Sampling theory and automated simulations for vertical sections, applied to human brain.

In recent years, there have been substantial developments in both magnetic resonance imaging techniques and automatic image analysis software. The purpose of this paper is to develop stereological image sampling theory (i.e. unbiased sampling rules) that can be used by image analysts for estimating geometric quantities such as surface area and volume, and to illustrate its implementation. The methods will ideally be applied automatically on segmented, properly sampled 2D images - although convenient manual application is always an option - and they are of wide applicability in many disciplines. In particular, the vertical sections design to estimate surface area is described in detail and applied to estimate the area of the pial surface and of the boundary between cortex and underlying white matter (i.e. subcortical surface area). For completeness, cortical volume and mean cortical thickness are also estimated. The aforementioned surfaces were triangulated in 3D with the aid of FreeSurfer software, which provided accurate surface area measures that served as gold standards. Furthermore, a software was developed to produce digitized trace curves of the triangulated target surfaces automatically from virtual sections. From such traces, a new method (called the 'lambda method') is presented to estimate surface area automatically. In addition, with the new software, intersections could be counted automatically between the relevant surface traces and a cycloid test grid for the classical design. This capability, together with the aforementioned gold standard, enabled us to thoroughly check the performance and the variability of the different estimators by Monte Carlo simulations for studying the human brain. In particular, new methods are offered to split the total error variance into the orientations, sectioning and cycloid components. The latter prediction was hitherto unavailable--one is proposed here and checked by way of simulations on a given set of digitized vertical sections with automatically superimposed cycloid grids of three different sizes. Concrete and detailed recommendations are given to implement the methods.

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.

Stereology of isolated objects with the invariator.

The invariator is a new stereological design to generate motion invariant test lines in three dimensions on an isotropic plane through a fixed point. The theory has been published recently. The purpose of this paper is to illustrate the application of the invariator on a group of rat brains to estimate brain volume and external surface area. Each brain was first split into its two hemispheres and then embedded into a ball filled with agar following a configuration named the antithetic isector, with the idea of reducing the error variance. After rolling the ball at random it was scanned by magnetic resonance imaging into a stack of parallel systematic sections: this is the isotropic Cavalieri design which, combined with the antithetic isector idea, proves to be very accurate. The invariator used only an equatorial section of the ball, and in the present case the coefficient of error of the volume and surface area estimators of an individual brain was about 30%. As it is design unbiased, the invariator may prove its strength mainly to estimate population means.

A general variance predictor for Cavalieri slices.

A general variance predictor is presented for a Cavalieri design with slices of an arbitrary thickness t >or= 0. So far, prediction formulae have been available either for measurement functions with smoothness constant q = 0, 1, ... , and t >or= 0, or for fractional q in [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 in [0, 1] and t >or= 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.

A new stereological principle for test lines in three-dimensional space.

A new principle is presented to generate isotropic uniform random (IUR) test lines hitting a geometric structure in three-dimensional space (3D). The principle therefore concerns the estimation of surface area, volume, membrane thickness, etc., of arbitrary structures with piecewise smooth boundary. The principle states that a point-sampled test line on an isotropic plane through a fixed point in 3D is effectively an invariant test line in 3D. Particular attention is devoted to the stereology of particles, where an alternative to the surfactor method is obtained to estimate surface area. An interesting case arises when the particle is convex. The methods are illustrated with synthetic examples.

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.

Precision of circular systematic sampling.

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.

Does lack of Cftr gene lead to developmental abnormalities in the lung?

Lung disease is the major cause of death in cystic fibrosis (CF), but the effect of gene mutation on the morphology of the main structural compartments of the lung is poorly understood. We show here, to our knowledge for the first time, a quantitative comparison of the fine pulmonary structures of cftr mutant versus non-cf mice. Pertinent volumes and surface areas were estimated in 10 homozygous cftrm1HGU mutants and 11 non-cf littermates by unbiased stereology at the light microscopic level. Our data did not reveal any statistical differences between group means for any of the 9 parameters considered. In other words, our data do not supply any significant evidence that the lack of the Cftr gene is accompanied by any developmental abnormalities in the lung, at least as far as the parameters studied are concerned.

