Compressive axial strain distributions in cancellous bone specimens

High-resolution local trabecular strain within trabecular structure under cyclic loading

Trabecular bone structure is a complex microstructure consisting of rods and plates, which poses challenges for its mechanical characterization. Digital image correlation (DIC) offers the possibility to characterize the strain response on the surface of trabecular bone. This study employed DIC equipped with a telecentric lens to investigate the strain state of individual trabeculae within their trabecular structure by assessing the longitudinal strain of the trabeculae at both the middle and near the edges of the trabeculae. Due to the high-resolution of the used DIC system, local surface strain of trabeculae was analyzed too. Lastly, the correlation between longitudinal trabecular strain and the orientation and slenderness of the trabeculae was investigated. The results showed that the strain magnification close to the edge of the trabeculae was higher and reached up to 8-folds the strain along the middle of the trabeculae. On the contrary, no strain magnification was found for most of the trabeculae between the longitudinal trabecular strain along the middle of the trabeculae and the globally applied strain. High-resolution full-field strain maps were obtained on the surface of trabeculae showing heterogeneous strain distribution with increasing load. No significant correlation was found between longitudinal trabecular strain and its orientation or slenderness. These findings and the applied methodology can be used to broaden our understanding of the deformation mechanisms of trabeculae within the trabecular network.

Anisotropy, Anatomical Region, and Additional Variables Influence Young's Modulus of Bone: A Systematic Review and Meta-Analysis

The importance of finite element analysis (FEA) is growing in orthopedic research, especially in implant design. However, Young's modulus (E) values, one of the most fundamental parameters, can range across a wide scale. Therefore, our study aimed to identify factors influencing E values in human bone specimens. We report our systematic review and meta-analysis based on the recommendation of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guideline. We conducted the analysis on November 21, 2021. We included studies investigating healthy human bone specimens and reported on E values regarding demographic data, specimen characteristics, and measurement specifics. In addition, we included study types reporting individual specimen measurements. From the acquired data, we created a cohort in which we performed an exploratory data analysis that included the explanatory variables selected by random forest and regression trees methods, and the comparison of groups using independent samples Welch's t test. A total of 756 entries were included from 48 articles. Eleven different bones of the human body were included in these articles. The range of E values is between 0.008 and 33.7 GPa. The E values were most heavily influenced by the cortical or cancellous type of bone tested. Measuring method (compression, tension, bending, and nanoindentation), the anatomical region within a bone, the position of the bone within the skeleton, and the bone specimen size had a decreasing impact on the E values. Bone anisotropy, specimen condition, patient age, and sex were selected as important variables considering the value of E. On the basis of our results, E values of a bone change with bone characteristics, measurement techniques, and demographic variables. Therefore, the evaluation of FEA should be performed after the standardization of in vitro measurement protocol. © 2023 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Effects of loading rate, age, and morphology on the material properties of human rib trabecular bone

The material and morphometric properties of trabecular bone have been studied extensively in bones bearing significant weight, such as the appendicular long bones and spine. Less attention has been devoted to the ribs, where quantification of material properties is vital to understanding thoracic injury. The objective of this study was to quantify the compressive material properties of human rib trabecular bone and assess the effects of loading rate, age, and morphology on the material properties. Material properties were quantified via uniaxial compression tests performed on trabecular bone samples at two loading rates: 0.005 s^-1 and 0.5 s^-1. Morphometric parameters of each sample were quantified before testing using micro-computed tomography. Rib trabecular bone material properties were lower on average compared to trabecular bone from other anatomical locations. Morphometric parameters indicated an anisotropic structure with low connectivity and a sparser density of trabeculae in the rib compared to other locations. No significant differences in material properties were observed between the tested loading rates. Material properties were only significantly correlated with age at the 0.005 s^-1 loading rate, and no morphometric parameter was significantly correlated with age. Trabecular separation and thickness were most strongly correlated with the material properties, indicating the sparser trabecular matrix likely contributed to the lower material property values compared to other sites. The novel trabecular bone material properties reported in this study can be used to improve the thoracic response and injury prediction of computational models.

Novel microcomposite implant for the controlled delivery of antibiotics in the treatment of osteomyelitis following total joint replacement

The objective of this study was to develop a novel microcomposite implant to be used in the treatment of osteomyelitis following total joint arthroplasty, with the dual purpose of releasing high local concentrations of antibiotic to eradicate the infection while providing adequate mechanical strength to maintain the dynamic or static spacer. Vancomycin-loaded microcomposite implants were fabricated by incorporating drug-loaded microparticles comprised of mesoporous silica into commonly employed polymethylmethacrylate (PMMA) bone cement, to yield a final drug loading of 10% w/w. In vitro release kinetics at 37°C were monitored by reverse-phase high-performance liquid chromatography, and compared to the release kinetics of current therapy implants consisting of drug alone incorporated at 10% w/w directly into PMMA bone cement. Results demonstrated a sevenfold improvement in the elution profile of microcomposite systems over current therapy implants. In vivo delivery of vancomycin to bone from microcomposite implants (70% of payload) was significantly higher than that from current therapy implants (approx. 22% of payload) and maintained significantly higher bone concentrations for up to 2 weeks duration. The elastic modulus showed no statistical difference between microcomposite implants and current standard therapy implants before drug elution, and maintenance of acceptable strength of microcomposite implants postdrug elution. These results demonstrate that we have developed a novel microcomposite spacer that will release continuously high antibiotic concentrations over a prolonged period of time, offering the possibility to eliminate infection and avoid the emergence of new resistant bacterial strains, while maintaining the requisite mechanical properties for proper space maintenance and joint fixation.

Sub-trabecular strain evolution in human trabecular bone

To comprehend the most detrimental characteristics behind bone fractures, it is key to understand the material and tissue level strain limits and their relation to failure sites. The aim of this study was to investigate the three-dimensional strain distribution and its evolution during loading at the sub-trabecular level in trabecular bone tissue. Human cadaver trabecular bone samples were compressed in situ until failure, while imaging with high-resolution synchrotron radiation X-ray tomography. Digital volume correlation was used to determine the strains inside the trabeculae. Regions without emerging damage were compared to those about to crack. Local strains in close vicinity of developing cracks were higher than previously reported for a whole trabecular structure and similar to those reported for single isolated trabeculae. Early literature on bone fracture strain thresholds at the tissue level seem to underestimate the maximum strain magnitudes in trabecular bone. Furthermore, we found lower strain levels and a reduced ability to capture detailed crack-paths with increased image voxel size. This highlights the dependence between the observed strain levels and the voxel size and that high-resolution is needed to investigate behavior of individual trabeculae. Furthermore, low trabecular thickness appears to be one predictor of developing cracks. In summary, this study investigated the local strains in whole trabecular structure at sub-trabecular resolution in human bone and confirmed the high strain magnitudes reported for single trabeculae under loading and, importantly extends its translation to the whole trabecular structure.

