Insights into the effects of tensile and compressive loadings on microstructure dependent fracture of trabecular bone

The micro-scale finite element models used in the past to understand yielding failure of trabecular bone have not addressed the microcrack formation and its effect on microstructure dependent fracture. An understanding of microcrack based failure mechanisms can be important to develop insights into response of trabecular bone to external loading before final failure. With this goal, we analyze tensile and compressive fracture failure at two different ages in two trabecular bone micrographs obtained from an ovine femur using a recently developed cohesive finite element method (CFEM) framework. The results and analyses indicate that examined trabecular microstructures are optimally designed for resisting compressive loading. Under tensile loading, initial damage in a microstructure is localized in a single random trabecula. Final microstructure failure occurs immediately after the failure of the trabecula. However, under compressive loading, failure of the first trabecula does not precede immediate complete failure of microstructure. Under compression the propagation fracture toughness (characterized by change in energy release rate as a function of crack density) increases with increase in crack density. However, under tension the propagation fracture toughness decreases with increasing crack density. The fracture mechanism remains unaffected by age variation. Effect of tissue property random variation on the variation in fracture strength diminishes under tension and increases under compression with increase in the age. Overall, results indicate that structural arrangement of the trabecular bone (besides the hierarchical chemical composition) can be an important contributor to its unique fracture resistance properties.     

Loss of trabeculae by mechano-biological means may explain rapid bone loss in osteoporosis.

Osteoporosis is characterized by rapid and irreversible loss of trabecular bone tissue leading to increased bone fragility. In this study, we hypothesize two causes for rapid loss of bone trabeculae; firstly, the perforation of trabeculae is caused by osteoclasts resorbing a cavity so deep that it cannot be refilled and, secondly, the increases in bone tissue elastic modulus lead to increased propensity for trabecular perforation. These hypotheses were tested using an algorithm that was based on two premises: (i) bone remodelling is a turnover process that repairs damaged bone tissue by resorbing and returning it to a homeostatic strain level and (ii) osteoblast attachment is under biochemical control. It was found that a mechano-biological algorithm based on these premises can simulate the remodelling cycle in a trabecular strut where damaged bone is resorbed to form a pit that is subsequently refilled with new bone. Furthermore, the simulation predicts that there is a depth of resorption cavity deeper than which refilling of the resorption pits is impossible and perforation inevitably occurs. However, perforation does not occur by a single fracture event but by continual removal of microdamage after it forms beneath the resorption pit. The simulation also predicts that perforations would occur more easily in trabeculae that are more highly mineralized (stiffer). Since both increased osteoclast activation rates and increased mineralization have been measured in osteoporotic bone, either or both may contribute to the rapid loss of trabecular bone mass observed in osteoporotic patients.     

High-speed photography of compressed human trabecular bone correlates whitening to microscopic damage

Mechanical testing of trabecular bone is mainly motivated by the huge impact of osteoporosis in post-menopausal women and the aged in society in terms of social and health care costs. Trabecular bone loss and impairment of its mechanical properties reduce bone strength and increase fracture risk, especially in vertebrae. It is generally accepted that in addition to bone mineral density, microarchitecture and material properties of bone also play important roles for bone strength and fracture risk. In order to overcome the limitations of standard mechanical tests delivering merely integral information about complicated samples, experiments were designed for step-wise mechanical testing with concurrent imaging of trabecular and cortical bone. In this communication we present an approach for real-time imaging of trabecular bone during compression using high-speed photography and investigate the hypothesis whether the whitening of deformed trabeculae is due to microdamage. Experiments on human trabecular bone samples from a healthy male donor revealed that failure of such samples is highly localized in fracture bands. Moreover, strongly deformed trabeculae were seen to whiten, an effect similar to stress whitening in polymers. Scanning Electron Microscopy of the same regions of interest revealed that whitened trabeculae were strongly damaged by microscopic cracks and mostly failed in delamination. Higher resolution images uncovered mineralized collagen fibrils spanning the cracks. The whitening partially faded after unloading of the samples, presumably due to partial crack closure. Overall, high-speed photography enables microdamage detection in real-time during a mechanical test and provides a correlation to recorded stress strain curves.     

