Estimation of the number of stellate cells in a liver with the smooth fractionator

To better evaluate the activation and proliferative response of hepatic stellate cells (HSC) in hepatic fibrosis, it is essential to have sound quantitative data in non‐pathological conditions. Our aim was to obtain the first precise and unbiased estimate of the total number of HSC in the adult rat, by combining the optical fractionator, in a smooth sampling design, with immunocytochemistry against glial fibrillary acidic protein. Moreover, we wanted to verify whether there was sufficiently relevant specimen inhomogeneity that could jeopardize the high expected estimate precision when using the smooth fractionator design for HSC. Finally, we wanted to address the question of what sampling scheme would be advisable a priori for future studies. Microscopical observations and quantitative data provided no evidence for inhomogeneity of tissue distribution of HSC. Under this scenario, we implemented a baseline sampling strategy estimating the number (N?) of HSC as 207E⁰⁶ (CV = 0.17). The coefficient of error [CE(N?)] was 0.04, as calculated by two formerly proposed approaches. The biological difference among animals contributed ? 95% to the observed variability, whereas methodological variance comprised the remaining 5%. We then carried out a half reduction of sampling effort, at the level of both sections and fields. In either occasion, the CE(N?) values were low (? 0.05) and the biological variance continued to be far more important than methodological variance. We concluded that our baseline sampling (counting 650–1000 cells/rat) would be appropriate to assess the lobular distribution and the N? of HSC. However, if the latter is the only parameter to be estimated, around half of our baseline sampling (counting 250–600 cells/rat) would still generate precise estimates [CE(N?) < 0.1], being in this case more efficient to reduce the number of sections than to reduce the sampled fields.     

A new fractionator principle with varying sampling fractions: exemplified by estimation of synapse number using electron microscopy

The quantification of ultrastructure has been permanently improved by the application of new stereological principles. Both precision and efficiency have been enhanced. Here we report for the first time a fractionator method that can be applied at the electron microscopy level. This new design incorporates a varying sampling fraction paradigm. The method allows for systematic random sampling from blocks of variable slab thickness, thereby eliminating the need for exhaustive serial sectioning through an entire containing space. This novel approach acknowledges the inaccuracy inherent in estimating the total object number using section sampling fractions based on the average thickness of sections of variable thicknesses. As an alternative, this approach estimates the correct particle section sampling probability based on an estimator of the Horvitz–Thompson type, resulting in a theoretically more satisfying and accurate estimate of the expected number of particles for the defined containing space.     

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.     

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.     

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.     

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%.     

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.     

Stereological estimation of mean linear intercept length using the vertical sections and trisector methods

A method for estimating the mean linear intercept length of anisotropic microstructures using vertical sections is presented. A test system of cycloids and points is overlaid on the vertical sections, and the mean linear intercept length is estimated from a simple counting procedure — no length measurements are required. The vertical direction is either arbitrarily chosen or chosen perpendicular to most of the surface boundaries of the objects of interest. A design with the latter choice of the vertical direction and three vertical sections — a trisector — will optimize the precision of the estimate from only three vertical sections. The method was applied to two metallic structures, but it may also be used in a biomedical context.     

Estimating the total number of lymphatic valves in infant lungs with the fractionator

The fractionator is illustrated by means of a biomedical example involving the estimation of the number of lymphatic valves in lungs of infants who had died from sudden infant death syndrome (SIDS) and other known causes. The method is unbiased irrespective of tissue deformations and it does not require external information such as section thickness. An upper bound of the coefficient of error of the estimate of the number of valves within one lung was 6.5%, despite the fact that the number of valves counted per lung at the last stage ranged between 11 and 37 only. The upper bound includes the biological variation of the number of valves among infant lungs. Some theoretical remarks are also made on the efficiency of the fractionator. It is suggested, for instance, that the initial sampling stages cause more impact on the precision of the final estimator than the subsequent stages, and that an optimal arrangement of fragments submitted to systematic sampling should have the smallest fragments at the ends, with fragment contents increasing smoothly toward the middle of the series.     

Automatic sampling for unbiased and efficient stereological estimation using the proportionator in biological studies

Quantification of tissue properties is improved using the general proportionator sampling and estimation procedure: automatic image analysis and non-uniform sampling with probability proportional to size (PPS). The complete region of interest is partitioned into fields of view, and every field of view is given a weight (the size) proportional to the total amount of requested image analysis features in it. The fields of view sampled with known probabilities proportional to individual weight are the only ones seen by the observer who provides the correct count. Even though the image analysis and feature detection is clearly biased, the estimator is strictly unbiased. The proportionator is compared to the commonly applied sampling technique (systematic uniform random sampling in 2D space or so-called meander sampling) using three biological examples: estimating total number of granule cells in rat cerebellum, total number of orexin positive neurons in transgenic mice brain, and estimating the absolute area and the areal fraction of β islet cells in dog pancreas. The proportionator was at least eight times more efficient (precision and time combined) than traditional computer controlled sampling.     

