Three-dimensional reconstruction of entire vertebral bodies

High-Resolution Episcopic Microscopy (HREM): Looking Back on 13 Years of Successful Generation of Digital Volume Data of Organic Material for 3D Visualisation and 3D Display

High-resolution episcopic microscopy (HREM) is an imaging technique that permits the simple and rapid generation of three-dimensional (3D) digital volume data of histologically embedded and physically sectioned specimens. The data can be immediately used for high-detail 3D analysis of a broad variety of organic materials with all modern methods of 3D visualisation and display. Since its first description in 2006, HREM has been adopted as a method for exploring organic specimens in many fields of science, and it has recruited a slowly but steadily growing user community. This review aims to briefly introduce the basic principles of HREM data generation and to provide an overview of scientific publications that have been published in the last 13 years involving HREM imaging. The studies to which we refer describe technical details and specimen-specific protocols, and provide examples of the successful use of HREM in biological, biomedical and medical research. Finally, the limitations, potentials and anticipated further improvements are briefly outlined.

Large-scale bone mineral histomorphometry-report of a simplified technique

AIMS

The aim of this study was the development of a simplified technique for bone mineral histomorphology on large undecalcified bone samples. Established techniques, such as undecalcified bone thin sectioning, ultrathin grinding, surface-stained block grinding and micro-computerized tomography (CT), are expensive, time-consuming and put very high demands on equipment, safety standards, personnel and laboratory facilities.

METHODS AND RESULTS

The method is based on the surface-stained block-grinding principle; however, its novelty lies in the selection of user-friendly, safe and low-cost materials, equipment and digitization techniques. We describe in detail the relevant steps, as well as many practical tips for their successful implementation: accurate bone cutting in thin sections with a customized arrangement on a commercial bandsaw, defatting with sodium hypochlorite, embedding in epoxy resin blocks at room temperature, silicon carbide paper grinding, von Kossa staining, flatbed scanner digitization and image processing.

CONCLUSION

We believe that the proposed methodology could contribute to the expansion of the study of bone tissue, as it enables the rapid examination of bone specimens on a large scale with minimal laboratory requirements and consumables costs.

Episcopic 3D Imaging Methods: Tools for Researching Gene Function

This work aims at describing episcopic 3D imaging methods and at discussing how these methods can contribute to researching the genetic mechanisms driving embryogenesis and tissue remodelling, and the genesis of pathologies. Several episcopic 3D imaging methods exist. The most advanced are capable of generating high-resolution volume data (voxel sizes from 0.5x0.5x1 µm upwards) of small to large embryos of model organisms and tissue samples. Beside anatomy and tissue architecture, gene expression and gene product patterns can be three dimensionally analyzed in their precise anatomical and histological context with the aid of whole mount in situ hybridization or whole mount immunohistochemical staining techniques. Episcopic 3D imaging techniques were and are employed for analyzing the precise morphological phenotype of experimentally malformed, randomly produced, or genetically engineered embryos of biomedical model organisms. It has been shown that episcopic 3D imaging also fits for describing the spatial distribution of genes and gene products during embryogenesis, and that it can be used for analyzing tissue samples of adult model animals and humans. The latter offers the possibility to use episcopic 3D imaging techniques for researching the causality and treatment of pathologies or for staging cancer. Such applications, however, are not yet routine and currently only preliminary results are available. We conclude that, although episcopic 3D imaging is in its very beginnings, it represents an upcoming methodology, which in short terms will become an indispensable tool for researching the genetic regulation of embryo development as well as the genesis of malformations and diseases.

Quantitative imaging of musculoskeletal tissue

Quantitative imaging of musculoskeletal tissue, including radiography, computed tomography (CT), and magnetic resonance imaging (MRI), has become the essential methodology in clinical practice for diagnosis and monitoring of various musculoskeletal conditions. Furthermore, quantitative imaging technologies have become indispensable for research and development in diseases of the human skeleton. Standardized methods of image analysis have been developed through the years to quantify measurements on bone and cartilage with high precision and accuracy. Key areas of musculoskeletal disease where quantitative imaging is currently employed are osteoporosis and arthritis.