Estimation of brain compartment volume from MR Cavalieri slices.

PURPOSE: Recent theory has been developed to estimate volume from a systematic sample of tissue slices of a given thickness and to predict the corresponding error. Our goal was to check the error prediction formulas by resampling and to determine the minimum number of MR slices required to estimate the volumes of the cerebrum and of the compartments of gray matter (GM) and white matter (WM) with prescribed errors. METHOD: Our working data set comprised the GM and WM segmentations obtained from a paradigmatic high signal-to-noise ratio 3D spoiled GRASS MR volume data set for a single healthy human subject. The data were classified using a fuzzy clustering minimum distance algorithm. We thereby obtained a stack of 183 serial coronal slices of 1 mm thickness encompassing the whole cerebrum. Empirical resampling was carried out using the corresponding data vectors, and the theoretical error predictors were thereby checked for slice thicknesses of 1, 3, 9, and 27 mm, with a distance of 45 mm between slice midplanes. RESULTS: Irrespective of slice thickness, a minimum of 3, 5, and 10 slices provided estimates of the true total volume of GM and WM in the cerebrum with coefficients of error (CEs) of 10, 5, and 3%, respectively, where CE(V)% = 100 x SE(V)/V. For the cerebrum, a minimum of two, three, and four slices were required for CEs of the same precision. CONCLUSION: In combination with high signal-to-noise ratio and enhanced tissue contrast, Cavalieri slices are the most appropriate for MRI, they supply unbiased and highly efficient volume estimates of brain compartments. For a given number of slices, CE(V) decreases rapidly when the slices are thicker than the gaps between them; when the slices are thinner than the gaps, then CE(V) is similar to that in the situation when the slice thickness is zero.

Application of the fractionator and vertical slices to estimate total capillary length in skeletal muscle.

A new stereological method is proposed which combines vertical slice projections with the fractionator to estimate the total capillary length in a skeletal muscle. The method was demonstrated on the soleus muscle of a Wistar rat. The implementation required capillary highlighting, tissue sampling, and data acquisition in the form of intersection counts between capillary projections and cycloid test lines. The capillaries were demonstrated using vascular perfusion (with gelatine) of the hind leg of the rat. The sampling procedure followed the fractionator design, namely a multistage systematic sampling design with a known sampling fraction at each stage. To make the design unbiased, vertical slices were used; for efficiency, the vertical axis was chosen parallel to the main axis of the muscle. As prescribed to avoid bias, the cycloid test lines were superimposed on the slice projections, viewed under the light microscope, with their minor axes normal to the vertical axis. The estimation precision was compared for different sampling and subsampling fractions. The proposed method was globally highly efficient, unbiased, and easy to implement.

Stereological assessment of the glial reaction to chronic deafferentation of the cochlear nuclei in the macaque monkey (Macaca fascicularis).

Neurectomy of the auditory nerve produces a massive deafferentation of the cochlear nuclei (CN) in the brainstem. Degenerating primary afferents are removed in the acute phase, and this is followed by a synaptic reorganization in the CN. As part of an ongoing study on the effect and applicability of auditory brain implants in the CN of Macaca fascicularis monkeys, we studied the chronic response of astrocytes in the CN to bilateral deafferentation of the VIIIth cranial nerve. Four control and five deafferentated animals were employed. The treated animals had a bilateral extradural section of the VIIIth cranial nerve and a survival of 3 months. Animals were euthanized and perfused, and the brainstem was serially sectioned. The astrocyte population of the CN was studied by glial fibrillary acidic protein (GFAP) immunohistochemistry and quantified by unbiased stereological methods. The total length of astrocyte processes, L(proc), was estimated as the product of nuclear volume V(nuc), which was estimated by the Cavalieri method, times the ratio L(V)(proc, nuc) of process length to nuclear volume. Mean nuclear volume was significantly lower in deafferented animals, whereas the mean ratio L(V)(proc, nuc) was higher (albeit no statistical significance was reached). However, the mean total astrocytic process length was virtually the same in both groups. The absence of a length increase in the glial processes indicates a decrease of the astrocytic reaction after the acute phase. No glial scar is present in the CN of the monkey after long-term deafferentation, so the usefulness of auditory brain implants to stimulate CN neurons directly as a means to overcome deafness resulting from direct damage to the VIIIth cranial nerve (i.e., acoustic neuromas) is plausible.

