Stereological measures of trabecular bone structure: comparison of 3D micro computed tomography with 2D histological sections in human proximal tibial bone biopsies

Stereology applied on histological sections is the ‘gold standard’ for obtaining quantitative information on cancellous bone structure. Recent advances in micro computed tomography (µCT) have made it possible to acquire three-dimensional (3D) data non-destructively. However, before the 3D methods can be used as a substitute for the current ‘gold standard’ they have to be verified against the existing standard. The aim of this study was to compare bone structural measures obtained from 3D µCT data sets with those obtained by stereology performed on conventional histological sections using human tibial bone biopsies. Furthermore, this study forms the first step in introducing the proximal tibia as a potential bone examination location by peripheral quantitative CT and CT. Twenty-nine trabecular bone biopsies were obtained from autopsy material at the medial side of the proximal tibial metaphysis. The biopsies were embedded in methylmetacrylate before µCT scanning in a Scanco µCT 40 scanner at a resolution of 20 × 20 × 20 µm³, and the 3D data sets were analysed with a computer program. After µCT scanning, 16 sections were cut from the central 2 mm of each biopsy and analysed with a computerized method. Trabecular bone volume (BV/TV) and connectivity density (CD) were estimated in both modalities, whereas trabecular bone pattern factor (TBPf) was estimated on the histological sections only. Trabecular thickness (Tb.Th), number (Tb.N) and separation (Tb.Sp), and structure model index (SMI) were estimated with the µCT method only. Excellent correlations were found between the two techniques for BV/TV (r = 0.95) and CD (r = 0.95). Additionally, an excellent relationship (r = 0.95) was ascertained between TBPf and SMI. The study revealed high correlations between measures of bone structure obtained from conventional 2D sections and 3D µCT data. This indicates that 3D µCT data sets can be used as a substitute for conventional histological sections for bone structural evaluations.     

Third-order aberration theory of Wien filters for monochromators and aberration correctors

Third-order aberrations at the first and the second focus planes of double focus Wien filters are derived in terms of the following electric and magnetic field components – dipole: E₁, B₁; quadrupole: E₂, B₂; hexapole: E₃, B₃ and octupole: E₄, B₄. The aberration coefficients are expressed under the second-order geometrical aberration free conditions of E₂ = −(m + 2)E₁/8R, B₂ = −mB₁/8R and E₃R²/E₁ − B₃R²/B₁ = m/16, where m is an arbitrary value common to all equations. Aberration figures under the conditions of zero x- and y-axes values show very small probe size and similar patterns to those obtained using a previous numerical simulation [G. Martínez & K. Tsuno (2004) Ultramicroscopy, 100 , 105–114]. Round beam conditions are obtained when B₃ = 5m²B₁/144R² and (E₄/E₁ − B₄/B₁)R³ = −29m²/1152. In this special case, aberration figures contain only chromatic and aperture aberrations at the second focus. The chromatic aberrations become zero when m = 2 and aperture aberrations become zero when m = 1.101 and 10.899 at the second focus. Negative chromatic aberrations are obtained when m < 2 and negative aperture aberrations for m < 1.101. The Wien filter functions not only as a monochromator but also as a corrector of both chromatic and aperture aberrations. There are two advantages in using a Wien filter aberration corrector. First, there is the simplicity that derives from it being a single component aberration correction system. Secondly, the aberration in the off-axis region varies very little from the on-axis figures. These characteristics make the corrector very easy to operate.     

A technique for studying one and the same section of a cell in sequence with the light and electron microscope

Methods for mounting and staining relatively thin sections on electron microscope grids, in order that one and the same section of a cell can be photographed in sequence with the light and electron microscope are described. Toluidine blue is used as a stain and hexachlorabuta-1,3 diene as a medium which enables the grid carrying the stained sections to be temporarily mounted under a coverslip and examined with an oil-immersion lens. Results obtained with pollen mother cells of Fritillaria lanceolata at zygotene are illustrated.     