A novel method for three-dimensional observation of the vascular networks in the whole mouse brain

A novel method for acquiring serial images suitable for three-dimensional reconstruction of vascular networks in the whole brain of mouse was developed. The brain infused with a White India ink-gelatin solution was fixed and embedded in paraffin containing Sudan Black B through xylene also containing Sudan Black B. Each sliced surface of the paraffin block was coated with liquid paraffin and its image was serially acquired. Coating with liquid paraffin extremely improved the quality of the image. The series of serial images was free of distortion and a three-dimensional image was reconstructed without the problem of the alignment and registration of adjacent images. The volume-rendered image indicated three-dimensional distribution of blood vessels in a whole brain. No ghost or shadow was observed on a volume-rendered image of the White India ink-gelatin infused brain. The z-axial resolution examined on the orthogonal sections reconstituted from serial images obtained at an interval of 5 mum showed no cross talk, indicating that the z-axial resolution was no larger than 5 mum. A proper understanding of the vascular system in a whole brain is indispensable to reveal the development of the vascular system in the brain of normal and genetically manipulated mouse and vascular alterations in pathological situation, such as stroke and neurodegenerative disease. Although simple and inexpensive, this method will provide fundamental information on the vascular system in a whole brain.

Quantifying the Directional Parameter of Structural Anisotropy in Porous Media

A new method has been developed to define the directional parameter and characterize the structural anisotropy of a highly porous structure with extensive pore interconnectivity and surface area, such as scaffolds in tissue engineering. This new method called intercept segment deviation (ISD) was validated through the comparison of structural anisotropy from ISD measurements with mechanical anisotropy from finite-element stress analysis. This was carried out on a generated two-dimensional (2D) image of a two-phase material and a real three-dimensional (3D) image of a tissue scaffold. The performance of other methods for quantification of the directional parameter was also assessed. The results indicate that the structural anisotropy obtained from this new method conforms to the actual mechanical anisotropy and provides a better prediction of the material orientation than the other methods for the 2D and 3D images studied.

Three-dimensional texture analysis of cancellous bone cores evaluated at clinical CT resolutions

The objective of this study was to determine if three-dimensional (3D) Haralick co-occurrence texture measures calculated from low-resolution CT images of trabecular bone correlate with 3D structural indices measured from high-resolution CT images. Thirty-three cubical regions of trabecular bone from human calcanei were analyzed using images obtained from a micro-computed tomography (micro-CT) scanner. 3D measures of bone architecture were calculated. The original images were then subsampled by factors of 5, 10, 15, and 20, and 3D texture features were calculated for each set of subsampled images. Linear regression models showed that co-occurrence texture features were significantly correlated with structural indices. Over 90% of the variation in three different structural indices was explained in two-variable regression models using texture features as predictors when the voxel side length was reduced by a factor of 10. Texture features calculated from clinical images may increase our ability to obtain trabecular bone architectural information when high-resolution images are unobtainable.

A comparison of structural and mechanical properties in cancellous bone from the femoral head and acetabulum

Mechanical interlock obtained by penetration of bone cement into cancellous bone is critical to the success of cemented total hip replacement (THR). Although acetabular component loosening is an important mode of THR failure, the properties of acetabular cancellous bone relevant to cement penetration are not well characterized. Bone biopsies (9mm diameter, 10mm long) were taken from the articular surfaces of the acetabulum and femoral head during total hip replacement. After mechanical and chemical defatting the two groups of bone specimens were characterized using flow measurement, mechanical testing and finally serial sectioning and three-dimensional computer reconstruction. The mean permeabilities of the acetabular group (1.064 × 10−10 m2) and femoral group (1.155x 10−10m2) were calculated from the flow measurements, which used saline solution and a static pressure of 9.8 kPa. The mean Young's modulus, measured non-destructively, was 47.4 MPa for the femoral group and 116.4MPa for the acetabular group. Three-dimensional computer reconstruction of the specimens showed no significant differences in connectivity and porosity between the groups. Results obtained using femoral head cancellous bone to investigate bone cement penetration and fixation are directly relevant to fixation in the acetabulum.

Cortical bone in the human femoral neck: three-dimensional appearance and porosity using synchrotron radiation

A high-resolution CT system using synchrotron radiation allowed visualization of the 3D cortical bone microarchitecture and measurement of intracortical porosity of femoral neck cortical bone specimens from 19 female cadavers imaged at 10.13-microm resolution. 3D reconstruction of specimens showed osteonal system arrangement. Mean porosity was 15.88%. This technique will provide insights into the mechanisms involved in osteoporotic hip fractures.

INTRODUCTION

The purpose of this study was to show that a high-resolution CT system using synchrotron radiation (SR) allows visualization of the 3D cortical bone microarchitecture of the human femoral neck and quantification of intracortical porosity.

