Predicting the structural integrity of bone defects repaired using bone graft materials

Bone defects create stress concentrations which can cause fracture under impact or cyclic loading. Defects are often repaired by filling them with a bone graft material; this will reduce the stress concentration, but not completely, because these materials have lower stiffness than bone. The fracture risk decreases over time as the graft material is replaced by living bone. Many new bone graft materials are being developed, using tissue engineering and other techniques, but currently there is no rational way to compare these materials and predict their effectiveness in repairing a given defect. This paper describes, for the first time, a theoretical model which can be used to predict failure by brittle fracture or fatigue, initiating at the defect. Preliminary results are presented, concentrating on the prediction of stress fracture during the crucial post-operative period. It is shown that the likelihood of fracture is strongly influenced by the shape of the defect as well as its size, and also by the level of post-operative exercise. The most important finding is that bone graft materials can be successful in preventing fracture even when their mechanical properties are greatly inferior to those of bone. Future uses of this technique include pre-clinical assessment of bone replacement materials and pre-operative planning in orthopaedic surgery.     

A critical distance study of stress concentrations in bone

The Theory of Critical Distances (TCD) is a method used to study the failure of material in situations where stress concentrations, such as holes and notches, are present. This method uses two material constants: a critical length and a critical stress. The elastic stress field close to the stress concentration is examined, applying a fracture criterion. The TCD has been applied to predict brittle fracture in various different materials and various types of notches but it has not previously been applied to bone. Since bone fails by brittle fracture with limited plasticity, it is expected that the TCD will be applicable. Experimental data were obtained from the literature on the effects of sharp notches and holes loaded in various ways (tension, torsion and bending). These tests were modelled using finite element analysis. It was found that the TCD could be successfully applied to predict the load required for brittle fracture as a function of the type and size of the stress concentration feature. The critical distance was found to be almost constant, about 0.3-0.4mm, for all types of bone studied: the critical stress was found to be related to the material's ultimate tensile strength by a constant factor of T=1.33. The results of this study will be of practical value in the assessment of stress concentration features introduced during surgery and of naturally occurring bone defects.     

Fracture toughness and fatigue crack propagation rate of short fiber reinforced epoxy composites for analogue cortical bone

Third-generation mechanical analogue bone models and synthetic analogue cortical bone materials manufactured by Pacific Research Laboratories, Inc. (PRL) are popular tools for use in mechanical testing of various orthopedic implants and biomaterials. A major issue with these models is that the current third-generation epoxy-short fiberglass based composite used as the cortical bone substitute is prone to crack formation and failure in fatigue or repeated quasistatic loading of the model. The purpose of the present study was to compare the tensile and fracture mechanics properties of the current baseline (established PRL "third-generation" E-glass-fiber-epoxy) composite analogue for cortical bone to a new composite material formulation proposed for use as an enhanced fourth-generation cortical bone analogue material. Standard tensile, plane strain fracture toughness, and fatigue crack propagation rate tests were performed on both the third- and fourth-generation composite material formulations using standard ASTM test techniques. Injection molding techniques were used to create random fiber orientation in all test specimens. Standard dog-bone style tensile specimens were tested to obtain ultimate tensile strength and stiffness. Compact tension fracture toughness specimens were utilized to determine plane strain fracture toughness values. Reduced thickness compact tension specimens were also used to determine fatigue crack propagation rate behavior for the two material groups. Literature values for the same parameters for human cortical bone were compared to results from the third- and fourth-generation cortical analogue bone materials. Tensile properties of the fourth-generation material were closer to that of average human cortical bone than the third-generation material. Fracture toughness was significantly increased by 48% in the fourth-generation composite as compared to the third-generation analogue bone. The threshold stress intensity to propagate the crack was much higher for the fourth-generation material than for the third-generation composite. Even at the higher stress intensity threshold, the fatigue crack propagation rate was significantly decreased in the fourth-generation composite compared to the third-generation composite. These results indicate that the bone analogue models made from the fourth-generation analogue cortical bone material may exhibit better performance in fracture and longer fatigue lives than similar models made of third-generation analogue cortical bone material. Further fatigue testing of the new composite material in clinically relevant use of bone models is still required for verification of these results. Biomechanical test models using the superior fourth-generation cortical analogue material are currently in development.     