剪切力对动脉血管平滑肌细胞增殖分化的影响

目的：探讨剪切力作用下人脐动脉血管平滑肌细胞的增殖分化的变化。方法：利用改进的灌流及流动培养装置,通过蠕动泵提供稳定的剪切力,同时提供静态培养所需的其它条件,建立体外人脐动脉血管平滑肌流动培养模型。分别对体外培养的人脐动脉血管平滑肌细胞加载3,4,5,8,10dyn／cm^2的定长流剪切力24h,同时以静态培养的细胞为对照组。相差倒置显微镜观察玻片上细胞的数量并作细胞计数,α—actin免疫组化染色．结果：细胞记数显示,同对照组相比,七刀应力各组的增殖能力都有所下降,5dyn／cm^2切应力作用下,细胞增殖缓慢最为明显．α—actin免疫组化染色提示切应力各组的分化程度较对照组高。结论：初步研究表明,剪切力对人脐动脉血管平滑肌细胞的增殖有一定抑制作用,并且可能促进了细胞的分化。     

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%.     

Stereological estimation of mean nuclear volume in prostatic cancer,the reproducibility and the possible value of estimations on repeated biopsies in the course of disease

The reproducibility of stereological estimates of mean nuclear volume by using the principle of volume estimation of particles of arbitrary shape is investigated together with the possible prognostic value of the estimates in the course of advanced prostatic cancer. Repeated transurethral resection of the prostate was performed 14–93 months after the first resection in 14 of 85 consecutive patients in whom prostatic cancer was newly diagnosed in the period 1979–1983. Twelve of these fourteen patients needed endocrine treatment because of progression of the metastatic disease. The reproducibility of the estimations was excellent as the variation of the method was less than 1 % when the estimation of the mean nuclear volume was repeated at random on the same specimens after a time-interval of 2 months. The progression of the disease was evidenced by a significant histological upgrading and by a highly significant increase of the mean nuclear volume from the first to the second transurethral resection of the prostate.     

Estimating the length of a bounded curve in three dimensions using total vertical projections

A new method is proposed to estimate the total length of a bounded, isolated linear feature in three dimensions from ‘total vertical projections’, obtained by rotating the curve about a fixed axis (arbitrarily called ‘vertical’) and projecting it onto a fixed vertical plane. No sections are required. Properly stained and embedded neuron dendrites, mycelial trees, fluorescent cytoskeletal filaments within a cell, etc., are candidate specimens for the method, especially in combination with the new devices for non-invasive three-dimensional microscopy. It is necessary that the specimen curve is rigid (i.e. of constant shape), that its length density is not too high (so that overlapping effects are not important) and that the embedding medium is fairly transparent. Given these requirements, the method can be very accurate and convenient to use, as is exemplified here.     

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 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.     

Role of parietal and principal gastric mucosa cells in the phenomenon of concentration of aluminum and indium

The subcellular behavior of aluminum and indium, used in medical and industrial fields, was studied in the gastric mucosa and the liver after their intragastric administration to rats, using, two of the most sensitive methods of observation and microanalysis, the transmission electron microscopy, and the secondary ion mass spectrometry. The ultrastructural study showed the presence of electron dense deposits, in the lysosomes of parietal and principal gastric mucosa cells but no loaded lysosomes were observed in the different studied hepatic territories. The microanalytical study allowed the identification of the chemical species present in those deposits as aluminum or indium isotopes and the cartography of their distribution. No modification was observed in control rats tissues. In comparison to previous studies describing the mechanism of aluminum concentration in the gastric mucosa and showing that this element was concentrated in the lysosomes of fundic and antral human gastric mucosa, our study provided additional informations about the types of cells involved in the phenomenon of concentration of aluminum and indium, which are the parietal and the principal cells of the gastric mucosa. Our study demonstrated that these cells have the ability to concentrate selectively aluminum and indium in their lysosomes, as a defensive reaction against intoxication by foreign elements.     

Combining quantitative 2D and 3D image analysis in the serial block face SEM: application to secretory organelles of pancreatic islet cells

A combination of two‐dimensional (2D) and three‐dimensional (3D) analyses of tissue volume ultrastructure acquired by serial block face scanning electron microscopy can greatly shorten the time required to obtain quantitative information from big data sets that contain many billions of voxels. Thus, to analyse the number of organelles of a specific type, or the total volume enclosed by a population of organelles within a cell, it is possible to estimate the number density or volume fraction of that organelle using a stereological approach to analyse randomly selected 2D block face views through the cells, and to combine such estimates with precise measurement of 3D cell volumes by delineating the plasma membrane in successive block face images. The validity of such an approach can be easily tested since the entire 3D tissue volume is available in the serial block face scanning electron microscopy data set. We have applied this hybrid 3D/2D technique to determine the number of secretory granules in the endocrine α and β cells of mouse pancreatic islets of Langerhans, and have been able to estimate the total insulin content of a β cell.