Multi-scale modelling of elastic moduli of trabecular bone

We model trabecular bone as a nanocomposite material with hierarchical structure and predict its elastic properties at different structural scales. The analysis involves a bottom-up multi-scale approach, starting with nanoscale (mineralized collagen fibril) and moving up the scales to sub-microscale (single lamella), microscale (single trabecula) and mesoscale (trabecular bone) levels. Continuum micromechanics methods, composite materials laminate theory and finite-element methods are used in the analysis. Good agreement is found between theoretical and experimental results.     

Bone tissue formation in sheep muscles induced by a biphasic calcium phosphate ceramic and fibrin glue composite

Some biomaterials are able to induce ectopic bone formation in muscles of large animals. The osteoinductive potential of macro- micro-porous biphasic calcium phosphate (MBCP) ceramic granules with fibrin glue was evaluated by intramuscular implantation for 6 months in six adult female sheep. The MBCP granules were 1–2 mm in size and were composed of hydroxyapatite (HA) and beta-tricalcium phosphate (β-TCP) in a 60/40 ratio. The fibrin glue was composed of fibrinogen, thrombin and other biological factors. After 6 months of implantation in the dorsal muscles of sheep, the explants were rigid. Histology, back-scattered electron microscopy and micro-computed tomography of the implants indicated that approximately 12% of mineralized bone had formed in between the MBCP granules. The ectopic bone appeared well-mineralized with mature osteocytes and Haversian structures. In addition, the number and thickness of bone trabeculae formed in between the MBCP particles were similar to those measured in trabecular bone in sheep. The overall results therefore confirmed the formation of well-mineralized ectopic bone tissue after intramuscular implantation of MBCP/fibrin glue composites. These bone substitutes exhibiting osteoinductive properties could be used for the reconstruction of large bone defects.     

Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone

The aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue''s mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue''s mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.     

Correlation of cancellous bone microarchitectural parameters from microCT to CT number and bone mechanical properties

Cancellous bone density alone is not a sufficient predictor of bone mechanical stiffness and strength. Microarchitectural parameters of bone may improve the accuracy of prediction. It is well established that bone density can be inferred from the intensities of clinical CT image datasets, however it is unknown if microarchitectural parameters manifest any relationship to the image intensities. Thirty-eight porcine cancellous bone cubes were subjected to clinical CT and microCT imaging to obtain the CT number and microarchitectural parameters respectively. They were subsequently compressed to failure to obtain the mechanical properties. Linear regression analyses were carried out for the three testing modalities to determine any possible correlations. Significant correlations (R² ≥ 0.5) were obtained between Hounsfield units and (1) volume fraction (BV/TV), (2) bone trabecular pattern (Tb.Pf), (3) trabeculae spacing (Tb.Sp), (4) structure model index (SMI) and (5) trabeculae number (Tb.N). Significant correlations were also discerned for microarchitectural parameters and mechanical properties. In conclusion, we established linear regression models between image-measured density in terms of Hounsfield units (HU) and microarchitectural parameters as well as models between cancellous bone microarchitectural parameters and mechanical properties. It should be noted that both density and microarchitectural parameters important to bone research could be inferred from clinical CT images.     

