A note on the stereological implications of irregular spacing of sections

Stereological methods for serial sections traditionally assume that the sections are exactly equally spaced. In reality, the spacing and thickness of sections can be quite irregular. This may affect the validity and accuracy of stereological techniques, especially the Cavalieri estimator of volume. We present a new formula for the accuracy of the Cavalieri estimator that includes the effect of random variability in section spacing. A modest amount of variability in section spacing can cause a substantial increase in estimator variance.     

Comparison of human and animal femoral head chondral properties and geometries

Investigations into tissue-preserving orthopaedic treatments should consider the tribology of articular cartilage; where simulations using animal joints are a predominant choice. However, very few studies have investigated the differences between human and animal cartilage. The aim of the present study was to characterise the differences in geometry and mechanical properties of human, porcine, bovine and ovine articular cartilage. Creep indentation was performed on osteochondral plugs taken from the superior region of femoral heads of all these species. Cartilage thickness was measured via the resistive force change of a needle descending through cartilage and bone. A biphasic finite element model was used to derive equilibrium elastic modulus and permeability. Results showed that human cartilage was significantly thicker than all other species tested. A positive correlation was found between femoral head diameter and cartilage thickness when comparing between species of quadrupeds. Human cartilage had the largest equilibrium elastic modulus, which was significant when comparing against porcine and bovine. However, porcine cartilage had significantly lower permeability. Significant differences in geometry and mechanical properties of articular cartilage were found between all species tested. It is necessary to consider these variations when choosing animal tissue to represent human.     

Stereological estimation of surface area and barrier thickness of fish gills in vertical sections

Previous morphometric methods for estimation of the volume of components, surface area and thickness of the diffusion barrier in fish gills have taken advantage of the highly ordered structure of these organs for sampling and surface area estimations, whereas the thickness of the diffusion barrier has been measured orthogonally on perpendicularly sectioned material at subjectively selected sites. Although intuitively logical, these procedures do not have a demonstrated mathematical basis, do not involve random sampling and measurement techniques, and are not applicable to the gills of all fish. The present stereological methods apply the principles of surface area estimation in vertical uniform random sections to the gills of the Brazilian teleost Arapaima gigas. The tissue was taken from the entire gill apparatus of the right‐hand or left‐hand side (selected at random) of the fish by systematic random sampling and embedded in glycol methacrylate for light microscopy. Arches from the other side were embedded in Epoxy resin. Reference volume was estimated by the Cavalieri method in the same vertical sections that were used for surface density and volume density measurements. The harmonic mean barrier thickness of the water‐blood diffusion barrier was calculated from measurements taken along randomly selected orientation lines that were sine‐weighted relative to the vertical axis. The values thus obtained for the anatomical diffusion factor (surface area divided by barrier thickness) compare favourably with those obtained for other sluggish fish using existing methods.     

Depth-dependent anisotropies of amides and sugar in perpendicular and parallel sections of articular cartilage by Fourier transform infrared imaging

Full thickness blocks of canine humeral cartilage were microtomed into both perpendicular sections and a series of 100 parallel sections, each 6 μm thick. Fourier transform infrared (IR) imaging was used to image each tissue section eleven times under different IR polarizations (from 0° to 180° polarization states in 20° increments and with an additional 90° polarization), at a spatial resolution of 6.25 μm and a wavenumber step of 8 cm^?1. With increasing depth from the articular surface, amide anisotropies increased in the perpendicular sections and decreased in the parallel sections. Both types of tissue sectioning identified a 90° difference between amide I and amide II in the superficial zone (SZ) of cartilage. The fibrillar distribution in the parallel sections from the SZ was shown to not be random. Sugar had a weak but recognizable anisotropy in the upper part of the radial zone (RZ) in the perpendicular sections. The depth‐dependent anisotropic data were fitted with a theoretical equation that contained three signature parameters, which illustrate the arcade structure of collagens with the aid of a fibril model. Fourier‐transform IR imaging of both perpendicular and parallel sections provides the possibility of determining the three‐dimensional macromolecular structures in articular cartilage. Being sensitive to the orientation of the macromolecular structure in healthy articular cartilage aids the prospect of detecting the early onset of the tissue degradation that may lead to pathological conditions such as osteoarthritis. Microsc. Res. Tech. 74:122–132, 2011. © 2010 Wiley‐Liss, Inc.     