Enhancement of three-dimensional appearance of freeze-fracture images by reversal processing of electron microscopy sheet film

Since sections intersect membranes at random angles, the mean distances measured between two such membranes are greater than the perpendicular distances between them. Errors of 10–20% will be usual. Equations are derived relating the true lengths with the various observed ones, and the accuracy of the various methods are indicated. These differ for block-stained and section-stained material. In the Appendix it is shown that in section-stained material, while it is the stain near the surface which is of overwhelming importance for the production of contrast, much of this stain lies in the section itself, rather than actually on the surface. This stained depth is shown to be ～4 nm deep, but this depth may include surface aggregates (～ 1 nm) as well.     

Orientation of medial smooth muscle in the wall of systemic muscular arteries.

The study was undertaken to determine the pattern of alignment of muscle cells in the tunica media of muscular arteries. Brachial and femoral arteries from two small Rhesus monkeys and renal arteries from two rabbits were fixed under pressure with formalin, or glutaraldehyde followed by formalin. Sections were cut at 7 micron thickness at specific angles varying from zero to 30 degrees, and then stained with haematoxylin and eosin. The end coordinates of the medial muscle nuclei (appearing dark with the H & E stain) were recorded using a digitizer. Analysis was done as suggested by a previous modelling study by one of the authors; lengths of the individual nuclei as they appeared on the section were plotted as a function of the distance around the perimeter of the vessel. The distribution of lengths was consistent with a truly circumferential pattern of alignment for the muscle nuclei in the wall of muscular arteries. The standard deviation about the average circumferential pattern was +/- 13 degrees in the plane of the histological sections cut in cross section. The number density Nv of 4.4 x 10(5) mm-3 was higher than determined previously for human brain arteries and the nuclear length was 20% shorter (30 micron).     

Three-dimensional volume reconstruction of extracellular matrix proteins in uveal melanoma from fluorescent confocal laser scanning microscope images

The distribution of looping patterns of laminin in uveal melanomas and other tumours has been associated with adverse outcome. Moreover, these patterns are generated by highly invasive tumour cells through the process of vasculogenic mimicry and are not therefore blood vessels. Nevertheless, these extravascular matrix patterns conduct plasma. The three‐dimensional (3D) configuration of these laminin‐rich patterns compared with blood vessels has been the subject of speculation and intensive investigation. We have developed a method for the 3D reconstruction of volume for these extravascular matrix proteins from serial paraffin sections cut at 4 µm thicknesses and stained with a fluorescently labelled antibody to laminin ( Maniotis et al., 2002 ). Each section was examined via confocal laser‐scanning focal microscopy (CLSM) and 13 images were recorded in the Z‐dimension for each slide. The input CLSM imagery is composed of a set of 3D subvolumes (stacks of 2D images) acquired at multiple confocal depths, from a sequence of consecutive slides. Steps for automated reconstruction included (1) unsupervised methods for selecting an image frame from a subvolume based on entropy and contrast criteria, (2) a fully automated registration technique for image alignment and (3) an improved histogram equalization method that compensates for spatially varying image intensities in CLSM imagery due to photo‐bleaching. We compared image alignment accuracy of a fully automated method with registration accuracy achieved by human subjects using a manual method. Automated 3D volume reconstruction was found to provide significant improvement in accuracy, consistency of results and performance time for CLSM images acquired from serial paraffin sections.     

