Application Of Stereology Research Articles

Rotational Crofton formulae with a fixed subspace

The classical Crofton formula explains how intrinsic volumes of a convex body K in n-dimensional Euclidean space can be obtained from integrating a measurement function at sections of K with invariantly moved affine flats. Motivated by stereological applications, we present variants of Crofton's formula, where the flats are constrained to contain a fixed linear subspace L0, but are otherwise invariantly rotated. This main result generalizes a known rotational Crofton formula, which only covers the case dim⁡L0=0. The proof combines a suitable Blaschke–Petkantschin formula with the classical Crofton formula. We also argue that our main result is best possible, in the sense that one cannot estimate intrinsic volumes of a set, based on lower-dimensional sections, other than those given by our result. Finally, we provide a proof for a well-established variant: an integral relation for vertical sections. Our formula is stated for intrinsic volumes of a given set, complementing the classical approach for Hausdorff measures.

Methodological Progress of Stereology in Cardiac Research and Its Application to Normal and Pathological Heart Development.

Design-based stereology is the gold standard for obtaining unbiased quantitative morphological data on volume, surface area, and length, as well as the number of tissues, cells or organelles. In cardiac research, the introduction of a stereological method to unbiasedly estimate the number of cardiomyocytes has considerably increased the use of stereology. Since its original description, various modifications to this method have been described. A particular field in which this method has been employed is the normal developmental life cycle of cardiomyocytes after birth, and particularly the question of when, during postnatal development, cardiomyocytes lose their capacity to divide and proliferate, and thus their inherent regenerative ability. This field is directly related to a second major application of stereology in recent years, addressing the question of what consequences intrauterine growth restriction has on the development of the heart, particularly of cardiomyocytes. Advances have also been made regarding the quantification of nerve fibers and collagen deposition as measures of heart innervation and fibrosis. In the present review article, we highlight the methodological progress made in the last 20 years and demonstrate how stereology has helped to gain insight into the process of normal cardiac development, and how it is affected by intrauterine growth restriction.

Application of Stereology in Liver Volume Measurements Using Computed Tomography Scan

Application of Stereology in Liver Volume Measurements Using Computed Tomography Scan

Quantification of random pore features of porous concrete mixes prepared with brick aggregate: An application of stereology and mathematical morphology

The present study deals with the pore feature analysis of porous concrete mixes based on image analysis technique. The porous concrete mixes are prepared with over-burnt brick aggregate having different sizes and different aggregate gradations. The scarcity of natural aggregates in Tripura, India has forced the researchers to use locally available waste bricks as a coarse aggregate in construction purposes. However, the application of bricks in porous concrete is very rare and the porous distribution of porous mixes made of brick aggregates are not well-known. Hence, in this paper, initiatives are made to characterize the porous features of pervious concrete mixes using bricks as coarse aggregates. Stereological analysis and mathematical morphology such as two-point correlation and granulometric distribution analysis are employed in this paper. Statistical analysis is also conducted to identify the distribution of the pores and is observed that the 3-parameter Weibull distribution is the best way to fit the pore diameters of the pervious concrete mixes. Finally, the relative mean pore size is identified and the permeability of the pervious mix is obtained based on this image analysis. From the overall analysis, it is found that the image analysis can be an efficient way to identify the pore features of the porous concrete mixes.

Filtering the good from the bad: A focus on kidney development and disease to celebrate John Bertram's long‐standing career in anatomy and renal research

Filtering the good from the bad: A focus on kidney development and disease to celebrate John Bertram's long‐standing career in anatomy and renal research

Global Trends in Application of Stereology as a Quantitative Tool in Biomedical Research.

