Influence of Osteocyte Lacunar-Canalicular Morphology and Network Architecture on Osteocyte Mechanosensitivity.

PURPOSE OF REVIEW: The goal of this review is to summarize recent findings related to modifications in osteocyte lacunar and canalicular morphology due to physiological and pathological conditions. In addition, this review aims to outline how these modifications may influence the local mechanical environment of osteocytes and their mechanosensitivity. RECENT FINDINGS: Reduction in lacunar density with age and increasing lacunar size with lactation are confirmed in multiple studies in human and murine bone. There is also evidence of a reduction in canalicular density, length, and branching, as well as increasing sphericity and smaller lacunae with aging and disease. However, while some studies have found modifications in lacunar density, size, shape, and orientation, as well as canalicular density, length, and size due to specific physiological and pathological conditions, others have not observed any differences. Recent finite element models provide insights into how observed modifications in the lacunar-canalicular network (lacunar and canalicular density) and lacunar-canalicular morphology (lacunar area/volume, shape, and orientation as well as canalicular diameter and length) may influence the fluid flow and local strains around the lacunar-canalicular network and modify the local mechanical environment of osteocytes. Modifications in the lacunar-canalicular network morphology may lead to significant changes in the strains received by osteocytes and may influence bone's response to mechanical stimulation as osteocytes are the primary mechanosensing bone cells. Further experimental and computational studies will continue to improve our understanding of the relationship between lacunar-canalicular network morphology and osteocyte mechanosensitivity.

Evaluating the Role of Canalicular Morphology and Perilacunar Region Properties on Local Mechanical Environment of Lacunar-Canalicular Network Using Finite Element Modeling.

Physiological and pathological processes such as aging, diseases, treatments, and lactation can alter lacunar-canalicular network (LCN) morphology and perilacunar region properties. These modifications can impact the mechanical environment of osteocytes which in turn can influence osteocyte mechanosensitivity and the remodeling process. In this study, we aim to evaluate how the modifications in the canalicular morphology, lacunar density, and the perilacunar region properties influence the local mechanical environment of LCN and the apparent bone properties using three-dimensional finite element (FE) modeling. The simulation results showed that a 50% reduction in perilacunar elastic modulus led to about 7% decrease in apparent elastic modulus of the bone. The increase in canalicular density, length, and diameter did not influence the strain amplification in the models but they increased the amount of highly strained bone around LCN. Change in lacunar density did not influence the strain amplification and the amount of highly strained regions on LCN surfaces. Reduction in perilacunar elastic modulus increased both the strain amplification and the volume of highly strained tissue around and on the surface of LCN. The FE models of LCN in this study can be utilized to quantify the influence of modifications in canalicular morphology, lacunar density, and perilacunar region properties on the apparent bone properties and the local mechanical environment of LCN. Although this is a numerical study with idealized models, it provides important information on how mechanical environment of osteocytes is influenced by the modifications in LCN morphology and perilacunar region properties due to physiological and pathological processes.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics.

PURPOSE OF REVIEW: The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale. RECENT FINDINGS: Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Interaction of Microcracks and Tissue Compositional Heterogeneity in Determining Fracture Resistance of Human Cortical Bone.

Recent studies demonstrated an association between atypical femoral fracture (AFF) and long-term bisphosphonate (BP) use for osteoporosis treatment. Due to BP treatment, bone undergoes alterations including increased microcrack density and reduced tissue compositional heterogeneity. However, the effect of these changes on the fracture response of bone is not well understood. As a result, the goal of the current study is to evaluate the individual and combined effects of microcracks and tissue compositional heterogeneity on fracture resistance of cortical bone using finite element modeling (FEM) of compact tension (CT) specimen tests with varying microcrack density, location, and clustering, and material heterogeneity in three different bone samples. The simulation results showed that an increase in microcrack density improved the fracture resistance irrespective of the local material property heterogeneity and microcrack distribution. A reduction in material property heterogeneity adversely affected the fracture resistance in models both with and without microcracks. When the combined changes in microcrack density and tissue material property heterogeneity representing BP treatment were evaluated, the models corresponding to BP-treated bone demonstrated reduced fracture resistance. The simulation results also showed that although microcrack location and clustering, and microstructure significantly influenced fracture resistance, the trends observed on the effect of microcrack density and tissue material property heterogeneity did not change. In summary, these results provide new information on the interaction of microcracks, tissue material property heterogeneity, and fracture resistance and may improve the understanding of the influence of mechanical changes due to prolonged BP use on the fracture behavior of cortical bone.