MATERIALS AND METHODS

Bone specimens from the inferior femoral neck were obtained from 19 female cadavers with no hip fracture (mean, 86.9 +/- 8.3 years). The specimens, consisting of embedded approximately 7 x 7 x 12-mm cortical bone parallelepipeds, were imaged using SR at 10.13-microm resolution. Commercial software was used to visualize both the 660 x 660 x 660-voxel volumes and the 2D axial slices through each volume. Qualitative examination of 2D axial slices focused on the appearance of the vessel canal system, presence of small bright zones (fully mineralized tissue) in the osseous matrix, and presence of cracks. A method was developed to automatically measure 3D intracortical porosity after separating pure bone from pores and cortical bone from trabecular bone.

RESULTS AND CONCLUSIONS

3D reconstruction of the specimens showed the entire structure and arrangement of the osteonal systems, parallel to the axis of the femoral neck. Bright zones were seen in the outer cortex. No cracks were observed. Porosity values varied widely from 4.96% to 38.87% (mean, 15.88 +/- 9.87%). This study establishes that SR microtomography can be used to display the 3D bone microstructure of the human femoral neck cortex and to quantify intracortical porosity. This technique will provide insights into the mechanisms involved in cortical bone loss and osteoporotic hip fractures.

Detecting and tracking local changes in the tibiae of individual rats: a novel method to analyse longitudinal in vivo micro-CT data

In this study we present the analysis of in vivo micro-CT scans using a new method based on image registration that accurately evaluates longitudinal micro-CT studies. We tested if detailed changes in the bone architecture could be detected and tracked in individual animals. A prototype in vivo micro-CT scanner (Skyscan 1076) was developed in which tibiae of rats that are lying on a bed under gas anaesthesia were scanned. For this study, three female Wistar rats were used: a sham-operated rat, an ovariectomised (OVX) rat and one rat that served as a reproducibility control. The reproducibility control rat was scanned twice in 1 day. The other animals were scanned at week 0, just before surgery, at week 4 and at week 14 after surgery. Architectural changes over time were detected by overlaying two data sets made at different time points using an algorithm that uses mutual information for optimal registration. The scans were segmented into binary data sets using a local thresholding algorithm. The reproducibility test showed small errors of less than 3% in bone volume measurements and errors less than 0.5% in measurements of trabecular thickness. The sham-operated rat showed no changes in total bone volume, though thinning and eventual loss of some small trabeculae could be detected, which could be related to the age of the animal. The OVX rat lost much trabecular bone volume, especially in the metaphysis (60% at week 4, 75% at week 14). The remaining trabeculae slowly increased in thickness. Following the different scans in time showed the forming of new trabecular structures. Additionally, small longitudinal growth at the growth plate could be detected after the first 4 weeks. Further, the OVX rat showed extensive modelling at the proximal endosteal lateral cortex. We have shown a new method that can detect and track changes in the local bone architecture and individual trabeculae in time, in an individual living animal. This method enables longitudinal in vivo micro-CT studies and has the potential to greatly contribute to experimental rat or mouse studies on pharmacological intervention and transgenic models.

A technique for quantitative three-dimensional analysis of microvascular structure

Research into angiogenesis and vascular microarchitecture has contributed to progress in a wide variety of biomedical fields, but increased understanding is limited, in part, by the available assays and imaging modalities. Techniques that allow quantitation of vascular microarchitecture are needed. A comprehensive method is presented that uses 6-microm-thick serial sections of frozen tissue samples, immunostaining for CD31, brightfield microscopy, automated alignment of two-dimensional serial sections, and volume rendering to produce high-resolution, three-dimensional, quantifiable images of microvascular structure. Application of the technique is shown by characterizing vascularization into a fibrin gel implanted against the skeletal muscle of rats and explanted after 7 days. Comparing measurements from automated and manually aligned MRI and fibrin samples verified quantitation. Automation removes concerns of observer bias or variation inherent in manual alignment and increases the speed of analysis. Analysis of the fibrin gel reveals a dense (4.3 +/- 1.1% endothelial cell density) network of tortuous (1.37 +/- 0.05 tortuosity) capillaries that replaces the gel as it degrades. There is a high level of void space (22.8 +/- 3.6%) in the gel, and average capillary length in the fibrovascular tissue was 93.0 +/- 7.4 microm. Data obtained from these automatically aligned images agreed with those obtained using manual analysis (no statistical difference), and the results are consistent with data from traditional methods.