Anxiogenic-like effects and reduced stereological counting of immunolabelled 5-hydroxytryptamine6 receptors in rat nucleus accumbens by antisense oligonucleotides.

The physiological role of 5-hydroxytryptamine6 receptors in the central nervous system has not yet been elucidated. The high affinity of various psychotropic drugs for 5-hydroxytryptamine6 receptors has led to the suggestion that this receptor type may be a novel target in neuropsychiatry. We have found that continuous intracerebroventricular administration of a 5-hydroxytryptamine6 receptor antisense oligonucleotide, but not of a missense oligonucleotide, produced an anxiogenic-like response in rats using two different models of anxiety, the social interaction test and the elevated plus-maze. Neither oligonucleotide treatment modified locomotor activity, rectal temperature or food intake, suggesting a low or null neurotoxicity. The effectiveness of the treatment with the designed antisense oligonucleotide to block the synthesis of the protein encoded by the target mRNA was assessed by immunolabelling 5-hydroxytryptamine6 receptors in the nucleus accumbens, where this receptor is highly expressed, using previously characterized specific antibodies. The density of the immunostaining was quantified by means of an unbiased three-dimensional stereologic procedure, which revealed a significant reduction (-25%) in the number of immunolabelled neuronal elements. These results suggest that, in addition to other 5-hydroxytryptamine receptor subtypes, 5-hydroxytryptamine6 receptors in the nucleus accumbens may participate in anxiety-related neurobiological mechanisms.

Precision of Cavalieri sections and slices with local errors.

Cavalieri sections--and more recently Cavalieri slices, especially in combination with non-invasive scanning--are widely used to estimate volumes. Physical Cavalieri slices are also increasingly used to estimate neuron numbers via the optical fractionator. In either case, the prediction of the error variance is important to assess optimal sample sizes. The error variance consists of two components, one due to the variation among the true contents of sections or slices, and the other due to local or 'nugget' errors. The latter may arise for instance estimating section areas by point counting discrete particles in slices or disectors. In this paper, a fairly comprehensive set of prediction formulae is presented to separate both variance components.

Hippocampal volume and neuronal number in Ts65Dn mice: a murine model of Down syndrome.

Ts65Dn mouse displays a partial triplication of chromosome 16 and is adopted as a model for Down syndrome (DS). It is known that Ts65Dn mice present memory deficiencies. In order to gain insight into the cause of these deficiencies, we studied the possibility of changes in volumes and neuronal numbers in different regions of the hippocampus (dentate gyrus, CA3, CA2 and CA1) in trisomic mice as compared to control littermates using stereological methods. The mean hippocampal volumes of Ts65Dn mice did not show significant differences as compared to controls, except in CA2 where there was a barely significant decrease. However, mean neuron number was significantly lower in Ts65Dn mice than in controls in dentate gyrus (43.7 x 10(4), CV 21%, n = 5, vs. 30.4 x 10(4), CV 18.1%, n = 4) and higher in CA3 (23.1 x 10(4), CV 18.9% vs. 33.3 x 10(4), CV 14.9%). These quantitative changes may account for the memory deficiencies observed in Ts65Dn mice.

Influence of ovariectomy on the canine striated external urethral sphincter (M. urethralis): a stereological analysis of slow and fast twitch fibres.

