A comparison between micro-CT and histology for the evaluation of cortical bone: effect of polymethylmethacrylate embedding on structural parameters

Cortical bone microstructure is an important parameter in the evaluation of bone strength. The aim of this study was to validate the characterization of human cortical bone microarchitecture using microcomputed tomography. In order to do this, microcomputed tomography structural measurements were compared with those obtained through histological examination (the gold standard). Moreover, to calculate structural parameters, microcomputed tomography images have to be binarized with the separation between bone and nonbone structures throughout a global thresholding. As the effect of the surrounding medium on the threshold value is not clear, an easy procedure to find the global uniform threshold for a given acquisition condition is applied. This work also compared the structural parameters of microcomputed tomography cortical sample scan in air or embedded in polymethylmethacrylate; histology was used as a reference. For each acquisition condition, a fixed threshold value was found and was applied on the corresponding microcomputed tomography image for the parameters assessment. Twenty cortical bone samples were collected from human femur and tibia diaphyses. All samples were microcomputed tomography scanned in air, embedded in polymethylmethacrylate, rescanned by microcomputed tomography, examined by histology and finally compared. A good correspondence between the microcomputed tomography images and the histological sections was found. Paired comparisons in cortical porosity, Haversian canal diameter and Haversian canal separation between histological sections and microcomputed tomography cross sections, first in air and then embedded in PolyMethylMethAcrylate, were made: no significant differences were found. None of the comparisons showed significant differences for cortical porosity, Haversian canal diameter and Haversian separation over a three-dimensional volume of interest, between microcomputed tomography scans in air and with samples embedded in PolyMethylMethAcrylate. The very good correlation between bone structural measures obtained from microcomputed tomography datasets and from two-dimensional histological sections confirms that microcomputed tomography may be an efficient tool for the characterization of cortical bone microstructure. Moreover, when the corresponding threshold value for each condition is used, structural parameters determined by microcomputed tomography are not affected by the surrounding medium (PolyMethylMethAcrylate).     

A physical phantom for the calibration of three-dimensional X-ray microtomography examination

X‐ray microtomography is rapidly gaining importance as a non‐destructive investigation technique, especially in the three‐dimensional examination of trabecular bone. Appropriate quantitative three‐dimensional parameters describing the investigated structure were introduced, such as the model‐independent thickness and the structure model index. The first parameter calculates a volume‐based thickness of the structure in three dimensions independent of an assumed structure type. The second parameter estimates the characteristic form of which the structure is composed, i.e. whether it is more plate‐like, rod‐like or even sphere‐like. These parameters are now experiencing a great diffusion and are rapidly growing in importance. To measure the accuracy of these three‐dimensional parameters, a physical three‐dimensional phantom containing different known geometries and thicknesses, resembling those of the examined structures, is needed. Unfortunately, such particular phantoms are not commonly available and neither does a consolidated standard exist. This work describes the realization of a calibration phantom for three‐dimensional X‐ray microtomography examination and reports an application example using an X‐ray microtomography system. The calibration phantom (external size 13 mm diameter, 23 mm height) was based on various aluminium inserts embedded in a cylinder of polymethylmethacrylate. The inserts had known geometries (wires, foils, meshes and spheres) and thicknesses (ranging from 20 µm to 1 mm). The phantom was successfully applied to an X‐ray microtomography device, providing imaging of the inserted structures and calculation of three‐dimensional parameters such as the model‐independent thickness and the structure model index. With the indications given in the present work it is possible to design a similar phantom in a histology laboratory and to adapt it to the requested applications.     

Non-destructive characterization of deer (Cervus Elaphus) antlers by X-ray microtomography coupled with image analysis

X-ray microtomography coupled with image analysis was tested as a non-destructive alternative method for the textural characterization of the trabecular part of deer antlers ( Cervus Elaphus ). As gas adsorption and mercury intrusion cannot be applied on this soft and spongy material, its pore texture was, up to now, determined from histological sections that give only two-dimensional information. In this work, X-ray microtomography is used to scan entire or half pieces of antlers and three-dimensional image analysis is performed in order to assess the differences between samples collected at various antler locations. Results clearly show a porosity profile along the sample diameter. The pore size distribution is showed to be dependent on the sample original site.     

