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.     

New variance expressions for systematic sampling: the filtering approach

We present a collection of variance models for estimators obtained by geometric systematic sampling with test points, quadrats, and n‐boxes in general, on a bounded domain in n‐dimensional Euclidean space ?ⁿ, n = 1, 2, ... , and for systematic rays and sectors on the circle. The approach adopted ? termed the filtering approach ? is new and different from the current transitive approach. This report is only preliminary, however, because it includes only variance models in terms of the covariogram of the measurement function. The estimation step is in preparation.     

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.     

Estimation error of Leydig cell numbers in atrophied rat testes due to the assumption of spherical nuclei

In this study, Leydig cell numbers in control and atrophied testes (induced via subcutaneous implants of testosterone plus 17β estradiol for 16 weeks; TE-implanted) of rats, estimated via the fractionator method (independent of any assumptions) were compared to those estimated via the disector (unbiased, but dependent on shrinkage) and Floderus (assumes spherical particles, dependent on shrinkage) methods. Estimates of Leydig cell numbers in control rats produced by all three stereological methods were similar. In rats with atrophied testes, both the fractionator and the disector methods produced significantly lower (P < 0.01; 47% and 41 % with fractionator and disector, respectively) Leydig cell number estimates per testis than in the controls. By contrast, the estimates of Leydig cell number in atrophied testes derived via the Floderus equation were not significantly different from those of controls, but larger than those obtained via the fractionator and the disector methods. These results suggested that the assumptions of the Floderus method were violated in the atrophied rat testes. Why was the Floderus method of estimating Leydig cell number applicable to control rats but not to the TE-implanted rats? In an attempt to answer this question the diameter measurement together with its correction factor used in the Floderus equation (i.e. D + t ? 2H) was also derived from the data collected for the disector method. The values for D + t ? 2H used in the Floderus method and also calculated via the disector method were found to be identical in controls, but for the TE-implanted rats a 32% lower value was obtained with the Floderus equation when compared to the disector. These findings suggested that this estimation error caused an overestimation of Leydig cell numbers in the TE-implanted rat testes.     

A general variance predictor for Cavalieri slices

A general variance predictor is presented for a Cavalieri design with slices of an arbitrary thickness t ≥ 0. So far, prediction formulae have been available either for measurement functions with smoothness constant q = 0, 1, … , and t ≥ 0, or for fractional q ∈ [0, 1] with t = 0. Because the possibility of using a fractional q adds flexibility to the variance prediction, we have extended the latter for any q ∈ [0, 1] and t ≥ 0. Empirical checks with previously published human brain data suggest an improved performance of the new prediction formula with respect to the hitherto available ones.     

Exact formulae for the precision of systematic sampling

A formula is given for the variance of the intersection of two geometric objects, S and T, under uniform, i.e. translation invariant, randomness. It involves an integral of the product of the point-pair distance distributions of S and T. In systematic sampling S is the specimen and T is the test system, for example a system of planes, lines, or dots in ?³ or ?². The general n-dimensional integral (or sum) is difficult to use, but for systematic sectioning, i.e. for a test system of parallel hyperplanes (planes in ?³ or lines in ?²) it can be reduced to a one-dimensional expression: this leads to Matheron's treatment in terms of ‘covariograms’ of the specimens. Under the condition of isotropy analogous simplifications lead to equations involving the distributions of scalar point-pair distances and to the approach developed by Matérn for sampling with point grids. The equations apply to arbitrary test systems, but they include fluctuating functions that require high precision in the numerical evaluation and make it difficult to pradict undamped variance oscillations of the volume estimator which occur for some specimen shapes but not for others. A generalized Euler method of successive partial integrations removes this difficulty and shows that, for a convex specimen, the undamped oscillations result from discontinuities in its chord-length density. The periodicities equal the ratios of the critical chord-lengths to the periodicities of the test system. Analogous relations apply to the covariogram. The formulae for the variance are extended also to the covariance of the volume estimators of paired specimens.     