Effect of vitamin K2 on three-dimensional trabecular microarchitecture in ovariectomized rats

Menatetrenone, a vitamin K2 with four isoprene units, has been reported to improve osteoporotic bone loss. The purpose of this investigation was to clarify the effect of menatetrenone on the three-dimensional (3D) trabecular microarchitecture in ovariectomized (OVX) rats by using microcomputed tomography (MCT). Forty-two 13-week-old female rats were used and divided into four groups: the OVX (OVX + MK-4) group treated with menatetrenone, the (OVX untreated) group, the sham-operated (Sham + MK-4) group treated with menatetrenone, and the sham-operated group not treated with menatetrenone (Sham untreated) group. OVX rats were fed a calcium-deficient diet. Menatetrenone treatment was begun just after the ovariectomy, and the mean menatetrenone oral intake over the 8-week period was adjusted to 30 mg/kg BW per day. The proximal metaphyseal region of the right tibia was evaluated by dual X-ray absorptiometry (DXA) and MCT. A parametric analysis of the reconstructed trabecular volume was carried out using bone volume fractions, the fractal dimension calculated by the 3D box-counting method, and the connectivity density as determined by topological analysis. Menatetrenone significantly increased the trabecular bone volume, fractal dimension, and connectivity in the OVX + MK-4 group compared with the OVX-untreated group (p < 0.01). Our results suggest that an 8-week administration of menatetrenone protects against the loss of trabecular bone volume and its connectivity when treatment is begun just after the ovariectomy. Despite this apparent protection, it remains unknown whether it is possible to reestablish trabecular connectivity if therapeutic intervention occurs after the trabecular connectivity has been lost.

Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture

The purpose of this work was to understand how fractal dimension of two-dimensional (2D) trabecular bone projection images could be related to three-dimensional (3D) trabecular bone properties such as porosity or connectivity. Two alteration processes were applied to trabecular bone images obtained by magnetic resonance imaging: a trabeculae dilation process and a trabeculae removal process. The trabeculae dilation process was applied from the 3D skeleton graph to the 3D initial structure with constant connectivity. The trabeculae removal process was applied from the initial structure to an altered structure having 99% of porosity, in which both porosity and connectivity were modified during this second process. Gray-level projection images of each of the altered structures were simply obtained by summation of voxels, and fractal dimension (Df) was calculated. Porosity (phi) and connectivity per unit volume (Cv) were calculated from the 3D structure. Significant relationships were found between Df, phi, and Cv. Df values increased when porosity increased (dilation and removal processes) and when connectivity decreased (only removal process). These variations were in accordance with all previous clinical studies, suggesting that fractal evaluation of trabecular bone projection has real meaning in terms of porosity and connectivity of the 3D architecture. Furthermore, there was a statistically significant linear dependence between Df and Cv when phi remained constant. Porosity is directly related to bone mineral density and fractal dimension can be easily evaluated in clinical routine. These two parameters could be associated to evaluate the connectivity of the structure.

Quantitative analysis of three-dimensional complexity and connectivity changes in trabecular microarchitecture in relation to aging, menopause, and inflammation

There are several types of bone loss besides that associated with normal aging, eg, that associated with the menopause, and that associated with chronic inflammation, and these are considered to be caused by different mechanisms. The microarchitecture that results from these different bone-loss mechanisms would not be the same. The purpose of this study was to investigate differences in the three-dimensional trabecular microarchitecture in various types of osteopenia, using microcomputed tomography (Micro-CT). Thirty-five Fisher 344 rats were divided into five groups (control, young, senile, ovariectomized [OVX], and inflammation-mediated osteopenia [IMO]) and distal femoral metaphysis was scanned by Micro-CT to nondestructively acquire a 3-D CT stack consisting of 50 consecutive slices at a spatial resolution of 26 microm. The volume of interest, consisting of the secondary spongiosa, was prepared to analyze the 3-D trabecular microarchitecture. A parametric analysis was carried out using bone volume fractions, fractal dimensions, and the first Betti number in order to quantitatively express the mass, complexity, and connectivity of the trabecular microarchitecture. Complexity tended to decrease with age, and decreased significantly in estrogen deficiency-induced and inflammation-mediated osteopenia. Connectivity did not appear to change with aging, but was significantly decreased in estrogen deficiency-induced and inflammation-mediated osteopenia. There was no significant difference between the OVX and the IMO groups.

