Human vertebral cancellous bone surface distribution

Predicting the Fracture Toughness of Human Cancellous Bone in Fractured Neck of Femur Patients Using Bone Volume and Micro-Architecture

The current protocol used to determine if an individual is osteoporotic relies on assessment of the individual's bone mineral density (BMD), which allows clinicians to judge the condition of a patient with respect to their peers. This, in essence, evaluates a person's fracture risk, because BMD is a good surrogate measure for strength and stiffness. In recent studies, the authors were the first to produce fracture toughness (FT) data from osteoporotic (OP) and osteoarthritic (OA) patients, by using a testing technique which basically analyzes the prerequisite stress conditions for the onset of growth of a major crack through cancellous bone tissue. FT depends mainly on bone quantity (BV/TV, bone volume/tissue volume), but also on bone micro-architecture (mArch), the inner trabecular design of the bone. The working research hypothesis of the present study is that mArch offers added prediction power to BV/TV in determining FT parameters. Consequently, our aim was to investigate the use of predictive models for fracture toughness and also to investigate if there are any significant differences between the models produced from samples loaded across (AC, transverse to) the main trabecular orientation and along (AL, in parallel) the trabeculae. In multilinear regression analysis, we found that the strength of the relationships varied for a crack growing in these two orthogonal directions. Adding mArch variables in the Ac direction helped to increase the R2 to 0.798. However, in the AL direction, adding the mArch parameters did not add any predictive power to using BV/TV alone; BV/TV on its own could produce R2 = 0.730. The present results also imply that the anisotropic layout of the trabeculae makes it more difficult for a major crack to grow transversely across them. Cancellous bone models and remodels itself in a certain way to resist fracture in a specific direction, and thus, we should be mindful that architectural quality as well as bone quantity are needed to understand the resistance to fracture.

Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

In biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R² ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).

Graphical Abstract

Synthetic open cell foams versus a healthy human vertebra: Anisotropy, fluid flow and μ-CT structural studies

Commercial synthetic open-cell foams are an alternative to human cadaveric bone to simulate in vitro different scenarios of bone infiltration properties. Unfortunately, these artificial foams do not reproduce the anisotropic microstructure of natural bone and, consequently, their suitability in these studies is highly questionable. In order to achieve scaffolds that successfully mimic human bone, microstructural studies of both natural porous media and current synthetic approaches are necessary at different length scales. In this line, the present research was conducted to improve the understanding of local anisotropy in natural vertebral bone and synthetic bone-like porous foams. To attain this objective, small volumes of interest within these materials were reconstructed via micro-computed tomography. The anisotropy of the microstructures was analysed by means of both their main local histomorphometric features and the behaviour of an internal flow computed via computational fluid dynamics. The results showed that the information obtained from each of the micro-volumes of interest could be scaled up to understand not only the macroscopic averaged isotropic and/or anisotropic behaviour of the samples studied, but also to improve the design of macroscopic porous implants better fitting specific local histomorphometric scenarios. The results also clarify the discrepancies in the permeability obtained in the different micro-volumes of interest analysed. STATEMENT OF SIGNIFICANCE: A deep insight comparative study between the porous microstructure of healthy vertebral bone and that of synthetic bone-like open-cell rigid foams used in in vitro permeability studies of bone cement has been performed. The results obtained are of fundamental relevance to computational studies because, in order to achieve convergence values, the computation process should be limited to small computation domains or micro-volumes of interest. This makes the results specific spatial dependent and for this reason computation studies cannot directly capture the macroscopic average behaviour of an anisotropic porous structure such as the one observed in natural bones. The results derived from this study are also important because we have been able to show that the specific spatial information contained in only one healthy vertebra is enough to capture, from a geometric point of view, the same information of "specific surface area vs. porosity" - in other words, the same basic law - that can also be found in other human bones for different patients, even at different biological ages. This is an important finding that, despite the efforts made and the controversies formulated by other authors, should be studied more thoroughly with other bone species and tissues (healthy and/or diseased). Moreover, our results should help to understand that, with the extensive capabilities of current 3D printing technologies, there is an enormous potential in the design of biomimetic porous bone-like scaffolds for bone tissue engineering applications.