Mapping cholesteryl ester analogue uptake and intracellular flow in Paramecium by confocal fluorescence microscopy

In Paramecium primaurelia the uptake and intracellular flow of cholesteryl ester was studied by fluorescence confocal laser scanning optical microscopy and by the fluorescent analogue cholesteryl‐BODIPY^® FL C₁₂ (BODIPY‐CE). The BODIPY FL fluorophore has the characteristic of emitting green fluorescence, which is red‐shifted as the probe concentrates. In cells incubated with 25 µm BODIPY‐CE for 30 s, fluorescence is found in vesicles located around the cytopharynx in the posterior half of the cell. Successively, the lipid is internalized by food vacuoles, the fluorescent vesicles are distributed throughout the cell and the intracellular membranes are labelled. The food vacuole number is maximum after 10–15 min of continuous labelling, then it decreases until no food vacuoles are found in 30‐min fed cells. BODIPY‐CE accumulates in red‐labelled cytoplasmic droplets located in the anterior half of the cell. When food vacuole formation is inhibited by trifluoperazine, fluorescence is found on cellular membranes and in small green‐labelled vesicles at the apical pole. The inhibition of clathrin‐mediated endocytosis does not interfere in P. primaurelia with BODIPY‐CE intracellular flow: intracellular membranes and storage droplets in the cell anterior part are dyed. Conversely, the use of sterol‐binding drugs prevents the lipid accumulation in droplets, stopping the lipid within the cytoplasmic membranes. Furthermore, the cells treated with monensin and cytochalasin B show a labelling of the cellular membranes and lipid droplets, whereas NH₄Cl reduces the lipid storage. Low temperature (4 °C) does not prevent the internalization of BODIPY‐CE that, however, is localized at the cytoplasmic membrane level and does not accumulate in storage droplets. In addition, BODIPY‐CE inhibits phagocytosis, as evidenced by comparing the kinetics of food vacuole formation of control cells, only fed with latex particles, with that of cells fed with latex particles and BODIPY‐CE. In conclusion, this study points out that in P. primaurelia the cholesteryl ester enters the cell via food vacuoles and through the plasma membrane and, inside the cell, it alters cell functions.     

Evaluation of the effective cross‐sections for recombination and trapping in the case of pure spinel

In this paper, we have investigated the evolution of the secondary electron emission in the case of pure spinel during electron irradiation, achieved in a scanning electron microscope at room temperature, which is derived from the measurement of the induced and the secondary electron currents. It was observed from the experimental results, that there are two regimes during the charging process: a plateau followed by a linear variation, which are better identified by plotting the logarithm of the secondary electron emission yield lnσ as function of the total surface density of trapped charges in the material Q_T. For positive charging, E₀ = 1.1 and 5 keV, the slope of the linear part, whose value is of about 10^?10 cm² charge^?1, is independent of the primary electron energy. It is interpreted as a microscopic cross section for electron–hole recombination. For negative charging of pure spinel, E₀ = 15 and 30 keV, the slope is associated with an electron trapping cross section close to 10^?14 cm² charge^?1, which can be assigned to the microscopic cross section for electron trapping. This trapping cross section is four orders of magnitude lower than the recombination one.     

Directional analysis of digitized planar sets by configuration counts

The oriented rose of normal directions of a random set Z can be used to quantify its anisotropy. A method for estimating this quantity from a digitization of Z in a sampling window, i.e. its pixel image, is presented. The image is analysed locally by considering pixel squares of size n × n. This allows us to count the number of different types of n × n configurations in the pixel image. We show that it suffices to restrict attention to the so‐called informative configurations. The number of informative configurations increases only polynomially in n. An algorithm to find these informative configurations is presented. Furthermore, estimators of the oriented rose based on counts of observed informative configurations are derived. The procedure is illustrated by a simulated example and an analysis of a microscopic image of steel.     