Empirical relationships between bone density and ultimate strength: A literature review

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

High-precision method for cyclic loading of small-animal vertebrae to assess bone quality

One potentially important bone quality characteristic is the response of bone to cyclic (repetitive) mechanical loading. In small animals, such as in rats and mice, cyclic loading experiments are particularly challenging to perform in a precise manner due to the small size of the bones and difficult-to-eliminate machine compliance. Addressing this issue, we developed a precise method for ex vivo cyclic compressive loading of isolated mouse vertebral bodies. The method has three key characteristics: 3D-printed support jigs for machining plano-parallel surfaces of the tiny vertebrae; pivotable loading platens to ensure uniform contact and loading of specimen surfaces; and specimen-specific micro-CT-based finite element analysis to measure stiffness to prescribe force levels that produce the same specified level of strain for all test specimens. To demonstrate utility, we measured fatigue life for three groups (n = 5–6 per group) of L5 vertebrae of C57BL/6J male mice, comparing our new method against two methods commonly used in the literature. We found reduced scatter of the mechanical behavior for this new method compared to the literature methods. In particular, for a controlled level of strain, the standard deviation of the measured fatigue life was up to 5-fold lower for the new method (F-ratio = 4.9; p < 0.01). The improved precision for this new method for biomechanical testing of small-animal vertebrae may help elucidate aspects of bone quality.

Standardizing compression testing for measuring the stiffness of human bone

Objectives

The ability to determine human bone stiffness is of clinical relevance in many fields, including bone quality assessment and orthopaedic prosthesis design. Stiffness can be measured using compression testing, an experimental technique commonly used to test bone specimens in vitro. This systematic review aims to determine how best to perform compression testing of human bone.

Methods

A keyword search of all English language articles up until December 2017 of compression testing of bone was undertaken in Medline, Embase, PubMed, and Scopus databases. Studies using bulk tissue, animal tissue, whole bone, or testing techniques other than compression testing were excluded.

Results

A total of 4712 abstracts were retrieved, with 177 papers included in the analysis; 20 studies directly analyzed the compression testing technique to improve the accuracy of testing. Several influencing factors should be considered when testing bone samples in compression. These include the method of data analysis, specimen storage, specimen preparation, testing configuration, and loading protocol.

Conclusion

Compression testing is a widely used technique for measuring the stiffness of bone but there is a great deal of inter-study variation in experimental techniques across the literature. Based on best evidence from the literature, suggestions for bone compression testing are made in this review, although further studies are needed to establish standardized bone testing techniques in order to increase the comparability and reliability of bone stiffness studies.

Cite this article: S. Zhao, M. Arnold, S. Ma, R. L. Abel, J. P. Cobb, U. Hansen, O. Boughton. Standardizing compression testing for measuring the stiffness of human bone. Bone Joint Res 2018;7:524–538. DOI: 10.1302/2046-3758.78.BJR-2018-0025.R1.

METHODS FOR THE CHARACTERIZATION OF THE LONG-TERM MECHANICAL PERFORMANCE OF CEMENTS FOR VERTEBROPLASTY AND KYPHOPLASTY: CRITICAL REVIEW AND SUGGESTIONS FOR TEST METHODS

There is a growing interest towards bone cements for use in vertebroplasty and kyphoplasty, as such spine procedures are becoming more and more common. Such cements feature different compositions, including both traditional acrylic cements and resorbable and bioactive materials. Due to the different compositions and intended use, the mechanical requirements of cements for spinal applications differ from those of traditional cements used in joint replacement. Because of the great clinical implications, it is very important to assess their long-term mechanical competence in terms of fatigue strength and creep. This paper aims at offering a critical overview of the methods currently adopted for such mechanical tests. The existing international standards and guidelines and the literature were searched for publications relevant to fatigue and creep of cements for vertebroplasty and kyphoplasty. While standard methods are available for traditional bone cements in general, no standard indicates specific methods or acceptance criteria for fatigue and creep of cements for vertebroplasty and kyphoplasty. Similarly, a large number of papers were published on cements for joint replacements, but only few cover fatigue and creep of cements for vertebroplasty and kyphoplasty. Furthermore, the literature was analyzed to provide some indications of tests parameters and acceptance criteria (number of cycles, duration in time, stress levels, acceptable amount of creep) for possible tests specifically relevant to cements for spinal applications.

Failure behaviour of rat vertebrae determined through simultaneous compression testing and micro-CT imaging

Skeletal fractures, including those resulting from osteoporosis, result in significant healthcare and societal costs on an annual basis. Therefore, it is important to understand the mechanisms by which these fractures occur. Incremental compression testing combined with micro-CT imaging has been used to visualize the progression of failure in trabecular bone samples; however, these studies have ignored the potential contributions of the cortical shell. In the current study, incremental compression testing with simultaneous micro-CT imaging was performed on rat vertebrae from multiple disease states (healthy control, osteoporotic, osteoporotic + treatment). These tests allowed the progression of failure through an entire vertebral body to be visualized for the first time. Three distinct failure modes were observed throughout all specimens, independent of disease state. Two of these failure modes (types I and II), which were observed in 93% of all specimens, were associated with the vascular apertures in the vertebrae's dorsal and ventral surfaces. This behaviour is likely caused by the stress concentrations in the cortical shell resulting from the apertures themselves, coupled with the reduced trabecular bone volume adjacent to them. These results suggest that the combined contributions of both the cortical shell and trabecular bone must be considered when studying the compressive failure behaviour of rat vertebrae.

The Tarsometatarsus of the Ostrich Struthio camelus: Anatomy, Bone Densities, and Structural Mechanics

Background

The ostrich Struthio camelus reaches the highest speeds of any extant biped, and has been an extraordinary subject for studies of soft-tissue anatomy and dynamics of locomotion. An elongate tarsometatarsus in adult ostriches contributes to their speed. The internal osteology of the tarsometatarsus, and its mechanical response to forces of running, are potentially revealing about ostrich foot function.

Methods/Principal Findings

Computed tomography (CT) reveals anatomy and bone densities in tarsometatarsi of an adult and a young juvenile ostrich. A finite element (FE) model for the adult was constructed with properties of compact and cancellous bone where these respective tissues predominate in the original specimen. The model was subjected to a quasi-static analysis under the midstance ground reaction and muscular forces of a fast run. Anatomy–Metatarsals are divided proximally and distally and unify around a single internal cavity in most adult tarsometatarsus shafts, but the juvenile retains an internal three-part division of metatarsals throughout the element. The juvenile has a sparsely ossified hypotarsus for insertion of the m. fibularis longus, as part of a proximally separate third metatarsal. Bone is denser in all regions of the adult tarsometatarsus, with cancellous bone concentrated at proximal and distal articulations, and highly dense compact bone throughout the shaft. Biomechanics–FE simulations show stress and strain are much greater at midshaft than at force applications, suggesting that shaft bending is the most important stressor of the tarsometatarsus. Contraction of digital flexors, inducing a posterior force at the TMT distal condyles, likely reduces buildup of tensile stresses in the bone by inducing compression at these locations, and counteracts bending loads. Safety factors are high for von Mises stress, consistent with faster running speeds known for ostriches.