Finite Element Analysis of Osteocytes Mechanosensitivity Under Simulated Microgravity

It was found that the mechanosensitivity of osteocytes could be altered under simulated microgravity. However, how the mechanical stimuli as the biomechanical origins cause the bioresponse in osteocytes under microgravity is unclear yet. Computational studies may help us to explore the mechanical deformation changes of osteocytes under microgravity. Here in this paper, we intend to use the computational simulation to investigate the mechanical behavior of osteocytes under simulated microgravity. In order to obtain the shape information of osteocytes, the biological experiment was conducted under simulated microgravity prior to the numerical simulation The cells were rotated by a clinostat for 6 hours or 5 days and fixed, the cytoskeleton and the nucleus were immunofluorescence stained and scanned, and the cell shape and the fluorescent intensity were measured from fluorescent images to get the dimension information of osteocytes The 3D finite element (FE) cell models were then established based on the scanned image stacks. Several components such as the actin cortex, the cytoplasm, the nucleus, the cytoskeleton of F-actin and microtubules were considered in the model. The cell models in both 6 hours and 5 days groups were then imposed by three magnitudes (0.5, 10 and 15 Pa) of simulating fluid shear stress, with cell total displacement and the internal discrete components deformation calculated. The results showed that under the simulated microgravity: (1) the nuclear area and height statistically significantly increased, which made the ratio of membrane-cortex height to nucleus height statistically significantly decreased; (2) the fluid shear stress-induced maximum displacements and average displacements in the whole cell decreased, with the deformation decreasing amplitude was largest when exposed to 1.5Pa of fluid shear stress; (3) the fluid shear stress-induced deformation of cell membrane-cortex and cytoskeleton decreased, while the fluid shear stress-induced deformation of nucleus increased. The results suggested the mechanical behavior of whole osteocyte cell body was suppressed by simulated microgravity, and this decrement was enlarged with either the increasing amplitude of fluid shear stress or the duration of simulated microgravity. What’s more, the mechanical behavior of membrane-cortex and cytoskeleton was suppressed by the simulated microgravity, which indicated the mechanotransduction process in the cell body may be further inhibited. On the contrary, the cell nucleus deformation increased under simulated microgravity, which may be related to either the decreased amount of cytoskeleton or the increased volume occupied proportion of nucleus in whole cell under the simulated microgravity. The numerical results supported our previous biological experiments, and showed particularly affected cellular components under the simulated microgravity. The computational study here may help us to better understand the mechanism of mechanosensitivity changes in osteocytes under simulated microgravity, and further to explore the mechanism of the bone loss in space flight.     

Microgravity and bone cell mechanosensitivity: FLOW experiment during the DELTA mission

The catabolic effects of microgravity on mineral metabolism in bone organ cultures might be explained as resulting from an exceptional form of disuse. It is possible that the mechanosensitivity of bone cells is altered under near weightlessness conditions, which likely contributes to disturbed bone metabolism observed in astronauts. In the experiment “FLOW”, we tested whether the production of early signaling molecules that are involved in the mechanical load-induced osteogenic response by bone cells is changed under microgravity conditions. FLOW was one of the Biological experiment entries to the Dutch Soyuz Mission “DELTA” (Dutch Expedition for Life Science, Technology and Atmospheric Research). FLOW was flown by the Soyuz craft, launched on April 19, 2004, on its way to the International Space Station. Primary osteocytes, osteoblasts, and periosteal fibroblasts were incubated in plunger boxes, developed by Centre for Concepts in Mechatronics, using plunger activation events for single pulse fluid shear stress stimulations. Due to unforeseen hardware complications, results from in-flight cultures are considered lost. Ground control experiments showed an accumulative increase of NO in medium for osteocytes (as well as for osteoblasts and periosteal fibroblasts). Data from the online-NO sensor showed that the NO produced in medium by osteocytes increased sharply after pulse shear stress stimulations. COX-2 mRNA expression revealed high levels in osteoblasts compared to the other cell types tested. In conclusion, preparations for the FLOW experiment and preliminary ground results indicate that the FLOW setup is viable for a future flight opportunity.     