Methodological principles for fractal analysis of trabecular bone

A standardized methodology for the fractal analysis of histological sections of trabecular bone has been established.
A modified box counting method has been developed for use on a PC-based image analyser. The effect of image analyser settings, magnification, image orientation and threshold levels was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to calculate objectively more than one fractal dimension from the modified Richardson plot.
The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ < 25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0.
It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than one fractal dimension, describing spatial structural entities. Fractal analysis is a model-independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and complements conventional histomorphometric and stereological techniques.     

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.     

Smooth surface micro finite element modelling of a cancellous bone analogue material

Tetrahedral finite element meshes with smooth surfaces can be created from computed tomography scans of cancellous bone in order to evaluate its mechanical properties. Image processing before creation of the mesh can affect the accuracy of determined mechanical properties. For a cancellous bone analogue, threshold, mesh density and surface smoothing parameters used in mesh generation were varied and the mechanical properties predicted by the resulting meshes were compared to experimental results. This study has shown that threshold selection is vital for accurate determination of volume fraction and resulting mechanical properties.     

Limitations of using micro-computed tomography to predict bone-implant contact and mechanical fixation

Fixation of metallic implants to bone through osseointegration is important in orthopaedics and dentistry. Model systems for studying this phenomenon would benefit from a non-destructive imaging modality so that mechanical and morphological endpoints can more readily be examined in the same specimens. The purpose of this study was to assess the utility of an automated microcomputed tomography (μCT) program for predicting bone-implant contact (BIC) and mechanical fixation strength in a rat model. Femurs in which 1.5-mm-diameter titanium implants had been in place for 4 weeks were either embedded in polymethylmethacrylate (PMMA) for preparation of 1-mm-thick cross-sectional slabs (16 femurs: 32 slabs) or were used for mechanical implant pull-out testing (n= 18 femurs). All samples were scanned by μCT at 70 kVp with 16 μm voxels and assessed by the manufacturer's software for assessing 'osseointegration volume per total volume' (OV/TV). OV/TV measures bone volume per total volume (BV/TV) in a 3-voxel-thick ring that by default excludes the 3 voxels immediately adjacent to the implant to avoid metal-induced artefacts. The plastic-embedded samples were also analysed by backscatter scanning electron microscopy (bSEM) to provide a direct comparison of OV/TV with a well-accepted technique for BIC. In μCT images in which the implant was directly embedded within PMMA, there was a zone of elevated attenuation (>50% of the attenuation value used to segment bone from marrow) which extended 48 μm away from the implant surface. Comparison of the bSEM and μCT images showed high correlations for BV/TV measurements in areas not affected by metal-induced artefacts. In addition for bSEM images, we found that there were high correlations between peri-implant BV/TV within 12 μm of the implant surface and BIC (correlation coefficients ≥0.8, p < 0.05). OV/TV as measured on μCT images was not significantly correlated with BIC as measured on the corresponding bSEM images. However, OV/TV was significantly, but weakly, correlated with implant pull-out strength (r= 0.401, p= 0.049) and energy to failure (r= 0.435, p= 0.035). Thus, the need for the 48-μm-thick exclusion zone in the OV/TV program to avoid metal-induced artefacts with the scanner used in this study means that it is not possible to make bone measurements sufficiently close to the implant surface to obtain an accurate assessment of BIC. Current generation laboratory-based μCT scanners typically have voxel sizes of 6-8 μm or larger which will still not overcome this limitation. Thus, peri-implant bone measurements at these resolutions should only be used as a guide to predict implant fixation and should not be over-interpreted as a measurement of BIC. Newer generation laboratory-based μCT scanners have several improvements including better spatial resolution and X-ray sources and appear to have less severe metal-induced artefacts, but will need appropriate validation as they become available to researchers. Regardless of the μCT scanner being used, we recommend that detailed validation studies be performed for any study using metal implants because variation in the composition and geometry of the particular implants used may lead to different artefact patterns.     