Stereology is a quantitative and comparative method that utilizes planes, lines, and points for the estimation of three-dimensional parameters in morphological studies. It primarily focuses on geometrical features of objects such as number, density, length, area, and volume. A scientometric study was conducted to analyze global research trends in application of stereology in biomedical research. Stereology has gained wide application resulting into design-based stereological methods. Data for this study were retrieved from the SCOPUS database. At least 5,732 publications employing stereology as analytical tool were produced in a period of 50 years between 1966 and 2016. Half (2,858; 49.87%) of these publications were produced in the last 12 years from 2005 to 2016. The relative growth rate (RGR) of publications decreased from 1967 (0.69) to 2016 (0.03) whereas the doubling time (DT) increased from 1.00 to 20.56 in the same period. A great majority (5,332; 93.02%) of the publications retrieved from SCOPUS were journal articles in various biomedical fields. The Journal of Microscopy tops the list of journals with at least 205 articles. The most productive country was USA with at least 1663 (23.10%) publications and Aarhus Universitet tops the list of institutions with at least 306 publications. J.R. Nyengaard was the most prolific author who contributed at least 125 publications. The highly cited article had a total of 2,054 citations with an average of over 82 citations per year. Given the growing importance of stereology in biomedical research, it is necessary to promote its application among scholars.

STEREOLOGY, AN UNBIASED METHODOLOGICAL APPROACH TO STUDY PLANT ANATOMY AND CYTOLOGY: PAST, PRESENT AND FUTURE

This review presents an historical overview of stereological methods used for the quantitative evaluation of plant anatomical and cytological structures. It includes the origins of these methods up to the most recent developments such as the application of stereology based on 3D images. We focus especially on leaf, as the vast majority of studies of plant microscopic structure examine this organ. An overview of plant cell ultrastructure measurements as well as plant anatomical characteristics (e.g. plant tissue volume density, internal leaf surface area, number and mean size of mesophyll cells and chloroplast number), which were estimated by stereological methods most frequently, is presented. We emphasize the importance of proper sampling needed for unbiased measurements. Furthermore, we mention other methods used for plant morphometric studies and briefly discuss their relevance, precision, unbiasedness and efficiency in comparison with unbiased stereology. Finally, we discuss reasons for the sparse use of stereology in plant anatomy and consider the future of stereology in plant research.

Application of stereology for two-phase flow structure validation in fluidized bed reactors

Paper describes a novel method for two-phase gas-solid flow structure validation in fluidized bed reactors. Investigation is based on application of stereology techniques. This is an innovative approach in the field of fluidization phenomena research. Study is focused on the analysis of flow structure images, obtained with high-speed visualization of the fluidization process. Fluidization is conducted in transparent narrow channel, where plastic balls are fluidized by air. Applied stereological analysis is grounded on the linear method and on the method of random and directed secants. This enables 2-dimensional image measurement and 3-dimensional stereological extrapolation. The major result is that for each two-phase gas-solid flow structure a set of stereological parameters exists. This enables quantification of the process. It has been found that the observation of inter-relation of all stereological parameters, during the changing of the flow structure, can be used for system control. The basic conclusion is that knowledge about the character of the changes may be used for constant process adjustment for various two phase systems such as gas-solid or gas-liquid.

Application of stereology in engineering of building materials

The article presents the literature review about the application of stereology and image analysis for quantitative evaluation of the building materials structure. At the outset, the development of stereological methods and computer image analysis techniques in the study of building materials was provided. Then quantitative structure parameters were defined and their methods of determining were showed. In the paper, the application of image analysis for the determination of properties of the cement composites was reported, including: an assessment of the porosity of the hardened concrete, determination of the aggregate distribution in the cementitious matrix, the crack analysis. It was found that the leading problem of image analysis is the process of sample preparation in order to obtain the correct extraction of examinated phase, and measurement automation process.

Basic Application of Stereology in Histology and Medical Sciences

Basic Application of Stereology in Histology and Medical Sciences

Digital stereology in neuropathology

Two-dimensional quantitative methods have frequently been used to address questions in neuropathological research; however, they face important limitations which design-based stereology may overcome by offering a set of methods to quantify two-dimensional histological sections into three-dimensional structural knowledge. Accordingly, stereology is a science based on statistical sampling principles and geometric measures. The application of stereology to neuropathological studies allows the researcher to efficiently obtain a precise estimate of various structural quantities. This neuropathological review will therefore present the relevant stereological estimators for obtaining reliable quantitative structural data from brains and peripheral nerves when using digital light microscopy. It is discussed how to obtain brain and nerve fibre samples to fulfil the requirements for the estimators. A presentation of design-based stereological probes for obtaining global volume, total number, local volume, total length, total surface area, cross-sectional area and diameter will be followed by discussion of the error variances of the methods. No mathematical equations or calculations are shown in this review.