Age Dependence of Systemic Bone Loss and Recovery Following Femur Fracture in Mice

The most reliable predictor of future fracture risk is a previous fracture of any kind. The etiology of this increased fracture risk is not fully known, but it is possible that fracture initiates systemic bone loss, leading to greater fracture risk at all skeletal sites. In this study, we investigated systemic bone loss and recovery after femoral fracture in young (3-month-old) and middle-aged (12-month-old) mice. Transverse femur fractures were created using a controlled impact, and whole-body bone mineral density (BMD), trabecular and cortical microstructure, bone mechanical properties, bone formation and resorption rates, mouse voluntary movement, and systemic inflammation were quantified at multiple time points post-fracture. We found that fracture led to decreased whole-body BMD in both young and middle-aged mice 2 weeks post-fracture; this bone loss was recovered by 6 weeks in young but not middle-aged mice. Similarly, trabecular bone volume fraction (BV/TV) of the L5 vertebral body was significantly reduced in fractured mice relative to control mice 2 weeks post-fracture (-11% for young mice, -18% for middle-aged mice); no significant differences were observed 6 weeks post-fracture. At 3 days post-fracture, we observed significant increases in serum levels of interleukin-6 and significant decreases in voluntary movement in fractured mice compared with control mice, with considerably greater changes in middle-aged mice than in young mice. At this time point, we also observed increased osteoclast number on L5 vertebral body trabecular bone of fractured mice compared with control mice. These data show that systemic bone loss occurs after fracture in both young and middle-aged mice, and recovery from this bone loss may vary with age. This systemic response could contribute to increased future fracture risk after fracture; these data may inform clinical treatment of fractures with respect to improving long-term skeletal health. © 2018 American Society for Bone and Mineral Research.

Trabecular bone loss at a distant skeletal site following noninvasive knee injury in mice

Traumatic injuries can have systemic consequences, as the early inflammatory response after trauma can lead to tissue destruction at sites not affected by the initial injury. This systemic catabolism may occur in the skeleton following traumatic injuries such as anterior cruciate ligament (ACL) rupture. However, bone loss following injury at distant,unrelated skeletal sites has not yet been established. In the current study, we utilized a mouse knee injury model to determine whether acute knee injury causes a mechanically significant trabecular bone loss at a distant, unrelated skeletal site (L5 vertebral body).Knee injury was noninvasively induced using either high-speed (HS; 500 mm/s) or lowspeed(LS; 1 mm/s) tibial compression overload. HS injury creates an ACL rupture by midsubstance tear, while LS injury creates an ACL rupture with an associated avulsion bone fracture. At 10 days post-injury, vertebral trabecular bone structure was quantified using high-resolution microcomputed tomography (lCT), and differences in mechanical properties were determined using finite element modeling (FEM) and compressive mechanical testing. We hypothesized that knee injury would initiate a loss of trabecular bone structure and strength at the L5 vertebral body. Consistent with our hypothesis, we found significant decreases in trabecular bone volume fraction (BV/TV) and trabecular number at the L5 vertebral body in LS injured mice compared to sham (8.8% and 5.0%, respectively), while HS injured mice exhibited a similar, but lower magnitude response (5.1% and 2.5%, respectively). Contrary to our hypothesis, this decrease intrabecular bone structure did not translate to a significant deficit in compressive stiffness or ultimate load of the full trabecular body assessed by mechanical testing or FEM. However,we were able to detect significant decreases in compressive stiffness in both HS and LS injured specimens when FE models were loaded directly through the trabecular bone region (9.9% and 8.1%, and 3, respectively). This finding may be particularly important for osteoporotic fracture risk, as damage within vertebral bodies has been shown to initiate within the trabecular bone compartment. Altogether, these data point to a systemic trabecular bone loss as a consequence of fracture or traumatic musculoskeletal injury, which may be an underlying mechanism contributing to increased risk of refracture following an initial injury. This finding may have consequences for treatment of acute musculoskeletal injuries and the prevention of future bone fragility.

The relationship between porosity and specific surface in human cortical bone is subject specific

A characteristic relationship for bone between bone volume fraction (BV/TV) and specific surface (BS/TV) has previously been proposed based on 2D histological measurements. This relationship has been suggested to be bone intrinsic, i.e., to not depend on bone type, bone site and health state. In these studies, only limited data comes from cortical bone. The aim of this paper was to investigate the relationship between BV/TV and BS/TV in human cortical bone using high-resolution micro-CT imaging and the correlations with subject-specific biometric data such as height, weight, age and sex. Images from femoral cortical bone samples of the Melbourne Femur Collection were obtained using synchrotron radiation micro-CT (SPring8, Japan). Sixteen bone samples from thirteen individuals were analysed in order to find bone volume fraction values ranging from 0.20 to 1. Finally, morphological models of the tissue microstructure were developed to help explain the relationship between BV/TV and BS/TV. Our experimental findings indicate that the BV/TV vs BS/TV relationship is subject specific rather than intrinsic. Sex and pore density were statistically correlated with the individual curves. However no correlation was found with body height, weight or age. Experimental cortical data points deviate from interpolating curves previously proposed in the literature. However, these curves are largely based on data points from trabecular bone samples. This finding challenges the universality of the curve: highly porous cortical bone is significantly different to trabecular bone of the same porosity. Finally, our morphological models suggest that changes in BV/TV within the same sample can be explained by an increase in pore area rather than in pore density. This is consistent with the proposed mechanisms of age-related endocortical bone loss. In addition, these morphological models highlight that the relationship between BV/TV and BS/TV is not linear at high BV/TV as suggested in the literature but is closer to a square root function.