The use of cranial bone grafts in the closure of alveolar and anterior palatal clefts

A method is described for harvesting cancellous bone from the diploic space. In our opinion, this is the material of choice for bone grafting alveolar clefts in the 7- to 11-year age group. The procedure could be performed at an earlier age if the maxillary segments are under orthopedic control and in proper alignment. Success of the procedure depends on proper orthodontic preparation of the maxillary segments and careful, complete closure of the soft tissues across the anterior palatal cleft, the nasal lining defect, and the anterior alveolus. Results have been encouraging in terms of bone formation, and tooth migration into the bone graft can be expected if there has been no damage to the dental sac. Closure of the alveolar defect at the time of the primary lip closure would preclude the eventual need for a bone graft, but it cannot be accomplished without early, precise alignment of the maxillary segments if extensive periosteal denudation is to be avoided. The age beyond which periosteal closure alone will be inadequate to provide sufficient bone formation and should be supplemented by a bone graft remains to be established.     

DEXA对骨髓炎骨缺损治疗中骨痂密度的评价

目的：探讨DEXA对骨髓炎骨缺损治疗中骨痂密度的评价及意义。方法：严格按照纳入排除标准,选取21例骨髓炎清创后伴大段皮质骨缺损一期植骨的病人。术后4,6,8,10个月后对骨折端骨痂行双能X线骨密度仪检测,并进行X摄片以及Enneking评分,从而明确植骨区愈合骨痂的密度变化趋势,骨愈合情况以及症状改善情况。结果：（1）X线摄片结果显示：4个月后：骨缺损区依然清晰可见,内有少量稀疏骨痂通过,少量外骨痂形成。6个月后：植骨区内骨痂含量明显增多,且外骨痂膨大。8个月：缺损区模糊,有较致密骨痂生成,且外骨痂逐渐减少。10个月：植骨区骨痂更加致密,且部份髓腔再通。（2）Enneking评分：患者术后第10个月功能恢复情况评估正常功能20例,20分以下的患者1例。（3）BMD测定：骨折端的骨密度及骨密度比率随时间延长而增加,植骨10个月后患侧的骨密度已可基本上达到正常对照侧的骨密度水平。结论：双能X线骨密度测量从一定程度上反映出骨痂的力学强度特性。在感染性骨缺损治疗中可以作为检测植骨区的恢复情况的参考。     

Reconstruction of orbital floor fracture using solvent-preserved bone graft

The orbital floor is one of the most frequently damaged parts of the maxillofacial skeleton during facial trauma. Unfavorable aesthetic and functional outcomes are frequent when it is treated inadequately. The treatment consists of spanning the floor defect with a material that can provide structural support and restore the orbital volume. This material should also be biocompatible with the surrounding tissues and easily reshaped to fit the orbital floor. Although various autografts or synthetic materials have been used, there is still no consensus on the ideal reconstruction method of orbital floor defects. This study evaluated the applicability of solvent-preserved cadaveric cranial bone graft and its preliminary results in the reconstruction of the orbital floor fractures. Twenty-five orbital floor fractures of 21 patients who underwent surgical repair with cadaveric bone graft during a 2-year period were included in this study. Pure blowout fractures were determined in nine patients, whereas 12 patients had other accompanying maxillofacial fractures. Of the 21 patients, 14 had clinically evident diplopia (66.7 percent), 12 of them had enophthalmos (57.1 percent), and two of them had gaze restriction preoperatively. Reconstruction of the floor of the orbit was performed following either the subciliary or the transconjunctival approach. A cranial allograft was placed over the defect after sufficient exposure. The mean follow-up period was 9 months. Postoperative diplopia, enophthalmos, eye motility, cosmetic appearance, and complications were documented. None of the patients had any evidence of diplopia, limited eye movement, inflammatory reactions in soft tissues, infection, or graft extrusion in the postoperative period. Providing sufficient orbital volume, no graft resorption was detected in computed tomography scan controls. None of the implants required removal for any reason. Enophthalmos was seen in one patient, and temporary scleral show lasting up to 3 to 6 weeks was detected in another three patients. Satisfactory cosmetic results were obtained in all patients. This study showed that solvent-preserved bone, which is a nonsynthetic, human-originated, processed bioimplant, can be safely used in orbital floor repair and can be considered as another reliable treatment alternative.     