The application of heat‐deproteinization to the morphological study of cortical bone: A contribution to the knowledge of the osteonal structure

Observation of heat‐deproteinized cortical bone specimens in incident light enabled the high definition documentation of the osteonal pattern of diaphyseal Haversian bone. This prompted a study to compare these images with those revealed by polarized light microscopy, carried out either on decalcified or thin, undecalcified, resin‐embedded sections. Different bone processing methods can reveal structural aspects of the intercellular matrix, depending on the light diffraction mode: birefringency in decalcified sections can be ascribed to the collagen fibrils orientation alone; in undecalcified sections, to both the ordered layout of collagen and the inorganic phase; in the heat‐deproteinized samples, exclusively to the hydroxyapatite crystals aggregation mode. The elemental chemical analysis documented low content of carbon and hydrogen, no detectable levels of nitrogen and significantly higher content of calcium and phosphorus in heat‐deproteinized samples, as compared with dehydrated controls. In both samples, the X‐ray diffraction (XRD) pattern did not show any significant difference in pattern of hydroxyapatite, with no peaks of any possible decomposition phases. Scanning electron microscopic (SEM) morphology of heat‐deproteinized samples could be documented with the fracturing technique facilitated by the bone brittleness. The structure of crystal aggregates, oriented in parallel and with marks of time periods, was documented. Comparative study of deproteinized and undecalcified samples showed that the matrix inorganic phase did not undergo a coarse grain thermal conversion until it reached 500°C, maintaining the original crystals structure and orientation. Incident light stereomicroscopy, combined with SEM analysis of deproteinized bone fractured surfaces, is a new enforceable technique which can be used in morphometric studies to improve the understanding of the osteonal dynamics. Microsc. Res. Tech. 79:691–699, 2016. © 2016 Wiley Periodicals, Inc.     

Feasibility of detecting trabecular bone around percutaneous titanium implants in rabbits by in vivo microfocus computed tomography

Objectives: The goal of this study was to examine the feasibility of in vivo imaging of trabecular bone around titanium implants by means of microfocus computed tomography (micro‐CT) and the use of rabbits for this purpose. Materials and Methods: Ten male rabbits type Hollander, received a titanium implant (1.7 mm diameter and 10 mm length) in the trabecular bone of the left tibia. Seven weeks later a micro‐CT scan was taken. Four rabbits were used to monitor potential harmful effects from X‐ray absorption until 4 weeks after scanning. A second group of six rabbits was used for testing the hypothesis that a good correlation exists between in vivo micro‐CT images and histological images of trabecular bone around titanium implants. The six rabbits were scanned and sacrificed immediately. The tibias were extracted and submitted to standard histological procedures. This resulted in a total of 12 histological sections and their corresponding 12 micro‐CT images. Bone area measurements were performed at the left and right side of the implant in three regions: 0–500, 500–1000 and 1000–1500 μm distance from the implant interface. Intra‐class correlations (ICC) were calculated between both techniques. Results: The four rabbits did not show any sign of radiodermatitis 4 weeks after scanning. In the micro‐CT images of the group of six rabbits, trabeculae are visible, but not well defined, due to the presence of noise in the image. The ICC for the right implant side were 0.44 for zone 0–500 μm, 0.48 for zone 500–1000 μm and 0.40 for zone 1000–1500 μm. The ICC for the left implant side could not be calculated. Conclusion: A low agreement was found between the bone measurements from histology and in vivo micro‐CT images. The use of the in vivo micro‐CT for trabecular bone imaging around metallic implants should be restricted to track tendencies in follow‐up studies.     