Study of two tungstates Ca0.5Cd0.5WO4 and Ca0.2Cd0.8WO4 by transmission electron microscopy

To better understand the role of crystal structures and local disorder in the photonic properties of the system (1 ? x)CaWO₄ ? xCdWO₄ with 0 < x < 1, two specific phases with compositions x = 0.5 (scheelite phase) and 0.8 (wolframite phase) have been studied by scanning and transmission electron microscopies. High‐resolution electron microscopy images and image simulations, associated with X‐ray diffraction data, allowed confirming the lattices and space groups I4₁/a and P2/c of the two scheelite and wolframite phases, at the local scale. The electron microscopy data show the existence of a high degree of crystallization associated with statistical distribution of Ca or Cd atoms on a Ca_1?xCd_x site in each lattice.     

An X-ray microscopy perspective on the effect of glutaraldehyde fixation on cells

X-ray microscopy (XRM) is the only microscopy technique that can provide high-resolution (30 nm) imaging of biological specimens without the need to fix, stain or section them. We aim to determine the effect, if any, of glutaraldehyde fixation on algae cells from the XRM perspective and thus provide beneficial information for both X-ray and electron microscopists on artefacts induced by glutaraldehyde fixation. Three species of microalgae, Microcystis aeruginosa, Anabaena spiroides and Chlorella vulgaris, were used in this study. XRM images were obtained from unfixed and glutaraldehyde-fixed cells and cell diameter and percentage X-ray absorbency were measured. The mean diameter of cells from fixed preparations was smaller than from unfixed preparations; the mean diameter of M. aeruginosa cells was significantly reduced from 3.92 µm in unfixed cells to 3.43 µm in fixed cells (P < 0.05); in C. vulgaris the diameter of cells was also significantly reduced from 3.50 µm in unfixed to 2.98 µm in fixed samples (P < 0.05); whereas there was no significant reduction in the diameter of A. spiroides cells (4.04–3.90 µm). The protein crosslinking mechanism of glutaraldehyde probably generated free water molecules, which play an important role in radiation damage induced by X-rays. This was seen as mass loss and cell shrinkage, which in the present study occurred more frequently in fixed cells than in unfixed cells. In addition, we demonstrated that the uptake of glutaraldehyde by cells makes all protein constituents in the cell organize into a closely packed configuration, thus causing a rise in the percentage of X-ray absorbency. In fixed cells, this rise was approximately by a factor of two compared with unfixed samples in which protein constituents inside the cell are arranged in their native form.     

Stereological length estimation using spherical probes

Lineal structures in biological tissue support a wide variety of physiological functions, including membrane stabilization, vascular perfusion, and cell‐to‐cell communication. In 1953, Smith and Guttman demonstrated a stereological method to estimate the total length density (L_v) of linear objects based on random intersections with a two‐dimensional sampling probe. Several methods have been developed to ensure the required isotropy of object–probe intersections, including isotropic‐uniform‐random (IUR) sections, vertical‐uniform‐random (VUR) slices, and isotropic virtual planes. The disadvantages of these methods are the requirements for inconvenient section orientations (IUR, VUR) or complex counting rules at multiple focal planes (isotropic virtual planes). To overcome these limitations we report a convenient and straightforward approach to estimate L_v and total length, L, for linear objects on tissue sections cut at any arbitrary orientation. The approach presented here uses spherical probes that are inherently isotropic, combined with unbiased fractionator sampling, to demonstrate total L estimation for thin nerve fibres in dorsal hippocampus of the mouse brain.     

Microinfrared reflection spectroscopic mapping: application to the detection of hydrogen-related species in natural quartz