Directional Tortuosity as a Predictor of Modulus Damage for Vertebral Cancellous Bone

There are many methods used to estimate the undamaged effective (apparent) moduli of cancellous bone as a function of bone volume fraction (BV/TV), mean intercept length (MIL), and other image based average microstructural measures. The MIL and BV/TV are both only functions of the cancellous microstructure and, therefore, cannot directly account for damage induced changes in the intrinsic trabecular hard tissue mechanical properties. Using a nonlinear finite element (FE) approximation for the degradation of effective modulus as a function of applied effective compressive strain, we demonstrate that a measurement of the directional tortuosity of undamaged trabecular hard tissue strongly predicts directional effective modulus (r2 > 0.90) and directional effective modulus degradation (r2 > 0.65). This novel measure of cancellous bone directional tortuosity has the potential for development into an anisotropic approach for calculating effective mechanical properties as a function of trabecular level material damage applicable to understanding how tissue microstructure and intrinsic hard tissue moduli interact to determine cancellous bone quality.

Biomechanical properties and microarchitecture parameters of trabecular bone are correlated with stochastic measures of 2D projection images

It is well known that loss of bone mass, quantified by areal bone mineral density (aBMD) using DXA, is associated with the increasing risk of bone fractures. However, bone mineral density alone cannot fully explain changes in fracture risks. On top of bone mass, bone architecture has been identified as another key contributor to fracture risk. In this study, we used a novel stochastic approach to assess the distribution of aBMD from 2D projection images of Micro-CT scans of trabecular bone specimens at a resolution comparable to DXA images. Sill variance, a stochastic measure of distribution of aBMD, had significant relationships with microarchitecture parameters of trabecular bone, including bone volume fraction, bone surface-to-volume ratio, trabecular thickness, trabecular number, trabecular separation and anisotropy. Accordingly, it showed significantly positive correlations with strength and elastic modulus of trabecular bone. Moreover, a combination of aBMD and sill variance derived from the 2D projection images (R2=0.85) predicted bone strength better than using aBMD alone (R2=0.63). Thus, it would be promising to extend the stochastic approach to routine DXA scans to assess the distribution of aBMD, offering a more clinically significant technique for predicting risks of bone fragility fractures.

Assessment of bone fragility with clinical imaging modalities

INTRODUCTION

Osteoporotic fractures are a vital public health concern and have created a great economic burden to our society. Therefore, early diagnosis of patients with high risk of osteoporotic fractures is essential. The current gold standard for assessment of fracture risk is the measurement of bone mineral density using dual-energy X-ray absorptiometry. However, such techniques are not very effective in the diagnosis of patients with osteopaenia. Doctors are usually unable to make an informed decision regarding the treatment plan of these patients. In addition to bone mineral density, advanced imaging modalities have been explored in recent years to assess bone quality in other contributing factors, such as microarchitecture of trabecular bone, mineralisation, microdamage and bone remodelling rates. Currently, the microarchitecture of trabecular bone can be evaluated in vivo by high-resolution peripheral quantitative computed tomography techniques, which have a resolution of 80 µm. However, such imaging techniques still remain a high-end research tool rather than a diagnostic tool for clinical applications. Thus, the limited accessibility and affordability of high-resolution peripheral quantitative computed tomography have become major concerns for the general public. Alternatively, combining bone mineral density measurements with stochastic assessments of spatial bone mineral density distribution from dual-energy X-ray absorptiometry images may offer an economic and efficient approach to non-invasively evaluate skeletal integrity and identify the at-risk population for osteoporotic fractures. The aim of this critical review is to assess bone fragility with clinical imaging modalities.

CONCLUSION

High-resolution quantitative computed tomography imaging technique may provide direct measurements of microarchitectures of trabecular bone in vivo. However, it is an expensive method of imaging modality.