Association between non-enzymatic glycation, resorption, and microdamage in human tibial cortices.

UNLABELLED: To better understand the association between different components of bone quality, we investigated the relationship among in vivo generated non-enzymatic glycation, resorption, and microdamage. The results showed negative correlation between advanced glycation end-products (AGEs) and resorption independent of age highlighting the interaction between these parameters that may lead to bone fragility. INTRODUCTION: Changes in the quality of bone material contribute significantly to bone fragility. In order to establish a better understanding of the interaction of the different components of bone quality and their influence on bone fragility, we investigated the relationship between non-enzymatic glycation, resorption, and microdamage generated in vivo in cortical bone using bone specimens from the same donors. METHODS: Total fluorescent advanced glycation end-products (AGEs) were measured in 96 human cortical bone samples from 83 donors. Resorption pit density, average resorption pit area, and percent resorption area were quantified in samples from 48 common donors with AGE measurements. Linear microcrack density and diffuse damage were measured in 21 common donors with AGE and resorption measurements. Correlation analyses were performed between all measured variables to establish the relationships among them and their variation with age. RESULTS: We found that average resorption pit area and percent resorption area decreased with increasing AGEs independently of age. Resorption pit density and percent resorption area demonstrated negative age-adjusted correlation with diffuse damage. Furthermore, average resorption pit area, resorption pit density, and percent resorption area were found to decrease significantly with age. CONCLUSIONS: The current study demonstrated the in vivo interrelationship between the organic constituents, remodeling, and damage formation in cortical bone. In addition to the age-related reduction in resorption, there is a negative correlation between AGEs and resorption independent of age. This inverse relationship indicates that AGEs alter the resorption process and/or accumulate in the tissue as a result of reduced resorption and may lead to bone fragility by adversely affecting fracture resistance through altered bone matrix properties.

Dilatational band formation in bone.

Toughening in hierarchically structured materials like bone arises from the arrangement of constituent material elements and their interactions. Unlike microcracking, which entails micrometer-level separation, there is no known evidence of fracture at the level of bone's nanostructure. Here, we show that the initiation of fracture occurs in bone at the nanometer scale by dilatational bands. Through fatigue and indentation tests and laser confocal, scanning electron, and atomic force microscopies on human and bovine bone specimens, we established that dilatational bands of the order of 100 nm form as ellipsoidal voids in between fused mineral aggregates and two adjacent proteins, osteocalcin (OC) and osteopontin (OPN). Laser microdissection and ELISA of bone microdamage support our claim that OC and OPN colocalize with dilatational bands. Fracture tests on bones from OC and/or OPN knockout mice (OC(-/-), OPN(-/-), OC-OPN(-/-;-/-)) confirm that these two proteins regulate dilatational band formation and bone matrix toughness. On the basis of these observations, we propose molecular deformation and fracture mechanics models, illustrating the role of OC and OPN in dilatational band formation, and predict that the nanometer scale of tissue organization, associated with dilatational bands, affects fracture at higher scales and determines fracture toughness of bone.

An integrated experimental-computational framework to assess the influence of microstructure and material properties on fracture toughness in clinical specimens of human femoral cortical bone.