Constitutive relationships of fabric, density, and elastic properties in cancellous bone architecture

The hypothesis that trabecular morphology can predict the elastic properties of cancellous bone has only partly been verified and no predictive analytical model is currently available. Such models are becoming increasingly relevant as the resolution levels of three-dimensional scanning techniques approach the size of trabeculae. This study took advantage of micro-finite-element methods and tested the aforementioned hypothesis in normal cancellous bone material collected at six anatomical locations from 56 individuals. Numerical analysis was based on high-resolution three-dimensional computer reconstructions of cancellous bone specimens from which the complete elastic characteristics and trabecular morphology, represented by three different fabric measures (the mean intercept length and two volume-based ones), were calculated. Each fabric measure was analyzed individually using the tensorial relationships derived by Cowin (Mech Mater 4:137-147; 1985). Models for both stiffness and compliance entries were developed. The models based on stiffness entries could explain 93.4%-95.6% of the variance, whereas those based on compliance entries could explain 89.2%-89.4%. When using the former model, the MIL (mean intercept length measure) performed slightly better than the two volume-based measures, VO (volume orientation) and SVD (star volume distribution), with 23% less remaining variance. The high correlations found strongly support the hypothesis and increase the hope that, on the basis of information on trabecular morphology, it will be possible to obtain considerably better estimates of bone quality in vivo compared with the rough two-dimensional density measurements used today.

The role of an effective isotropic tissue modulus in the elastic properties of cancellous bone

Conceptually, the elastic characteristics of cancellous bone could be predicted directly from the trabecular morphology--or architecture--and by the elastic properties of the tissue itself. Although hardly any experimental evidence exists, it is often implicitly assumed that tissue anisotropy has a negligible effect on the apparent elastic properties of cancellous bone. The question addressed in this paper is whether this is actually true. If it is, then micromechanical finite element analysis (micro-FEA) models, representing trabecular architecture, using an 'effective isotropic tissue modulus' should be able to predict apparent elastic properties of cancellous bone. To test this, accurate multi-axial compressive mechanical tests of 29 whale bone specimens were simulated with specimen-specific micro-FEA computer models built from true three-dimensional reconstructions. By scaling the micro-FEA predictions by a constant tissue modulus, 92% of the variation of Young's moduli determined experimentally could be explained. The correlation even increased to 95% when the micro-FEA moduli were scaled to the isotropic tissue moduli of individual specimens. Excellent agreement was also found in the elastic symmetry axes and anisotropy ratios. The prediction of Poisson's ratios was somewhat less precise at 85% correlation. The results support the hypothesis; for practical purposes, the concept of an 'effective isotropic tissue modulus' concept is a viable one. They also suggest that the value of such a modulus for individual cases might be inferred from the average tissue density, hence the degree of mineralization. Future studies must clarify how specific the tissue modulus should be for different types of bone if adequate predictions of elastic behavior are to be made in this way.

Connectivity and the elastic properties of cancellous bone

This study addresses the possible significance of trabecular connectivity for the mechanical quality of cancellous bone. A total of 141 cubic trabecular bone specimens collected from autopsy material from 56 individuals without any known bone or metastatic diseases were used. Age variation was in the range of 14-91 years and a wide range of trabecular architecture was found. Each specimen was three-dimensionally reconstructed with a voxel size of either 20 or 25 microm. Using the detailed three-dimensional reconstructions as input for microstructural finite-element models, the complete elastic properties of the trabecular architecture were obtained and maximum and mean stiffness could be calculated. Volume fraction and true three-dimensional architectural measurements of connectivity density and surface density were determined. Connectivity density was determined in an unbiased manner by the Euler number, which is a topological property. Using multiple regression analysis it was found that volume fraction explained by far the greatest part (84%-94%) of the variation in both mean and maximum stiffness. When connectivity density and surface density were included, the correlations increased marginally to 89%-95%. Noticeably negative regression coefficients were found for connectivity density. The results suggest that, in normal cancellous bone, the connectivity density has very limited value for assessment of elastic properties by morphological variables, but if a relation exists then stiffness decreases with increasing connectivity.

Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions

A quantitative assessment of bone tissue stresses and strains is essential for the understanding of failure mechanisms associated with osteoporosis, osteoarthritis, loosening of implants and cell-mediated adaptive bone-remodeling processes. According to Wolff's trajectorial hypothesis, the trabecular architecture is such that minimal tissue stresses are paired with minimal weight. This paradigm at least suggests that, normally, stresses and strains should be distributed rather evenly over the trabecular architecture. Although bone stresses at the apparent level were determined with finite element analysis (FEA), by assuming it to be continuous, there is no data available on trabecular tissue stresses or strains of bones in situ under physiological loading conditions. The objectives of this project were to supply reasonable estimates of these quantities for the canine femur, to compare trabecular-tissue to apparent stresses, and to test Wolff's hypothesis in a quantitative sense. For that purpose, the newly developed method of large-scale micro-FEA was applied in conjunction with micro-CT structural measurements. A three-dimensional high-resolution computer reconstruction of a proximal canine femur was made using a micro-CT scanner. This was converted to a large-scale FE-model with 7.6 million elements, adequately refined to represent individual trabeculae. Using a special-purpose FE-solver, analyses were conducted for three different orthogonal hip-joint loading cases, one of which represented the stance-phase of walking. By superimposing the results, the tissue stress and strain distributions could also be calculated for other force directions. Further analyses of results were concentrated on a trabecular volume of interest (VOI) located in the center of the head. For the stance phase of walking an average tissue principal strain in the VOI of 279 strain was found, with a standard deviation of 212 microstrain. The standard deviation depended not only on the hip-force magnitude, but also on its direction. In more than 95% of the tissue volume the principal stresses and strains were in a range from zero to three times the averages, for all hip-force directions. This indicates that no single load creates even stress or strain distributions in the trabecular architecture. Nevertheless, excessive values occurred at few locations only, and the maximum tissue stress was approximately half the value reported for the tissue fatigue strength. These results thus indicate that trabecular bone tissue has a safety factor of approximately two for hip-joint loads that occur during normal activities.