Elemental distributions in femoral bone of rat under osteoporosis preventive treatments

One of the abnormalities of bone architecture is osteoporosis as occurring in post‐menopausal women. Especially long bones, such as femur, become more fragile and more prone to fracture. The efficiency of several osteoporosis preventative treatments based on oestrogen and progestin in bone structure and mineral recovery was studied using ovariectomized Wistar rats as an osteoporosis experimental model. Diagonal cross‐sections of the proximal epiphysis of femoral bones were analysed using nuclear microscopy techniques in order to map and determine the concentration profiles of P, Ca, S, Fe and Zn from the epiphysis to diaphysis and across the cortical and trabecular bone structures. In control animals (not ovariectomized), the S and Zn contents significantly characterized differences between cortical and trabecular bone structures, whereas P and Ca showed increased gradients from the epiphyseal region to the diaphysis. After ovariectomy the differences observed were differential according to the type of hormonal supplementation. A significant decrease in P and Ca contents and depletion of minor and trace minerals, such as S, Fe and Zn, were found for both cortical and trabecular bone structures after ovariectomy relative to controls. Bone mineral contents were reversed to control levels by synthetic oestrogen supplementation, and combined oestrogen and progesterone treatment. Recovery was more evident in the femoral epiphysis and neck than in the diaphysis. The use of oestrogen alone did not lead to bone recovery after ovariectomy. Alterations in bone mineral composition observed for animals receiving synthetic oestrogen and combined oestrogen and progesterone supplement might reflect beneficial structural changes in critical regions of long bones, mostly affected in post‐menopausal osteoporosis.     

Automated reconstruction of curvilinear fibres from 3D datasets acquired by X-ray microtomography

The characterization of fibrous structures is important in both composites and textiles research for relating to the bulk properties of the material. However, the microscopic nature of the fibres and their high densities make them very difficult to characterize. Many techniques have been developed for the measurement and characterization of fibrous structures but they tend to be restricted to measurements on the sample surface or within physical cross‐sections. X‐ray microtomography can be used to non‐destructively probe the internal structure of a range of fibrous materials, providing large amounts of 3D data. A technique has been developed for tracing fibres within 3D datasets acquired by X‐ray microtomography and this has been applied to a glass fibre reinforced composite and also a non‐woven textile sample. The 3D fibrous structures of both samples were successfully reconstructed and their fibre orientation distributions calculated. This technique enables novel characterizations, such as the through‐thickness variation of fibre orientation in non‐wovens.     

Imaging connected porosity of crystalline rock by contrast agent‐aided X‐ray microtomography and scanning electron microscopy

We set out to study connected porosity of crystalline rock using X‐ray microtomography and scanning electron microscopy with energy dispersive X‐ray spectroscopy (SEM‐EDS) with caesium chloride as a contrast agent. Caesium is an important radionuclide regarding the final deposition of nuclear waste and also forms dense phases that can be readily distinguished by X‐ray microtomography and SEM‐EDS. Six samples from two sites, Olkiluoto (Finland) and Grimsel (Switzerland), where transport properties of crystalline rock are being studied in situ, were investigated using X‐ray microtomography and SEM‐EDS. The samples were imaged with X‐ray microtomography, immersed in a saturated caesium chloride (CsCl) solution for 141, 249 and 365 days and imaged again with X‐ray microtomography. CsCl inside the samples was successfully detected with X‐ray microtomography and it had completely penetrated all six samples. SEM‐EDS elemental mapping was used to study the location of caesium in the samples in detail with quantitative mineral information. Precipitated CsCl was found in the connected pore space in Olkiluoto veined gneiss and in lesser amounts in Grimsel granodiorite. Only a very small amount of precipitated CsCl was observed in the Grimsel granodiorite samples. In Olkiluoto veined gneiss caesium was found in pinitised areas of cordierite grains. In the pinitised areas caesium was found in notable excess compared to chloride, possibly due to the combination of small pore size and negatively charged surfaces. In addition, elevated concentrations of caesium were found in kaolinite and sphalerite phases. The findings concerning the location of CsCl were congruent with X‐ray microtomography.     