Microstructural and compositional changes that occur due to aging, pathological conditions, or pharmacological treatments alter cortical bone fracture resistance. However, the relative importance of these changes to the fracture resistance of cortical bone has not been quantified in detail. In this technical note, we developed an integrated experimental-computational framework utilizing human femoral cortical bone biopsies to advance the understanding of how fracture resistance of cortical bone is modulated due to modifications in its microstructure and material properties. Four human biopsy samples from individuals with varying fragility fracture history and osteoporosis treatment status were converted to finite element models incorporating specimen-specific material properties and were analyzed using fracture mechanics-based modeling. The results showed that cement line density and osteonal volume had a significant effect on crack volume. The removal of cement lines substantially increased the crack volume in the osteons and interstitial bone, representing straight crack growth, compared to models with cement lines due to the lack of crack deflection in the models without cement lines. Crack volume in the osteons and interstitial bone increased when mean elastic modulus and ultimate strength increased and mean fracture toughness decreased. Crack volume in the osteons and interstitial bone was reduced when material property heterogeneity was incorporated in the models. Although both the microstructure and the heterogeneity of the material properties of the cortical bone independently increased the fracture toughness, the relative contribution of the microstructure was more significant. The integrated experimental-computational framework developed here can identify the most critical microscale features of cortical bone modulated by pathological processes or pharmacological treatments that drive changes in fracture resistance and improve our understanding of the relative influence of microstructure and material properties on fracture resistance of cortical bone.

Quantifying how altered lacunar morphology and perilacunar tissue properties influence local mechanical environment of osteocyte lacunae using finite element modeling.

Previous studies have demonstrated that osteocyte lacunar morphology and perilacunar bone tissue properties undergo alterations due to physiological and pathological processes such as aging, lactation, diseases, and treatments. However, the influence of these alterations on the apparent mechanical properties of the bone and the local mechanical environment of osteocyte lacunae has not been evaluated in detail. The goal of this study is to quantify the influence of osteocyte lacunar morphology and perilacunar tissue properties on local mechanical environment around lacunae and the apparent mechanical properties of the bone using three-dimensional FE models of lacunae networks with varying lacunar morphology and perilacunar properties based on previously reported experimental data. To attain this goal, a parametric study using models with different lacunar/perilacunar properties, including lacunar density (Lc.D), orientation (Lc.Φ), volume (Lc.V), and equancy (Lc.Eq), as well as perilacunar modulus (Pl.E), and size (Pl.S) was carried out. In addition, a specific case study using models derived from aged and young bone specimens was performed. Our results showed that the highly strained tissue around lacunae increased linearly with increasing Lc.D and Lc.V, reduced exponentially with decreasing angle of major axis of lacunae from the loading direction and with increasing Pl.E, and increased exponentially with increasing Pl.S. The change in apparent elastic modulus with modifications in lacunar morphology was very small whereas the change in perilacunar modulus had a more substantial influence on the apparent elastic modulus. Lacunar strain amplification was reduced by increasing Lc.Φ, and Pl.E and increased with increasing Lc.V within the range of 1.5 and 2.3. No significant difference was seen in the apparent elastic modulus of models derived from young and aged bone models. However, young bone showed substantially larger amount of highly strained tissue around lacunae compared to the aged bone. This difference was amplified when the perilacunar tissue property modifications were incorporated in the models. In summary, the results indicate that modifications in the osteocyte lacunar morphology and perilacunar tissue properties can significantly alter local tissue deformation around lacunae which may impact osteocyte mechanosensitivity.

Structural role of osteocyte lacunae on mechanical properties of bone matrix: A cohesive finite element study.

Despite the extensive studies on biological function of osteocytes, there are limited studies that evaluated the structural role of osteocyte lacunae on local mechanical properties of the bone matrix. As a result, the goal of this study was to elucidate the independent contribution of osteocyte lacunae structure on mechanical properties and fracture behavior of the bone matrix uncoupled from its biological effects and bone tissue composition variation. This study combined cohesive finite element modeling with experimental data from a lactation rat model to evaluate the influence of osteocyte lacunar area porosity, density, size, axis ratio, and orientation on the elastic modulus, ultimate strength, and ultimate strain of the bone matrix as well as on local crack formation and propagation. It also performed a parametric study to isolate the influence of a single osteocyte lacunae structural property on the mechanical properties of the bone matrix. The experimental measurements demonstrated statistically significant differences in lacunar size between ovariectomized rats with lactation history and virgin groups (both ovariectomized and intact) and in axis ratio between rats with lactation history and virgins. There were no differences in mechanical properties between virgin and lactation groups as determined by the finite element simulations. However, there were statistically significant linear relationships between the physiological range of osteocyte lacunar area porosity, density, size, and orientation and the elastic modulus and ultimate strength of the bone matrix in virgin and lactation rats. The parametric study also revealed similar but stronger relationships between elastic modulus and ultimate strength and lacunar density, size, and orientation. The simulations also demonstrated that the osteocyte lacunae guided the crack propagation through local stress concentrations. In summary, this study enhanced the limited knowledge on the structural role of osteocyte lacunae on local mechanical properties of the bone matrix. These data are important in gaining a better understanding of the mechanical implications of the local modifications due to osteocytes in the bone matrix.