Calibration of trabecular bone structure measurements of in vivo three-dimensional peripheral quantitative computed tomography with 28-microm-resolution microcomputed tomography

It has recently been shown that high-resolution computed tomography and magnetic resonance imaging have the potential to assess information about the microarchitecture of bone in a noninvasive way. However, due to the limited spatial resolution of the in vivo measurements, the individual trabeculae are not depicted with their true thickness. Nevertheless, the spacing of the structural elements allows the assessment of trabecular number. In a previous publication, the ridge number density (RND) was introduced as a measure for this structural index. It can be extracted from high-resolution three-dimensional (3D) images of patients and shows a reproducibility of 1.6%. In this work the Ridge extraction procedure is compared to and calibrated with microcomputed tomography (microCT) measurements. Three-dimensional measurements of 15 bone biopsies are made with a 28-microm-resolution microCT scanner as well as with a 165-microm-resolution peripheral quantitative computed tomography (pQCT) scanner. For the latter, the same settings are used as for patient examinations. The 15 pairs of measurements are analyzed and the resulting structural indices are compared. The results show that structural indices such as trabecular number, mean thickness, and mean separation can be determined from the 3D pQCT data with an r2 of between 0.81 and 0.96 if the microCT data are taken as the gold standard. The calibration equation found for the bone volume fraction has an intercept of 0.04 and a slope of 0.86 (r2 = 0.98), and trabecular number as the main additional structural index shows a nonsignificant intercept and a calibration slope of 0.91 with the microCT. The calibration procedure can be used directly for patient examinations. Applied to time-series measurements it may be of value for monitoring and quantifying microarchitectural changes due to therapy or aging.

Glenoid bone architecture

This article describes regional variations in trabecular bone architecture in terms of density and orientation within six glenoid specimens. The mean donor age was 56 years and ranged from 31 to 72 years. An automated imaging technique based on 3-dimensional serial sectioning was used for the direct examination of the glenoid cancellous bone structures. Subchondral plate thickness was on average 1.9 mm and ranged from 1.2 mm to 2.9 mm. The volume fraction of trabecular bone varied from 11% to 45% with peak values at the posterior glenoid vault. On graphic 3-dimensional reconstructions, the glenoid appeared as platelike trabeculae, radially oriented perpendicular to the subchondral plate and interconnected by thin rods. These views also displayed regional variations throughout the glenoid, reflecting differences in the macroscopic appearance. Quantitative structural analysis revealed different degrees of anisotropy at the glenoid cancellous region, predominantly transverse isotropy. Resemblance to direct weight-bearing cancellous bone such as the proximal tibia was evident.

Relationships between bone morphology and bone elastic properties can be accurately quantified using high-resolution computer reconstructions