Dependence of trabecular structure on bone quantity: a comparison between osteoarthritic and non-pathological bone

BACKGROUND

The mechanical characterization of trabecular bone is related to its structure. In order to describe the trabecular structure and to study the mechanical behavior of the trabecular tissue, several parameters are presented in the literature. Some studies suggest a possible dependence of the structure on bone volume fraction; this dependence could bias the validity of previous studies. The problem increases its complexity when pathological bone such as osteoarthritic tissue is studied, where the organization of the trabecular structure could be different if compared to the non-pathological tissue. The primary aim of this study was to evaluate the dependence between trabecular structure and bone volume fraction. The secondary aim was to compare osteoarthritic and non-pathological bone considering the correlation between structure and bone volume fraction.

METHODS

Sixty trabecular bone specimens were extracted from femoral heads of two groups of 30 Caucasian donors; an osteoarthritic group and a non-pathological group. Several structural parameters, such as bone volume fraction, direct trabecular thickness, fabric tensor eigenvalues and their normalizations, were calculated from micro-CT analysis. A statistical analysis was carried out to identify the dependences between structural parameters and bone volume fraction. The comparison between osteoarthritic bone and non-pathological bone was also performed.

FINDINGS

Only the normalized eigenvalues of the fabric tensor were not correlated to bone volume fraction (R<0.5). The first and second normalized eigenvalues were significantly different between osteoarthritic bone and non-pathological bone (respectively P<0.05 and P<0.001).

INTERPRETATION

In conclusion, orientation and anisotropy of the trabecular structure do not depend on bone volume fraction. Moreover, differences in the first and second normalized fabric tensor eigenvalues suggest in the osteoarthritic group a structure more oriented along the main trabecular direction.

Cancellous bone properties and matrix content of TGF-beta2 and IGF-I in human tibia: a pilot study

Transforming and insulin-like growth factors are important in regulating bone mass. Thus, one would anticipate correlations between matrix concentrations of growth factors and functional properties of bone. We therefore investigated the relationships of (1) TGF-beta2 and (2) IGF-I matrix concentrations with the trabecular microstructure, stress distribution, and mechanical properties of tibial cancellous bone from six male human cadavers. Trabecular stress amplification (VMExp/sigma(app)) and variability (VMCOV) were calculated using microcomputed tomography (muCT)-based finite element simulations. Bone volume fraction (BV/TV), surface/volume ratio (BS/BV), trabecular thickness (Tb.Th), number (Tb.N) and separation (Tb.Sp), connectivity (Eu.N), and anisotropy (DA) were measured using 3-D morphometry. Bone stiffness and strength were measured by mechanical testing. Matrix concentrations of TGF-beta2 and IGF-I were measured by ELISA. We found higher matrix concentrations of TGF-beta2 were associated with higher Tb.Sp and VMExp/sigma(app) for pooled data and within subjects. Similarly, a higher matrix concentration of IGF-I was associated with lower stiffness, strength, BV/TV and Tb.Th and with higher BS/BV, Tb.Sp, VMExp/sigma(app) and VMCOV for pooled data and within subjects. IGF-I and Tb.N were negatively associated within subjects. It appears variations of the stress distribution in cancellous bone correlate with the variation of the concentrations of TGF-beta2 and IGF-I in bone matrix: increased local matrix concentrations of growth factors are associated with poor biomechanical and architectural properties of tibial cancellous bone.

Numerical modeling of bone tissue adaptation--a hierarchical approach for bone apparent density and trabecular structure

In this work, a three-dimensional model for bone remodeling is presented, taking into account the hierarchical structure of bone. The process of bone tissue adaptation is mathematically described with respect to functional demands, both mechanical and biological, to obtain the bone apparent density distribution (at the macroscale) and the trabecular structure (at the microscale). At global scale bone is assumed as a continuum material characterized by equivalent (homogenized) mechanical properties. At local scale a periodic cellular material model approaches bone trabecular anisotropy as well as bone surface area density. For each scale there is a material distribution problem governed by density-based design variables which at the global level can be identified with bone relative density. In order to show the potential of the model, a three-dimensional example of the proximal femur illustrates the distribution of bone apparent density as well as microstructural designs characterizing both anisotropy and bone surface area density. The bone apparent density numerical results show a good agreement with Dual-energy X-ray Absorptiometry (DXA) exams. The material symmetry distributions obtained are comparable to real bone microstructures depending on the local stress field. Furthermore, the compact bone porosity is modeled giving a transversal isotropic behavior close to the experimental data. Since, some computed microstructures have no permeability one concludes that bone tissue arrangement is not a simple stiffness maximization issue but biological factors also play an important role.

