Computed tomography porosity and spherical indentation for determining cortical bone millimetre-scale mechanical properties

Preclinical Rodent Models for Human Bone Disease, Including a Focus on Cortical Bone

Preclinical models (typically ovariectomized rats and genetically altered mice) have underpinned much of what we know about skeletal biology. They have been pivotal for developing therapies for osteoporosis and monogenic skeletal conditions, including osteogenesis imperfecta, achondroplasia, hypophosphatasia, and craniodysplasias. Further therapeutic advances, particularly to improve cortical strength, require improved understanding and more rigorous use and reporting. We describe here how trabecular and cortical bone structure develop, are maintained, and degenerate with aging in mice, rats, and humans, and how cortical bone structure is changed in some preclinical models of endocrine conditions (eg, postmenopausal osteoporosis, chronic kidney disease, hyperparathyroidism, diabetes). We provide examples of preclinical models used to identify and test current therapies for osteoporosis, and discuss common concerns raised when comparing rodent preclinical models to the human skeleton. We focus especially on cortical bone, because it differs between small and larger mammals in its organizational structure. We discuss mechanisms common to mouse and human controlling cortical bone strength and structure, including recent examples revealing genetic contributors to cortical porosity and osteocyte network configurations during growth, maturity, and aging. We conclude with guidelines for clear reporting on mouse models with a goal for better consistency in the use and interpretation of these models.

Calcium Phosphate Cements as Carriers of Functional Substances for the Treatment of Bone Tissue

Interest in calcium phosphate cements as materials for the restoration and treatment of bone tissue defects is still high. Despite commercialization and use in the clinic, the calcium phosphate cements have great potential for development. Existing approaches to the production of calcium phosphate cements as drugs are analyzed. A description of the pathogenesis of the main diseases of bone tissue (trauma, osteomyelitis, osteoporosis and tumor) and effective common treatment strategies are presented in the review. An analysis of the modern understanding of the complex action of the cement matrix and the additives and drugs distributed in it in relation to the successful treatment of bone defects is given. The mechanisms of biological action of functional substances determine the effectiveness of use in certain clinical cases. An important direction of using calcium phosphate cements as a carrier of functional substances is the volumetric incorporation of anti-inflammatory, antitumor, antiresorptive and osteogenic functional substances. The main functionalization requirement for carrier materials is prolonged elution. Various release factors related to the matrix, functional substances and elution conditions are considered in the work. It is shown that cements are a complex system. Changing one of the many initial parameters in a wide range changes the final characteristics of the matrix and, accordingly, the kinetics. The main approaches to the effective functionalization of calcium phosphate cements are considered in the review.

Research on Determining Elastic-Plastic Constitutive Parameters of Materials from Load Depth Curves Based on Nanoindentation Technology

It is of great significance for structural design and engineering evaluation to obtain the elastic-plastic parameters of materials. The inverse estimation of elastic-plastic parameters of materials based on nanoindentation technology has been applied in many pieces of research, but it has proved to be difficult to determine the elastic-plastic properties of materials by only using a single indentation curve. A new optimal inversion strategy based on a spherical indentation curve was proposed to obtain the elastoplastic parameters (the Young's modulus E, yield strength σ_y, and hardening exponent n) of materials in this study. A high-precision finite element model of indentation with a spherical indenter (radius R = 20 µm) was established, and the relationship between the three parameters and indentation response was analyzed using the design of experiment (DOE) method. The well-posed problem of inverse estimation under different maximum indentation depths (h_max1 = 0.06 R, h_max2 = 0.1 R, h_max3 = 0.2 R, h_max4 = 0.3 R) was explored based on numerical simulations. The results show that the unique solution with high accuracy can be obtained under different maximum press-in depths (the minimum error was within 0.2% and the maximum error was up to 1.5%). Next, the load-depth curves of Q355 were obtained by a cyclic loading nanoindentation experiment, and the elastic-plastic parameters of Q355 were determined by the proposed inverse-estimation strategy based on the average indentation load-depth curve. The results showed that the optimized load-depth curve was in good agreement with the experimental curve, and the optimized stress-strain curve was slightly different from the tensile test, and the obtained parameters were basically consistent with the existing research.