Femoral head apparent density distribution predicted from bone stresses

A new theory relating bone morphology to applied stress is used to predict the apparent density distribution in the femoral head and neck. Cancellous bone is modeled as a self-optimizing material and cortical bone as a saturated (maximum possible bone density) response to stress in the bone tissue. Three different approaches are implemented relating bone apparent density to: (1) the von Mises stress, (2) the strain energy density in the mineralized tissue and (3) a defined closed effective stress (spherical stress). An iterative nonlinear three-dimensional finite element model is used to predict the apparent density distribution in the femoral head and neck for each of the three approaches. It is shown that the von Mises stress (an open effective stress) cannot accurately predict bone apparent density. It is shown that strain energy density and the defined closed effective stress can predict apparent density and that they give predictions consistent with the observed density pattern in the femoral head and neck.     

Segmental bone defects: from cellular and molecular pathways to the development of novel biological treatments

Several conditions in clinical orthopaedic practice can lead to the development of a diaphyseal segmental bone defect, which cannot heal without intervention. Segmental bone defects have been traditionally treated with bone grafting and/or distraction osteogenesis, methods that have many advantages, but also major drawbacks, such as limited availability, risk of disease transmission and prolonged treatment. In order to overcome such limitations, biological treatments have been developed based on specific pathways of bone physiology and healing. Bone tissue engineering is a dynamic field of research, combining osteogenic cells, osteoinductive factors, such as bone morphogenetic proteins, and scaffolds with osteoconductive and osteoinductive attributes, to produce constructs that could be used as bone graft substitutes for the treatment of segmental bone defects. Scaffolds are usually made of ceramic or polymeric biomaterials, or combinations of both in composite materials. The purpose of the present review is to discuss in detail the molecular and cellular basis for the development of bone tissue engineering constructs.     

Bone grafts and bone morphogenetic proteins in spine fusion

Spinal fusions are being performed for various pathologies of the spine. Stabilizing vertebral segments by eliminating motion across those segments becomes critical in dealing with pathologies of the spine that lead to instability. The use of autograft has been the gold standard for spine fusion. However, due to complications such as donor site morbidity, increased operating time, and limited supply, the use of allograft as a graft extender has become an acceptable practice especially in fusions spanning multiple segments. The discovery and isolation of novel proteins (i.e., bone morphogenetic proteins, BMPs), which initiate the molecular cascade of bone formation, have experimentally been shown in numerous animal studies to be as effective as autografts. Although the use of BMPs has exciting applications in spine surgery, long-term clinical studies must be evaluated for its efficacy in various applications in humans. The use of biomimetic materials such as hydroxyapatite (HA), or tricalcium phosphate (TCP) has also been examined in several animal models as bone graft substitutes or carriers. Although these materials have shown some promise in specific site applications, more work remains in elucidating an efficacious combination of these materials and BMPs that can be as effective as autografts. This review will present the status of bone grafts, bone morphogenetic proteins, gene therapy, and work that has been done to facilitate spinal fusion and simultaneously eliminate the need for bone graft. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effects of mechanical loading patterns,bone graft,and proximity to periosteum on bone defect healing

The goal of this study is to elucidate whether mechanobiological factors, including mechanical loading patterns, presence of bone graft, and proximity to the periosteum, correlate to de novo tissue generation and healing in critical sized long bone defects, which are enveloped by periosteum in situ and are bridged at 16 weeks, in sheep femora. Quantitative histomorphometric measures of defect cross sections show that, along the axis least able to resist bending loads (minor centroidal axis, CA), bone laid down in the first two weeks after surgery exhibits more mineralization albeit less total area compared to bone along the axis most able to resist bending loads (major CA). Similarly, areas of the cross section along the minor CA show a higher degree of perfusion albeit less total area of perfusion compared to bone along the major CA. Furthermore, proximity to the periosteal niche, in conjunction with the presence of bone graft and predominant loading patterns, relates significantly to the radial distribution of early bone apposition and perfusion of bone at 16 weeks after surgery (linear regression with R²>0.80). In the absence of graft, early bone density is relatively evenly distributed in the defect zone, as is the intensity of perfused tissue. As measured by a steeper average slope in intensity of fluorochrome (new bone) distribution between the periosteum and the IM nail, the presence of bone graft retards initial bone formation in the defect zone and is associated with less evenly distributed tissue perfusion (steeper slope) persisting 16 weeks after surgery. Finally, although the mean area of bone resorption is not significantly different within or between groups defined by the presence of graft and/or mechanical loading patterns in the defect zone, the mean area of infilling resorption spaces is significantly higher in areas of the defect zone least able to resist bending (minor CA) but is not significantly related to the presence of bone graft. To our knowledge, the use of the major and minor centroidal axes to relate prevailing mechanical loading patterns to area and density of early bone generation in bone defects has not been reported prior to this study and may provide a new means to assess structure–function relationships in de novo bone generation and healing of bone defects.     