Conclusions/Significance

High safety factors suggest that bone densities and anatomy of the ostrich tarsometatarsus confer strength for selectively critical activities, such as fleeing and kicking predators. Anatomical results and FE modeling of the ostrich tarsometatarsus are a useful baseline for testing the structure’s capabilities and constraints for locomotion, through ontogeny and the full step cycle. With this foundation, future analyses can incorporate behaviorally realistic strain rates and distal joint forces, experimental validation, and proximal elements of the ostrich hind limb.

Comparative biomechanical and microstructural analysis of native versus peracetic acid-ethanol treated cancellous bone graft

Bone transplantation is frequently used for the treatment of large osseous defects. The availability of autologous bone grafts as the current biological gold standard is limited and there is a risk of donor site morbidity. Allogenic bone grafts are an appealing alternative, but disinfection should be considered to reduce transmission of infection disorders. Peracetic acid-ethanol (PE) treatment has been proven reliable and effective for disinfection of human bone allografts. The purpose of this study was to evaluate the effects of PE treatment on the biomechanical properties and microstructure of cancellous bone grafts (CBG). Forty-eight human CBG cylinders were either treated by PE or frozen at −20°C and subjected to compression testing and histological and scanning electron microscopy (SEM) analysis. The levels of compressive strength, stiffness (Young's modulus), and fracture energy were significantly decreased upon PE treatment by 54%, 59%, and 36%, respectively. Furthermore, PE-treated CBG demonstrated a 42% increase in ultimate strain. SEM revealed a modified microstructure of CBG with an exposed collagen fiber network after PE treatment. We conclude that the observed reduced compressive strength and reduced stiffness may be beneficial during tissue remodeling thereby explaining the excellent clinical performance of PE-treated CBG.

Patient-specific modelling of bone and bone-implant systems: the challenges

In the past three decades, finite element (FE) modelling has provided considerable understanding to the area of musculoskeletal biomechanics. However, most of this understanding has been generated using generic, standardised or idealised models. Patient-specific modelling (PSM) is almost never used for making clinical decisions. Imaging technologies have made it possible to create patient-specific geometries and FE meshes for modelling. While these have brought us closer to PSM, several challenges associated with the definition of material properties, loads, boundary conditions and interaction between components still need to be overcome. This study reviews the current status of PSM with respect to defining material behaviour and prescribing boundary conditions and interactions. With regard to the constitutive modelling of bone, it is seen that imaging is being increasingly used to define elastic properties (isotropic as well as anisotropic). However, the post-elastic and time-dependent behaviour, important for several modelling situations, is mostly obtained from in vitro experiments. Strain-based plasticity, not commonly available in FE codes, appears to have the potential of reducing an element of patient-specificity in modelling the yielding behaviour of bone. PSM of real boundary conditions that include muscles and ligaments continues to remain a challenge; many clinically relevant questions can be, however, answered without their inclusion. Simulation techniques to undertake PSM of interactions between bone and uncemented implants are available. Interference fit employed in both joint replacement fracture treatments induces considerable preload whose inclusion in models is important for the prediction of interface behaviour.

High-Speed Photography of Human Trabecular Bone during Compression

The mechanical properties of healthy and diseased bone tissue are extensively studied in mechanical tests. Most of this research is motivated by the immense costs of health care and social impacts due to osteoporosis in post-menopausal women and the aged. Osteoporosis results in bone loss and change of trabecular architecture, causing a decrease in bone strength. To address the problem of assessing local failure behavior of bone, we combined mechanical compression testing of trabecular bone samples with high-speed photography. In this exploratory study, we investigated healthy, osteoarthritic, and osteoporotic human vertebral trabecular bone compressed at high strain rates simulating conditions experienced in individuals during falls. Apparent strains were found to translate to a broad range of local strains. Moreover, strained trabeculae were seen to whiten with increasing strain. We hypothesize that the effect seen is due to microcrack formation in these areas, similar to stress whitening seen in synthetic polymers. From the results of a motion energy filter applied to the recorded movies, we saw that the whitened areas are, presumably, also of high deformation. We believe that this method will allow further insights into bone failure mechanisms, and help toward a better understanding of the processes involved in bone failure.

Microarchitectural adaptations in aging and osteoarthrotic subchondral bone issues

The human skeleton optimizes its microarchitecture by elaborate adaptations to mechanical loading during development and growth. The mechanisms for adaptation involve a multistep process of cellular mechanotransduction stimulating bone modelling, and remodeling resulting in either bone formation or resorption. This process causes appropriate microarchitectural changes tending to adjust and improve the bone structure to its prevailing mechanical environment. Normal individual reaches peak bone mass at age between 25 and 30 years, and thereafter bone mass declines with age in both genders. The bone loss is accompanied by microarchitectural deterioration resulting in reduced mechanical strength likely leading to fragility fractures. With aging, inevitable bone loss occurs, which is frequently the cause of osteoporosis; and inevitable bone and joint degeneration happens, which often results in osteoarthrosis. These diseases are among the major health care problems in terms of socio-economic costs. The overall goals of the current series of studies were to investigate the age-related and osteoarthrosis (OA) related changes in the 3-D microarchitectural properties, mechanical properties, collagen and mineral quality of subchondral cancellous and cortical bone tissues. The studies included mainly two parts. For human subjects: aging- (I–IV) and early OArelated (V–VI) changes in cancellous bone properties were assessed. For OA guinea pig models (VII–IX), three topics were studied: firstly, the spontaneous, age-related development of guinea pig OA; secondly, the potential effects of hyaluronan on OA subchondral bone tissues; and thirdly, the effects on OA progression of an increase in subchondral bone density by inhibition of bone remodeling with a bisphosphonate. These investigations aimed to obtain more insight into the age-related and OA-related subchondral bone adaptations.

TGFbeta3 and loading increases osteocyte survival in human cancellous bone cultured ex vivo

The goal of this study was to assess the effect of the addition of TGFbeta(3), alone or in combination with loading, on the survival of osteocytes in 3D human explant cancellous bone during long-term culture in an ex vivo loading bioreactor. Human cancellous bone explants were cultured for up to 14 days with or without TGFbeta(3) (15 ng ml(-1)) and with or without loading (300 cycles, at 1 Hz, producing 4000 microstrain). Bone core response was visualized using undecalcified histology with morphological methods after embedding with Technovit 9100 New resin. Histological examination revealed normal gross level bone structure with or without the application of load or the addition of TGFbeta(3). The viability of the osteocytes within the bone was assessed by lactate dehydrogenase (LDH) activity. We demonstrate that this ex vivo loading bioreactor is able to maintain a high percentage (over 50%) of viable osteocytes throughout the bone explants after 14 days in ex vivo culture. Further to this, the combination of daily loading and TGFbeta(3) administration produced superior osteocyte survival at the core centres when compared to loading or TGFbeta alone.