A new method for three-dimensional skeleton graph analysis of porous media: application to trabecular bone microarchitecture

This paper introduces a new three-dimensional analysis of complex disordered porous media. Skeleton graph analysis is described and applied to trabecular bone images obtained by high resolution magnetic resonance imaging. This technique was developed bearing in mind topological considerations. The correspondence between vertices and branches of the skeleton graph and trabeculae is used in order to get local information on trabecular bone microarchitecture. In addition to real topological parameters, local structural information about trabeculae, such as length and volume distributions, are obtained. This method is applied to two sets of samples: six osteoporosis and six osteoarthritis bone samples. We demonstrate that skeleton graph analysis is a powerful technique to describe trabecular bone microarchitecture.     

Three‐dimensional digital reconstruction of skin epidermis and dermis

This study describes how three‐dimensional (3D) human skin tissue is reconstructed, and provides digital anatomical data for the physiological structure of human skin tissue based on large‐scale thin serial sections. Human skin samples embedded in paraffin were cut serially into thin sections and then stained with hematoxylin‐eosin. Images of serial sections obtained from lighting microscopy were scanned and aligned by the scale‐invariant feature transform algorithm. 3D reconstruction of the skin tissue was generated using Mimics software. Fibre content, porosity, average pore diameter and specific surface area of dermis were analysed using the ImageJ analysis system. The root mean square error and mutual information based on the scale‐invariant feature transform algorithm registration were significantly greater than those based on the manual registration. Fibre distribution gradually decreased from top to bottom; while porosity showed an opposite trend with irregular average pore diameter distribution. A specific surface area of the dermis showed a ‘V’ shape trend. Our data suggested that 3D reconstruction of human skin tissue based on large‐scale serial sections could be a valuable tool for providing a highly accurate histological structure for analysis of skin tissue. Moreover, this technology could be utilized to produce tissue‐engineered skin via a 3D bioprinter in the future.     

Platelet‐rich fibrin and collagen membrane in the preservation of the alveolar bone: Feasibility of the elemental inorganic composition and scanning electron microscopy analysis

The success of dental implants is related to the amount, quality, and composition of the alveolar bone. The placement of platelet‐rich fibrin (PRF) clot associated with a resorbable collagen membrane (RCM) in a postextraction alveolus is a technique used for ridge preservation. This case report study analyzed the ultrastructural characteristics of cross‐sectioned alveolar bone that received PRF and RCM using scanning electron microscopy and the inorganic composition using “energy dispersive X‐ray spectrometry,” in order to explore the feasibility of this method to clinical studies. Three alveolar bone samples from two male patients (37 and 58 years old), obtained in the procedure of placing the dental implant, were analyzed. Two bone samples previously received PRF and RCM (M37 and M58), the third sample represented a physiological bone formation without treatment (M37‐control). The bone sample M37 showed irregularly shaped islets of calcified material intermingled with connective tissue. The other samples, from the 58‐year‐old patient with PRF and RCM (M58); and the other untreated bone sample from the same 37‐year‐old patient (M37‐control) showed similar ultrastructural morphology with trabecular conformation without islets agglomerations. The inorganic composition analysis showed higher concentrations of calcium and phosphorus in both samples treated with PRF and RCM in comparison to the untreated bone sample. The Ca/P ratio was higher in the M37 sample compared to the others samples. The results showed morphology and inorganic composition differences among the treatments used, suggesting that this method is feasible to analyze parameters of the alveolar bone tissue.     