Spatial and temporal changes of subchondral bone proceed to articular cartilage degeneration in rats subjected to knee immobilization

This study was aimed to investigate the spatial and temporal changes of subchondral bone and its overlying articular cartilage in rats following knee immobilization. A total of 36 male Wistar rats (11–13 months old) were assigned randomly and evenly into 3 groups. For each group, knee joints in 6 rats were immobilized unilaterally for 1, 4, or 8 weeks, respectively, while the remaining rats were allowed free activity and served as external control groups. For each animal, femurs at both sides were dissected after sacrificed. The distal part of femur was examined by micro‐CT. Subsequently, femoral condyles were collected for further histological observation and analysis. For articular cartilage, significant changes were observed only at 4 and 8 weeks of immobilization. The thickness of articular cartilage and chondrocytes numbers decreased with time. However, significant changes in subchondral bone were defined by micro‐CT following immobilization in a time‐dependent manner. Immobilization led to a thinner and more porous subchondral bone plate, as well as a reduction in trabecular thickness and separation with a more rod‐like architecture. Changes in subchondral bone occurred earlier than in articular cartilage. More importantly, immobilization‐induced changes in subchondral bone may contribute, at least partially, to changes in its overlying articular cartilage. Microsc. Res. Tech. 79:209–218, 2016. © 2016 Wiley Periodicals, Inc.     

Stereological estimation of eye volume using the Pappus method

The estimation of object volume from rotationally randomised sections relies on an ancient geometrical principle due to the Alexandrian mathematician Pappus. In this paper we describe two studies that make estimates of eye volume using a stereological version of the Pappus principle. The first study uses a design-based version of the Pappus theorem to make estimates of eye volume in Sprague–Dawley rats and the second uses a model-based implementation for estimating eye volume in juvenile Dover sole. In the sole study we compare the estimates of volume with estimates made using the Cavalieri method and show that the Pappus method gives identical volume estimates with a markedly lower coefficient of variation (2.5%) than the Cavalieri method (13.5%).     

Prediction of the variance of stereological volume estimates from systematic sections using computer-intensive methods

The Cavalieri method is an unbiased estimator of the total volume of a body from its transectional areas on systematic sections. The coefficient of error (CE) of the Cavalieri estimator was predicted by a computer‐intensive method. The method is based on polynomial regression of area values on section number and simulation of systematic sectioning. The measurement function is modelled as a quadratic polynomial, with an error term superimposed. The relative influence of the trend and the error component is estimated by techniques of analysis of variance. This predictor was compared with two established short‐cut estimators of the CE based on transitive theory. First, all predictors were applied to data sets from six deterministic models with analytically known CE. For these models, the CE was best predicted by the older short‐cut estimator and by the computer‐intensive approach, if the measurement function had finite jumps. The best prediction was provided by the newer short‐cut estimator when the measurement function was continuous. The predictors were also applied to published empirical datasets. The first data set consisted of 10 series of areas of systematically sectioned rat hearts with 10–13 items, the second data set consisted of 13 series of systematically sampled transectional areas of various biological structures with 38–90 items. On the whole, similar mean values for the predicted CE were obtained with the older short‐cut estimator and the computer‐intensive method. These ranged in the same order of magnitude as resampling estimates of the CE from the empirical data sets, which were used as a cross‐check. The mean values according to the newer short‐cut CE estimator ranged distinctly lower than the resampling estimates. However, for individual data sets, it happened that the closest prediction as compared to the cross‐check value could be provided by any of the three methods. This finding is discussed in terms of the statistical variability of the resampling estimate itself.     