Free surface density and microdamage in the bone remodeling equation: Theoretical considerations

Bone is maintained through a coupled process of bone resorption and bone formation, in a continuous process called bone remodeling. An imbalance in this process caused by disease, abnormal mechanical demands, or fatigue may predispose bone to fracture injuries. The remodeling process is generally viewed as a material response to functional demands. Here, we propose a new set of constitutive equations for the bone remodeling process and contains the specific surface, instead of volume fraction, and the degree of microcracking in the constitutive equations. The rate of remodeling is related to mechanical stimuli, free surface density and a microcrack factor. In this approach, the effect of mechanical stimuli, rate of mechanical stimuli, and integration of mechanical stimuli on bone remodeling can be evaluated simultaneously in the remodeling equation. Specific examples are given for illustration of the model.     

Development of a unifying theory for mechanical adaptation and maintenance of trabecular bone

Trabecular bone is a tissue with a complex 3D structure, consisting of struts and plates, which attains its mature morphology during growth in a process called ‘modeling’. In maturity, the tissue is renewed continuously by local bone resorption and subsequent formation in a process called ‘remodeling’. Both these metabolic activities are executed by bone-resorbing osteoclastic and bone-forming osteoblastic cells. It is known that bone mass and trabecular orientation are adapted to the external forces and that alternative loading conditions lead to adaptations of the internal tissue architecture. The question is how the characteristics of external loads are sensed in the bone, and how they are translated to structural adaptation of the tissue. The time scale of the underlying processes is on the order of months, or even years. This aspect makes bone a complex research topic. In this paper, we discuss the application of computer simulation to investigate the remarkable adaptive processes. We describe our developments of empirical models in the past 15 years, able to predict bone adaptation to external loads from a macroscopic level towards a cell-based level, in which the most important relationships of the cellular processes are captured. The latest model explains the morphological phenomena observed in trabecular bone at a microscopic level.     

Bone remodelling in the pores and around load bearing transchondral isoelastic porous-coated glassy carbon implants: Experimental study in rabbits

Cylinders of porous-coated glassy carbon were implanted into drill holes made through the articular surface of the medial condyle of both tibiae of ten rabbits for six and 12 weeks. Bone ingrowth and remodelling was examined by radiographic, histologic, oxytetracycline-fluorescence and microradiographic methods. Bone ingrowth into pores and load bearing implants was seen by all examination methods. Bone ingrowth occurred earlier when the pores were facing cancellous bone than cortical bone. Appositional bone formation occurred on the trabeculae a few millimetres from the interface during the early phase of remodelling at six weeks. At 12 weeks resorptive remodelling had occurred both in the surroundings and in those pores that face cancellous bone, whereas the amount of bone still increased in the pores facing cortical bone. In its porous-coated form glassy carbon functions well as a frame for ingrowing bone and it shows good osteoconductivity. Its mechanical properties are suitable for functioning as a structural bone substitute in places where the loads are mainly compressive. The difference between findings at six and 12 weeks indicated physiologic stress distribution and the adverse effects of stiff materials on bone remodelling were avoided by using this isoelastic material.     

Trabecular bone adaptation in a finite element frame model using load dependent fabric tensors

Most human bones are divided into an external cortical and an internal trabecular substance. Both kinds of bone tissue are capable of adapting their strength to the loads acting upon them; they are in a state of continuous remodelling. The present study introduces a new method for modelling the functional adaptation of the trabecular bone by means of a finite element frame model, where each trabecula is represented by one beam element in order to achieve a relatively simple model with a low element number. The model is generated in a stochastic way, thus avoiding the need for CT imaging. For the purpose of the remodelling simulations a structure consisting of two kinds of beam elements is used. The elements involved in carrying loads are called ‘active’ beams, while those not working are regarded as ‘passive’ beams. Any modification in the structure is executed by changing the active elements into passive or vice versa according to the eigenvalues of node-by-node defined fabric tensors. The algorithm generates anisotropic structures, with load-directed beam orientations similar to the living trabecular bone tissue.     