Automated thresholding and analysis of microCT scanned bread dough

Computer aided x‐ray microtomography is an increasingly popular method to investigate the structure of materials. Continuing improvements in the technique are resulting in increasingly larger data sets. The analysis of these data sets generally involves executing a static workflow for multiple samples and is generally performed manually by researchers. Executing these processes requires a significant time investment. A workflow which is able to automate the activities of the user would be useful. In this work, we have developed an automated workflow for the analysis of microtomography scanned bread dough data sets averaging 5 GB in size. Comparing the automated workflow with the manual workflow indicates a significant amount of the time spent (33% in the case of bread dough) on user interactions in manual method. Both workflows return similar results for porosity and pore frequency distribution. Finally, by implementing an automated workflow, users save the time which would be required to manually execute the workflow. This time can be spent on more productive tasks.     

Correlative light and backscattered electron microscopy of bone--Part I: Specimen preparation methods

A method for preparing nondecalcified bone and tooth specimens for imaging by both light microscopy (LM) and backscattered electron microscopy in the scanning electron microscope (BSE-SEM) is presented. Bone blocks are embedded in a polymethylmethacrylate (PMMA) mixture and mounted on glass slides using components of a light-cured dental adhesive system. This method of slide preparation allows correlative studies to be carried out between different microscopy modes, using the same histologic section. It also represents a large time savings relative to other mounting methods whose media require long cure times.     

Technical advances in the sectioning of dental tissue and of on‐section cross‐linked collagen detection in mineralized teeth

Immunohistochemical detection of cross‐linked fibrillar collagens in mineralized tissues is much desired for exploring the mechanisms of biomineralization in health and disease. Mineralized teeth are impossible to section when embedded in conventional media, thus limiting on‐section characterization of matrix proteins by immunohistochemistry. We hypothesized that by using an especially formulated acrylic resin suitable for mineralized dental tissues, not only sectioning of teeth would be possible, but also our recently developed immunofluorescence labeling technique would be amenable to fully calcified tissues for characterization of dentinal fibrillar collagens, which remains elusive. The hypothesis was tested on fixed rodent teeth embedded in Technovit 9100 New®. It was possible to cut thin (1 μm) sections of mineralized teeth, and immunofluorescence characterization of cross‐linked type I fibrillar collagen was selected due to its abundance in dentine. Decalcified samples of teeth embedded in paraffin wax were also used to compare immunolabeling from either method using the same immunoreagents in equivalent concentrations. In the decalcified tissue sections, type I collagen labeling in the dentine along the tubules was “patchy” and the signal in the predentine was very weak. However, enhanced signal in mineralized samples with type I collagen was detected not only in the predentine but also at the limit between intertubular dentine, within the elements of the enamel organ and subgingival stroma. This report offers advances in sectioning mineralized dental tissues and allows the application of immunofluorescence not only for on‐section protein detection but importantly for detecting cross‐linked fibrous collagens in both soft and mineralized tissue sections. Microsc. Res. Tech. 73:741–745, 2010. © 2009 Wiley‐Liss, Inc.     

A new method for the two-dimensional analysis of bone structure in human iliac crest biopsies

A new method is described for the analysis of the two-dimensional structural pattern of trabecular bone in human iliac crest biopsies. 8 μm thick undecalcified sections stained with the von Kossa technique were examined at a magnification of ×9. Using an Ibas II image analyser, the ratio of nodes to free ends and the length of different strut types (cortex to free end, node or cortex, free end to free end and node to node, loop or free end) expressed as a percentage of total strut length were assessed. The reproducibility of the method was good for most of the measured indices but inter-observer and inter-section variation were greater. Comparison of biopsy sections obtained from eleven young healthy control subjects and eleven patients with hepatic osteoporosis revealed a significantly higher node to free end ratio, node to loop and node to node strut length and significantly lower cortex to free end and free end to free end strut length in the controls. No significant differences were seen in node to free end, cortex to cortex or cortex to node strut length. This approach to trabecular bone structure analysis should prove useful in determining patterns of bone loss in health and disease and in examining the effects of treatment on bone structure in osteoporosis.     

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.