3D extrusion printing of density gradients by variation of sinusoidal printing paths for tissue engineering and beyond

During extrusion printing of pasty biomaterials, internal geometries are mainly adjusted by positioning of straightly deposited strands which does not allow realization of spatially adaptable density gradients in x-, y- and z-direction for anisotropic scaffolds or anatomically shaped constructs. Herein, an alternative concept for printing patterns based on sinusoidal curves was evaluated using a clinically approved calcium phosphate cement (CPC). Infill density in scaffolds was adjusted by varying wavelength and amplitude of a sinus curve. Both wavelength and amplitude factors were defined by multitudes of the applied nozzle diameter. For CPC as a biomaterial ink in bone application, porosity, mechanical stiffness and biological response by seeded immortalized human mesenchymal stem cells - adhesion and pore bridging behavior - were investigated. The internal structure of a xyz-gradient scaffold was proven via X-ray based micro computed tomography (µCT). Silicone was used as a model material to investigate the impact of printing velocity and strand distance on the shape fidelity of the sinus pattern for soft matter printing. The impact of different sinus patterns on mechanical properties was assessed. Density and mechanical properties of CPC scaffolds were successfully adjusted without an adverse effect on adhesion and cell number development. In a proof-of-concept experiment, a sinus-adjusted density gradient in an anatomically shaped construct (human vertebral body) defined via clinical computed tomography (CT) data was demonstrated. This fills a technological gap for extrusion-based printing of freely adjustable, continuously guidable infill density gradients in all spatial directions. STATEMENT OF SIGNIFICANCE: 3D extrusion printing of biomaterials allows the generation of anatomically shaped, patient-specific implants or tissue engineering scaffolds. The density of such a structure is typically adjusted by the strand-to-strand distance of parallel, straight-meandered strands in each deposited layer. By printing in a sinusoidal pattern, design of density gradients is possible with a free, spatial resolution in x-, y- and z-direction. We demonstrated that porosity and mechanical properties can be freely adapted in this way without an adverse effect on cell adhesion. With the example of a CT dataset of a human spine, the anisotropic pattern of a vertebral body was resembled by this printing technique that can be translated to various patterns, materials and application.

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

Can guided wave ultrasound predict bone mechanical properties at the femoral neck in patients undergoing hip arthroplasty?

The bone quality of patients undergoing hip replacement surgery is poorly predicted by radiographs alone. With better bone quality information available to a surgeon, the operation can be performed more safely. The aim of this study was to investigate whether ultrasound signals of cortical bone at peripheral sites such as the tibia and radius can be used to predict the compressive mechanical properties of cortical bone at the femoral neck. We recruited 19 patients undergoing elective hip arthroplasty and assessed the radius and tibia of these patients with the Azalée guided wave ultrasound to estimate the porosity and thickness of the cortex. Excess bone tissues were collected from the femoral neck and the compressive mechanical properties of the cortex were characterised under a mechanical loading rig to determine stiffness, ultimate strength, and density. The correlations between the ultrasound measurements and mechanical properties were analysed using linear regression, Pearson correlation statistics, and multiple regression analysis. Cortical mechanical properties were weakly to moderately correlated with the ultrasound measurements at various sites (R2 = 0.00-0.36). The significant correlations found were not consistent across all 4 peripheral measurement sites. Additionally, weak to moderate ability of the ultrasound to predict mechanical properties at the neck of femur with multiple regression analysis was found (R2 = 0.00-0.48). Again, this was inconsistent across the different anatomical sites. Overall, the results demonstrate the need for ultrasound scans to be collected directly from clinically relevant sites such as the femoral neck due to the inconsistency of mechanical properties across various sites.

Bone hydration: How we can evaluate it, what can it tell us, and is it an effective therapeutic target?

