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The nucleator is a method to estimate the volume of a particle, i.e. a compact subset of ℝ3, which is widely used in Stereology. It is based on geometric sampling and known to be unbiased. However, the prediction of the variance of this estimator is non-trivial and depends on the underlying sampling scheme. We propose well established tools from quasi-Monte Carlo integration to address this problem. In particular, we show how the theory of reproducing kernel Hilbert spaces can be used for variance prediction and how the variance of estimators based on the nucleator idea can be reduced using lattice (or lattice-like) points. We illustrate and test our results on various examples.

The nucleator is a design unbiased method of local stereology for estimating the volume of a bounded object. The only information required lies in the intersection of the object with an isotropic random ray emanating from a fixed point (called the pivotal point) associated with the object. For instance, the volume of a neuron can be estimated from a random ray emanating from its nucleolus. The nucleator is extensively used in biosciences because it is efficient and easy to apply. The estimator variance can be reduced by increasing the number of rays. In an earlier paper a systematic sampling design was proposed, and theoretical variance predictors were derived, for the corresponding volume estimator. Being the only variance predictors hitherto available for the nucleator, our basic goal was to check their statistical performance by means of Monte Carlo resampling on computer reconstructions of real objects. As a plus, the empirical distribution of the volume estimator revealed statistical properties of practical relevance.

Purpose The main aim of this study was to research new treatments following peripheral nerve injury involving melatonin (Mel), acetyl- l -carnitine (ALCAR), and leptin (Lep) using updated unbiased methods at the stereological and electron microscopic levels. Materials and methods Wistar albino rats were randomly divided into nine equal groups; control (Cont), obese control (OG), obese group exposed to sciatic nerve resection (Gap) (OGG), obese group injected intraperitoneally (i.p.) with Mel (OMG), obese group injected with Mel i.p. with gap (OMGG), obese group injected with Lep i.p. (OLG), obese group injected with Lep i.p. with gap (OLGG), obese group injected with ALCAR i.p. (OAG), and obese group injected with ALCAR i.p. with gap (OAGG). Electromyography (EMG) procedures were performed. Following routine histological procedures, stereological analysis was performed for each group. Results In terms of the number of myelinated axons, high significant increase in OGG was observed compared to OG and Cont (p < 0.01). In addition, a highly significant increase in axon surface area and myelin thickness of OGG compared to OG and Cont (p < 0.01) was noted. A significant decrease in myelin thickness/axon diameter ratio of OGG was found in comparison with the other groups. In terms of latency, there was a highly significant decrease in OGG compared to Cont and OG (p < 0.01). Myelinated axon numbers in OAGG, OMGG and OLGG increased highly significantly compared to other groups (p < 0.01). Latency in OMGG, a highly significant increase, was determined in OMG compared to Cont (p < 0.01). In addition, latency values in OGG were highly significantly greater than in OAC and OAGG (p < 0.01). Conclusion In particular, administration of Lep, Mel and ALCAR as neuroprotective agents may make a positive contribution to regeneration and myelination in obese rats. [ABSTRACT FROM AUTHOR]

The porcine liver is frequently used as a large animal model for verification of surgical techniques, as well as experimental therapies. Often, a histological evaluation is required that include measurements of the size, nuclearity or density of hepatocytes. Our aims were to assess the mean number-weighted volume of hepatocytes, the numerical density of hepatocytes, and the fraction of binuclear hepatocytes (Bn HEP) in the porcine liver, and compare the distribution of these parameters among hepatic lobes and macroscopic regions of interest ( ROIs) with different positions related to the liver vasculature. Using disector and nucleator as design-based stereological methods, the morphometry of hepatocytes was quantified in seven healthy piglets. The samples were obtained from all six hepatic lobes and three ROIs (peripheral, paracaval and paraportal) within each lobe. Histological sections (thickness 16 μm) of formalin-fixed paraffin-embedded material were stained with the periodic acid-Schiff reaction to indicate the cell outlines and were assessed in a series of 3-μm-thick optical sections. The mean number-weighted volume of mononuclear hepatocytes (Mn HEP) in all samples was 3670 ± 805 μm3 (mean ± SD). The mean number-weighted volume of Bn HEP was 7050 ± 2550 μm3. The fraction of Bn HEP was 4 ± 2%. The numerical density of all hepatocytes was 146 997 ± 15 738 cells mm−3 of liver parenchyma. The porcine hepatic lobes contained hepatocytes of a comparable size, nuclearity and density. No significant differences were identified between the lobes. The peripheral ROIs of the hepatic lobes contained the largest Mn HEP with the smallest numerical density. The distribution of a larger Mn HEP was correlated with a larger volume of Bn HEP and a smaller numerical density of all hepatocytes. Practical recommendations for designing studies that involve stereological evaluations of the size, nuclearity and density of hepatocytes in porcine liver are provided. [ABSTRACT FROM AUTHOR]

It is shown that, for a three dimensional particle (namely an arbitrary compact domain with piecewise smooth boundary in R^3) the mean wedge volume defined on a given pivotal section is equal to the average nucleator estimator of the particle volume defined on that section. Further, if the particle is convex and it contains the pivotal point, then the flower area of a given pivotal section equals the average surfactor estimator defined on that section. These results are intended to throw some light on the standing conjecture that the functional defined on a pivotal section according to the invariator has a unique general expression. As a plus, the former result leads to a computational formula for the mean wedge volume of a convex polygon which is much simpler than the one published recently, and it is valid whether the fixed pivotal point is interior or exterior to the particle.