Regional variations of vertebral trabecular bone microstructure with age and gender

The vertebral trabecular bone has a complex three-dimensional (3D) microstructure, with inhomogeneous morphology. A thorough understanding of regional variations in the microstructural properties is crucial for evaluating age- and gender-related bone loss of the vertebra, and may help us to gain more insight into the mechanism of the occurrence of vertebral osteoporosis and the related fracture risks.

INTRODUCTION

The aim of this study was to identify regional differences in 3D microstructure of vertebral trabecular bone with age and gender, using micro-computed tomography (micro-CT) and scanning electron microscopy (SEM).

METHODS

We used 56 fourth lumbar vertebral bodies from 28 women and men (57-98 years of age) cadaver donors. The subjects were chosen to give an even age and gender distribution. Both women and men were divided into three age groups, 62-, 77- and 92-year-old groups. Five cubic specimens were prepared from anterosuperior, anteroinferior, central, posterosuperior and posteroinferior regions at sagittal section. Bone specimens were examined by using micro-CT and SEM.

RESULTS

Reduced bone volume (BV/TV), trabecular number (Tb.N) and connectivity density (Conn.D), and increased structure model index (SMI) were found between ages 62 and 77 years, and between ages 77 and 92 years. As compared with women, men had higher Tb.N in the 77-year-old group and higher Conn.D in the 62- and 77-year-old groups. The central and anterosuperior regions had lower BV/TV and Conn.D than their corresponding posteroinferior region. Increased resorbing surfaces, perforated or disconnected trabeculae and microcallus formations were found with age.

CONCLUSION

Vertebral trabeculae are microstructurally heterogeneous. Decreases in BV/TV and Conn.D with age are similar in women and men. Significant differences between women and men are observed at some microstructural parameters. Age-related vertebral trabecular bone loss may be caused by increased activity of resorption. These findings illustrate potential mechanisms underlying vertebral fractures.

Vertebral osteoporosis and trabecular bone quality

Vertebral fractures due to osteoporosis commonly occur under non-traumatic loading conditions. This problem affects more than 1 in 3 women and 1 in 10 men over a lifetime. Measurement of bone mineral density (BMD) has traditionally been used as a method for diagnosis of vertebral osteoporosis. However, this method does not fully account for the influence of changes in the trabecular bone quality, such as micro-architecture, tissue properties and levels of microdamage, on the strength of the vertebra. Studies have shown that deterioration of the vertebral trabecular architecture results in a more anisotropic structure which has a greater susceptibility to fracture. Transverse trabeculae are preferentially thinned and perforated while the remaining vertical trabeculae maintain their thickness. Such a structure is likely to be more susceptible to buckling under normal compression loads and has a decreased ability to withstand unusual or off-axis loads. Changes in tissue material mechanical properties and levels of microdamage due to osteoporosis may also compromise the fracture resistance of vertebral trabecular bone. New diagnostic techniques are required which will account for the influence of these changes in bone quality. This paper reviews the influence of the trabecular architecture, tissue properties and microdamage on fracture risk for vertebral osteoporosis. The morphological characteristics of normal and osteoporotic architectures are compared and their potential influence on the strength of the vertebra is examined. The limitations of current diagnostic methods for osteoporosis are identified and areas for future research are outlined.

Three-dimensional imaging using microcomputed tomography for studying tooth macromorphology

BACKGROUND

The authors conducted a study to demonstrate potential applications of microcomputed tomography (microCT) in the analysis of tooth morphology.

METHODS

The authors selected for microCT analysis five maxillary first molars with a second canal in the mesiobuccal (MB) root, five mandibular first molars with a mesial root possessing a considerable curvature and five single-canal premolars with complicated apical anatomy. The hardware device used in this study was a desktop X-ray microfocus CT scanner (SkyScan 1072, SkyScan bvba, Aartselaar, Belgium).

RESULTS

The authors obtained a three-dimensional image from each of the 15 teeth. In three cases, the MB canals coalesced into one canal, while in the other two molars the canals were separate. Four of the five mandibular molars exhibited a single canal in the mesial root, which had a broad, flat appearance in a mesiodistal dimension. In the premolar teeth, the canals were independent; however, the apical delta and ramifications of the root canals were obvious, yet intricate.

CONCLUSIONS

MicroCT offers a reproducible technique for 3-D noninvasive assessment of root canal systems.

CLINICAL IMPLICATIONS

While this technique is not suitable for clinical use, it can be applied to improve preclinical training and analysis of fundamental procedures in endodontic and restorative treatment.