A new method of microinfrared reflection spectroscopy and mapping analysis is briefly introduced. It was used to detect distributions and structures of hydrogen‐related species (e.g. H₂O, SiOH and SiH) in plastically deformed natural quartz. We used a Fourier transform‐infrared spectrometer with a microscopic imaging system fully automated for all microscope functions (e.g. focusing, aperture, stage motion and measurements). Mapping can be made in thin sections with a thickness of 50 µm at room temperature and low temperatures (77 K) using a liquid N₂ cooling system. Infrared reflection spectra were obtained by five scans for each point with a range from 4000 to 400 cm^?1. The spectra were measured five times within about 2.5 s at each position. The scanning interval was 100–150 µm using a 100 × 100 µm² aperture. All obtained spectral data were stored in computer memory to construct two‐dimensional mappings of infrared absorption. From the comparisons between infrared mapping images and deformation microstructures, in addition to the molecular H₂O around 3600–3400 cm^?1, the hydrogen‐related point defects (i.e. SiOH and SiH) around 970–900 cm^?1 within quartz grains and between grain boundaries increased with decreasing grain sizes (increasing plastic strain). The method can detect the SiOH and SiH along grain boundaries that enhance the hydrolytic weakening of natural quartz.     

Morphological and immunohistochemical analysis of the biocompatibility of resin‐modified cements

The aim of this double‐blind randomized study was to evaluate the biocompatibility of resin‐modified glass ionomer cements (RMGIC) by means of morphological and immunohistochemical analyses. RMGICs were selected and divided into four groups: Group CK (Crosslink Orthodontic Band Cement); Group RS (Resilience Light Cure Band Cement) Group RMO (RMO Band Cement), Group TP (Transbond Plus Light Cure Band), and Group C (Control‐polyethylene). The materials were implanted in rat subcutaneous tissues, randomly selected for this study. After time intervals of 7, 15, and 30 days the tissues were submitted to morphological analysis. In immunohistochemical analysis, the immuno‐marking of antibody CD68 was evaluated. The results obtained were statistically analyzed by the Kruskal–Wallis and Dunn tests (p < .05). In the morphological analysis after 7 days, Groups RS, RMO and TP showed more intense inflammatory infiltrate (p = .004) and only Group RMO presented greater intensity of multinucleated giant cells (p = .027). In the immunohistochemical analysis, Groups RMO and RS were observed to present a larger quantity of CD68+ (p = .004) in the time interval of 7 days and only Group RMO presented statistically significant difference for this parameter after 15 days (p = .026). In the time interval of 30 days, Group RMO presented the largest quantity of multinucleated giant cells (p < .004). The RMGICS Crosslink and Transbond Plus provided significantly better tissue biocompatibility than the Resilience and RMO Cements.     

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.     

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.     

Evaluation of variance models for fractionator sampling of trees

We compared the performance of several models for predicting, from small samples, the precision of estimates of the total number of blossoms on fruit trees obtained using a three‐stage fractionator, in which the sampling units were defined by the tree structure: (1) primary branches and stem (2) secondary branches and shoots and (3) flowering buds. The models considered were the semiempirical models of Cruz‐Orive (1990, 2004 ) (CO), a random sample model (SR), a Poisson model (P), successive differences (D) and repeated systematic sampling (R). Procedures that relied upon a single sample and a model of the variance (SR, P, D) were not able to predict the estimator variance because the considered structures strongly violated model assumptions. The semiempirical CO model performed acceptably in some cases where model assumptions were violated to a moderate degree. The repeated systematic sampling procedure, which does not rely upon a model of the variance, usually provided very good predictions when the resampling terms were distributed appropriately across more than one sampling stage.     

The influences of process parameters on the preliminary roll-forging process of the AISI-1045 automobile front axle beam

Roll-forging process is widely used to fabricate the automobile front axle beams. The reasonable selection of the process parameters is significant to ensure the quality and improve the property of the automobile front axle beam owing to the complexity and importance of the preliminary roll-forging process. This paper developed a 3D Finite element (FE) model of the preliminary roll-forging process of the AISI-1045 automobile front axle beam under the Deform-3D platform. A corresponding experiment is subsequently conducted. Good agreement between the experimental and simulative results validates the employed model. Based on this dependable FE model, the influences of initial temperature of billet T ₀ , rotational speed of rolls n and friction factor m on the geometric dimension, temperature inhomogeneity, deformation inhomogeneity, and roll-forging load are investigated comprehensively. The results can provide reliable guidelines for the selection of process parameters.

     

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.