In vitro study investigating the mechanical properties of acrylic bone cement containing calcium carbonate nanoparticles

A successful total hip replacement has an expected service life of 10-20 years with over 75% of failures due to aseptic loosening which is directly related to cement mantle failure. The aim of the present study was to investigate the addition of nanoparticles of calcium carbonate to acrylic bone cement. It was anticipated that an improvement in mechanical performance of the resultant nanocomposite bone cement would be achieved. A design of experiment approach was adopted to maximise the mechanical properties of the bone cement containing nanoparticles of calcium carbonate and to determine the constituents and preparation methods for which these occur. The selected conditions provided improvements of 21% in energy to maximum load, 10% in elastic modulus, 7% in bending strength and 8% in bending modulus when compared with bone cement without nanoparticles. Although cement containing nanoCaCO(3) coated in sodium citrate also enhanced the energy to maximum load by 28% and the elastic modulus by 14% when compared with control cement, it is not recommended as a factor in the production of nanocomposite bone cement due to reduction in the bending properties of the final bone cement.     

Electron microscopic investigation on the osteogenesis at titanium implant/bone marrow interface under masticatory loading

Electron microscopic investigation on osteogenetic process at the implant surface of threadless rod-type titanium implants with different surface roughness of Ra 0.4 ± 0.01 μm, Sm 2.6 ± 0.3 μm and Ra 2.0 ± 0.12 μm, Sm 36 ± 9.1 μm was performed at the early stage of 21 and 42 days post implantation into the jawbones of four beagles under the load bearing condition of functional mastication. The implant surfaces were covered with a blood clot and haematopoietic stem cells (HSC) including phagocytic monocytes immediately after the implantation. Successively, osteogenic stem cells (OSC) migrated from cortical and/or trabecular endosteum to the HSC-layer on the implant surface. The new bone formation at the implant/bone marrow interface was developed by collaboration of osteomediator cells (OMC) differentiated from monocytes of HSC and osteoblast phenotype cells of OSC derived from endosteum of cortical bone and/or trabecular. The new bone layer at the implant surface consisted of two layers, solution-mediated calcification layer of pseudo bone and cell (osteoblast) -mediated calcification layer of true bone. The pseudo bone was produced by solution-mediated calcification of OMC- and HSC-remnants near by the implant surface. The bone healing process at the implant/bone marrow interface depended upon two factors; the migration of OSC from cortical and/or trabecular endosteum to the implant surface and the healing potentiality. Topographic dependency upon the bone healing potential at implant/bone marrow interface was not confirmed in this experiment under the load bearing condition of functional mastication.     

Effect of expanded bone marrow-derived osteoprogenitor cells seeded into polycaprolactone/tricalcium phosphate scaffolds in new bone regeneration of rabbit mandibular defects

The purpose of this study was to assess and evaluate new bone formation in rabbit marginal mandibular defects using expanded bone marrow-derived osteoprogenitor cells seeded in three-dimensional scaffolds of polycaprolactone/tricalcium phosphate (PCL/TCP). Bone marrow was harvested from the rabbit ilium and rabbit bone marrow-derived osteoprogenitor cells were isolated and expanded in standard culture medium and osteogenic medium supplement. The cells were then seeded into the PCL/TCP scaffolds and the cell/scaffold constructions were implanted into prepared defects in rabbit mandibles. PCL/TCP scaffold alone and autogenous bone graft from the mandible were also implanted into the other prepared defects. The specimens were evaluated at 4 and 8 weeks after the implantation using clinical, radiographic, and histological techniques. The results of the experimental group demonstrated more newly formed bone on the surface and in the pores of the PCL/TCP scaffolds. In addition, the osteoblasts, osteocytes, and new bone trabeculae were identified throughout the defects that were implanted with the cell/scaffold constructions. The PCL/TCP alone group was filled mostly with fibrous cells particularly in the middle region with less bone formation. These results would suggest that the derived osteotoprogenitor cells have the potential to form bone tissue when seeded onto PCL/TCP scaffolds.     