Biomechanical mechanisms of atypical femoral fracture.

Antiresorptives such as bisphosphonates (BP) and denosumab are commonly used osteoporosis treatments that are effective in preventing osteoporotic fractures by suppressing bone turnover. Although these treatments reduce fracture risk, their long-term use has been associated with atypical femoral fracture (AFF), a rare potential side effect. Despite its rare occurrence, AFF has had a disproportionately significant adverse impact on society due to its severe outcomes such as loss of function and delayed healing. These severe outcomes have led to the decrease in the use and prescription of osteoporosis treatment drugs due to patient anxiety and clinician reluctance. This creates the risk for increasing osteoporotic fracture rates in the population. The existing information on the pathogenesis of AFF primarily relies on retrospective observational studies. However, these studies do not explain the underlying mechanisms that contribute to AFF, and therefore the mechanistic origins of AFF are still poorly understood. The purpose of this review is to outline the current state of knowledge of the mechanical mechanisms of AFF. The review focuses on three major potential mechanical mechanisms of AFF based on the current literature which are (1) macroscale femoral geometry which influences the stress/strain distribution in the femur under loading; (2) bone matrix composition, potentially altered by long-term remodeling suppression by BPs, which directly influences the material properties of bone and its mechanical behavior; and (3) microstructure, potentially altered by long-term remodeling suppression by BPs, which impacts fracture resistance through interaction with crack propagation. In addition, this review presents the critical knowledge gaps in understanding AFF and also discusses approaches to closing the knowledge gap in understanding the underlying mechanisms of AFF.

Finite element modeling of the influence of hand position and bone properties on the Colles' fracture load during a fall.

Distal forearm fracture is one of the most frequently observed osteoporotic fractures, which may occur as a result of low energy falls such as falls from a standing height and may be linked to the osteoporotic nature of the bone, especially in the elderly. In order to prevent the occurrence of radius fractures and their adverse outcomes, understanding the effect of both extrinsic and intrinsic contributors to fracture risk is essential. In this study, a nonlinear fracture mechanics-based finite element model is applied to human radius to assess the influence of extrinsic factors (load orientation and load distribution between scaphoid and lunate) and intrinsic bone properties (age-related changes in fracture properties and bone geometry) on the Colles' fracture load. Seven three-dimensional finite element models of radius were created, and the fracture loads were determined by using cohesive finite element modeling, which explicitly represented the crack and the fracture process zone behavior. The simulation results showed that the load direction with respect to the longitudinal and dorsal axes of the radius influenced the fracture load. The fracture load increased with larger angles between the resultant load and the dorsal axis, and with smaller angles between the resultant load and longitudinal axis. The fracture load also varied as a function of the load ratio between the lunate and scaphoid, however, not as drastically as with the load orientation. The fracture load decreased as the load ratio (lunate/scaphoid) increased. Multiple regression analysis showed that the bone geometry and the load orientation are the most important variables that contribute to the prediction of the fracture load. The findings in this study establish a robust computational fracture risk assessment method that combines the effects of intrinsic properties of bone with extrinsic factors associated with a fall, and may be elemental in the identification of high fracture risk individuals as well as in the development of fracture prevention methods including protective falling techniques. The additional information that this study brings to fracture identification and prevention highlights the promise of fracture mechanics-based finite element modeling in fracture risk assessment.

A three-dimensional multiscale finite element model of bone coupling mineralized collagen fibril networks and lamellae.

