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

Simulation analysis of surgical neck fractures of the humerus related to bone degeneration

The most common type of proximal humerus fracture is surgical neck fracture. The purpose of this paper is to study the mechanical mechanism and the effect of bone degeneration on humeral surgical neck fractures. The right humerus finite element models were established based on CT computed tomography. The stress values and crack propagation process under an axial force were obtained. Three indexes (mechanical property, cortical bone thickness of diaphysis and cancellous bone volume fraction) in this article were used to describe bone degeneration. The results showed that the three models group with different index had the same conclusions. The calculation results showed that the higher the bone degeneration level, the shorter the fracture time and the lower the fracture stress. The crack initiated from the medial side of the humerus, then gradually grew toward lateral side along the both sides, and finally broke. The medial crack was flat and single like "a thin line", while the lateral fracture of the humerus was irregular and crushed into fragments. The medial humerus cracks were generated by tensile stress, while the lateral cracks were generated by compressive stress. The thickness of humerus diaphysis might be used as the index of fracture risk due to direct readability from clinical images and quantitative relation of fracture risk. This article would provide reference data for the treatment and prevention of humeral surgical neck fracture.

Analysis and validation of a 3D finite element model for human forearm fracture

Most researchers have performed finite element (FE) analysis of the human forearm fracture by exploring the strength and load transmission of the bones. However, few studies concentrated a complete simulation of the whole forearm complex including ligaments. This paper aims to investigate the load transmission through the bones, contact stress at the joints and strain in the ligaments by using an elaborate FE model, further validating the fracture condition for human forearm. The interosseous ligament was separated into three regions based on the distance to the proximal and distal ends. The FE simulation results were slightly more or less than a previous experimental data in the literature, but generally provided a close approximation of the bone and ligament behaviors. Compared with the experiment results under different loading conditions, maximum contact stress at the proximal radio ulnar joint (PRUJ) and distal radio ulnar joint (DRUJ) of the simulations was higher with an average of 13.4%, and peak strain in the interosseous ligament (IOL) was lower with an average of 11.0%. Under 10 kg load, the maximum stress in the radius (2.25 MPa) was less than double the value in the ulna (1.43 MPa). Finally, the FE model has been validated with the onset and location of the Colles' fracture in the literature. This study will provide a great benefit in terms of surgical and medical applications related to forearm fracture that require an extensive knowledge of the behavior of the bones and ligaments under various loading conditions.

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.

Understanding the Patterns of Deformity of Wrist Fractures Using Computer Analysis

Computer modeling of the wrist has followed other fields in the search for descriptive methods to understand the biomechanics of injury. Using patient-specific 3D computer models, we may better understand the biomechanics of wrist fractures in order to plan better care. We may better estimate fracture morphology and stability and evaluate surgical indications, design more adequate or effective surgical approaches and develop novel methods of therapy. The purpose of this review is to question the actual advances made in the understanding of wrist fractures using computer models.

Smaller Radius Width in Women With Distal Radius Fractures Compared to Women Without Fractures

Introduction

Bone mineral density (BMD) measured using dual-energy x-ray absorptiometry (DXA) is typically used to assess fracture risk. However, other factors such as bone size and the forward momentum of a fall (a function of body size) can also potentially influence fracture risk, but are understudied. This report describes the characteristics of a cohort of Caucasian pre- and postmenopausal women with distal radius fractures (DRF) after falling onto an outstretched hand.

Methods

The fracture cohort comprised entries in an institutional review board-approved registry of study patients who had had DXA scans. For patients with DRF, the contralateral radius was scanned and BMD, T-scores (used to define bone status as normal, osteopenic, or osteoporotic), and radius width were recorded. Generally, side-to-side (left-right) differences in bone size and BMD are small and, hence, the contralateral radius was considered a surrogate for bone status of the fractured radius. Apparently healthy women without fractures were used as race-, age-, and BMI-matched controls.  

Results

Premenopausal women < 49 years of age (mean age, 38 years) with DRF had significanty smaller radii width compared to matched controls. Mean radius BMD was in the normal range. As a group, the cohort was overweight based on mean BMI. Postmenopausal women > 50 years (mean age, 64 years) with DRF also had low radius width, but in contrast to the first group, this group had low peripheral and central BMD.

Conclusions

Women with DRF had contralateral and presumably fractured radii of bone width smaller than matched controls. As a group, these women were also overweight based on BMI. The smaller radius width may increase the risk for fracture irrespective of BMD, especially since larger body size would result in greater inertial force when falling while ambulating.  