Water constitutes roughly a quarter of the cortical bone by volume yet can greatly influence mechanical properties and tissue quality. There is a growing appreciation for how water can dynamically change due to age, disease, and treatment. A key emerging area related to bone mechanical and tissue properties lies in differentiating the role of water in its four different compartments, including free/pore water, water loosely bound at the collagen/mineral interfaces, water tightly bound within collagen triple helices, and structural water within the mineral. This review summarizes our current knowledge of bone water across the four functional compartments and discusses how alterations in each compartment relate to mechanical changes. It provides an overview on the advent of- and improvements to- imaging and spectroscopic techniques able to probe nano-and molecular scales of bone water. These technical advances have led to an emerging understanding of how bone water changes in various conditions, of which aging, chronic kidney disease, diabetes, osteoporosis, and osteogenesis imperfecta are reviewed. Finally, it summarizes work focused on therapeutically targeting water to improve mechanical properties.

Mechanical and morphological properties of parietal bone in patients with sagittal craniosynostosis

Limited information is available on the effect of sagittal craniosynostosis (CS) on morphological and material properties of the parietal bone. Understanding these properties would not only provide an insight into bone response to surgical procedures but also improve the accuracy of computational models simulating these surgeries. The aim of the present study was to characterise the mechanical and microstructural properties of the cortical table and diploe in parietal bone of patients affected by sagittal CS. Twelve samples were collected from pediatric patients (11 males, and 1 female; age 5.2 ± 1.3 months) surgically treated for sagittal CS. Samples were imaged using micro-computed tomography (micro-CT); and mechanical properties were extracted by means of micro-CT based finite element modelling (micro-FE) of three-point bending test, calibrated using sample-specific experimental data. Reference point indentation (RPI) was used to validate the micro-FE output. Bone samples were classified based on their macrostructure as unilaminar or trilaminar (sandwich) structure. The elastic moduli obtained using RPI and micro-FE approaches for cortical tables (E_RPI 3973.33 ± 268.45 MPa and E_micro-FE 3438.11 ± 387.38 MPa) in the sandwich structure and diploe (E_RPI1958.17 ± 563.79 MPa and E_micro-FE 1960.66 ± 492.44 MPa) in unilaminar samples were in strong agreement (r = 0.86, p < .01). We found that the elastic modulus of cortical tables and diploe were correlated with bone mineral density. Changes in the microstructure and mechanical properties of bone specimens were found to be irrespective of patients' age. Although younger patients are reported to benefit more from surgical intervention as skull is more malleable, understanding the material properties is critical to better predict the surgical outcome in patients <1 year old since age-related changes were minimal.

Structure-function relationships of the human vertebral endplate

BACKGROUND

Although deformation and fracture of the vertebral endplate have been implicated in spinal conditions such as vertebral fracture and disc degeneration, few biomechanical studies of this structure are available. The goal of this study was to quantify the mechanical behavior of the vertebral endplate.

METHODS

Eight-five rectangular specimens were dissected from the superior and/or inferior central endplates of human lumbar spine segments L1 to L4. Micro-computed tomography (μCT) imaging, four-point-bend testing, and ashing were performed to quantify the apparent elastic modulus and yield stress (modulus and yield stress, respectively, of the porous vertebral endplate), tissue yield stress (yield stress of the tissue of the vertebral endplate, excluding pores), ultimate strain, fracture strain, bone volume fraction (BV/TV), bone mineral density (BMD), and various measures of tissue density and composition (tissue mineral density, ash fraction, and ash density). Regression was used to assess the dependence of mechanical properties on density and composition.

RESULTS

Wide variations in elastic and failure properties, and in density and tissue composition, were observed. BMD and BV/TV were good predictors of many of the apparent-level mechanical properties, including modulus, yield stress, and in the case of the inferior vertebral endplate, failure strains. Similar values of the mechanical properties were noted between superior and inferior vertebral endplates. In contrast to the dependence of apparent stiffness and strength on BMD and BV/TV, none of the mechanical properties depended on any of the tissue-level density measurements.