Can the theory of critical distances predict the failure of shape memory alloys?

Components made from shape memory alloys (SMAs) such as nitinol often fail from stress concentrations and defects such as notches and cracks. It is shown here for the first time that these failures can be predicted using the theory of critical distances (TCDs), a method which has previously been used to study fracture and fatigue in other materials. The TCD uses the stress at a certain distance ahead of the notch to predict the failure of the material due to the stress concentration. The critical distance is believed to be a material property which is related to the microstructure of the material. The TCD is simply applied to a linear model of the material without the need to model the complication of its non-linear behaviour. The non-linear behaviour of the material at fracture is represented in the critical stress. The effect of notches and short cracks on the fracture of SMA NiTi was studied by analysing experimental data from the literature. Using a finite element model with elastic material behaviour, it is shown that the TCD can predict the effect of crack length and notch geometry on the critical stress and stress intensity for fracture, with prediction errors of less than 5%. The value of the critical distance obtained for this material was L?=?90?μm; this may be related to its grain size. The effects of short cracks on stress intensity were studied. It was shown that the same value of the critical distance (L?=?90?μm) could estimate the experimental data for both notches and short cracks.     

Volume maintenance of inlay bone grafts in the craniofacial skeleton

Although the clinical use of inlay bone grafts is widespread in craniofacial surgery, the dynamics of inlay bone grafting to the craniofacial skeleton have never been well characterized. Previous work demonstrated that volume maintenance of bone grafts in the onlay position is a consequence of their microarchitectural features, rather than their embryological origins. The purpose of this study was to investigate whether the properties determining the volume maintenance of bone grafts in the onlay position in the craniofacial skeleton could be extended to bone grafts in the inlay position. It was hypothesized that volume maintenance of an inlay bone graft could be better explained on the basis of the microarchitectural features of the graft (cortical versus cancellous composition), rather than its embryological origin (membranous versus endochondral), and that the primary determinant of bone graft behavior is the interaction between the microarchitectural features of the bone graft and the local mechanical environment in which the bone graft is placed. Cortical and cancellous bone grafts were harvested from the iliac crest (endochondral origin) of 25 New Zealand white rabbits, and cortical bone was harvested from the mandible (membranous origin) of each rabbit. Four 7-mm trephine holes were made in the cranium of each rabbit, posterior to the coronal suture. Each defect was filled with endochondral cortical bone, endochondral cancellous bone, or membranous cortical bone or was left as an ungrafted control specimen. Animals were killed at 3, 8, or 16 weeks. Crania were subjected to micro-computed tomographic and histological assessments. Micro-computed tomographic analysis demonstrated significant increases in actual bone volume from time 0 to the time of death for all types of grafts. Cortical bone demonstrated significant increases in space-occupying volume at all time points. By 16 weeks, no statistically significant difference in either the actual bone volume or the space-occupying volume according to graft type could be detected. There was no resorption of the inlay bone grafts; in fact, all bone types exhibited increased volume. Cancellous bone demonstrated the greatest capacity to increase actual bone volume. All bone graft types seemed to reach a steady-state bone volume, as if controlled by a local regulator. The regulator is likely the local mechanical environment in which the grafts were placed, as corroborated by the findings that the bone grafts seemed to recapitulate the characteristics of the bone in which they were placed, rather than maintaining their native characteristics.     

A musculoskeletal model of the equine forelimb for determining surface stresses and strains in the humerus--part I. Mathematical modeling