Elastic strains in antler trabecular bone determined by synchrotron X-ray diffraction

The microstructure and associated mechanical properties of antler trabecular bone have been studied using a variety of techniques. The local trabeculae properties, as well as the three-dimensional architecture were characterized using nanoindentation and X-ray microtomography, respectively. An elastic modulus of 10.9+/-1.1 GPa is reported for dry bone, compared with 5.4+/-0.9 GPa for fully hydrated bone. Trabeculae thickness and separation were found to be comparable to those of bovine trabecular bone. Uniaxial compression conducted in situ during X-ray microtomography showed that antler can undergo significant architectural rearrangement, dominated by trabeculae bending and buckling, due to its low mineral content. High-energy synchrotron X-ray diffraction was used to measure elastic strains in the apatite crystals of the trabeculae, also under in situ uniaxial compression. During elastic loading, strain was found to be accommodated largely by trabeculae aligned parallel to the loading direction. Prior to the macroscopic yield point, internal strains increased as trabeculae deformed by bending, and load was also found to be redistributed to trabeculae aligned non-parallel to the loading direction. Significant bending of trabecular walls resulted in tensile strains developing in trabeculae aligned along the loading direction.

The mechanical integrity of in vivo engineered heterotopic bone

Recent advances in tissue engineering have aroused interest in growth of heterotopic bone for the repair of skeletal defects. This study demonstrates an in vivo method in minipigs of engineering individual human-sized mandible replacements of heterotopic bone with a mechanical integrity similar to natural bone. Ten individualized mandible replacement scaffolds were created using computer-aided design (CAD) techniques. Five had a resorbable external scaffold made of polylactite mesh (test group 1) and five had had a non-resorbable external scaffold of titanium mesh (test group 2). The mesh scaffolds were loaded each with five BioOss blocks serving as internal scaffolds and 3.5 mg recombinant human Bone Morphogenetic Protein-7. The loaded mesh scaffolds were implanted into the latissimus dorsi muscles of five infant minipigs. After 6 weeks the mandible replacements were harvested. Core biopsy cylinders were taken from the replacements of both test groups and from the natural pig mandibles (control 1). Also, core biopsies from plain BioOss Blocks were gained (control 2). The core biopsy cylinders were loaded axially into a compression test device to evaluate the mechanical compression resistance. Additional specimen underwent histological examination. Both test groups resulted in successful bone induction with degrees of compression resistance [Test 1: 1.62 MPa (SD+/-0.73); Test 2: 1.51 MPa (SD+/-0.56)] statistically insignificant when compared to natural porcine mandibular bone [1.75 MPa (SD+/-0.69)]. This differed significantly from the much lower compression resistance seen in the unadulterated BioOss [0.92 MPa (SD+/-0.04)]. Following this, the in vivo engineered bone has a similar mechanical compression stability as natural bone.

Comparison of the Linear Finite Element Prediction of Deformation and Strain of Human Cancellous Bone to 3D Digital Volume Correlation Measurements

The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.

Propriétés mécaniques de greffons humains provenant de têtes fémorales et traitées par un procédé d’épuration physico-chimique (Ostéopure™)

PURPOSE OF THE STUDY

Bone grafts and bone substitutes must be biocompatible osteoconductors with satisfactory mechanical properties similar to native bone. When the bone treatment is conducted under specific conditions, the elasticity module under infra-maximal loading can be optimized to achieve reproducible values. The purpose of this work was to determine the effect of the cleaning and sterilization process using Osteopure on the biomechanical properties of trabecular bone harvested from human femoral heads.

MATERIAL AND METHOD

Seventy trabecular bone samples were tested: group 1F (fresh samples); group 1N (after application of Osteopure cleaning); group 1S (after Osteopure cleaning and sterilization). Non-destructive and destructive tests (group 1D) were performed. Two fresh femoral heads were used as controls for the destructive test (group 2). The first non-destructive test was applied directly after section (group 1F). Other samples were then purified with Osteopure treatment and a second non-destructive test was conducted (group 1N). A third non-destructive test was conducted after sterilization with 25 kgray radiation (group 1S). Treatments 1 and 2 were performed by OST Developpement SA (Clermont-Ferrand). Finally a destruction test was applied along the directional axis (group 1D). For the 31 samples in group 2 (control) the destructive test was applied along the directional axis immediately after section. Compression tests were performed at a deformation speed of 3 mm/min for 0.3% deformation.

RESULTS

The Young module did not exhibit any significant difference between the three steps of the testing in the three orthogonal directions. The Young module was not significantly different between group 1F and group 2 (controls). Maximal force of compression was significantly different (P<0.01). There was a linear relationship between maximal force at rupture and the Young module obtained during destructive tests, for groups 1D and 2 respectively. The compression curves obtained from sterilized samples (group 1D) were not significantly different from those observed for fresh trabecular bone in group 2 (controls).

DISCUSSION

The Young module values measured from 70-673 MPa. For non-destructive tests, the module values were to the order of 64% of those obtained for destructive tests. Decreased maximal force of rupture observed for treated samples in comparison with fresh samples can be explained by the extraction of most of the lipids.

CONCLUSION

The Osteopure method does not alter stiffness of bone allografts. The elasticity module observed in treated bones is close to that observed in fresh bones. Mechanical resistance to compression is however only half the force of compression observed in the hip joint for daily activities. The linear relationship between the elasticity mode and loading required for rupture is not affected by treatment with Osteopure. The advantages related to elimination of prions or viral contamination appear by far to be more important than the minor changes observed in the mechanical characteristics of allografts.

A Finite Element Beam-model for Efficient Simulation of Large-scale Porous Structures

This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.

Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone

The objective of this study was to report our quantitative computed tomography (QCT) density-mechanical property regressions for trabecular bone for use in biomechanical modelling of the human spine. Cylindrical specimens of human vertebral trabecular bone (from T10 to L4) were cored from 32 cadavers (mean +/- SD age = 70.1 +/- 16.8; 13 females, 19 males) and scanned using QCT. Mechanical tests were conducted using a protocol that minimized end-artifacts over the apparent density range tested (0.09-0.38 g/cm3). To account for the presence of multiple specimens per donor in this data set, donor was treated as a random effect in the regression model. Mean modulus (319 +/- 189 MPa) was higher and mean yield strain (0.78 +/- 0.06%) was lower than typical values reported previously due to minimization of the end-artifact errors. QCT density showed a strong positive correlation with modulus (n = 76) and yield stress (r2 = 0.90-0.95, n = 53, p < 0.001). There was a weak positive linear correlation with yield strain (r2 = 0.58, n = 53, p = 0.07). Prediction errors, incurred when estimating modulus or strength for specimens from a new donor, were 30-36% of the mean values of these properties. Direct QCT density-mechanical property regressions gave more precise predictions of mechanical properties than if physically measured wet apparent density was used as an intermediate variable to predict mechanical properties from QCT density. Use of these QCT density-mechanical property regressions should improve the fidelity of QCT-based biomechanical models of the human spine for whole bone and bone-implant analyses.