CONCLUSION

The dependence of many of the mechanical properties of the vertebral endplate on BV/TV and BMD suggests possibilities for noninvasive assessment of how this region of the spine behaves during habitual and injurious loading. Further study of the nonmineral components of the endplate tissue is required to understand how the composition of this tissue may influence the overall mechanical behavior of the vertebral endplate.

Bulk Wave Velocities in Cortical Bone Reflect Porosity and Compression Strength

The goal of this study was to evaluate whether ultrasonic velocities in cortical bone can be considered as a proxy for mechanical quality of cortical bone tissue reflected by porosity and compression strength. Micro-computed tomography, compression mechanical testing and resonant ultrasound spectroscopy were used to assess, respectively, porosity, strength and velocity of bulk waves of both shear and longitudinal polarisations propagating along and perpendicular to osteons, in 92 cortical bone specimens from tibia and femur of elderly human donors. All velocities were significantly associated with strength (r = 0.65-0.83) and porosity (r = -0.64 to -0.77). Roughly, according to linear regression models, a decrease in velocity of 100 m/s corresponded to a loss of 20 MPa in strength (which is approximately 10% of the largest strength value) and to an increase in porosity of 5%. These results provide a rationale for the in vivo measurement of one or several velocities for the diagnosis of bone fragility.

Reversing cortical porosity: Cortical pore infilling in preclinical models of chronic kidney disease

PURPOSE

Chronic kidney disease (CKD) patients have a high incidence of fracture due in part to cortical porosity. The goal of this study was to study cortical pore infilling utilizing two rodent models of progressive CKD.

METHODS

Exp 1: Female C57Bl/6J mice (16-week-old) were given dietary adenine (0.2%) to induce CKD for 10 weeks after which calcium water supplementation (Ca-H2O; 1.5% and 3%) was given to suppress PTH for another 4 weeks. Exp 2: Male Cy/+ rats were aged to ~30 weeks with baseline porosity assessed using in vivo μCT. A second in vivo scan followed 5-weeks of Ca-H2O (3%) supplementation.

RESULTS

Exp 1: Untreated adenine mice had elevated blood urea nitrogen (BUN), parathyroid hormone (PTH), and cortical porosity (~2.6% porosity) while Ca-H2O lowered PTH and cortical porosity (0.5-0.8% porosity). Exp 2: Male Cy/+ rats at baseline had variable porosity (0.5%-10%), but after PTH suppression via Ca-H2O, cortical porosity in all rats was lower than 0.5%. Individual pore dynamics measured via a custom MATLAB code demonstrated that 85% of pores infilled while 12% contracted in size.

CONCLUSION

Ca-H2O supplementation causes net cortical pore infilling over time and imparted mechanical benefits. While calcium supplementation is not a viable clinical treatment for CKD, these data demonstrate pore infilling is possible and further research is required to examine clinically relevant therapeutics that may cause net pore infilling in CKD.

Excessive salt consumption causes systemic calcium mishandling and worsens microarchitecture and strength of long bones in rats

Excessive salt intake has been associated with the development of non-communicable diseases, including hypertension with several cardiovascular consequences. Although the detrimental effects of high salt on the skeleton have been reported, longitudinal assessment of calcium balance together with changes in bone microarchitecture and strength under salt loading has not been fully demonstrated. To address these unanswered issues, male Sprague-Dawley rats were fed normal salt diet (NSD; 0.8% NaCl) or high salt diet (HSD; 8% NaCl) for 5 months. Elevation of blood pressure, cardiac hypertrophy and glomerular deterioration were observed in HSD, thus validating the model. The balance studies were performed to monitor calcium input and output upon HSD challenge. The HSD-induced increase in calcium losses in urine and feces together with reduced fractional calcium absorption led to a decrease in calcium retention. With these calcium imbalances, we therefore examined microstructural changes of long bones of the hind limbs. Using the synchrotron radiation x-ray tomographic microscopy, we showed that trabecular structure of tibia and femur of HSD displayed a marked increase in porosity. Consistently, the volumetric micro-computed tomography also demonstrated a significant decrease in trabecular bone mineral density with expansion of endosteal perimeter in the tibia. Interestingly, bone histomorphometric analyses indicated that salt loading caused an increase in osteoclast number together with decreases in osteoblast number and osteoid volume. This uncoupling process of bone remodeling in HSD might underlie an accelerated bone loss and bone structural changes. In conclusion, long-term excessive salt consumption leads to impairment of skeletal mass and integrity possibly through negative calcium balance.