Knowledge of the forces that act upon the equine humerus while the horse is standing and the resulting strains experienced by the bone is useful for the prevention and treatment of fractures and for assessing the proximolateral aspect of the bone as a site for obtaining autogenous bone graft material. The first objective was to develop a mathematical model to predict the loads on the proximal half of the humerus created by the surrounding musculature and ground reaction forces while the horse is standing. The second objective was to calculate surface bone stresses and strains at three cross sections on the humerus corresponding to the donor site for bone grafts, a site predisposed to stress fracture, and the middle of the diaphysis. A three-dimensional mathematical model employing optimization techniques and asymmetrical beam analysis was used to calculate shoulder muscle forces and surface strains on the proximal and mid-diaphyseal aspects of the humerus. The active shoulder muscles, which included the supraspinatus, infraspinatus, subscapularis, and short head of the deltoid, produced small forces while the horse is standing; all of which were limited to 4.3% of their corresponding maximum voluntary contraction. As a result, the strains calculated at the proximal cross sections of the humerus were small, with maximum compressive strains of -104microepsilon at the cranial aspect of the bone graft donor cross section. The middle of the diaphysis experienced larger strain magnitudes with compressive strains at the lateral and the caudal aspects and tensile strains at the medial and cranial aspects (-377microepsilon and 258microepsilon maximum values, respectively) while the horse is standing. Small strains at the donor bone graft site do not rule out using this location to harvest bone graft tissue, although strains while rising to a standing position during recovery from anesthesia are unknown. At the site common to stress fractures, small strains imply that the stresses seen by this region while the horse is standing, although applied for long periods of time, are not a cause of fracture in this location. Knowing the specific regions of the middle of the diaphysis of the humerus that experience tensile and compressive strains is valuable in determining optimum placement of internal fixation devices for the treatment of complete fractures.     

Atypical subtrochanteric femoral shaft fractures: role for mechanics and bone quality

Bisphosphonates are highly effective agents for reducing osteoporotic fractures in women and men, decreasing fracture incidence at the hip and spine up to 50%. In a small subset of patients, however, these agents have recently been associated with ''atypical femoral fractures'' (AFFs) in the subtrochanteric region or the diaphysis. These fractures have several atypical characteristics, including occurrence with minimal trauma; younger age than typical osteoporotic fractures; occurrence at cortical, rather than cancellous sites; early radiographic appearance similar to that of a stress fracture; transverse fracture pattern rather than the familiar spiral or transverse-oblique morphologies; initiation on the lateral cortex; and high risk of fracture on the contralateral side, at the same location as the initial fracture. Fracture is a mechanical phenomenon that occurs when the loads applied to a structure such as a long bone exceed its load-bearing capacity, either due to a single catastrophic overload (traumatic failure) or as a result of accumulated damage and crack propagation at sub-failure loads (fatigue failure). The association of AFFs with no or minimal trauma suggests a fatigue-based mechanism that depends on cortical cross-sectional geometry and tissue material properties. In the case of AFFs, bisphosphonate treatment may alter cortical tissue properties, as these agents are known to alter bone remodeling. This review discusses the use of bisphosphonates, their effects on bone remodeling, mechanics and tissue composition, their significance as an effective therapy for osteoporosis, and why these agents may increase fracture risk in a small population of patients.     

Summary--Measuring "bone quality"

The idea of bone quality is well-established in the literature and represents a real conundrum in the treatment of osteoporosis. On the one hand, there are measurements for patients that predict fracture risk for the population as a whole, but between individual patients, one will fracture but another will not, despite the fact that all of the technical measurements we use to predict fracture risk are the same. There are, of course, many aspects of bone mechanical properties that cannot yet be measured in patients. The session began with a discussion of what bone quality is, then the speakers presented work on novel aspects of bone properties that could help explain why fracture prediction in vivo is inexact.     

Application of fracture mechanics to failure in manatee rib bone

BACKGROUND: The Florida manatee (Trichechus manatus latirostris) is listed as endangered by the U.S. Department of the Interior. Manatee ribs have different microstructure from the compact bone of other mammals. Biomechanical properties of the manatee ribs need to be better understood. Fracture toughness (K(C)) has been shown to be a good index to assess the mechanical performance of bone. Quantitative fractography can be used in concert with fracture mechanics equations to identify fracture initiating defects/cracks and to calculate the fracture toughness of bone materials. METHOD OF APPROACH: Fractography is a standard technique for analyzing fracture behavior of brittle and quasi-brittle materials. Manatee ribs are highly mineralized and fracture in a manner similar to quasi-brittle materials. Therefore, quantitative fractography was applied to determine the fracture toughness of manatee ribs. RESULTS: Average fracture toughness values of small flexure specimens from six different sizes of manatees ranged from 1.3 to 2.6 MPa(m)(12). Scanning electron microscope (SEM) images show most of the fracture origins were at openings for blood vessels and interlayer spaces. CONCLUSIONS: Quantitative fractography and fracture mechanics can be combined to estimate the fracture toughness of the material in manatee rib bone. Fracture toughness of subadult and calf manatees appears to increase as the size of the manatee increases. Average fracture toughness of the manatee rib bone materials is less than the transverse fracture toughness of human and bovine tibia and femur.     