Biomechanics of trabecular bone

Trabecular bone is a complex material with substantial heterogeneity. Its elastic and strength properties vary widely across anatomic sites, and with aging and disease. Although these properties depend very much on density, the role of architecture and tissue material properties remain uncertain. It is interesting that the strains at which the bone fails are almost independent of density. Current work addresses the underlying structure-function relations for such behavior, as well as more complex mechanical behavior, such as multiaxial loading, time-dependent failure, and damage accumulation. A unique tool for studying such behavior is the microstructural class of finite element models, particularly the "high-resolution" models. It is expected that with continued progress in this field, substantial insight will be gained into such important problems as osteoporosis, bone fracture, bone remodeling, and design/analysis of bone-implant systems. This article reviews the state of the art in trabecular bone biomechanics, focusing on the mechanical aspects, and attempts to identify important areas of current and future research.

The prospects of estimating trabecular bone tissue properties from the combination of ultrasound, dual-energy X-ray absorptiometry, microcomputed tomography, and microfinite element analysis

Osteoporosis commonly is assessed by bone quantity, using bone mineral density (BMD) measurements from dual-energy X-ray absorptiometry (DXA). However, such a measure gives neither information about the integrity of the trabecular architecture nor about the mechanical properties of the constituting trabeculae. We investigated the feasibility of deriving the elastic modulus of the trabeculae (the tissue modulus) from computer simulation of mechanical testing by microfinite element analysis (muFEA) in combination with measurements of ultrasound speed of sound (SOS) and BMD measurements. This approach was tested on 15 postmortem bovine bone cubes. The apparent elastic modulus of the specimens was estimated from SOS measurements in combination with BMD. Then the trabecular morphology was reconstructed using microcomputed tomography (muCT). From the reconstruction a mesh for muFEA was derived, used to simulate mechanical testing. The tissue modulus was found by correlating the apparent moduli of the specimens as assessed by ultrasound with the ones as determined with muFEA. A mean tissue modulus of 4.5 GPa (SD, 0.69) was found. When adjusting the muFEA-determined elastic moduli of the entire specimens with their calculated tissue modulus, an overall correlation of R2 = 96% with ultrasound-predicted values was obtained. We conclude that the apparent elastic stiffness characteristics as determined from ultrasound correlate linearly with those from muFEA. From both methods in combination, the elastic stiffness of the mineralized tissue can be determined as an estimator for mechanical tissue quality. This method can already be used for biopsy specimens, and potentially could be applicable in vivo as well, when clinical CT or magnetic resonance imaging (MRI) tools with adequate resolution reach the market. In this way, mechanical bone quality could be estimated more accurately in clinical practice.

Measurement of strain distributions within vertebral body sections by texture correlation

STUDY DESIGN

A high-resolution strain measurement technique was applied to axially loaded parasagittal sections from thoracic spinal segments.

OBJECTIVES

To establish a new experimental technique, develop data analysis procedures, characterize intrasample shear strain distributions, and measure intersample variability within a group of morphologically diverse samples.

SUMMARY OF BACKGROUND DATA

Compression of intact vertebral bodies yields structural stiffness and strength, but not strain patterns within the trabecular bone. Finite element models yield trabecular strains but require uncertain boundary conditions and material properties.

METHODS

Six spinal segments (T8-T10) were sliced in parasagittal sections 6-mm thick. Axial compression was applied in 25-N increments up to sample failure, then the load was removed. Contact radiographs of the samples were made at each loading level. Strain distributions within the central vertebral body were measured from the contact radiographs by an image correlation procedure.

RESULTS

Intrasample shear strain probability distributions were log-normal at all load levels. Shear strains were concentrated directly inferior to the superior end-plate and adjacent to the anterior cortex, in regions where fractures are commonly seen clinically. Load removal restored overall sample shape, but measurable residual strains remained.

CONCLUSIONS

This experimental model is a suitable means of studying low-energy vertebral fractures. The methods of data interpretation are consistent and reliable, and strain patterns correlate with clinical fracture patterns. Quantification of intersample variability provides guidelines for the design of future experiments, and the strain patterns form a basis for validation of finite element models. The results imply that strain uniformity is an important criterion in assessing risk of vertebral failure.

Mechanical properties of vertebrate hard tissues

The main mechanical properties of bone and dentine are reviewed.

The effect of boundary conditions on experimentally measured trabecular strain in the thoracic spine

Vertebral bodies are the primary structural entities of the spine, and trabecular bone is the dominant material from which vertebral bodies are composed. Understanding the mechanical characteristics of vertebral trabecular bone, therefore, is of critical importance in the many clinical conditions that affect the spine. Numerous studies have loaded vertebral bodies to investigate the influence of trabecular bone characteristics on deformation and failure patterns, but the methods of load application have been inconsistent. These differences in the method of load application are a potential confounding factor in the interpretation of the experimental results. We investigated this problem by measuring the distribution of minimum principal strain and maximum shear strain magnitude within 6.35 mm thick samples cut from thoracic spine segments (T8-T10) and loaded to simulate three common experimental configurations. Measurements were made using the texture correlation technique, which extracts deformation patterns from digitized contact radiographs of samples under load. The three loading configurations examined were a three-body construct, a single vertebral body loaded through sectioned intervertebral discs, and polymethylmethacrylate molded directly to the endplates. Results indicate that from both probability and spatial distribution standpoints the best simulation of in vivo loading generates the least uniform strains. Loading through disc remnants or through plastic molded to the endplates causes increasing degrees of strain homogenization. This result has implications not only for the design of experiments involving spinal loading, but also for theories concerning the adaptation of trabecular bone to functional loads.

Stereological analysis of bone architecture in the pig zygomatic arch

BACKGROUND

Stereological analysis of trabecular bone structure may reveal information about regional variations in stress distribution, especially in areas like the zygomatic arch in which those variations are difficult to assess mechanically. This study investigates regional differences in trabecular orientation, thickness, and density in the zygomatic and squamosal bones of pigs.

METHODS

Zygomatic arches were serially sectioned frontally (n = 4), horizontally (n = 4), or parasagittally (n = 4), at a thickness of 0.8 mm. Sections were viewed under a stereomicroscope; video-images were digitized and analyzed with an automated program.