Matrix concentration of insulin-like growth factor I (IGF-I) is negatively associated with biomechanical properties of human tibial cancellous bone within individual subjects

Insulin-like growth factor-I (IGF-I), abundant in bone matrix, is believed to play an important role during bone development and remodeling. To our knowledge, however, few studies have addressed the relationship between the concentration of IGF-I in bone matrix and the biomechanical properties of bone tissue. In this study, forty-five cylindrical specimens of cancellous bone were harvested from six human tibiae and scanned using micro-computed tomography (microCT). The bone volume fraction (BV/TV) was calculated from three-dimensional (3D) microCT images. Mechanical tests were then performed on a servohydraulic testing system to determine the strength and stiffness of cancellous bone. Following mechanical testing, the concentration of IGF-I in bone matrix was measured by using an enzyme-linked immunoabsorbent assay (ELISA). Within each subject, the concentration of IGF-I in bone matrix had significant (P<0.01) negative correlations with the bone volume fraction, strength, and stiffness of cancellous bone. In particular, the anterior quadrant of the proximal tibia was significantly (P<0.02) greater in IGF-I matrix concentration and marginally significantly lower in strength (P=0.053) and stiffness (P=0.059) than the posterior quadrant. The negative correlations between the cancellous bone matrix concentration of IGF-I and cancellous bone biomechanical properties within subjects found in this study may help us understand the variation of the biomechanical properties of cancellous bone in proximal human tibiae.

An orientation distribution function for trabecular bone

We describe a new method for quantifying the orientation of trabecular bone from three-dimensional images. Trabecular lattices from five human vertebrae were decomposed into individual trabecular elements, and the orientation, mass, and thickness of each element were recorded. Continuous functions that described the total mass (M(phi,theta)) and mean thickness (tau(phi,theta)) of all trabeculae as a function of orientation were derived. The results were compared with experimental measurements of the elastic modulus in three principal anatomic directions. A power law scaling relationship between the anisotropies in mass and elastic modulus was observed; the scaling exponent was 1.41 (R2=0.88). As expected, the preponderance of trabecular mass was oriented along the cranial-caudal direction; on average, there was 3.4 times more mass oriented vertically than horizontally. Moreover, the vertical trabeculae were 30% thicker, on average, than the horizontal trabeculae. The vertical trabecular thickness was inversely related to connectivity (R2=0.70; P=0.07), suggesting a possible organization into either few, thick trabeculae or many thin trabeculae. The method, which accounts for the mechanical connectedness of the lattice, provides a rapid way to both visualize and quantify the three-dimensional organization of trabecular bone.

Finite element calculated uniaxial apparent stiffness is a consistent predictor of uniaxial apparent strength in human vertebral cancellous bone tested with different boundary conditions

Strong correspondence between the uniaxial apparent strength and stiffness of cancellous bone allows the use of stiffness as a predictor of bone strength. Measured values of mechanical properties in cancellous bone can be different between experiments due to different experimental conditions. In the current study, bone volume fraction, experimentally determined and finite element (FE) predicted stiffness were examined as predictors of cancellous bone ultimate strength in two different groups each of which was tested using a different end constraint. It is demonstrated that, although always significant, the relationships of strength with bone volume fraction and experimentally determined stiffness are different between test groups. Apparent stiffness, estimated by FE modeling, predicts the ultimate strength of human cancellous bone consistently for all examined experimental protocols.

Structural development of the mineralized tissue in the human L4 vertebral body

Knowledge of the structural development of the human vertebrae from non-weight-bearing before birth to weight-bearing after birth is still poor. We studied the mineralized tissue of the developing lumbar L4 vertebral body at ages 15 weeks postconception to 97 years from the tissue level (trabecular architecture) to the material level (micro- and nanostructure). Trabecular architecture was investigated by 2D histomorphometry and the material level was examined by quantitative backscattered electron imaging (for typical calcium content, CaMaxFreq) and scanning small-angle X-ray scattering (for mean mineral particle thickness). During early development, the trabecular orientation changed from a radial to a vertical/horizontal pattern. For bone area per tissue area and trabecular width in postnatal cancellous bone, the maximum was reached at adolescence (20 years), while for trabecular number the maximum was reached at childhood (approximately 1 year). CaMaxFreq was lower in early bone (approximately 21 wt%) than in mineralized cartilage (approximately 29 wt%) and adolescent bone (approximately 23 wt%). In conclusion, the changes at the tissue level were observed to continue throughout life while the development of bone at the material level (CaMaxFreq, mineral particle thickness and orientation) is essentially complete after the first years of life. CaMaxFreq and mean particle thickness increase rapidly during the first years and reach saturation. Remarkably, when these parameters are plotted versus logarithm of age, they appear linear.