Septal fracture in simple nasal bone fracture

SUMMARY: Nasal bone fractures are the most common type of facial fractures. Previous studies have shown that most nasal fractures involve the septum, which can provide an obstacle to the successful reduction of nasal bone fractures. In particular, septal fractures in combination with simple nasal bone fractures are usually unrecognized and untreated at the time of injury. Furthermore, systemized treatment protocols and diagnostic tools for septal fractures in the case of simple nasal bone fracture have not previously been presented. In this study, the clinical findings of septal fractures in cases of simple nasal bone fracture were correlated with symptoms, signs, and computed tomography findings and assessed statistically. The patterns of septal fractures in simple nasal bone fractures were assessed by direct vision via hemitransfixion incision. Of the 52 patients with simple nasal bone fracture who presented over a 3-year period and were included in this study, 10 were female and 42 were male, with an average age of 33.8 years (age range, 18 to 61 years). Fifty of these patients (96.2 percent) showed septal fractures, and septoplasty or submucosal resection was performed on 41 patients (78.8 percent) who manifested severe septal fractures of perioperative septal grade 3 or higher. Closed reduction of the nasal bone fracture only was performed on the remaining 11 patients. Among the signs evident at physical examination, mucosal tearing was found to be statistically significant for septal fracture. Computed tomography was found to be very helpful in diagnosing septal fracture but could not predict its severity accurately (Spearman correlation coefficient between computed tomography septal grading and perioperative septal grading, 33.5 percent). Therefore, computed tomography could not be used as a definitive diagnostic modality for septal fractures in terms of deciding whether septoplasty or submucous resection was needed. It is evident that septal fractures are frequent in simple nasal bone fractures that are not combined with other facial bone fractures. This study confirms that there are differences between radiologic findings and perioperative findings. To reduce the incidence of posttraumatic nasal deformity, meticulous physical examinations with subsequent septoplasty or submucosal resection are needed in the treatment of simple nasal bone fracture.     

Advances in the fracture mechanics of cortical bone

As cortical bone is a semi-brittle solid, its fracture is dependent not only on the magnitude of the applied stress, but also on the nature of any intrinsic or introduced cracks. Consequently a variety of fracture mechanics techniques have been utilised to evaluate the fracture toughness of cortical bone, including the single edge notched, centre notched cylindrical and compact tension methods, and values have been established for the critical stress intensity factor (Kc) and the critical strain energy release rate (Gc). The Kc and Gc values obtained depend on the orientation of the cortical bone, as well as on bone density, the velocity of crack propagation and specimen geometry. The significance of these fracture mechanics parameters for cortical bone is critically reviewed.     

Fracture in human cortical bone: local fracture criteria and toughening mechanisms

Micromechanical models for fracture initiation that incorporate local failure criteria have been widely developed for metallic and ceramic materials; however, few such micromechanical models have been developed for the fracture of bone. In fact, although the fracture event in "hard" mineralized tissues such as bone is commonly believed to be locally strain-controlled, only recently has there been experimental evidence (using double-notched four-point bend testing) to support this widely held belief. In the present study, we seek to shed further light on the nature of the local cracking events that precede catastrophic fracture in human cortical bone, and to define their relationship to the microstructure. Specifically, numerical computations are reported that demonstrate that the stress and strain states ahead of such a notch are qualitatively similar irrespective of the deformation mechanism (pressure-insensitive plasticity vs. pressure-sensitive microcracking). Furthermore, we use the double-notched test to examine crack-microstructure interactions from a perspective of determining the salient toughening mechanisms in bone and to characterize how these may affect the anisotropy in fracture properties. Based on preliminary micromechanical models of these processes, the relative contributions of various toughening mechanisms are established. In particular, crack deflection and uncracked-ligament bridging are identified as the major mechanisms of toughening in cortical bone.     

A fabric-dependent fracture criterion for bone.

A fracture criterion for bone tissue is proposed. Bone material is considered to be anisotropic and its properties are described by invoking the concept of directional variation of porosity. The fracture criterion is expressed as a scalar-valued function of the stress tensor and it incorporates an orientation-dependent distribution of compressive/tensile strength. The proposed mathematical framework is applied to a numerical analysis of fracture in the proximal femur due to a fall from standing height. The risk of fracture is assessed in the context of two different porosity distributions, simulating a healthy and an osteoporotic bone.