RESULTS

All regions were anisotropic. Predominant orientation of trabeculae differed between and within bones. Three main patterns were seen. Anteriorly, zygomatic trabeculae were mainly arranged vertically and anteroposteriorly (relative to the occlusal plane). Posteriorly, including the jaw joint region, the squamosal featured primarily mediolateral trabeculae. In the midsection of the arch, where the two bones overlap, the trabeculae displayed a predominantly anteroposterior orientation with a secondary mediolateral peak. Trabeculae were typically 0.3-0.4 mm wide and occupied 40-50% of the area of the sections with few regional variations.

CONCLUSIONS

Trabecular bone in the pig zygomatic arch is arranged orthogonally, relative to the occlusal plane. In conjunction with information from strain gauge recording, these data suggest that the zygomatic bone is bent in the parasagittal plane whereas the squamosal is bent out-of-plane. The mediolateral trabeculae in the posterior regions are consistent with a cantilever effect at the jaw joint.

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.

Systematic and random errors in compression testing of trabecular bone

We sought to quantify the systematic and random errors associated with end-artifacts in the platens compression test for trabecular bone. Our hypothesis was that while errors may depend on anatomic site, they do not depend on apparent density and therefore have substantial random components. Trabecular bone specimens were first tested nondestructively using newly developed accurate protocols and then were tested again using the platens compression test. Percentage differences in modulus between the techniques (bovine proximal tibia [n = 18] and humerus [n = 17] and human lumbar spine, [n = 9]) were in the range of 4-86%. These differences did not depend on anatomic site (p = 0.21) and were only weakly dependent on apparent density and specimen aspect ratio (r2 < 0.10). The mean percentage difference in modulus was 32.6%, representing the systematic component of the end-artifact error. Neglecting the minor variations explained by density and specimen size (approximately 10%), an upper bound on the random error from end-artifacts in this experiment was taken as the SD of the modulus difference (+/-18.2%). Based on a synthesis of data taken from this study and from the literature, we concluded that the systematic underestimation error in the platens compression test can be only approximated and is in the range of 20-40%; the substantial random error (+/-12.5%) confounds correction, particularly when the sample size is small. These errors should be considered when interpreting results from the platens test, and more accurate testing techniques should be used when such errors are not acceptable.

Anatomic and directional variation in the mechanical properties of the mandibular condyle in pigs

Stereologic studies of trabecular architecture suggest that the pig mandibular condyle is strongest when loaded supero-inferiorly, and that stress is concentrated in the antero-inferior region (Teng and Herring, 1995). To test these hypotheses, we investigated the uni-axial mechanical properties of 22 pig mandibular condyles in three loading directions at a mean strain rate of 0.14 (+/- 0.12)% s-1. A total of 91 rectangular beam specimens (averaging 9.0 mm x 6.0 mm x 5.0 mm) was tested. For each specimen, 5 or 6 non-destructive tests were performed before compressive failure. Strain in both longitudinal and transverse directions was measured by foil strain gauges on the central part of the specimen. Data were normalized at a strain rate of 0.1% s-1, specimen length of 9 mm, and cross-sectional area of 30.25 mm2. Generally, modulus of elasticity (E) and ultimate stress (sigma u) in the anterior regions of the condyle were greater than those in the posterior. E, sigma u, and Poisson's ratio (upsilon) were significantly different among the test directions, but ultimate strain (epsilon u) was not. The highest values of E (4.04 GPa), sigma u (14.97 MPa), and rho (0.81 g/cm3) were seen in the anterior inferior/middle region under supero-inferior loading. The lowest values (0.94 GPa for E, 2.38 MPa for sigma u, and 0.52 g/cm3 for rho) were found in the inferior/posterior region in medio-lateral loading. Although the mechanical properties of the condyle vary depending upon location, these results verify that the condyle is strongest and stiffest under compressive loads in the supero-inferior direction, and that the anterior-inferior region is particularly strong and stiff.

Postfailure compressive behavior of tibial trabecular bone in three anatomic directions

To obtain information describing the postfailure behavior of human proximal tibial trabecular bone, cube specimens of bone were mechanically tested in compression beyond the point of failure. Tests were performed in the three anatomic directions, plots of stress versus strain were obtained, and measures to describe the stress-strain relations before, during, and after failure were defined. These measures included elastic modulus, strength, postfailure slope, strain during maximum stress, and first postfailure minimum stress. For each anatomic direction, analyses were performed to correlate these parameters with ash density. Each of these measures was significantly correlated with ash density at the p < 0.05 level for all test directions, except for postfailure slope, which was correlated in the mediolateral and superior-inferior directions, and strain during maximum stress, which was correlated only in the superior-inferior direction. The data from this study enable trilinear stress-strain relations to be estimated for proximal tibial trabecular bone of various densities, and can serve as a first step toward modeling the behavior of trabecular bone before, during, and after failure.

Texture correlation: a method for the measurement of detailed strain distributions within trabecular bone

A new technique, termed texture correlation, is described for the measurement of displacement and strain patterns within samples of trabecular bone. Texture correlation is a modification of digital image correlation, a method for analysis of deformation in objects marked with random surface speckle. Instead of surface speckle, the trabecular pattern itself is used as a basis for correlation. Digitized contact radiographs of samples in unloaded and loaded states are compared by computer to determine displacements of a grid of points. Displacements are filtered with Savitsky-Golay polynomial-convolution filters to reduce noise, and then strain is calculated with finite element techniques. The method is conceptually similar to the manual measurement of surface markers but has numerous advantages: no marking of the sample is required, displacements are measured automatically by computer, measurement of thousands of displacements is practical, and filtering allows calculation of strain over small regions of the sample. The validity of the technique is demonstrated by comparison of strain patterns measured by texture correlation at low resolution with the same patterns measured by a surface marker technique in six samples of trabecular bone from a human femoral head. The results of texture correlation at full resolution then are presented to demonstrate the capabilities of the method.

Characterization of three formulations of a synthetic foam as models for a range of human cancellous bone types

Porous polyurethane foams were prepared from Daro foam components with a range of mechanical properties to simulate human trabecular bone. Ratios of 10.0:5.0, 10.0:7.9, and 10.0:10.0 isocyanate to resin were mixed, cured, and cut into cubes. Properties were determined from uniaxial compression to 50% of the original cube height at a strain rate of 1.2 mm/s. Electron microscopy was used to characterize the foam structure. Average compressive yield stress values, ultimate compressive stresses, and elastic moduli ranged from 4.44 to 2.79, 5.61 to 3.28, and 134.0 to 110.1 MPa, respectively, for the three formulations. The foam materials showed a similar morphology of spherical bubbles, and the average bubble size tended to decrease as the ratio of isocyanate to resin increased even though the bubble size differences were not statistically significant. The results indicate that large blocks of foam can be prepared with consistent mechanical properties simulating a range of trabecular bone properties so that implants can be tested for various patient populations.