Slow and fast twitch fibres were stereologically analysed in the morphologically defined and most strongly developed ventral and ventrolateral region of the external urethral sphincter (M. urethralis) using five sexually intact anestrous and five ovariectomized nulliparous beagles. The estimated mean total cross-sectional area of the investigated part of the muscle consisted of 4.2 mm2 (15.1%) type I fibre, 10.0 mm2 (32.1%) type II fibre, and 16.3 mm2 (52.8%) connective tissue in the control group. The corresponding absolute mean value of type I fibres (3.7 mm2/13.5%) was statistically lower in ovariectomized animals. No significant difference between groups was observed in the relative number of transverse profiles of type I and II fibres; type I fibres comprised 23.8% and type II 76.2% of all muscle fibres in the sexually intact group, but 21.8% and 78.2% in the ovariectomy group, respectively. The ovariectomized dogs exhibited a statistically significant lower type I and II fibre number and a concomitant slightly larger mean single profile area (diameter) of fibre type II compared with the control animals. The significantly reduced number and decreased total cross-sectional area of the fatigue-resistant type I fibres in ovariectomized dogs suggest a predominant weakening of the fibre type I portion of the M. urethralis as consequence of ovariectomy. The effect could be mediated by sex hormonal factors and may contribute to the development of postspaying urinary incontinence in female dogs.

Comparison of the phagocytosis of two types of cyclosporin (SDZ OXL 400 and SDZ IMM 125) by alveolar macrophages from hamsters.

The aim of this study was to compare two types of cyclosporin (Cs) particles, SDZ OXL 400 and SDZ IMM 125, the latter being more hydrophilic, to understand their uptake by airway macrophages. Alveolar macrophages (AM), harvested by bronchoalveolar lavage (BAL) of hamster lungs, were cultured with two different doses (0.1 mg and 0.5 mg) for 1 h, 6 h, and 24 h. Control incubations without Cs particles or with latex particles were carried out simultaneously. Cell viability, cell activation (i.e., respiratory burst, interleukin-6 (IL-6) synthesis) and mean volume of particles phagocytosed per macrophage were measured. Both types of Cs particles did not modify the AM viability, and failed to induce IL-6 synthesis during phagocytosis but slightly decreased the cell oxidative respiratory burst. The comparison between SDZ OXL 400 and SDZ IMM 125 showed that for the lower dose the mean volume of both Cs types phagocytosed was similar at 1 h and 6 h. At 24 h an increase of the mean volume phagocytosed was seen for SDZ IMM 125 but not for SDZ OXL 400. For the higher dose the mean volume of SDZ IMM 125 phagocytosed was higher than SDZ OXL 400 at 1 h and 6 h and comparable for both types at 24 h. SDZ IMM 125 particles were phagocytosed more rapidly than SDZ OXL 400. The mean volume of phagocytosed latex particles increased with time and dose and was higher than for both Cs particle types. In conclusion, AM were seen to phagocytose particles of different physical properties (i.e., form, size, and shape), chemical properties (i.e., inert or peptidic) and degrees of hydrophilicity in a different manner.

Comparison of the rate of phagocytosis of orthorhombic cyclosporine A (CsA) and latex particles by alveolar macrophages from hamsters.

The aim of this study was to develop an in vitro model to estimate the clearance of pulmonary administered cyclosporine A (CsA). To do this we estimated the volume of CsA particles phagocytosed by alveolar macrophages (AM) lavaged from hamsters. AM were cultured with CsA particles at two doses of particles (0.1 mg or 0.5 mg) and at three incubation times (1 h, 6 h or 24 h). The AM were also incubated with or without latex particles. After incubation, AM were processed for light and electron microscopy and the mean volume of phagocytosed particles was estimated stereologically from micrographs of the cells. Here, however, the CsA particles were dissolved during the embedding process and only their negative images (vacuoles) could be detected. An indirect method was therefore developed. The volume of cytoplasmic vacuoles (called 'background' vacuoles) was estimated in control macrophages (without particles or with latex particles and subtracted from the total volume of vacuoles in macrophages incubated with CsA, which gave the volume of phagocytosed CsA. The volume of the 'background' vacuoles remained constant in all study conditions. At a dose of 0.1 mg CsA the volume phagocytosed per macrophage was 13.83 microns3 at 1 h, 8.43 microns3 at 6 h and 4.50 microns3 at 24 h. At a dose of 0.5 mg CsA, the volume phagocytosed varied from 26.59 microns3 at 1 h, to 4.13 microns3 at 6 h and 49.10 microns3 at 24 h. These results show no statistically significant dependence on time for either dose, and a statistically significant dose effect only at 24 h. With latex particles, the phagocytosed volume increased significantly with time and dose and was significantly higher than for CsA particles. This study showed that CsA particles are phagocytosed by AM from hamsters but to a lesser extent than latex particles. This difference could be correlated with physical properties, i.e. a difference between particle size and shape and/or chemical properties, latex particles being inert and CsA particles being peptidic. Moreover, different surface receptors on AM could be involved in the process of phagocytosis of CsA and latex particles.

