A brief update on lung stereology

Lung stereology has a long and successful tradition. From mice to men, the application of new stereological methods at several levels (alveoli, parenchymal cells, organelles, proteins) has led to new insights into normal lung architecture, parenchymal remodelling in emphysema‐like pathology, alveolar type II cell hyperplasia and hypertrophy and intracellular surfactant alterations as well as distribution of surfactant proteins. The Euler number of the network of alveolar openings, estimated using physical disectors at the light microscopic level, is an unbiased and direct estimate of alveolar number. Surfactant‐producing alveolar type II cells can be counted and sampled for local size estimation with physical disectors at a high magnification light microscopic level. The number of their surfactant storage organelles, lamellar bodies, can be estimated using physical disectors at the EM level. By immunoelectron microscopy, surfactant protein distribution can be analysed with the relative labelling index. Together with the well‐established classical stereological methods, these design‐based methods now allow for a complete quantitative phenotype analysis in lung development and disease, including the structural characterization of gene‐manipulated mice, at the light and electron microscopic level.     

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.     

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.     

Precision of the fractionator from Cavalieri designs

A popular procedure to predict the variance of the fractionator consists in splitting the initial collection of fragments into two subsets, in order to use the corresponding particle counts (or any other pertinent measure), in the calculation. The current formula does not account for local or ‘nugget’ errors inherent in the estimation of fragment contents, however. Moreover, it does not account for the fact that the contribution of the variability between fragments or slices should rapidly decrease as the sampling fraction increases. For these reasons, an update to the formula is overdue. It should be stressed, however, that the formula applies to Cavalieri slices designs – its application for arbitrary partition designs is therefore not warranted.     

Estimating the number of complex particles using the ConnEulor principle

An unbiased counting rule for the number of topologically simple objects of any shape, size and distribution in 3D space is a pertinent problem in stereology. Combining the disector principle with the object's 3D Euler number makes possible number estimation, which until now has been obtainable only by exhaustive serial sections. The disector is a set of two sections where the object's profiles in one section are compared with its profiles on the neighbouring section, and the number of new 2D topological events is recorded. In a disector of known volume the sum of topological events is a direct estimate of the disector contribution to the total Euler number, which forms the basis for an ultimate number estimator in 3D, the ConnEulor. The method is illustrated by an electron microscopic study of the number of mitochondria in the exocrine cells of the pancreas.     

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%.     

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.     

Stereological estimation using vertical sections in a complex tissue

A method designed for stereological estimation in a very complex tissue using vertical sections is presented. In some tissues, the random rotation of the tissue for vertical sections may obscure recognition of the anatomical structures of interest. The present method overcomes this problem by generating sections with both a particular orientation, 'mapping sections', and ordinary random vertical sections usable for the required observations. A map describing the positions of the vertical sections is produced to make the complex reference space recognizable. The method is illustrated by estimating the number and size of neurones in the dorsal raphe nucleus of the human brainstem with its dense packing of roughly 100 nuclei within a volume less than 50 cm³.     

Direct and efficient stereological estimation of total cell quantities using electron microscopy

Stereological estimation of total subcellular quantities in bioscience is presented in this report. Special emphasis is placed on the use of electron microscopy, which under certain circumstances may be combined with light microscopy. Three strategies based on the Cavalieri principle, the disector and local stereological probes through arbitrarily fixed points for estimation of total quantities inside cells are presented. The quantities comprise (total) number, length, surface area, volume or 3D spatial distribution for organelles as well as total amount of gold particles, various compounds or certain cytochemical markers.     

The total number of neurons in the human neocortex unbiasedly estimated using optical disectors

An efficient method is presented for obtaining, in under 4h, an unbiased estimate of the total number of neurons in the human neocortex, with a coefficient of error on the estimate of ～ 5%. The novel sampling scheme used in this study is unbiased and was designed so that only a small amount of neocortical grey matter had to be removed. Hence, the majority of the cerebral grey matter and all the internal grey matter was left intact for further resampling and analysis. Each cerebral hemisphere was subdivided into the four major neocortical regions, sliced coronally at 7-mm intervals and the volume of the neocortex determined using Cavalieri's principle. Uniform sampling of neocortex was performed in the hemisphere followed by regional subsampling with a varying sampling fraction being taken from each region. Neuronal density estimates were made in thick plastic sections using optical disectors. Shrinkage estimates were made in parallel with the number estimates and found to be negligible. The total number of neocortical neurons in the right hemisphere of five normal 80-year-old men was found to be 13·7 × 10⁹ with an inter-individual coefficient of variation of 12%.     