The interface region between articular cartilage and bone by μMRI and PLM at microscopic resolutions

This dual-modality microscopic imaging study quantifies the interface region between the noncalcified cartilage and the subchondral bone plate, which includes the deep portion of the noncalcified articular cartilage and the zone of calcified cartilage (ZCC). This interface region is typically not visible in routine MRI but becomes visible in MRI with the application of an ultra-short echo time (UTE) sequence. A number of cartilage-bone blocks from a well-documented canine humeral head were harvested for imaging by microscopic MRI (μMRI) and PLM (polarized light microscopy). In μMRI, T2 anisotropic images were acquired by 2D gradient-echo, magnetization-prepared spin-echo and UTE sequences at the 0° and 55° (the magic angle) orientations at 11.7 μm/pixel resolution. In PLM, quantitative optical retardation (nm) and collagen orientation (°) were mapped from the thin sections from the same μMRI specimens at 0.5–2 μm pixel resolutions. The orientational and organizational architecture of the collagen matrix in this interface region was quantified and correlated between the complementary imaging. The magic angle effect as seen in the noncalcified cartilage was statistically confirmed in ZCC in μMRI, which was further supported by quantitative PLM. With an enhanced understanding of the tissue properties in this important interface region, it will potentially be possible to monitor the changes of this tissue region which is instrumental to the initiation and development of osteoarthritis and other joint diseases.     

Unbiased estimation of human body composition by the Cavalieri method using magnetic resonance imaging

The classical methods for estimating the volume of human body compartments in vivo (e.g. skin-fold thickness for fat, radioisotope counting for different compartments, etc.) are generally indirect and rely on essentially empirical relationships — hence they are biased to unknown degrees. The advent of modern non-invasive scanning techniques, such as X-ray computed tomography (CT) and magnetic resonance imaging (MRI) is now widening the scope of volume quantification, especially in combination with stereological methods. Apart from its superior soft tissue contrast, MRI enjoys the distinct advantage of not using ionizing radiations. By a proper landmarking and control of the scanner couch, an adult male volunteer was scanned exhaustively into parallel systematic MR ‘sections’. Four compartments were defined, namely bone, muscle, organs and fat (which included the skin), and their corresponding volumes were easily and efficiently estimated by the Cavalieri method: the total section area of a compartment times the section interval estimates the volume of the compartment without bias. Formulae and nomograms are given to predict the errors and to optimize the design. To estimate an individual's muscle volume with a 5% coefficient of error, 10 sections and less than 10min point counting (to estimate the relevant section areas) are required. Bone and fat require about twice as much work. To estimate the mean muscle volume of a population with the same error contribution, from a random sample of six subjects, the workload per subject can be divided by √6, namely 4 min per subject. For a given number of sections planimetry would be as accurate but far more time consuming than point counting.     

Chondrocytes interconnecting tracks and cytoplasmic projections observed within the superficial zone of normal human articular cartilage--a transmission electron microscopy, atomic force microscopy, and two-photon excitation microscopy studies

The morphology of the normal human and rat articular cartilage was assessed using transmission electron microscopy (TEM), atomic force microscopy (AFM), and two-photon excitation (2PE) microscopy. Spurr-embedded sections from fixed human cartilage were simultaneously evaluated using TEM and AFM. The presences of tracks among the chondrocytes from the superficial zone of the cartilage were observed. In order to ratify the presence of interconnecting tracks among superficial zone chondrocytes, whole fixed human and rat cartilage, as well as fresh whole rat cartilage, were examined under the 2PE. In all cases, these tracks were observed. In addition, porous matrix, well-defined lacunae, and cytoplasmic projections anchored to the extracellular matrix (ECM) were also detected. We conclude that normal human and rat flattened superficial chondrocytes might be interconnected by tracks running through the ECM. In addition, cytoplasmic projections were observed anchored to the ECM. All these structures may possibly be related to cell/cell and ECM/chondrocytes signaling. Our findings provide new information that possibly will be of relevant importance for a more profound study of normal cartilage physiology and eventually, the pathogenesis of osteoarthritis.     