It would be advantageous if the mechanical properties of trabecular bone could be directly inferred from stereomorphometric parameters. For that purpose, apparent density and mean intercept length, as measures of bone mass and directionality (fabric), are commonly correlated with the elastic characteristics of bone samples, as determined in compression tests. However, complete and accurate relationships have not yet been established in this way. This may be due not only to the occurrence of artifacts in both the stereomorphometric and the mechanical assessments but also to an inherent inadequacy of mean intercept length in characterizing the full mechanical significance of bone architecture or nonhomogeneities in trabecular tissue properties not accounted for in stereomorphometry. In this study, we introduce a computer modeling approach allowing these biases to be eliminated. With use of high-resolution three-dimensional computer reconstructions of trabecular bone specimens for stereomorphometry and for microstructural finite element models to simulate mechanical tests, unbiased comparisons become feasible. The purpose was to investigate if accurate and complete relationships can be established in this way. Four different fabric measures were considered: mean intercept length and three volume-based ones. Compliance matrices were calculated from fabric tensors, with use of the mathematical relationship proposed by Cowin for 29 vertebral whale-bone specimens. These were correlated with the compliance constants determined directly from the microstructural finite element model simulation. The nine orthotropic elastic constants of all 29 specimens were well predicted from their stereomorphometric fabric and volume fraction values, with correlation coefficients ranging from R2adj = 0.9934 to 0.9963. When individual compliance components were considered (1/Ei, 1/Gij, or -v[ij]/Ei), correlation coefficients ranged from R2adj = 0.924 to 0.982. All four fabric measures performed equally well. It is concluded that volume fraction and fabric measures correlate highly with the apparent elastic properties of bone samples, provided that anisotropy and nonhomogeneity in the elastic properties of the trabecular tissue itself have negligible effects on the apparent properties. Whether this is true for bone in general remains to be seen, as only a subset was analyzed here. These methods, however, can be valuable in similar assessments of other subsets.

Structure and function of vertebral trabecular bone

STUDY DESIGN

A combined morphologic and finite-element study on vertebral trabecular bone.

OBJECTIVE

To relate the form and function of vertebral trabecular bone, in an attempt to better understand the mechanical function of a lumbar vertebra.

SUMMARY OF BACKGROUND DATA

The architecture of bone is closely related to its mechanical function (Wolff's Law). In the human spine, vertebrae are subjected to a large variety of loads. Yet, these bones show a typical architecture, which means that they carry typical loads.

METHODS

Five trabecular bone cubes from specific sites of a lumbar vertebra were 3D-reconstructed for computerized analysis. The architecture of the specimens was quantified by the bone volume fraction and a measure of anisotropy, the mean bone length. A finite element model was used to calculate internal stresses within a homogeneous vertebral body under basic loads. For each load case, bone volume fraction of the specimens was compared with the equivalent von Mises stress, and mean bone length was compared with the principal stress directions.

RESULTS

Bone volume fraction poorly related to the von Mises stress in the physiologic load case of axial compression. However, high bone volume fractions exist at locations where multiple load situations occur (e.g., near the pedicles and endplates). Remarkably, these sites also show finer architectures. Comparison of mean bone length with principal stresses revealed that the vertebral trabecular bone architecture particularly, but not entirely, corresponds to the stress field under axial compression. The horizontal struts near the end-plates were found to be due to the function of the healthy intervertebral disc, and facetal joint loads introduce stress components that relate well with the bone structures near the pedicle bases.

CONCLUSIONS

The trabecular bone architecture and the vertical orientation of the facet joints suggest that walking may be the main activity that determines the lumbar vertebral bone architecture.

Three-dimensional imaging of trabecular bone using the computer numerically controlled milling technique

Although various techniques exist for high-resolution, three-dimensional imaging of trabecular bone, a common limitation is that resolution depends on specimen size. Most techniques also have limited availability due to their expense and complexity. We therefore developed a simple, accurate technique that has a resolution that is independent of specimen size. Thin layers are serially removed from an embedded bone specimen using a computer numerically controlled (CNC) milling machine, and each exposed cross section is imaged using a low-magnification digital camera. Precise positioning of the specimen under the camera is achieved using the programmable feature of the CNC milling machine. Large specimens are imaged without loss of resolution by moving the specimen under the camera such that an array of field-of-views spans the full cross section. The images from each field-of-view are easily assembled and registered in the postprocessing. High-contrast sections are achieved by staining the bone black with silver nitrate and embedding it in whitened methylmethacrylate. Due to the high contrast nature and high resolution of the images, thresholding at a single value yielded excellent predictions of morphological parameters such as bone volume fraction (mean +/- SD percent error = 0.70 +/- 4.28%). The main limitations of this fully automated "CNC milling technique" are that the specimen is destroyed and the process is relatively slow. However, because of its accuracy, independence of image resolution from specimen size, and ease of implementation, this new technique is an excellent method for ex situ imaging of trabecular architecture, particularly when high resolution is required.