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.     

Quantification of micrometre-sized porosity in quasicrystals using coherent synchrotron radiation imaging

The ability to image phase distributions with high spatial resolution is a key capability of microscopy systems. Consequently, the development and use of phase microscopy has been an important aspect of microscopy research and development. Most phase microscopy is based on a form of interference. Some phase imaging techniques, such as differential interference microscopy or phase microscopy, have a low coherence requirement, which enables high‐resolution imaging but in effect prevents the acquisition of quantitative phase information. These techniques are therefore used mainly for phase visualization. On the other hand, interference microscopy and holography are able to yield quantitative phase measurements but cannot offer the highest resolution. A new approach to phase microscopy, quantitative phase‐amplitude microscopy (QPAM) has recently been proposed that relies on observing the manner in which intensity images change with small defocuses and using these intensity changes to recover the phase. The method is easily understood when an object is thin, meaning its thickness is much less than the depth of field of the imaging system. However, in practice, objects will not often be thin, leading to the question of what precisely is being measured when QPAM is applied to a thick object. The optical transfer function formalism previously developed uses three‐dimensional (3D) optical transfer functions under the Born approximation. In this paper we use the 3D optical transfer function approach of Streibl not for the analysis of 3D imaging methods, such as tomography, but rather for the problem of analysing 2D phase images of thick objects. We go on to test the theoretical predictions experimentally. The two are found to be in excellent agreement and we show that the 3D imaging properties of QPAM can be reliably predicted using the optical transfer function formalism.     

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.     

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.     

Characterization of biomolecule immobilization by scanning force microscopy using a wet-masking technique

The assemblage of molecular layers was investigated using scanning force microscopy (SFM). A wet-masking technique was used for the preparation of monolayer steps by partial masking of the substrate with an elastomeric mask during incubation in the modification buffers. The subsequent adsorption of biotin, streptavidin, and biotiny lated beads onto a gold substrate was investigated by SFM visualization of the created steps. The molecular layers were characterized based on measurements of step height and surface roughness. The simultaneous visualization of the surface before and after modification minimizes artifacts introduced by changes in tip shape or imaging parameters.     

Comparative evaluation of retrospective shading correction methods

Because of the inherent imperfections of the image formation process, microscopical images are often corrupted by spurious intensity variations. This phenomenon, known as shading or intensity inhomogeneity, may have an adverse affect on automatic image processing, such as segmentation and registration. Shading correction methods may be prospective or retrospective. The former require an acquisition protocol tuned to shading correction, whereas the latter can be applied to any image, because they only use the information already present in an image. Nine retrospective shading correction methods were implemented, evaluated and compared on three sets of differently structured synthetic shaded and shading‐free images and on three sets of real microscopical images acquired by different acquisition set‐ups. The performance of a method was expressed quantitatively by the coefficient of joint variations between two different object classes. The results show that all methods, except the entropy minimization method, work well for certain images, but perform poorly for others. The entropy minimization method outperforms the other methods in terms of reduction of true intensity variations and preservation of intensity characteristics of shading‐free images. The strength of the entropy minimization method is especially apparent when applied to images containing large‐scale objects.     

Characterization of human ovarian teratoma hair by using AFM, FT-IR, and Raman spectroscopy

The structural, physical, and chemical properties of hair taken from an ovarian teratoma (teratoma hair) was first examined by atomic force microscopy (AFM), Fourier transform infrared (FT-IR), and Raman spectroscopy. The similarities and differences between the teratoma hair and scalp hair were also investigated. Teratoma hair showed a similar morphology and chemical composition to scalp hair. Teratoma hair was covered with a cuticle in the same manner as scalp hair and showed the same amide bonding modes as scalp hair according to FT-IR and Raman spectroscopy. On the other hand, teratoma hair showed different physical properties and cysteic acid bands from scalp hair: the surface was rougher and the adhesive force was lower than the scalp hair. The cystine oxides modes did not change with the position unlike scalp hair. These differences can be understood by environmental effects not by the intrinsic properties of the teratoma hair.     

The efficient and unbiased estimation of nuclear size variability using the ‘selector’

The selector was used to make an unbiased estimation of nuclear size variability in one benign naevocellular skin tumour and one cutaneous malignant melanoma. The results showed that the estimates obtained using the selector were comparable to those obtained using the more time consuming Cavalieri-disector approach. Employing ‘optical sections’, the selector was found to be between five and ten times more efficient than the Cavalieri-disector method when using physical sections.