Trabecular shear stress in human vertebral cancellous bone: intra- and inter-individual variations

Correlation of the mean and standard deviation of trabecular stresses has been proposed as a mechanism by which a strong relationship between the apparent strength and stiffness of cancellous bone can be achieved. The current study examined whether the relationship between the mean and standard deviation of trabecular von Mises stresses can be generalized for any group of cancellous bone. Cylindrical human vertebral cancellous bone specimens were cut in the infero-superior direction from T12 of 23 individuals (inter-individual group). Thirty nine additional specimens were prepared similarly from the T4-T12 and L2-L5 vertebrae of a 63 year old male (intra-individual group). The specimens were scanned by micro-computed tomography (microCT) and trabecular von Mises stresses were calculated using finite element modeling. The expected value, standard deviation and coefficient of variation of the von Mises stress were calculated form a three-parameter Weibull function fitted to von Mises stress data from each specimen. It was found that the average and standard deviation of trabecular von Mises shear stress were: (i) correlated with each other, supporting the idea that high correlation between the apparent strength and stiffness of cancellous bone can be achieved through controlling the trabecular level shear stress variations, (ii) dependent on anatomical site and sample group, suggesting that the variation of stresses are correlated to the mean stress to different degrees between vertebrae and individuals, and (iii) dependent on bone volume fraction, consistent with the idea that shear stress is less well controlled in bones with low BV/TV. The conversion of infero-superior loading into trabecular von Mises stresses was maximum for the tissue at the junction of the thoracic and lumbar spine (T12-L1) consistent with this junction being a common site of vertebral fracture.

NACOB presentation Keynote lecture. Cancellous bone biomechanics. North American Congress on Biomechanics

Cancellous bone is both a biological and a mechanical structure. The interaction between these two aspects of cancellous bone is sufficiently strong that understanding the mechanical properties of the tissue is not possible without consideration of the biology. This manuscript is a mathematical expansion of a portion of the first author's Keynote lecture at the 1998 NACOB presentation. The cellular activity of cancellous bone proceeds in part by the transport of metabolites between trabecular hard tissue and marrow. The anatomical observation is that human trabeculae are seldom internally served by a blood supply, suggesting that the transport mechanisms for trabecular survival are diffusion and a collection of mechanisms for active transport of metabolites independent of blood flow. It will be demonstrated that metabolite transport by diffusion can explain two notable empirical relationships for bone: (a) the close relationship between the bone surface and the bone volume, and (b) the exponential decline in the bone volume fraction during periods of mechanical disuse. A mathematical model is also developed showing how mechanical loading can effect bone volume fraction by increasing metabolite transport between the tissue compartments.

External and internal macromorphology in 3D-reconstructed maxillary molars using computerized X-ray microtomography

AIM

The aim of this study was to perform a qualitative analysis of the relationship between the external and internal macromorphology of the root complex and to use fractal dimension analysis to determine the correlation between the shape of the outer surface of the root and the shape of the root canal.

METHODOLOGY

On the basis of X-ray computed transaxial microtomography, a qualitative and quantitative analysis of the external and internal macromorphology of the root complex in permanent maxillary molars was performed using well-defined macromorphological variables and fractal dimension analysis. Five maxillary molars were placed between a microfocus X-ray tube with a focal spot size of 0.07 mm, a Thomson-SCF image intensifier, and a CCD camera compromising a detector for the tomograph. Between 100 and 240 tomographic 2D slices were made of each tooth. Assembling slices for 3D volume was carried out with subsequent median noise filtering. Segmentation into enamel, dentine and pulp space was achieved through thresholding followed by morphological filtering. Surface representations were then constructed. A useful visualization of the tooth was created by making the dental hard tissues transparent and the pulp chamber and root-canal system opaque. On this basis it became possible to assess the relationship between the external and internal macromorphology of the crown and root complex.

RESULTS

There was strong agreement between the number, position and cross-section of the root canals and the number, position and degree of manifestation of the root complex macrostructures. Data from a fractal dimension analysis also showed a high correlation between the shape of the root canals and the corresponding roots.

CONCLUSIONS

It is suggested that these types of 3D volumes constitute a platform for preclinical training in fundamental endodontic procedures.