ESTIMATING A RATIO OF MEANS FROM BIVARIATE COUNTS WITH APPLICATIONS IN STEREOLOGY

Summary In survey sampling and in stereology, it is often desirable to estimate the ratio of means θ= E(Y)/E(X) from bivariate count data (X, Y) with unknown joint distribution. We review methods that are available for this problem, with particular reference to stereological applications. We also develop new methods based on explicit statistical models for the data, and associated model diagnostics. The methods are tested on a stereological dataset. For point-count data, binomial regression and bivariate binomial models are generally adequate. Intercept-count data are often overdispersed relative to Poisson regression models, but adequately fitted by negative binomial regression.

Microscopy-based quantitative analysis of lung structure: application in diagnosis

Stereology provides a set of methods that are appropriate for a microscopy-based quantitative assessment of lung structure. In general, the aim of stereology is to obtain information on three-dimensional structures from two-dimensional sections of these structures. The inherent impartiality of stereological principles is critical in order to meet the requirements of 'good laboratory practice'. This article is a systematic review of the applications of stereology to characterize pathological alterations of emphysema, fibrosis, acute lung injury and tumor grading. The reader is provided with a general overview of unbiased or design-based stereology and is provided with some examples of how these methods could be integrated into a diagnostic work-up of lung diseases in humans and animal models. The article also reviews the implications of a published statement, which defines standards for quantitative assessment of lung structure based on stereology, by the American Thoracic Society and the European Respiratory Society. In view of the recently published standards for quantitative assessment of lung structure, unbiased stereological methods are strongly recommended, particularly as they provide valuable information in diagnosing lung diseases and allow a statistically valid quantitative comparison between different groups. Future developments will make the application of stereology in lung biology and pathology even more efficient. Moreover, there is also the potential for combing the principles of stereology with other imaging modalities (e.g., radiological), which will allow for non-invasive lung stereology.

THE PIVOTAL TESSELLATION

The tessellation studied here is motivated by some stereological applications of a new expression for the motion invariant density of straight lines in R3. The term 'pivotal' stems from the fact that the tessellation is constructed within a plane which is isotropic through a fixed, 'pivotal' origin. Consider either a stationary point process, or a stationary random lattice of points in that plane. Through each point event draw a straight line which is perpendicular to the axis determined by the origin and the point event. The union of all such lines (called p-lines) constitutes the mentioned tessellation. We concentrate on the pivotal tessellation based on a stationary and isotropic planar Poisson point process; we show that this tessellation is not stationary.

Flowers and wedges for the stereology of particles

Recently, a new decomposition has been found for the motion invariant density of straight lines in, with applications in stereology. The new principle, called the invariator, leads to new rotational formulae which express the surface area and the volume of a bounded subset (called a 'particle') in terms of an observable functional defined in an isotropically oriented section (called a pivotal section) through a fixed point (called the pivotal point). The results have been extended to intrinsic volumes of manifolds in general space forms. The purpose of this paper is to present new results and computational formulae for three-dimensional particles. Explicit estimators are obtained for a convex polyhedral particle with a pivotal point in its interior, in terms of the coordinates of the vertices of the pivotal section. The results are applied to a population of polyhedral grains from a cemented carbide which was studied earlier by alternative methods.

