counting windows is designed such that a large portion of the volume close to the primary particle is examined and a smaller portion of the volume as the distance to the primary object increases. The experimenter can determine the relation between these volumina as a function of the distance by adjusting the parameters of the window graph, and thus reach a good balance between workload and obtained information. Estimation formulae based on the Horvitz-Thompson theorem are derived for both isotropic uniform random and vertical uniform random designs. The method is illustrated with an example where the radial number density of neurons and glial cells around neurons in the human neocortex is estimated using thick vertical sections for light microscopy. The results indicate that the glial cells are clustered around the neurons and the neurons have a tendency towards repulsion from each other.     

Cylindrical diameters method for calibrating section thickness in serial electron microscopy

An estimate of section thickness is required for measuring structures in serial section microscopy. Mean section thickness is estimated reliably by averaging the ratios of the diameters of cylindrical objects, such as mitochondria, to the number of sections they span. This cylindrical diameters method improves the accuracy of section thickness as inferred from the colour of sections floating in water. The cylindrical diameters method gives the same answer as that obtained by the minimal folds method. It is preferable because it can be done in a series that has no folds that can distort and obscure the objects that are being measured.     

High resolution optical microscopy of animal tissues by the use of sub-micrometer thick sections and a new stain

The introduction of 1 micron-thick sections from plastic embedded material represents a great technical improvement for the study of tissues under the optical microscope. However, even sections of this thickness appear too thick when observed with oil immersion objectives of high numerical aperture. The extremely shallow depth of field of these lenses allows them to differentiate several focal planes within a one micron thick section. This in turn results in ghost images being formed from out of focus structures, a problem particularly vexing when photomicrography is attempted. To circumvent this difficulty, we reduced the thickness of the sections down to an optimum of 0.4 micron. These thinner sections do require a very energetic stain to give enough contrast to the cellular structures; Stevenel Blue, a stain recently adapted for plastic sections [del Cerro et al., Microsc. Acta 83, (2), 117--121 (1980)] proved to be the most suitable for this purpose of several stains tested. In summary, submicrometer thick sections stained with Stevenel Blue allow to reach the limits of visibility permitted by the best available objectives and effectively merge the realm of optical microscopy with that of low power electron microscopy.     

Cryoultramicrotomy of muscle: improved preservation and resolution of muscle ultrastructure using negatively stained ultrathin cryosections

Ultrathin sections of rapidly frozen, briefly pre-treated muscle tissue are cut and thereafter are thawed and contrasted using a negative staining technique. The method has provided micrographs in which the in-vivo order in the muscle fibres has been preserved well enough to enable both a more complete interpretation of X-ray diffraction evidence from muscle, and also a gain of new ultrastructural information on aspects of myofibril and myofilament architecture in different types of fibre. Examples here are taken from chicken, rabbit and fish muscles and show both the M-band and the bridge region of the A-band in great detail. To enhance the detail in the original images, one-dimensional (1-D) and 2-D averaging techniques (lateral smearing and step averaging, respectively) are used. Although there is major shrinkage in section thickness to about one-third of its original value, demonstrated here for the first time is the fact that the characteristic A-band lattice planes are preserved in these sections in 3-D. This confirms the usefulness of cryosections not just for 1-D and 2-D image processing, but also for 3-D reconstruction. Thus, in combination with techniques of image processing, cryoultramicrotomy can give the muscle morphologist the detailed data that are needed to match the molecular biologists, biochemists and immunologists in the interpretation of their data about physiological and pathophysiological events in muscle fibres at the macromolecular level.     

Evaluation of characterization methods for thin sections of silver halide microcrystals by analytical electron microscopy

Silver halide microcrystals are usually composed of different phases with varying halide compositions. These microcrystals can be sectioned with an ultramicrotome with a certain thickness in a specific direction. The scanning electron microscopical analysis of these sections provides information on the internal halide profile.
During sample sectioning, many deformations can be induced in the material, and usually dominate the different scanning electron images.
By acquiring X-ray maps, it is possible to locate the different phases in the sections. This technique, however, is very time-consuming, and can only be used when the local halide variations are very high.
When an EDX line scan is acquired over the section, information on the position of the phases with different halide composition is obtained in a reasonable time, and shows no dependence on the section deformations. From this knowledge, several positions on the section are selected where local X-ray analyses are performed. After quantifying the results, the internal halide distribution is obtained. The analytical lateral resolution is about 30 nm for sections ≈100 nm thick.