Correlation between friction of articular cartilage and reflectance intensity from superficial images

The lubrication mechanism of articular cartilage is characterized by an efficient performance. In this work, friction of articular cartilage was evaluated with in-site images of articular surface. The images were captured with the laser light reflected at the interface between a prism and articular cartilage. The attenuation of reflectance was associated with the increase of the contact of collagen network of articular cartilage. The light reflectance and friction coefficient for short sliding presented a significant positive correlation. Friction tests were also carried out for short (30 s) and long (300 s) preloading times. The results indicate that depletion of fluid film is responsible for the increase of friction and the recovery of the fluid film was observed for the long preloading after the early stage of sliding.     

Imaging of the Surface of Human and Bovine Articular Cartilage with ESEM and AFM

The surface of human and bovine articular cartilage was imaged with environmental SEM and AFM. The effective modulus of the surface, from force--distance curves obtained with AFM, remained constant at 9±2 kPa in the presence of synovial fluid. Extensive washing of the cartilage surface with phosphate buffered saline (PBS) removed a superficial gel-like layer, leaving a granular layer intact. Force--distance curves showed that the chemical and mechanical properties of the gel exposed to PBS changed over time. The effective modulus at the surface dropped from 481 to 4 kPa over an hour. The results suggest that the gel-like layer, having partly lost water through evaporation on removal from the joint, absorbs water from PBS. It becomes softer and eventually begins to dissolve. The low effective modulus of the gel-like layer in synovial fluid indicates that it is too soft to influence the surface roughness. Imprints of the surface under pressure were taken using a low viscosity dental kit. Imaging of the imprint surface indicated that the topography of the cartilage under pressure was similar to that of the surface after removal of the gel-like layer. In conclusion, imaging of articular cartilage with ESEM and AFM revealed two distinct non-fibrous layers, which are granular and gel-like, and cover the fibrous collagen matrix.     

Head replacement, head rotation, and surface damage effects on metal-on-metal total hip replacements: a hip simulator study

The possibility of replacing the femoral head alone, in either solid or articular surface replacement form, during revision operations on metal-on-metal total hip replacements remains an attractive feature of such implants. In the present investigation, laboratory simulator studies of the influence upon volumetric wear of inserting a new femoral head, of introducing some head rotation, and of damaging the femoral head by scratches have all been explored. New and rotated heads both involve an additional running-in period, but the experimental studies show that the volumetric wear associated with this process is less than the initial running-in wear. The beneficial effects upon volumetric wear of small clearances have been confirmed, while the processing of high-carbon Co-Cr-Mo materials appears to be much less influential. Scratches did not affect wear as much as head replacement or head rotation, but the ongoing wear rates were somewhat higher.     

The Fractal Structure of Equine Articular Cartilage

The naturally occurring structure of articular cartilage has proven to be an effective means for the facilitation of motion and load support in equine and other animal joints. Cartilage has been found to be a complex and dynamic medium, which has led to an incomplete understanding of the nature and operating mechanisms acting within a joint. Although cartilage has biphasic and triphasic properties, it is believed that the performance of equine articular joints is influenced by the surface roughness of the joint cartilage (Ateshian et al., '98; Chan et al., 2011; Yao and Unsworth, '93). Various joint types with different motions and regimes of lubrication have altered demands on the articular surface that may affect cartilage surface properties. In research performed on freshly harvested samples, equine articular cartilage has been shown to possess a multiscale structure and a fractal dimension. It is thought that by determining the fractal dimension (D) of articular cartilage, a better understanding of the friction, wear, and lubrication mechanisms for biomechanic surfaces can eventually be reached. This study looks at the fractal dimensions of three different articular cartilage surfaces in the equine carpus: the radiocarpal, midcarpal, and carpometacarpal surfaces. The three surfaces provide an ideal comparison of fractal dimensions for a different range of motion, geometry, and loading. In each sample, identical treatment was performed during measurement by a stylus profilometer. SCANNING 34: 418–426, 2012. © 2012 Wiley Periodicals, Inc.     