Despite evidence of contribution of mineralized collagen fibrils (MCF) to both the microscale elastic and fracture response of bone, the extent of influence of MCF orientation and material property variation on the lamellar scale mechanical properties is still not well quantified. To this end, in this study, we developed a three-dimensional multiscale finite element model that linked submicroscale models of MCF networks to microscale models of several lamellae. The developed models evaluated the individual and relative influence of MCF orientation as well as material property variation due to MCF mineral distribution and interaction on the lamellar scale mechanical response of bone. The simulation results showed that the elastic modulus, ultimate strength, and fracture energy at the lamellar scale decreased as the angle between the main axis of MCFs and loading direction increased. The heterogeneity in mineral distribution along MCFs did not lead to a significant difference in the mechanical behavior at the lamellar scale compared to the material property heterogeneity introduced in the models due to MCF orientation variation. Variation in the interaction between MCFs at the submicroscale had a substantial influence on the lamellar scale mechanical properties. In summary, this study established a multiscale model that linked MCFs to lamellae providing the capability of quantifying the relative influence of modifications in material and organizational properties of MCFs due to age, diseases, and treatments on the fracture processes at the lamellar length scale.

Assessment of the multifactorial causes of atypical femoral fractures using a novel multiscale finite element approach.

Atypical femoral fracture (AFF), which is a low energy fracture in the subtrochanteric or diaphysis region of the femur, has multifactorial causes that span macro- to microscale mechanisms including femoral geometry, cortical bone composition and structure. However, the extent of individual and combined influence of these factors on AFF is still not well understood. As a result, the aim of this study is to develop a multiscale fracture mechanics-based finite element modeling framework that is capable of quantifying the individual and combined influence of macroscale femoral geometrical properties as well as cortical bone microscale material properties and structure on AFF. In this study, three different femoral geometries with two different cortical bone microstructures, and two different material property distributions were investigated by first determining the critical AFF locations in the femur using macroscale stress analysis and then performing coupled macro-microscale fracture simulations. The simulation results showed that femoral geometry led to substantial differences in crack growth independent of cortical microstructure and tissue level material properties. The results suggest that multiple femoral geometrical properties, including neck-shaft angle and curvature, may contribute to the fracture behavior at AFF sites rather than a single macroscale geometrical feature. Osteonal area had a significant effect on microcrack propagation at AFF sites independent of microscale material property distribution and femoral geometry. In addition, cortical bone tissue level material heterogeneity improved the fracture resistance independent of femoral geometry and cortical microstructure. In summary, the computational approach developed in this study identified the individual, combined, and relative influence of multiscale factors on AFF risk. The new framework developed in this study could help identify the governing multiscale mechanisms of AFF and bring additional insight into the possible association of long-term bisphosphate treatment with AFF.

Prediction of Colles' fracture load in human radius using cohesive finite element modeling.

Osteoporotic and age-related fractures are a significant public health problem. One of the most common osteoporotic fracture sites in the aging population is distal radius. There is evidence in the literature that distal radius fractures (Colles' fracture) are an indicative of increased risk of future spine and hip fractures. In this study, a nonlinear fracture mechanics-based finite element method is applied to human radius to assess its fracture load as a function of cortical bone geometry and material properties. Seven three-dimensional finite element models of radius were created and the fracture loads were determined by using cohesive finite element modeling which explicitly represents the crack and the fracture process zone behavior. The fracture loads found in the simulations (731-6793 N) were in the range of experimental values reported in the literature. The fracture loads predicted by the simulations decreased by 4-5% per decade based only on material level changes and by 6-20% per decade when geometrical changes were also included. Cortical polar moment of inertia at 15% distal radius showed the highest correlation to fracture load (r(2)=0.97). These findings demonstrate the strength of fracture mechanics-based finite element modeling and show that combining geometrical and material properties provides a better assessment of fracture risk in human radius.

A finite element study evaluating the influence of mineralization distribution and content on the tensile mechanical response of mineralized collagen fibril networks.