Analysis of cardiac function by MRI and stereology.

Design-based stereology and phase contrast magnetic resonance imaging (MRI) were combined to monitor changes in the volume of the four chambers of the human heart during the cardiac cycle. The data set consisted of 18 adjacent slices (or 'scanning levels') of 0.5 cm thickness, perpendicular to the long axis of the body, and encompassing the whole heart of a healthy volunteer. At each scanning level, a cardiac gated MR image was obtained at each of 16 equally spaced time frames within the cardiac cycle. Given stationarity with respect to time, absence of image artefacts and appropriate definition of chamber boundaries, for each time frame unbiased estimates of total blood volume in the relevant heart chambers were efficiently obtained using the Cavalieri method and point counting. Combined with a proper MRI acquisition, modern stereological methods constitute an efficient and reliable tool to quantify cardiac function noninvasively.

Efficiency of airway macrophage recovery by bronchoalveolar lavage in hamsters: a stereological approach.

Macrophages play a central role in the defence of the respiratory tract against deposited particles. In addition to the well-studied alveolar macrophages, airway macrophages have been recognized as an important clearance factor. Bronchoalveolar lavage (BAL) has been used for functional and morphological investigations of macrophages in vitro, assuming that all macrophages are removed with equal probability from the lung surface. Airway macrophages have been found in close contact with the epithelial cells. These macrophages may not be easily removed by lavage, and they might constitute a functionally different macrophage population. We have tested the hypothesis that there exists a population of macrophages in the conducting airways that resists removal by lavage. We lavaged the lungs of four hamsters and fixed the lungs, thereafter, by intravascular perfusion. The number of macrophages in the intrapulmonary conducting airways was estimated with an unbiased stereological technique, the fractionator, and compared to the number of macrophages in the airways of four hamsters whose lungs had not been lavaged prior to fixation. This in situ study revealed that, in hamster lungs, 42% of the airway macrophages were not removed by BAL and that about 5% of all macrophages in the BAL fluid were airway macrophages. Additionally, ultrastructural alterations of the airway epithelium were found. It is concluded that there exists a population of airway macrophages that resists lavage. This is an aspect which has to be considered in studies performed with macrophages obtained by BAL, since they could represent a functionally different macrophage population.

Paradoxical effects of bleomycin and heavy water (D2O) in mice.

Bleomycin (BLM) lacks many side effects of other cytostatic drugs. Pulmonary toxicity is the major dose-limiting effect of BLM. This is based in part on generation of free radicals. It is conceivable that deuterium in body fluids lessens the production of free radicals, thus preventing or diminishing the morphologic expression of pulmonary BLM toxicity. We therefore studied the effect of moderate deuteration of body fluids on BLM-induced lung damage in BALB/c-mice. In addition to conventional histopathological methods, we used a vertical sectioning design for stereological estimation of pulmonary volumes and surface areas. BLM (low/medium/high dose: 25/50/75 IU/kg body weight) was injected i.p. once a week for 6 weeks. Half the mice drank deuterated water before, during and after BLM treatment. Three weeks after the last injection, the lungs were fixed by airway instillation. Deuterated animals treated with BLM lacked signs of irreversible BLM-induced pulmonary damage. Conversely, focal sub-pleural fibrosis and fibrosing alveolitis were present in BLM-treated mice drinking tap water. Deuterated mice had stereological values for almost all lung parameters that were lower than in non-deuterated mice. The organ-specific advantage of deuteration was offset by marked enhancement of systemic toxicity of BLM. We conclude that (1) moderate concentrations of deuterium may prevent the development of fibrosing alveolitis in BLM-treated mice, possibly by reducing proliferation of alveolar fibroblasts, and, less probably, by impairing generation or enhancing capture of free radicals; (2) the toxicity of BLM was enhanced by ingestion of deuterium, resulting in morphological liver alterations and increased mortality.