Loss of bone density and bone strength following premenopausal risk-reducing bilateral salpingo-oophorectomy: a prospective controlled study (WHAM Study)

Prophylactic oophorectomy is recommended for women at high risk for ovarian cancer, but the associated impact on bone health is of clinical concern. This prospective, controlled study demonstrated substantial loss of bone density and bone strength following surgical menopause. Postoperative hormone therapy alleviated, but not fully prevented, spinal bone loss.

INTRODUCTION

This prospective study investigated bone health in women following premenopausal oophorectomy.

METHODS

Dual-energy x-ray absorptiometry (DXA), peripheral quantitative computed tomography (pQCT), and pQCT-based finite element analysis (pQCT-FEA) were used to assess bone health between systemic hormone therapy (HT) users and non-users after premenopausal risk-reducing bilateral salpingo-oophorectomy (RRBSO) compared with premenopausal controls over 24-month follow-up.

RESULTS

Mean age was 42.4 ± 2.6 years (n = 30) for the surgery group and 40.2 ± 6.3 years for controls (n = 42), and baseline bone measures were similar between groups. Compromised bone variables were observed at 24 months after RRBSO, among which areal bone mineral density (aBMD) at the lumbar spine, tibial volumetric cortical density (Crt vBMD), and tibial bending stiffness (k_bend) had decreased by 4.7%, 1.0%, and 12.1%, respectively (all p < 0.01). In non-HT users, significant losses in lumbar spine (5.8%), total hip (5.2%), femoral neck (6.0%) aBMD, tibial Crt vBMD (2.3%), and k_bend (14.8%) were observed at 24 months (all p < 0.01). HT prevented losses in k_bend, tibial Crt vBMD, and aBMD, except for modest 2.3% loss at the lumbar spine (p = 0.01).

CONCLUSION

This prospective, controlled study of bone health following RRBSO or premenopausal oophorectomy demonstrated substantial loss of bone density and bone strength following RRBSO. HT prevented loss of bone density and bone stiffness, although there was still a modest decrease in lumbar spine aBMD in HT users. These findings may inform decision-making about RRBSO and clinical management following premenopausal oophorectomy.

Biological Effects of a Three-Dimensionally Printed Ti6Al4V Scaffold Coated with Piezoelectric BaTiO3 Nanoparticles on Bone Formation

Bone defect repair at load-bearing sites is a challenging clinical problem for orthopedists. Defect reconstruction with implants is the most common treatment; however, it requires the implant to have good mechanical properties and the capacity to promote bone formation. In recent years, the piezoelectric effect, in which electrical activity can be generated due to mechanical deformation, of native bone, which promotes bone formation, has been increasingly valued. Therefore, implants with piezoelectric effects have also attracted great attention from orthopedists. In this study, we developed a bioactive composite scaffold consisting of BaTiO₃, a piezoelectric ceramic material, coated on porous Ti6Al4V. This composite scaffold showed not only appropriate mechanical properties, sufficient bone and blood vessel ingrowth space, and a suitable material surface topography but also a reconstructed electromagnetic microenvironment. The osteoconductive and osteoinductive properties of the scaffold were reflected by the proliferation, migration, and osteogenic differentiation of mesenchymal stem cells. The ability of the scaffold to support vascularization was reflected by the proliferation and migration of human umbilical vein endothelial cells and their secretion of VEGF and PDGF-BB. A well-established sheep spinal fusion model was used to evaluate bony fusion in vivo. Sheep underwent implantation with different scaffolds, and X-ray, micro-computed tomography, van Gieson staining, and elemental energy-dispersive spectroscopy were used to analyze bone formation. Isolated cervical angiography and visualization analysis were used to assess angiogenesis at 4 and 8 months after transplantation. The results of cellular and animal studies showed that the piezoelectric effect could significantly reinforce osteogenesis and angiogenesis. Furthermore, we also discuss the molecular mechanism by which the piezoelectric effect promotes osteogenic differentiation and vascularization. In summary, Ti6Al4V scaffold coated with BaTiO₃ is a promising composite biomaterial for repairing bone defects, especially at load-bearing sites, that may have great clinical translation potential.