Autologous resurfacing

Background: There is a discrepancy between the interest in joint‐reconstructions and the current knowledge about the healing‐processes involved. Major reconstructions are performed with osteosynthesized allografts and fresh allografts for cartilage. Objectives: The main question to be answered is: what do we know about metaphyseal and epiphyseal cancellous bone healing, contact healing of the subchondral bone and its influence on cartilage healing? Can we achieve healing of all four compartments in contact? Purpose: The purpose is to systematically investigate through animal testing the healing processes of metaphyseal and epiphyseal bone, including the subchondral bone and the healing of cartilage of press‐fit‐inserted grafts, considering nondemineralized high‐resolution histology. Material and Methods: Primary cancellous‐bone healing of osteosynthesized hemi‐osteotomies was studied in 13 canine tibial heads, the contact healing was investigated in 7 dogs and 18 giant‐rabbits comparing contact‐healing of press‐fit‐inserted autologs cylindrical grafts with empty defects applying the wet‐grinding diamond‐technology. Bench‐experiments on the epiphyseal bones of swine including pullout‐tests of cylindrical grafts formed the basis for validation of that press‐fit diamond technology. Results: Primary metaphyseal and epiphyseal contact healing, including hyaline cartilage, was found in all compartments of the meta‐and epiphysis in the precisely performed experiments. The press‐fit principle, which employs cylindrical grafts and diamond instrumentation featuring a difference of 15/100 mm between graft and recipient bed, achieved high loads between 73.48 and 178.95 N (mean value 118.16 and standard deviation 32.79) in the pullout tests. Conclusion: Autologous press‐fit grafting with alignment of the bony baseplate using wet‐grinding precision has attained promising histo‐morphological results. Microsc. Res. Tech., 78:40–51, 2015. © 2014 Wiley Periodicals, Inc.     

Alteration of cartilage matrix morphology with histological processing

An interlacunar network in the extracellular matrix of femoral head articular cartilage of neontal rats was seen by light microscopy to: (1) consist of elements, 0·5 μm thick, which occurred as individual elements, as bundles of elements, and as fused elements, (2) stain intensely with toluidine blue, methylene blue, and safranin O, and (3) connect chondrocytes by inserting on the chondrocyte capsules which were composed of morphologically and cytochemically similar material. By electron microscopy, the single elements were seen to be composed of thicker, denser staining areas of the honeycomb appearing matrix and the fused elements appeared as non-membrane bound channels containing granular material. Articular cartilage was processed using combinations of fixatives, dehydrating agents, and embedding media. Regardless of fixation, demineralization, or embedding, the network was not seen after dehydration of the cartilage with methanol, ethanol, acetone or tert-butanol but was seen after dehydration with aqueous solutions of glycol methacrylate, propylene oxide, 2-propanol or 2,2-dimethoxypropane. Network visualization following a variety of methods demonstrated that no single fixative, dehydrating agent, or embedding medium caused its formation. The presence of the network in different cartilage zones, its consistent morphology by light and electron microscopy, the uniformity of the elements in their connection with the chondrocytes, and presence in fresh-frozen sections suggest the network may be real, but rigorous evidence for its existence in vivo is still required. Since cartilage morphology was altered by histological methods, especially dehydration, common methods used in studying connective tissue matrix should be evaluated to determine their effect on matrix morphology.     

Design-based estimation of surface area in thick tissue sections of arbitrary orientation using virtual cycloids

Surface area is a first‐order stereological parameter with important biological applications, particularly at the intersection of biological phases. To deal with the inherent anisotropy of biological surfaces, state‐of‐the‐art design‐based methods require tissue rotation around at least one axis prior to sectioning. This paper describes the use of virtual cycloids for surface area estimation of objects and regions in thick, transparent tissue sections cut at any arbitrary (convenient) orientation. Based on the vertical section approach of Baddeley et al., the present approach specifies the vertical axis as the direction of sectioning (i.e. the direction perpendicular to the tissue section), and applies computer‐generated cycloids (virtual cycloids) with their minor axis parallel to the vertical axis. The number of surface‐cycloid intersections counted on focal planes scanned through the z‐axis is proportional to the surface area of interest in the tissue, with no further assumptions about size, shape or orientation. Optimal efficiency at each x–y location can be achieved by three virtual cycloids orientated with their major axes (which are parallel to the observation planes) mutually at an angle of 120°. The major practical advantage of the present approach is that estimates of total surface area (S) and surface density (S_V) can be obtained in tissue sections cut at any convenient orientation through the reference space.     