One of the key length scales of interest in bone's hierarchical structure is the submicroscale which has been shown to influence the fracture behavior of bone at larger length scales. At the submicroscale, the building block of bone is mineralized collagen fibrils (MCF). The mineral distribution and content of MCFs as well as the interaction between MCFs influence the mechanical response of bone at the submicroscale. However, to what extent these factors influence the submicroscale damage and failure processes in bone has not been quantified. The goal of this study is to evaluate the influence of varying mineral distribution, mineral content, and interaction between MCFs on the submicroscale mechanical and fracture response of bone using a novel finite element model incorporating a 3D network of MCFs under both transverse (representing MCF separation) and longitudinal (representing MCF rupture) tensile loading. The results showed that the apparent mechanical properties (elastic modulus, ultimate strength and fracture energy) of the MCF networks increased both with increasing uniformity of mineral distribution and with stronger interactions between MCFs under longitudinal loading whereas under transverse loading only interactions between MCFs but not the mineral distribution influenced the apparent properties of MCF networks. The mechanical properties demonstrated an exponential variation with mineral distribution under both longitudinal and transverse loading. An increase in total volume fraction of minerals at full mineralization resulted in a modest increase in the mechanical properties of MCF networks. These results provide new insights into how changes in mineral content and distribution as well as interaction between MCFs modify the submicroscale mechanical properties of bone. The unique information gained from this study cannot be directly accessible with experiments and single MCF computational models. This new information has the potential to provide a better understanding of the underlying mechanisms of damage in MCF networks which may help identify the effect of tissue modifications at the submicroscale due to disease, age-related changes, and treatments on bone fracture risk.

Effect of modifications in mineralized collagen fibril and extra-fibrillar matrix material properties on submicroscale mechanical behavior of cortical bone.

A key length scale of interest in assessing the fracture resistance of bone is the submicroscale which is composed of mineralized collagen fibrils (MCF) and extra-fibrillar matrix (EFM). Although the processes through which the submicroscale constituents of bone contribute to the fracture resistance in bone have been identified, the extent of the modifications in submicroscale mechanical response due to the changes in individual properties of MCFs and EFM has not been determined. As a result, this study aims to quantify the influence of individual MCF and EFM material property modifications on the mechanical behavior (elastic modulus, ultimate strength, and resistance to failure) of bone at the submicroscale using a novel finite element modeling approach that incorporate 3D networks of MCFs with three different orientations as well as explicit representation of EFM. The models were evaluated under tensile loading in transverse (representing MCF separation) and longitudinal (representing MCF rupture) directions. The results showed that the apparent elastic modulus at the submicroscale under both loading directions for all orientations was only affected by the change in the elastic modulus of MCFs. MCF separation and rupture strengths were mainly dependent on the ultimate strength of EFM and MCFs, respectively, with minimal influence of other material properties. The extent of damage during MCF separation increased with increasing ultimate strength of EFM and decreased with increasing fracture energy of EFM with minimal contribution from elastic modulus of MCFs. For MCF rupture, there was an almost one-to-one linear relationship between the percent change in fracture energy of MCFs and the percent change in the apparent submicroscale fracture energy. The ultimate strength and elastic modulus of MCFs had moderate to limited influence on the MCF rupture fracture energy. The results of this study quantified the extent of changes that may be seen in the energy dissipation processes during MCF rupture and separation relative to the changes in the individual constituents of the tissue. This new knowledge significantly contributes to improving the understanding of how the material property alterations at the submicroscale that can occur due to diseases, age-related changes, and treatments affect the fracture processes at larger length scales.

Mineralized collagen fibril network spatial arrangement influences cortical bone fracture behavior.

Bone is a hierarchical material exhibiting different fracture mechanisms at each length scale. At the submicroscale, the bone is composed of mineralized collagen fibrils (MCF). At this scale, the fracture processes in cortical bone have not been extensively studied in the literature. In this study, the influence of MCF size and orientation on the fracture behavior of bone under both transverse and longitudinal loading was investigated using novel 3D models of MCF networks with explicit representation of extra-fibrillar matrix. The simulation results showed that separation between MCFs was the main cause of damage and failure under transverse loading whereas under longitudinal loading, the main damage and failure mechanism was MCF rupture. When the MCF network was loaded in the transverse direction the mechanical properties increased as the orientation of fibrils deviated farther from the main fibril orientation whereas the opposite trend was observed under longitudinal loading. The fracture energy was much larger in longitudinal than transverse loading. MCF diameter variation did not affect the mechanical properties under longitudinal loading but led to higher mechanical properties with increasing MCF diameter under transverse loading. The new modeling framework established in this study generate unique information on the effect of MCF network spatial arrangement on the fracture behavior of bone at the submicroscale which is not currently possible to measure via experiments. This unique information may improve the understanding of how structural alterations at the submicroscale due to disease, age-related changes, and treatments affect the fracture processes at larger length scales.