A finite macro-element for corroded reinforced concrete

This paper proposes a model of the mechanical behaviour of corroded reinforced concrete members subjected to bending under service load. The model is based on the formulation of a macro-element to be used in FEM analysis, having a length equal to the distance between two consecutive flexural cracks and a cross-section equal to the member cross-section. The mechanical formulation is directly written in generalized variables (bending moment and curvature) and is based on the concept of the transfer length necessary for the transmission of tensile load from re-bar to tensile concrete thanks to the bond. It is thus possible to take into account the effect of reinforcement corrosion on the bond between re-bar and concrete, by increasing the transfer length versus intensity of corrosion. The variation of the transfer length versus corrosion is expressed using a scalar damage parameter. A first experimental validation is performed on a 17-year-old beam kept in a chloride environment under its service load.     

Nanostructural analysis of trabecular bone

The mechanical properties of bone are dictated by the size, shape and organization of the mineral and matrix phases at multiple levels of hierarchy. While much is known about structure–function relations at the macroscopic level, less is known at the nanoscale, especially for trabecular bone. In this study, high resolution transmission electron microscopy (HRTEM) was carried out to analyze shape and orientation of apatite crystals in murine femoral trabecular bone. The distribution and orientation of mineral apatites in trabecular bone were different from lamellar bone and the c-axis of the tablet-like mineral apatite crystals in trabecular bone was arranged with no preferred orientation. The difference in the orientation distribution of apatite crystals of trabecular bone in the present study compared with that of lamellar bone found in the literature can be attributed to the more complex local stress state in trabecular bone. Apatite crystals were also found to be multi-crystalline, not single crystalline, from dark field image analysis. From the observations of this study, it is suggested that Wolff’s law can be applicable to the nanostructural orientation and distribution of apatite crystals in trabecular bone. It was also found that small round crystalline particles observed adjacent to collagen fibrils were similar in size and shape to the apatite crystals in biomimetically nucleated synthetic amorphous calcium phosphate, which suggests that they are bone mineral apatite nuclei.     

A bone adaptation integrated approach using BEM

An algorithm for the mathematical representation of bone adaptation is proposed. This model can be used at bone tissue level (local level) as well as at whole bone level (global level). The boundary element method is used for the numerical analysis of trabecular bone tissue together with the remodeling algorithm presented by (Fridez P., Rakotomanana L., Terrier A., Leyvraz P.F., Three dimensional model of bone external adaptation, Comput Methods Biomech Biomed Eng, 2, 189–196, 1998, [1]). Some numerical examples are given to show the versatility and power of the algorithm here discussed. Additionally, the method converges rapidly to the solution, which is one of the main advantages of the proposed numerical scheme.     

动物骨折治疗用金属骨板局部增量成形新工艺

目的目前动物骨折常用的锁定骨板内固定技术(Point-contact Reconstruction Compress Locking, PRCL)需要采用多个工具配合手动完成骨板成形,针对该过程中精度不可控、效率低等问题,提出一种弯扭复合成形模具,发展一种局部增量成形金属骨板的方法。方法 PRCL骨板固定治疗中,为了贴合受伤骨骼,治疗前骨板需经过面内弯曲、弯曲以及扭转3类变形。通过调整弯扭复合成形模具的空间位置及模具不同组成部分的相对位置,实现不同区域内不同变形量的面内弯曲、弯曲或扭转。应用数值方法分析验证弯扭复合成形模具及成形方法的适用性,基于DEFORM软件建立工业纯钛TA2骨板局部增量成形过程有限元模型,分析具有两个成形区的TA2骨板局部增量成形特征。结果塑性变形仅发生在复合模具附近,对已变形区无影响,会引起未成形区的刚性位移;骨板长度方向受力小于其宽度和厚度方向受力,面内弯曲需要较大的成形载荷。结论所发展的模具和方法可实现预期的骨板成形,也适用于其他PRCL金属骨板的成形。