Fabric and elastic principal directions of cancellous bone are closely related

Cancellous bone architecture and mechanics are intimately related. The trabecular architecture of cancellous bone is considered determined by its mechanical environment (Wolff's law), and the mechanical properties of cancellous bone are inversely determined by the trabecular architecture and material properties. Much effort has been spent in expressing these relations, but the techniques and variables necessary for this have not been fully identified. It is obvious, however, that some measure of architectural anisotropy (fabric) is needed. Within the last few years, volume-based measures of fabric have been introduced as alternatives to the mean intercept length method, which has some theoretical problems. This paper seeks to answer which of four different fabric measures best predicts finite element calculated mechanical anisotropy directions. Twenty-nine cancellous bone specimens were three-dimensionally reconstructed using the automated serial sectioning technique. A series of large-scale finite-element analyses were performed on each of the three-dimensional reconstructions to calculate the compliance matrix for each specimen, from which the mechanical principal directions were derived. The architectural anisotropy was determined in three-dimensional space for each specimen using mean intercept length (MIL), volume orientation (VO), star volume distribution (SVD) and star length distribution (SLD). Each of the architectural anisotropy results were expressed by a fabric tensor. Architectural main directions were determined from the fabric tensors and compared with the FE-calculated mechanical anisotropy directions. All architectural measures predicted the mechanical main directions rather well, which supports the assumption that mechanical anisotropy directions are aligned with fabric directions. MIL showed a significant, though very small (1.4 degrees), deviation from the primary mechanical direction. VO had difficulty in determining secondary and tertiary mechanical directions; its mean deviation was 8.9 degrees. SVD and SLD provided marginally better predictors of mechanical anisotropy directions than MIL and VO.

Three-dimensional methods for quantification of cancellous bone architecture

Recent development in three-dimensional (3-D) imaging of cancellous bone has made possible true 3-D quantification of trabecular architecture. This provides a significant improvement of the tools available for studying and understanding the mechanical functions of cancellous bone. This article reviews the different techniques for 3-D imaging, which include serial sectioning, X-ray tomographic methods, and NMR scanning. Basic architectural features of cancellous bone are discussed, and it is argued that connectivity and architectural anisotropy (fabric) are of special interest in mechanics-architecture relations. A full characterization of elastic mechanical properties is, with traditional mechanical testing, virtually impossible, but 3-D reconstruction in combination with newly developed methods for large-scale finite element analysis allow calculations of all elastic properties at the cancellous bone continuum level. Connectivity has traditionally been approached by various 2-D methods, but none of these methods have any known relation to 3-D connectivity. A topological approach allows unbiased quantification of connectivity, and this further allows expressions of the mean size of individual trabeculae, which has previously also been approached by a number of uncertain 2-D methods. Anisotropy may be quantified by fundamentally different methods. The well-known mean intercept length method is an interface-based method, whereas the volume orientation method is representative of volume-based methods. Recent studies indicate that volume-based methods are at least as good as interface-based methods in predicting mechanical anisotropy. Any other architectural property may be quantified from 3-D reconstructions of cancellous bone specimens as long as an explicit definition of the property can be given. This challenges intuitive and vaguely defined architectural properties and forces bone scientists toward 3-D thinking.

Determination of connectivity density in human iliac crest bone biopsies assessed by a computerized method

The aim of the present study was to design a computer program (based on the ConnEulor principle) for direct measurement of 3-D connectivity density in iliac crest bone sections, as used for conventional histomorphometry. We used the physical disector principle and developed an algorithm for nonlinear alignment of the disector pairs. 3-D connectivity was evaluated in transiliac specimens from 30 nonselected autopsy cases of 14 men (age range 20-84 years) and 16 women (age range 20-96 years). In order to visualize the findings from the disector pairs, 3-D reconstruction was performed for two of the iliac crest biopsies. The designed computer program aligns the two sections forming a disector pair and automatically depicts the differences between the images, thereby making correct, direct connectivity density measurements available for conventional bone research.

A microtomographic system for the nondestructive evaluation of bone architecture

Microtomography (micro-computed-tomography, mu-CT) is a method to image and quantify trabecular bone. It has the capability to address the role of trabecular architecture on the mechanical properties of bone and to study trabecular bone remodeling. The system described in this work is based on a compact fan-beam type tomograph that can work in spiral scanning or multislice mode. An X-ray tube with a microfocus is used as a source, a CCD-array as a detector. Samples with diameters from a few millimeters to a maximum of 14 mm can be measured, typically, bone biopsies with a diameter of 8 mm and a length of approximately 10 mm are measured. Spatial resolution is 28 microns. Usually the volume of interest contains 4 x 4 x 4 mm3 and is represented in 14 x 14 x 14 microns3 voxels. 3D stereological indices are extracted according to the standard definitions used in histomorphometry. Triangular surface representation is effected with an extended marching cube algorithm and forms a convenient basis for finite element analysis. Microtomographic measurements may be employed to "calibrate" lower-dose, lower-resolution images in vivo as well as to nondestructively assess unprocessed surgical bone biopsy specimens. These specimens remain intact for mechanical or histological testing.