Human vertebral body apparent and hard tissue stiffness

Cancellous bone apparent stiffness and strength are dependent upon material properties at the tissue level and trabecular architecture. Microstructurally accurate, large-scale finite element (LS-FE) models were used to predict the experimental apparent stiffness of human vertebral cancellous bone and to estimate the trabecular hard tissue stiffness. Twenty-eight LS-FE models of cylindrical human vertebral cancellous bone specimens (8 mm in diameter, 9.5 mm in height, one each from twenty-eight individuals) were generated directly from microcomputed tomography images and solved by a special purpose iterative finite element program. The experimental apparent stiffness and strength of the specimens were determined by mechanical testing to failure in the infero superior direction. Morphometric measurements including bone volume fraction (BV/TV), three eigenvalues of the fabric tensor and average P(L) were also calculated. The finite element estimate of apparent stiffness explained much of the variance in both experimental apparent stiffness (r2=0.89) and experimental apparent strength (r2=0.87). Stepwise linear regression analysis demonstrated that the LS-FE estimated apparent stiffness was the only significant predictor of experimental apparent stiffness and strength when it was included with all measured morphometric values. Hard tissue stiffness was quite variable between individuals (mean, 5.7 GPa; S.D. 1.6 GPa), but was not significantly related to age, sex, race, weight or morphometric measures for this sample.

Modeling the mechanical behavior of vertebral trabecular bone: effects of age-related changes in microstructure

Age-related reductions in the thickness and number of trabeculae in vertebral trabecular bone have been documented by several workers, yet the relative effects of these changes on mechanical properties are not known. We developed a two-dimensional model of human vertebral trabecular bone and investigated its mechanical behavior using finite element analysis. The stress-strain behavior, failure mode, and strain distributions predicted using the model were consistent with those observed for vertebral trabecular bone under compressive loading. Random reductions in the number of trabeculae reduced the modulus and strength of the models two to five times more than uniform reductions in the thickness of trabeculae that caused the same loss of bone volume. For example, randomly removing longitudinal trabeculae to achieve a reduction in density of 10% reduced the strength by approximately 70%, whereas removing the same amount of bone by uniformly reducing the thickness of the longitudinal trabeculae only reduced the strength by approximately 20%. For a simulation of aged bone, in which the thickness and number of trabeculae were reduced concurrently, the strength was 23% of its intact ("young") value. When the bone mass of the aged model was restored to its intact level by increasing the thickness but not the number of trabeculae, the strength increased by 60%, but was still only 37% of its intact value. These combined findings, based on a two-dimensional, idealized model of vertebral trabecular bone, illustrate the importance of maintaining trabecular number and suggest that it may not be possible to restore bone strength following a period of advanced bone loss if a substantial number of trabeculae have been resorbed. Thus, until treatments exist that can increase trabecular number, the most effective treatment strategy is to prevent the degradation of bone strength by maintaining the number of trabeculae at a healthy level.

Quantitative analysis of trabecular morphogenesis in the human costochondral junction during the postnatal period in normal subjects

BACKGROUND

Quantitative histomorphometric features of the bone growth plate in the human rib have been investigated in infants, ranging in age from 3-36 weeks (mean 18.6 weeks) to provide data currently not available.

METHODS

Measurements were taken in each histological zone of the growth plate. Data from 20 cases were pooled and parameters describing the characteristic features of trabecular bone calculated using morphometric formulae. The measurements were made from the resting zone of the cartilage to the secondary spongiosa, 3.78 mm from the starting point.

RESULTS

Cartilage volume fraction decreased from 78% in the resting zone to a bone volume fraction of between 20% and 30% in the secondary cancellous bone. Cartilage matrix surface increased rapidly in the cartilage and bone mineral surface declined in correspondence with the development of primary bone. The distance between chondrocyte lacunae was observed to decrease throughout the cartilage to a transverse septa thickness of 18 microns in the hypertrophic zone. A rapid increase in trabecular thickness to 128 microns was observed in the primary spongiosa, the secondary spongiosa ranging between 137 microns and 168 microns. Spacing, chondrocyte profile transverse diameter, increased to 30 microns in the hypertrophic zone, following which an increase in trabecular separation to 347 microns was observed in the primary spongiosa. The number of transverse intervals between individual chondrocyte lacunae was observed to increase in the cartilage to a maximum of 21.3 cartilaginous or mineralised septa per mm of growth plate length in the hypertrophic zone. Trabeculae in the metaphysis then decreased in number to approximately 1.5 trabeculae per mm in the secondary spongiosa.

CONCLUSIONS

These data thus provide new insight into the development of trabecular structure during growth and normal values for the comparison of tissue from skeletal dysplasias and growth disorders.