A new method of comparative bone strength measurement

Most investigations of the material properties of bone have been concerned with the measurement of absolute values for various mechanical parameters. It can be necessary, however, to produce test samples with similar mechanical properties in order to assess the effect on these properties of particular treatments. Absolute values for these properties may not be as important as any changes observed. We describe here a new method whereby many bone test samples with very similar mechanical properties can be produced. If the femoral shaft at the diaphysis is cut in transverse section, it is possible to produce many similar shaped rings of bone. We compared the material properties of 48 ring samples with 65 beam specimens. Both were tested in three-point bending. Global estimates of coefficient of variation (CV) for each parameter were used to assess similarity within each group. All the rings had very similar ash weights (1.98%), thicknesses (1.97%), and diameters (< 0.01%). Values of load/deflection of the rings were more similar than the values of Young's modulus (E) for the beams (7.06 versus 9.9%), and the maximum loads sustainable by the rings were more similar than the bending strengths of the beams (5.7 versus 13.6%). The energy absorbed by the ring samples were more consistent than the beams (14.31 versus 34.41%). We suggest that there is improved similarity in mechanical characteristics within groups of samples produced in this manner than with more conventional sample configurations.

Estimation of material properties in the equine metacarpus with use of quantitative computed tomography

The purpose of this study was to investigate the relationships between data obtained from quantitative computed tomography and mechanical properties in the equine metacarpus, as measured in vitro in bone specimens. Three hundred and fifty-five bone specimens from the metacarpi of 10 horses were machined into right cylinders aligned with the long axis of the bone. A computed tomographic scan of the specimens, along with a Cann-Genant K2HPO4 calibration standard, was obtained. The specimens then were compressed to failure, and the elastic modulus, yield stress, yield strain, strain energy density at yield, ultimate stress, ultimate strain, and strain energy density at ultimate failure were calculated. The specimens were dried and ashed. Quantitative computed tomography-derived K2HPO4 equivalent density proved to be an excellent estimator (r2 > 0.9) of elastic modulus, yield stress, ultimate stress, wet density, dry density, and ash density; a moderately good estimator (0.4 < r2 < 0.9) of strain energy density at yield and at ultimate failure; and a poor estimator (r2 < 0.2) of yield strain and ultimate strain. It was concluded that the relationships between quantitative computed tomography data and mechanical properties of the equine metacarpus were strong enough to justify the use of these data in automated finite element modeling.

Mechanical behavior of damaged trabecular bone

The mechanical behavior of damaged trabecular bone may play a role in the etiology of age-related spine fractures since damaged bone exists in and may weaken the elderly vertebral body. To describe some characteristics of damaged trabecular bone, we measured the changes in modulus and strength that occur when bovine trabecular bone is loaded in compression to various strains beyond its elastic range. Twenty-three reduced-section specimens, taken from 17 different bones, were loaded from 0-X-0-9% strain, where X was one of four strains: 1.0% (n = 7), 2.5% (n = 6), 4.0% (n = 5), or 5.5% (n = 5). We found that modulus was reduced for all applied strains, whereas strength was reduced only for strain levels > or = 2.5%; the percentage changes in modulus and strength were independent of Young's modulus but were highly dependent on the magnitude of the applied strains; modulus was always reduced more than strength; and simple statistical models, using knowledge of only the applied strains, predicted well the percentage reductions in modulus (r2 = 0.97) and strength (r2 = 0.74). The modulus reductions reported here are in qualitative agreement with those for cortical bone in tensile loading, supporting the concept that the damage behaviors of cortical and trabecular bone are similar for low strains (< or = 4.0%). In addition, because modulus was always reduced more than strength, damaged trabecular bone may be stress protected in vivo by redistribution of stresses to undamaged bone.

Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures

To compare the numerous modulus-density and strength-density relations that have been found for human trabecular bone from the proximal tibia, correlations between various measures of density were sought. Hydrated and dry apparent density, ash density, and density from quantitative computed tomography (QCT) were determined for cubic trabecular specimens taken from the proximal portion of human tibiae, and correlations between these measures were found (r > 0.99, P < .001). Orthogonal moduli and strengths of the specimens were measured mechanically, and were significantly correlated with ash density according to power relations (r > or = 0.85, P < .001). The strong correlation between density from QCT and ash density indicates that these measures can be used with nearly equal precision in estimating modulus and strength of tibial trabecular bone. Equations between mechanical properties and density reported in previous studies were converted to use a common density measure and, after considering the effects of specimen size, were in general agreement with results of the present study.

Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus

The conflicting conclusions regarding the relationship between the tensile and compressive strengths of trabecular bone remain unexplained. To help resolve this issue, we compared measurements of the tensile (n = 22) and compressive (n = 22) yield strengths, and yield strains, of trabecular bone specimens taken from 38 bovine proximal tibiae. We also studied how these failure properties depended on modulus and apparent density. To enhance accuracy, trabecular orientation was controlled, and each specimen had a reduced section where strains were measured with a miniature extensometer. We found that the mean yield strength was 30% lower for tensile loading. However, the difference between individual values of the tensile and compressive strengths increased linearly with increasing modulus and density, being negligible for low moduli, but substantial for high moduli. By contrast, both the tensile and compressive yield strains were independent of modulus and density, with the yield strain being 30% lower for tensile loading. Thus, the difference between the tensile and compressive strengths of bovine tibial trabecular bone depends on the modulus, but the difference between yield strains does not. This phenomenon may explain in part that conflicting conclusions reached previously on the tensile and compressive strengths of trabecular bone since the mean modulus has varied among different studies. Realizing that our data pertain only directly to bovine tibial trabecular bone for longitudinal loading, our results nevertheless suggest that failure parameters based on strains may provide more powerful and general comparisons of the failure properties for trabecular bone than measures based on stress.

Trabecular bone exhibits fully linear elastic behavior and yields at low strains

Using a protocol designed to reduce experimental artifacts associated with the conventional compression test for trabecular bone, we performed in vitro mechanical testing on bovine tibial trabecular bone to obtain accurate descriptions of the elastic and yield behaviors. Reduced-section cylindrical specimens were preconditioned for eight tension-compression (+/- 0.5% strain) cycles and then loaded to failure either in tension (n = 15) or compression (n = 14). We found that the pre-yield behavior for every specimen was fully linear, indicating that the initial nonlinear 'toe' is an experimental artifact. Analysis of variance on the moduli indicated that there was no significant difference between the tensile and compressive moduli before preconditioning. However, preconditioning decreased the tensile and compressive moduli on average by 8.8% (p < 0.01) and 5.3% (p < 0.01), respectively, with the decrease in tensile modulus being larger (p < 0.01). These small but significant decreases in modulus suggest that initial yielding involves microstructural damage (as opposed to plastic slip) of individual trabeculae and also indicate that the tensile and/or the compressive yield strain of (bovine tibial) trabecular bone is less than 0.5%. The mean tensile strength was approximately 70% of the mean compressive strength, although this difference in strengths may have been affected by the preconditioning-induced damage. Taken together, these results suggest that there are more similarities between the elastic and yield behaviors of trabecular and cortical bone than had been assumed previously.