A perimeter algorithm applied to lung pathology

A new image analyser, the NS 2000, explores the image using 256 photodiodes and, according to an adjustable threshold, converts it into a set of digital points of logical level 0 or 1. The method of fitting squares of increasing size consists of checking the presence of a square of a given size and of a given logical value throughout the image studied and gives the areas of successive erosions of the image. Using the parameters provided by the device one can obtain the total boundary B_A per unit area for the phase studied, which is proportional to the number of squares having points of the two logical levels. Errors in length measurement as a function of orientation and for isotropic structures are compared to other automatic perimeter algorithms and to manual square grid measurement. Using the parameters provided by the device for the quantitative evaluation of lesions of elastase induced emphysema in hamster lungs, the values obtained for internal surface area (ISA) of alveoli, are lower by about 40% in elastase treated hamsters when compared to normal controls. This difference is highly significant (P < 0.001) and the results obtained by the described method are in good agreement with those obtained by the classical manual procedure. Efficiency, defined as the precision of the estimate per unit measurement time on a given set of sample units (pictures in this paper), is given for both NS 2000 and manual procedures. The results obtained show comparable values but the automatic procedure includes a statistical treatment and it is significantly faster on histological sections than on micrographs, which was not the case with the manual method.     

Three-dimensional analysis of neuronal geometry using HVEM

There is a need for an electron microscopic method for visualization of selectively stained neurons and neuronal processes with higher resolution than can be obtained with the light microscope, but using thick sections that allow visualization of the three-dimensional structure of the neuron. Such a method is required for measurement of the geometry of neurons, and this information is needed to test theoretical predictions on the way in which electrical signals of synaptic origin are processed by the cells. The high voltage electron microscope (HVEM) is well suited to this application, because of its high resolution and ability to form images of thick sections. Use of this instrument requires development of selective stains that can produce diffuse cytoplasmic staining of specific cells or cell populations on the basis of their functional properties. Several such methods currently being employed for light microscopic work can be used directly in the high voltage electron microscope or can be made useful by relatively minor alterations. These include intracellular staining with horseradish peroxidase, axonal tracing with Phaseolus vulgaris leukoagglutinin (PHA-L), and immunocytochemical staining for specific cell markers known to stain the cytoplasm of certain cell populations. Cells stained intracellularly by microinjection of horseradish peroxidase during physiological recording experiments may be stained in thick (ca. 50 μm) sections cut on a vibratome or similar instrument and stained in the standard way, using methods designed for light microscopy. The sections are then postfixed in osmium tetroxide and embedded in epoxy plastic. Sections cut from these blocks at thicknesses of from 1 to 5 μm using a dry glass knife may be examined directly in the HVEM with no further staining. This produces a very clear image of the cell on a relatively unstained background. This method provides more than adequate resolution of the boundary of the neuron, allowing measurement of neuronal processes to better than 10-nm precision. Similar results are obtained when the same method is applied to axonal tracing using PHA-L. In this case, the exogenously applied marker is used to label a small population of nearby neurons and to trace their connections with other cells at a distance. The lectin is detected by immunocytochemistry, but the selective contrast of the image is adjustable because the concentration of antigen in the cell is largely controlled by the experimenter. The lectin is distributed diffusely in the cytoplasm in a pattern identical to that of intracellular staining, so like intracellular staining, it reveals the overall shape of the cell. Immunocytochemical labelling using endogenous antigens known to be distributed in the cytoplasm of specific neurons produced inadequate control of selective contrast when prepared in this manner. Instead, 1–10μm sections cut from blocks of nervous tissue were embedded in polyethylene glycol, stained using a combedded in polyethylene glycol, stained using a combination of immunocytochemistry and histochemical intensification methods, and embedded in plastic on the grid. This method, which is also suited for staining with poorly penetrating markers such as colloidal gold, may also prove useful in a variety of other situations requiring the intensification of selective contrast.     

The use of silver nitrate as a stain for scanning electron microscopy of arterial intima and paraffin sections of kidney

The suitability of silver nitrate as a stain for scanning electron microscopy was investigated. Accordingly en face preparations of arterial intima were impregnated with silver nitrate, fixed with formalin, and coated with platinum-palladium alloy. In SEM images, the silver lines surrounding the endothelial cells, and the deposits on the intima appear as white lines or dots on a darker background. Similar results were noted for nitrocellulose-embedded endothelium. Paraffin sections of kidney treated with silver nitrate (von Kossa's stain) were also examined. Deposits of the calcium salts of phosphates and carbonates (stained with silver nitrate) were easily differentiated from other tissue components. Results were compared with those obtained with the light microscope. The scanning electron microscopic examination provided a finer definition of the silver granules relative to the surrounding architecture. The limitations and advantages of these techniques and possible further applications of silver nitrate as a stain for scanning electron microscopy are discussed. The use of silver nitrate as a stain for some SEM preparations is recommended.     