Application of stereology to study the effects of pneumoperitoneum on peritoneum

Scanning electron microscopy is unable to provide sufficient data to obtain definitive results for research into the morphologic effect of pneumoperitoneum on peritoneum. To overcome this difficulty, we adopted stereology to examine the effect of the type of gas insufflated, pressure, duration, and gas flow on morphologic alterations of peritoneum. Fifty SD rats were divided into ten groups. One group served as control. Pneumoperitoneum was established at 5 mmHg and 1.0 l/min gas flow for 1, 2 or 3 h with CO2 (in groups C1h, C2h, and C3h, respectively) or with He (in groups H1h, H2h, and H3h, respectively). CO2 pneumoperitoneum was further established at 8 mmHg and 1.0 l/min gas flow for 1 h (group C8p), at 5 mmHg and 2.0 l/min gas flow for 1 h (group C2f), and at 5 mmHg and 3.0 l/min gas flow for 1 h (group C3f). After the procedures, five specimens were sampled from anterior peritoneum and measured by stereological and electron-microscopic techniques. Groups H1h and C1h, H2h and C2h, and H3h and C3h, respectively, were the same in terms of area fraction of basal lamina exposed and diameter of mesothelial cells (P>0.05). The magnitudes of peritoneal trauma in groups C2h, C3h, C8p, C2f, and C3f were significantly higher than that in group C1h (P<0.01), and the same result was observed in groups H2h and H3h against group H1h (P<0.01), and in group C3f against group C2f (P<0.01). Furthermore, the area fractions of basal lamina exposed in groups C3h and H3h were remarkably higher than those in groups C2h and H2h, respectively (P<0.01). The mechanism of basal lamina exposure comprises mesothelial cell desquamation and plasmatorrhexis. Peritoneal morphologic trauma during pneumoperitoneum can be attributed to the pressure, duration, and gas flow instead of the type of gas insufflated.

Application of stereology to dermatological research

Stereology is a set of mathematical and statistical tools to estimate three-dimensional (3-D) characteristics of objects from regular two-dimensional (2-D) sections. In medicine and biology, it can be used to estimate features such as cell volume, cell membrane surface area, total length of blood vessels per volume tissue and total number of cells. The unbiased quantification of these 3-D features allows for a better understanding of morphology in vivo compared with 2-D methods. This review provides an introduction to the field of stereology with specific emphasis on the application of stereology to dermatological research by supplying a short insight into the theoretical basis behind the technique and presenting previous dermatological studies in which stereology was an integral part. Both the theory supporting stereology and a practical approach in a dermatological setting are reviewed with the aim to provide the reader with the capability to better assess papers employing stereological estimators and to design stereological studies independently.

A new expression for the density of totally geodesic submanifolds in space forms, with stereological applications

Integral section formulae for totally geodesic submanifolds (planes) intersecting a compact submanifold in a space form are available from appropriate representations of the motion invariant density (measure) of these planes. Here we present a new decomposition of the invariant density of planes in space forms. We apply the new decomposition to rewrite Santaló's sectioning formula and thereby to obtain new mean values for lines meeting a convex body. In particular we extend to space forms a recently published stereological formula valid for isotropic plane sections through a fixed point of a convex body in R 3 .

Application of Stereology on Neodymium-Doped Yttrium Aluminum Garnet (Nd:YAG) Transparent Ceramics

Nd:YAG precursor powders were synthesized by homogeneous precipitation, and Nd:YAG transparent ceramics were prepared by vacuum sintering at 1700 °C for 5 h. The ceramic materials were characterized by light transmittance and field emission gun-environment scanning microscope. Using statistics and stereology theory, study was carried out on the quantitative relationships between light transmittance and stereological parameters in three-dimensional Euclidean space. It is found that the transmittance of Nd:YAG with 1 mm in thickness is about 45% and 58% in visible and near-infrared wavelength, respectively. The transmittance linearly increases with increasing equivalent sphere diameter and reaches the theoretical value of single crystal when the equivalent sphere diameter is 20 μm. The transmittance decreases with the increasing of mean specific area per unit volume of grain and discrete grains, and the transmittance decreases with increasing mean free distance of grains in Nd:YAG ceramics.

Application of stereology to the statistical description of the spatial distribution of composition and other scalar properties in three dimensional space

The composition distribution in a chemically nonuniform system may be described as a set of scalar fields X k ( x, y, z), one for each component k, where X k is the atom fraction of component k. For each component statistical information about this spatial distribution may be obtained by combining a sampling of microprobe line traces with stereological analysis. This analysis yields the volume weighted concentration distribution function, f v ( X k ), where f v ( X k ) dX k is the fraction of the volume of the system that has compositions in the range X k to X k + dX k , and S v ( X k ), the area per unit volume of structure of the isocomposition contour at each composition. The harmonic mean of the distribution of concentration gradients over each isocomposition contour can be computed from this information. The methodology also can be applied to the analysis of the distribution of any scalar property that is nonuniform in a structure.