Estimating mean particle volume and number from random sections by sampling profile boundaries

We describe some new shape-independent stereological estimates of particle mean volume and surface area. Finding volumes or surface areas of cell nuclei, from electron micrographs of random thin sections, is a central problem of biological stereology. The well-known point-sampled intercept (PSI) method samples profile interiors to find the volume-weighted mean volume. This can be used in place of the true mean volume, but to do so introduces bias when volumes vary a great deal, as they do in fixed specimens. Jensen and Gundersen quite recently extended the PSI estimator to provide particle surface area, with no bias in the case of uniform surface areas. Here we extend the PSI volume estimator in a different way, sampling profile boundaries rather than their interiors. We obtain a boundary-sampled intercept (BSI) volume estimator, simpler than the PSI surface area estimator, but also unbiased for uniform surface areas. Both of these estimators are attractive, for example, in measuring and counting cell nuclei, where membrane surface area varies less than volume. Furthermore, they have no shape bias whatsoever. This paper also examines the general relationship between boundary- and area-sampled estimates, and we clarify the formal connection between our volume estimator and the PSI surface area estimator. We also calculate and compare their theoretical efficiencies.     

Utilizing confocal microscopy to measure refractive index of articular cartilage

This study proposes a method for measuring the refractive index of articular cartilage within a thin and small specimen slice. The cartilage specimen, with a thickness of about 50 μm, was put next to a thin film of immersion oil of similar thickness. Both the articular cartilage and immersion oil were scanned along the depth direction using a confocal microscope. The refractive index mismatch between the cartilage and the immersion oil induced a slight axial deformation in the confocal images of the cartilage specimen that was accurately measured by a subpixel edge‐detection‐based technique. A theoretical model was built to quantify the focal shift of confocal microscopy caused by the refractive index mismatch. With the quantitative deformations of cartilage images and the quantified function of focal shift, the refractive index of articular cartilage was accurately interpolated. At 561 nm, 0.1 MPa and 20 °C, the overall refractive index of the six cartilage plugs was 1.3975 ± 0.0156. The overall coefficient of variation of all cartilage specimens was 0.68%, which indicated the high repeatability of our method. The verification experiments using distilled water showed a minimal relative error of 0.02%.     

Quantitative zonal differentiation of articular cartilage by microscopic magnetic resonance imaging,polarized light microscopy,and Fourier‐transform infrared imaging

This study aimed to synchronize the zonal differentiation of the full‐thickness articular cartilage by three micro‐imaging techniques, namely microscopic magnetic resonance imaging (µMRI), polarized light microscopy (PLM), and Fourier‐transform infrared imaging (FTIRI). Eighteen cartilage‐bone blocks from three canine humeral joints were imaged by: (a) µMRI T₂ relaxation at 0° and 55° orientations in a 7 T magnetic field, (b) PLM optical retardation and azimuthal angle, and (c) FTIRI amide I and amide II anisotropies at 0° and 90° polarizations relative to the articular surface. In addition, µMRI T₁ relaxation was imaged before and after the tissue being immersed in gadolinium (contrast agent) solution, to calculate the proteoglycan concentration. A set of previously established criteria in cartilage imaging was revised. The new criteria could simultaneously correlate the thicknesses of the three consecutive subtissue zones in articular cartilage among these imaging techniques. Microsc. Res. Tech. 76:625–632, 2013. © 2013 Wiley Periodicals, Inc.