Automated identification of neurons and their locations

Individual locations of many neuronal cell bodies (>10⁴) are needed to enable statistically significant measurements of spatial organization within the brain such as nearest‐neighbour and microcolumnarity measurements. In this paper, we introduce an Automated Neuron Recognition Algorithm (ANRA) which obtains the (x, y) location of individual neurons within digitized images of Nissl‐stained, 30 μm thick, frozen sections of the cerebral cortex of the Rhesus monkey. Identification of neurons within such Nissl‐stained sections is inherently difficult due to the variability in neuron staining, the overlap of neurons, the presence of partial or damaged neurons at tissue surfaces, and the presence of non‐neuron objects, such as glial cells, blood vessels, and random artefacts. To overcome these challenges and identify neurons, ANRA applies a combination of image segmentation and machine learning. The steps involve active contour segmentation to find outlines of potential neuron cell bodies followed by artificial neural network training using the segmentation properties (size, optical density, gyration, etc.) to distinguish between neuron and non‐neuron segmentations. ANRA positively identifies 86 ± 5% neurons with 15 ± 8% error (mean ± SD) on a wide range of Nissl‐stained images, whereas semi‐automatic methods obtain 80 ± 7%/17 ± 12%. A further advantage of ANRA is that it affords an unlimited increase in speed from semi‐automatic methods, and is computationally efficient, with the ability to recognize ～100 neurons per minute using a standard personal computer. ANRA is amenable to analysis of huge photo‐montages of Nissl‐stained tissue, thereby opening the door to fast, efficient and quantitative analysis of vast stores of archival material that exist in laboratories and research collections around the world.     

Boolean random functions

A Boolean function f in Rⁿ is the supremum of upper semi-continuous random functions f'i which are almost surely positive, bounded with compact support and centred at the Poisson points (i). They generalize to functions of classical Boolean model for sets. The Boolean function f may be studied via its subgraph, i.e. as a random set in Rⁿ x R. The key notion is then the functional Q(Bt), i.e. the probability that a compact set Bt centred at altitude t misses the subgraph of f. The general expression of Q(Bt) is given, and followed by a series of important derivations (volumes, gradients, numbers of summits, etc). Theorems of structure are given: they concern the properties of infinite divisibility for the sup, and domains of attraction for Boolean functions. The last sections are devoted to the study of two particular Boolean functions; emphasis is put on the stereological implications of the approach. A critical example illustrates the theory.     

Descriptors of flatness and roughness

The two notions of flatness and roughness refer to local properties of the profiles and of the surfaces. They are defined in two- and three-dimensional spaces. Flatness is the ratio of the measure of the surface divided by its projection, and roughness the average of the square of the mean curvature of the surface per unit area. Whatever the number of dimensions of the space is, both parameters are accessible from vertical plane sections. The problem of their digital version is discussed, and algorithms are given. The approach also applies for grey tone functions, in R² and in R³. Finally the results are extended to the n-dimensional case.     