Morphology-mechanical property relations in trabecular bone of the osteoarthritic proximal tibia

Alteration of morphologic and mechanical properties of trabecular bone in the osteoarthritic proximal tibia may be a contributing factor in tibial component loosening. To explore this issue, the authors performed tissue property measurements, morphologic analysis, and mechanical testing of subchondral, epiphyseal, and metaphyseal trabecular bone specimens retrieved from six human proximal tibias exhibiting a range of medial unicondylar osteoarthritic degeneration. Apparent density in the proximal tibia was altered according to varus misalignment and medial subluxation associated with medial osteoarthritis of the knee. In subchondral bone, a decrease in tissue mineralization contributed to a significant reduction in axial mechanical properties with degenerative disease (P < .0005). In epiphyseal and metaphyseal bone, trabecular thickness and the number of trabeculae increased linearly with volume fraction, providing a power law relationship between axial elastic modulus and apparent density (R2 = .84). Average elastic properties of the tibial epiphysis and metaphysis were not reduced by degenerative disease (P < .05). The results suggest that absolute minimization of tibial resection might not be an optimal strategy for tibial component fixation and that mechanical properties of the tibial resection surface are more homogeneous in planes parallel to the joint surface than in a plane normal to the longitudinal axis of the tibia.

Trabecular bone modulus and strength can depend on specimen geometry

We performed a series of uniaxial compression tests on wet bovine trabecular bone to compare both modulus and strength when measured using 2:1 aspect ratio (10 mm long, 5 mm diameter) cylinders (n = 30) and 5 mm cubes (n = 29). We also compared the correlation coefficients in the resulting modulus-density and strength-density regressions and the standard errors of the estimate. When comparing the mean values of modulus and strength for each group, the confounding variations in apparent density were accounted for with an analysis of covariance. The Fisher's Z transformation was used to compare the correlation coefficients statistically. Results from the analysis of covariance indicated that the modulus and strength of the cubes were higher by 36% (p < 0.01) and 18% (p < 0.05), respectively, with respect to the 2:1 cylinder values. The correlation coefficients in the modulus-density and strength-density regressions were not sensitive to the regression model (linear versus power law). However, correlation coefficients for both modulus-density and strength-density regressions were higher (p < 0.05) for the 2:1 cylinders (r = 0.90, modulus; r = 0.94, strength) than for the cubes (r = 0.57, modulus; r = 0.82, strength). In addition, the standard errors of the estimate in both modulus and strength were substantially lower for the 2:1 cylinders. These data indicate that both modulus and strength can depend on the specimen geometry when using conventional compression testing techniques. We conclude, therefore, that inter-study comparisons of modulus and strength may be invalid if these confounding effects of different specimen geometries are not addressed. Our data also indicate that density can better explain the observed variance in modulus and strength when 2:1 cylinders are used as opposed to cubes. Using this phenomenon as a rationale for choosing a standard specimen gometry, we recommend that the 2:1 cylinder be used as a standard specimen in studies designed to determine the effects of various treatments on the uniaxial compressive modulus and strength of trabecular bone.

Compressive fatigue behavior of bovine trabecular bone

We studied the fatigue behavior of bovine trabecular bone specimens under stress control using a sinusoidal uniaxial compressive load profile with a frequency of 2 Hz. The stress range was determined from the corresponding initial global platen-to-platen strain range, where the maximum initial strain was between 0.8 and 2.1% and the minimum strain was 0.6%. The local strain distribution was measured on the same type of specimen by affixing glass spheres and photographing them in the unloaded and loaded positions using multiple exposures. The number of cycles to failure (defined as a 5% decrease in secant modulus) was strongly correlated with the initial global maximum strain (r2 = 0.78) and ranged from 20 cycles at 2.1% strain to 400,000 cycles at 0.8% strain. All of the fatigue specimens showed a region of transverse failure approximately 1 mm from the end of the specimen. Microscopic examination of the failure zones revealed two failure modes: a straight transverse brittle-like fracture through the trabeculae, most often found in trabeculae transverse to the loading direction, and buckling-like failure, common in oblique trabeculae, involving bending and splitting. The local strain increased towards the ends of the specimens to a value 2-4 times that in the middle. Modulus degradation with the number of cycles was distinctively different for high-cycle and low-cycle fatigue, suggesting the possibility that both creep and damage accumulation contribute to fatigue failure of trabecular bone.

Theoretical analysis of the experimental artifact in trabecular bone compressive modulus

A theoretical analysis was performed to characterize potential experimental artifacts in conventional compression testing of trabecular bone, where strains are based on the relative displacements of the two loading platens. We assumed that the total experimental artifact for modulus was the sum of a damage and friction artifact and derived equations to describe these artifacts. The two unknown constants in these equations were found using a combination of data derived from linear finite element analyses and in vitro uniaxial compression tests. Subsequent finite element analyses allowed estimation of the artifacts for a wide range of specimens (cube, 1:4-3:1 aspect ratio cylinders). If friction is completely eliminated at the specimen-platen interface, the Young's modulus of a 5 mm sized (1:1 aspect ratio dimension) specimen which has a damage artifact due to machining may be underestimated by at least 45% regardless of specimen geometry; otherwise, the platens modulus may vary from less than 30 to over 175% of the Young's modulus, depending upon the specimen geometry and Poisson's ratio of the bone. Increasing the specimen size reduces the artifact only slightly. Since Poisson's ratio can be large for trabecular bone and is rarely known a priori, the precision of the conventional compression test will, therefore, be poor unless friction is completely eliminated at the specimen-platen interface. However, without friction at the interface, the platens modulus will always underestimate Young's modulus, thereby reducing the accuracy of this test. There was also evidence that the strength may be affected by these artifacts.(ABSTRACT TRUNCATED AT 250 WORDS)

Comparison of mechanical properties of human, bovine bone and a new processed bone xenograft

The study compared the mechanical properties of human bone, fresh bovine bone and a new highly purified bone xenograft: T650 (Lubboc-Laddec). Destructive, compressive tests were performed to determine Young's modulus and ultimate strength, with a constant deformation rate of 0.025 mm min-1. The stress-strain curves obtained from all the non-human specimens especially the T650, did not differ significantly from those observed with human bone. Human and fresh bovine samples presented a significantly different Young's modulus. The T650 samples, depending upon their trabecular texture (dense or medium) also differed significantly from each other (132.9 +/- 52.3 versus 80.0 +/- 37.3 MPa, P < 0.05). Their moduli were similar to those of bovine and human cancellous bone, respectively (117.49 +/- 61.53 versus 77.36 +/- 54.96. P < 0.05). The ultimate strength of T650 dense (9.6 +/- 3.7 MPa) was similar to bovine (8.5 +/- 4.2 MPa) and human bone (8.78 +/- 5.2 MPa): the T650 medium (5.9 +/- 2.8 MPa) was significantly different from the other specimens.