We investigated the microscopic structure of transverse sections of the oculomotor, trochlear and abducens nerves of Arabian foals using stereological methods. Bilateral nerve pairs from 2-month-old female Arabian foals were analyzed. The tissues were embedded in plastic blocks, then 1 µm thick sections were cut and stained with osmium tetroxide and methylene blue-azure II. Stereology was performed using light microscopy. Morphometry showed that the right and left pairs of nerves were similar. The transverse sectional areas of the oculomotor, trochlear and abducens nerves were 1.93 ± 0.19 mm2, 0.32 ± 0.06 mm2and 0.70 ± 0.08 mm2, respectively. The oculomotor nerve exhibited a significantly greater number of myelinated axons (16755 ± 1279) and trochlear (2656 ± 494) and the abducens nerves (4468 ± 447). The ratio of the axon diameter to myelinated nerve fiber diameter was 0.58, 0.55 and 0.55 for the oculomotor, trochlear and abducens nerves, respectively. Of the three nerves studied, the abducens nerve exhibited the greatest nerve fiber area, myelin area, nerve and axon diameters, and myelin thickness. The ratio of small myelinated nerve fibers was greatest in the oculomotor nerve. [ABSTRACT FROM AUTHOR]

Abstract: Guanidinopropionic acid (GPA) increases AMPK activity, mitochondrial function and biogenesis in muscle and improves physiological function, for example during aging. Mitochondrial dysfunction is a major contributor to the pathogenesis of Parkinson''s disease. Here we tested whether GPA prevents neurodegeneration of the nigrostriatal dopamine system in MPTP-treated mice. Mice were fed a diet of 1% GPA or normal chow for 4weeks and then treated with either MPTP or saline. Indices of nigrostriatal function were examined by HPLC, immunohistochemistry, stereology, electron microscopy and mitochondrial respiration. MPTP intoxication decreased TH neurons in the SNpc of normal chow-fed mice; however GPA-fed mice remarkably exhibited no loss of TH neurons in the SNpc. MPTP caused a decrease in striatal dopamine of both normal chow- and GPA-fed mice, although this effect was significantly attenuated in GPA-fed mice. GPA-fed mice showed increased AMPK activity, mitochondrial respiration and mitochondrial number in nigrostriatal TH neurons, suggesting that the neuroprotective effects of GPA involved AMPK-dependent increases in mitochondrial function and biogenesis. MPTP treatment produced a decrease in mitochondrial number and volume in normal chow-fed mice but not GPA-fed mice. Our results show the neuroprotective properties of GPA in a mouse model of Parkinson''s disease are partially mediated by AMPK and mitochondrial function. Mitochondrial dysfunction is a common problem in neurodegeneration and thus GPA may slow disease progression in other models of neurodegeneration. [Copyright &y& Elsevier]

Bovine cumulus-oocyte complexes (COCs) aspirated from slaughterhouse ovaries are used for in vitro maturation and fertilization after selection on the basis of morphological appearance of the cumulus and ooplasm. In this context, a quantitative characterization of COCs could provide additional criteria for selecting the most competent complexes. Bovine COCs from small (1–4 mm) antral follicles were aspirated from metestrous and proestrous stage ovaries of Holstein–Friesian cows, fixed in glutaraldehyde, randomly embedded in glycol-methacrylate, and sectioned at 20 μm. The unbiased nucleator principle of stereology was used for estimating the mean volumes of complexes, oocytes, cumulus cells, and nuclei of oocytes and cumulus cells. The thickness of the zona pellucida and the relative numerical percentages of the several morphological types (C1, C2 and C3) of cumulus cells were also evaluated. The optical dissector procedure was used for cumulus cell sampling. Quantitative data show that the variability among complexes is generally high, especially for the volume of COCs. There were no linear correlations between the studied parameters, except between the volume of the oocyte and nucleus at metestrus. At proestrus, the volumes of COCs, oocytes and nuclei of oocytes, the volume of follicular cells and the thickness of the inner zona pellucida, were significantly higher than at metestrus. The relative numerical frequency of follicular type C1 cells was lower whereas that of type C3 cells was higher at proestrus than at metestrus. In conclusion, small antral follicles had larger COCs and oocytes at proestrus compared to metestrus and the COCs also had a higher percentage of follicular type C3 cells. Results suggest that for the same type of follicle size there may exist different functional populations of COCs at distinct stages of the bovine ovarian cycle. [Copyright &y& Elsevier]

Summary In design stereology, many estimators require isotropic orientation of a test probe relative to the object in order to attain unbiasedness. In such cases, systematic sampling of orientations becomes imperative on grounds of efficiency and practical applicability. For instance, the planar nucleator and the vertical rotator imply systematic sampling on the circle, whereas the Buffon–Steinhaus method to estimate curve length in the plane, or the vertical designs to estimate surface area and curve length, imply systematic sampling on the semicircle. This leads to the need for predicting the precision of systematic sampling on the circle and the semicircle from a single sample. There are two main prediction approaches, namely the classical one of G. Matheron for non-necessarily periodic measurement functions, and a recent approach based on a global symmetric model of the covariogram, more specific for periodic measurement functions. The latter approach seems at least as satisfactory as the former for small sample sizes, and it is developed here incorporating local errors. Detailed examples illustrating common stereological tools are included. [ABSTRACT FROM AUTHOR]