Spherical depth-sensing nanoindentation of human anterior skull base bones: Establishment of a test protocol

The mechanical properties of anterior skull base (ASB) bones are not well understood due to their complex geometry and deep location. However, it is of particular interest for skull base surgeons to appraise the force range they can apply during procedures and know what kind of haptic feedback a simulation device should produce in order to be realistic for trainees. The aim of this study was to establish a measurement protocol to set the level of hydration state, temperature and curve analysis method for spherical depth sensing nanoindentation of ASB bones. A definitive screening design method was used to test the different possible combinations of these factors. Two samples of ASB bones from the heads of two human body donors (two specimens) were selected according to their microstructure as assessed by micro-CT (microtomography): low-porosity (16.87%, sphenoid bone) and high-porosity (79.85%, ethmoid bone). Depth measurement series of 36 nanoindentations (n = 288) were performed on specimen 1 according to the L8 Taguchi orthogonal array to study the effect of temperature (two levels: 20 or 37 °C), hydration state (dry or immerged in physiological saline sodium chloride), and loading curve analysis according to the Hertzian contact theory (fitting at the start or at the end). The mean values of reduced Young's (E*) modulus varied significantly depending on the hydration status and bone microstructure. In order to obtain the physiological properties of ASB bones, we thus propose performing immersion tests. To simplify the experimentation protocol, future experiments must include a room temperature level and a fit of the curve at the end of the load. A validation series was performed on the second specimen to assess the set of parameters. The E* in dry bone gave mean values of 994.68 MPa, versus 409.79 MPa in immerged bones (p < 0.00001). This is the first time a study has been carried out on ASB bones, defining the experimental parameters related to physiological conditions.

Impaction technique influences implant stability in low-density bone model

Aims

Cementless acetabular components rely on press-fit fixation for initial stability. In certain cases, initial stability is more difficult to obtain (such as during revision). No current study evaluates how a surgeon’s impaction technique (mallet mass, mallet velocity, and number of strikes) may affect component fixation. This study seeks to answer the following research questions: 1) how does impaction technique affect a) bone strain generation and deterioration (and hence implant stability) and b) seating in different density bones?; and 2) can an impaction technique be recommended to minimize risk of implant loosening while ensuring seating of the acetabular component?

Methods

A custom drop tower was used to simulate surgical strikes seating acetabular components into synthetic bone. Strike velocity and drop mass were varied. Synthetic bone strain was measured using strain gauges and stability was assessed via push-out tests. Polar gap was measured using optical trackers.

Results

A phenomenon of strain deterioration was identified if an excessive number of strikes was used to seat a component. This effect was most pronounced in low-density bone at high strike velocities. Polar gap was reduced with increasing strike mass and velocity.

Conclusion

A high mallet mass with low strike velocity resulted in satisfactory implant stability and polar gap, while minimizing the risk of losing stability due to over-striking. Extreme caution not to over-strike must be exercised when using high velocity strikes in low-density bone for any mallet mass.

Cite this article: Bone Joint Res 2020;9(7):386–393.

A method for fracture toughness measurement in trabecular bone using computed tomography, image correlation and finite element methods

The fracture resistance of load-bearing trabecular bone is adversely affected by diseases such as osteoporosis. However, there are few published measurements of trabecular bone fracture toughness due to the difficulty of conducting reliable tests in small specimens of this highly porous material. A new approach is demonstrated that uses digital volume correlation of X-ray computed tomographs to measure 3D displacement fields in which the crack shape and size can be objectively identified using a phase congruency analysis. The criteria for crack propagation, i.e. fracture toughness, can then be derived by finite element simulation, with knowledge of the elastic properties.