A detailed morphological study of the vomeronasal organ and the accessory olfactory bulb of cats

The organization of the vomeronasal system (VNS) of fetal, newborn, and adult cats was investigated by microdissection and microscopic examination of sections stained conventionally or with lectins (UEA-1, LEA) or antibodies against proteins Gα(i2) (associated with vomeronasal receptor type1) and Gα(o) (associated with receptor vomeronasal receptor type2). The feline VNS is morphologically similar to that of other mammals. Staining with lectins and anti-Gα(i2) was uniform throughout the sensory epithelium of the vomeronasal organ, and throughout the nervous and glomerular layers of the accessory olfactory bulb (AOB); anti-Gα(o) stained no VNS tissue. This organization places the cat together with several other domestic or farm animals (dog, horse, sheep, goat, pig) in a group of mammals with just a single path of communication between the sensory epithelium of the vomeronasal organ and AOB, in contrast to the two-path model found in rodents and other mammals (in which apical and basal sensory epithelium layers project to rostral and caudal AOB areas, respectively). However, the cat differs from the sheep and pig in that the development of its VNS is still incomplete at birth.     

Direct visualization of receptor arrays in frozen-hydrated sections and plunge-frozen specimens of E. coli engineered to overproduce the chemotaxis receptor Tsr

We have recently reported electron tomographic studies of sections obtained from chemically fixed E. coli cells overproducing the 60‐kDa chemotaxis receptor Tsr. Membrane extracts from these cells prepared in the presence of Tween‐80 display hexagonally close‐packed microcrystalline assemblies of Tsr, with a repeating unit large enough to accommodate six Tsr molecules arranged as trimers of receptor dimers. Here, we report the direct visualization of the Tsr receptor clusters in (i) vitrified cell suspensions of cells overproducing Tsr, prepared by rapid plunge‐freezing, and (ii) frozen‐hydrated sections obtained from cells frozen under high pressure. The frozen‐hydrated sections were generated by sectioning at ?150 °C using a diamond knife with a 25° knife angle, with nominal thicknesses ranging from 20 to 60 nm. There is excellent correspondence between the spatial arrangement of receptors in thin frozen‐hydrated sections and the arrangements found in negatively stained membrane extracts and plunge‐frozen cells, highlighting the potential of using frozen‐hydrated sections for the study of macromolecular assemblies within cells under near‐native conditions.     

Lamellar subcomponents of the cuticular cell membrane complex of mammalian keratin fibres show friction and hardness contrast by AFM

There is a substantial body of information indicating that 18‐methyleicosanoic acid (18‐MEA) is covalently linked to the outer surface of all mammalian keratin fibres and also forms the outer β‐layer of the cuticular cell membrane complex (CCMC) which separates the cuticle cells from each other. Low cohesive forces are expected between the lipid‐containing outer β‐layer and the δ‐layer of the CCMC, thus providing a weak point for cuticular delamination and presenting a fresh layer of 18‐MEA to the newly exposed surface. We have used lateral force microscopy and force modulation atomic force microscopy (AFM) to examine human hair fibres in which the non‐covalently linked fatty acids have been removed. Examination of the lateral force images of new cuticle surfaces revealed by the attrition of overlying cuticle layers showed three separate zones of clearly defined frictional contrast. These are thought to correspond with the δ‐layer, the proteinaceous epicuticle and outer β‐layers of the CCMC. The δ‐layer was found to have a thickness of 16 nm (SD = 1 nm, n = 25), comparable to the 18.0 nm thickness measured from transverse cross‐sections of fibres with transmission electron microscopy. Force modulation AFM showed that the outer β‐layer was softer than the epicuticle and the δ‐layer. The frictional contrast was removed following treatment with methanolic KOH (0.1 mol dm^?3) at 25 °C for 30 min, suggesting the hydrolysis of the thioester linkage and removal of 18‐MEA from the surface.     

Precision of area estimation: a numerical study

After listing some general formulae for sampling in n-dimensional space, the author considers the one-dimensional case: the estimation of the length of a line segment by counting the number of points that happen to fall within the segment. If the points are equidistantly located, the variance of the estimate is a strictly periodic function of the length of the segment. This systematic sample has a higher efficiency than simple and stratified random samples of the same intensity. With some modifications, the results carry over to the two-dimensional case: the estimation of the area of a plane figure by counting the number of sample points falling inside the figure. However, the strict periodicity of the variance in the one-dimensional systematic case is replaced by a ‘Zitterbewegung’. The magnitude of this oscillation is seen to be very different for figures of different shapes. Some results are presented also for the estimation of areas by line transects, and for the estimation of volumes by aid of lattices of points in R³, and R⁴. Some comments are also given on the practical implications of the results for sampling in the plane.     