Material heterogeneity, microstructure, and microcracks demonstrate differential influence on crack initiation and propagation in cortical bone.

The recent studies have shown that long-term bisphosphonate use may result in a number of mechanical alterations in the bone tissue including a reduction in compositional heterogeneity and an increase in microcrack density. There are limited number of experimental and computational studies in the literature that evaluated how these modifications affect crack initiation and propagation in cortical bone. Therefore, in this study, the entire crack growth process including initiation and propagation was simulated at the microscale by using the cohesive extended finite element method. Models with homogeneous and heterogeneous material properties (represented at the microscale capturing the variability in material property values and their distribution) as well as different microcrack density and microstructure were compared. The results showed that initiation fracture resistance was higher in models with homogeneous material properties compared to heterogeneous ones, whereas an opposite trend was observed in propagation fracture resistance. The increase in material heterogeneity level up to 10 different material property sets increased the propagation fracture resistance beyond which a decrease was observed while still remaining higher than the homogeneous material distribution. The simulation results also showed that the total osteonal area influenced crack propagation and the local osteonal area near the initial crack affected the crack initiation behavior. In addition, the initiation fracture resistance was higher in models representing bisphosphonate treated bone (low material heterogeneity, high microcrack density) compared to untreated bone models (high material heterogeneity, low microcrack density), whereas an opposite trend was observed at later stages of crack growth. In summary, the results demonstrated that tissue material heterogeneity, microstructure, and microcrack density influenced crack initiation and propagation differently. The findings also elucidate how possible modifications in material heterogeneity and microcrack density due to bisphosphonate treatment may influence the initiation and propagation fracture resistance of cortical bone.

Anisotropy of age-related toughness loss in human cortical bone: a finite element study.

A mechanistic understanding of the role of bone quality on fracture processes is essential for determining the underlying causes of age-related changes in the mechanical response of the human bone. In this study, a previously developed cohesive finite element model was used to investigate the effects of age-related changes and the orientation of crack growth on the toughening behavior of human cortical bone. The change in the anisotropy of toughening mechanisms with age was also studied. Finite element method (FEM) simulations showed that the initiation toughness decreased by 3% and 8%/decade for transverse and longitudinal crack growth, respectively. In contrast, fracture resistance curve slope for transverse and longitudinal crack growth decreased by 2% and 3%/decade, respectively. Initiation fracture toughness values were higher for the transverse than for the longitudinal for a given age. On the other hand, propagation fracture toughness values were higher for longitudinal than for transverse crack growth for a given age. With respect to age, the toughness ratio for crack initiation decreased by 6%/decade, but that for propagation showed almost no change (less than 1%). In light of these findings, an analytical model evaluating the crack arresting feature of cement lines, is proposed to explain the factors that determine crack penetration into osteons or its deflection by cement lines.

Interactions between microstructural and geometrical adaptation in human cortical bone.

With aging and in disease, the changes in bone microstructure and geometry influence the mechanical properties of cortical bone, however, the level of interaction between the two is not known. Here, we investigate the interaction between the changes in microstructural and geometrical properties of the aging male tibia in proximal and distal middiaphysis. The microstructural measurements include variables related to the size and density of osteons and intracortical porosity. The macroscopic geometrical properties include variables related to bone surfaces (periosteal and endosteal) and cross section (area, moment of inertia). Site-specific correlations were found between the microstructural and geometrical properties along the bone length and at different bone surfaces. In contrast to the proximal middiaphysis of male tibia, where no correlation existed, significant (p<0.05) correlations were found in the distal middiaphysis of tibia. The changes in parameters partially related to bone formation in the cortex, including the osteonal area, showed positive correlations with an increase in the periosteal diameter. Similarly, parameters related to bone resorption and/or failed formation in the cortex, including porosity and pore size, showed significant correlations with cortical thinning. These findings support the concept that, with aging, anabolic and catabolic responses in the human tibia at microstructural and macrostructural levels are spatially related and site specific.