Characterization of coals by automated optical image analysis 1. Vitrinite reflectance

An increasing awareness of the importance of petrographic characterization of coals to efficient selection of coals for pulverized coal combustion and metallurgical coking, has highlighted the need to improve slow and subjective optical microscopic procedures. Automated image-analysis procedures to measure vitrinite random reflectance are examined here in some detail, giving particular attention to inertinite-rich coals. It is shown by consideration of intra- and inter-particle reflectance variance that a given accuracy for vitrinite mean random reflectance (R_v) can be achieved by selection of an appropriate surface sampling procedure. The repeatability of R_v for single coals is similar to that for manual microscopy, but the reproducibility, as established by an international interchange exercise, is not yet good enough to specify a standard procedure. In some coals even vitrinite sub-macerals can be distinguished; however, caution is required when extending this method to vitrinite reflectance distributions of blends containing different rank coals or of heat-altered coals.     

Contrast in the transmission mode of a low-voltage scanning electron microscope

The contrast thicknesses (x_k) of thin carbon and platinum films have been measured in the transmission mode of a low-voltage scanning electron microscope for apertures of 40 and 100 mrad and electron energies (E) between 1 and 30 keV. The measured values overlap with those previously measured for E (≥ 17keV) in a transmission electron microscope. Differences in the decrease of x_k with decreasing E between carbon and platinum agree with Wentzel-Kramer-Brillouin calculations of the elastic cross-sections. Knowing the value of x_k allows the exponential decrease ∝ exp(—x/x_k) in transmission with increasing mass-thickness (x = ρt) of the specimen and the increasing gain of contrast for stained biological sections with decreasing electron energy to be calculated for brightfield and darkfield modes.     

Silver impregnation applied to striated muscle: The sarcoplasmic reticulum

The classical black reaction developed by Camillo Golgi is shown to impregnate the tubules and fenestrations of the sarcoplasmic reticulum (SR) in striated muscle. This is a double impregnation of chromate and silver, which usually fills extracellular spaces. The method is difficult insofar as long incubation times are required, and location of the successfully “stained” SR in plastic-embedded tissue blocks is unpredictable. The light microscope is absolutely necessary to find the good regions which can then be cut from the blocks in 1-μm-thick sections and examined in the electron microscope. Stereo pairs give the best results since these resolve overlap problems common to thick sections. A variety of artifacts are illustrated which can help avoid erroneous interpretations. The Golgi-“stained” SR shows this elusive network with unsurpassed contrast and should benefit the morphological studies of muscle-membrane enthusiasts.     

Applications of medium-voltage STEM for the 3-D study of organelles within very thick sections

Scanning transmission electron microscopy at 300 kV enables the visualization of nucleolar silver-stained structures within thick sections (3–8 μm) of Epon-embedded cells at high tilt angles (–50°; + 50°). Thick sections coated with gold particles were used to determine the best conditions for obtaining images with high contrast and good resolution. For a 6-μm-thick section the values of thinning and shrinkage under the beam are 35 to 10%, respectively. At the electron density used in these experiments (100e^—/Å₂/s) it is estimated that these modifications of the section stabilized in less than 10 min. The broadening of the beam through the section was measured and calculations indicated that the subsequent resolution reached 100 nm for objects localized near the lower side of 4-μm-thick sections with a spot-size of 5·6 nm. Comparing the same biological samples, viewed alternately in CTEM and STEM, demonstrated that images obtained in STEM have a better resolution and contrast for sections thicker than 3 μm. Therefore, the visualization of densely stained structures, observed through very thick sections in the STEM mode, will be very useful in the near future for microtomographic reconstruction of cellular organelles.