Microstructure of the Distal Radius and Its Relevance to Distal Radius Fractures

Background  There is a paucity of information on the microstructure of the distal radius, and how this relates to its morphology and function. Purpose  This study aims to assess the microanatomical structure of the distal radius, and relate this to its morphology, function, and modes of failure. Methods  Six dry adult skeletal distal radii were examined with microcomputed tomography scan and analyzed with specialist computer software. From 3D and 2D images, the subchondral, cortical, and medullary trabecular were assessed and interpreted based on the overall morphology of the radius. Results  The expanded distal radial metaphysis provides a wide articular surface for distributing the articular load. The extrinsic wrist ligaments are positioned around the articular perimeter, except on the dorsal radial corner. The subchondral bone plate is a 2 mm multilaminar lattice structure, which is thicker below the areas of the maximal articular load. There are spherical voids distally, which become ovoid proximally, which assist in absorbing articular impact. It does not have Haversian canals. From the volar aspect of the lunate facet, there are thick trabecular columns that insert into the volar cortex of the radius at the metaphyseal-diaphyseal junction. For the remainder of the subchondral bone plate, there is an intermediate trabecular network, which transmits the load to the intermediate trabeculae and then to the trabecular arches. The arches pass proximally and coalesce with the ridges of the diaphyseal cortex. Conclusion  The distal radius morphology is similar to an arch bridge. The subchondral bone plate resembles the smooth deck of the bridge that interacts with the mobile load. The load is transmitted to the rim, intermediate struts, and arches. The metaphyseal arches allow the joint loading forces to be transmitted proximally and laterally, providing compression at all levels and avoiding tension. The arches have a natural ability to absorb the impact which protects the articular surface. The distal radius absorbs and transmits the articular impact to the medullary cortex and intermediate trabeculae. The medullary arches are positioned to transmit the load from the intermediate trabeculae to the diaphysis. Clinical Relevance  The microstructure of the distal radius is likely to be important for physiological loading of the radius. The subchondral bone plate is a unique structure that is different to the cancellous and cortical bone. All three bone types have different functions. The unique morphology and microstructure of the distal radius allow it to transmit load and protect the articular cartilage.

Relationship Between Ulnar Variance, Cortical Bone Density, and Load to Failure in the Distal Radius at the Typical Site of Fracture Initiation

PURPOSE

Increased ulnar variance has been shown to lead to diminished load borne by the distal radius. The purpose of this study was to determine the correlations among ulnar variance, bone mineral density, and load to failure at the distal radius.

METHODS

Posteroanterior radiographs and computed tomographic scans were taken of 12 cadaveric forearms in neutral rotation. Ulnar variance was measured for each wrist by the method of perpendiculars. Measurements of cortical, trabecular, and combined bone density were made at the distal radius. We performed linear regression analysis and correlation analysis to determine the relationship between bone densities and ulnar variance measurements. Next, we loaded the 12 cadaveric radii to failure under axial compression. Linear regression analysis and correlation analysis were then performed to determine the relationship between load to failure and both ulnar variance and cortical density.

RESULTS

Increased ulnar variance was significantly correlated with decreased cortical bone density at the distal radius and both were correlated with decreased load to failure. We found no correlation between ulnar variance and trabecular density or combined trabecular and cortical bone density at the distal radius.

CONCLUSIONS

Our study found that increased ulnar variance and decreased cortical bone mineral density correlates with decreased load to failure under axial compression.

CLINICAL RELEVANCE

Ulnar variance is linked to both bone quality and load to failure at the distal radius.

Assessment of the effect of reduced compositional heterogeneity on fracture resistance of human cortical bone using finite element modeling

The recent reports of atypical femoral fracture (AFF) and its possible association with prolonged bisphosphonate (BP) use highlighted the importance of a thorough understanding of mechanical modifications in bone due to bisphosphonate treatment. The reduced compositional heterogeneity is one of the modifications in bone due to extensive suppression of bone turnover. Although experimental evaluations suggested that compositional changes lead to a reduction in the heterogeneity of elastic properties, there is limited information on the extent of influence of reduced heterogeneity on fracture resistance of cortical bone. As a result, the goal of the current study is to evaluate the influence of varying the number of unique elastic and fracture properties for osteons, interstitial bone, and cement lines on fracture resistance across seven different human cortical bone specimens using finite element modeling. Fracture resistance of seven human cortical bone samples under homogeneous and three different heterogeneous material levels was evaluated using a compact tension test setup. The simulation results predicted that the crack volume was the highest for the models with homogeneous material properties. Increasing heterogeneity resulted in a lower amount of crack volume indicating an increase in fracture resistance of cortical bone. This reduction was observed up to a certain level of heterogeneity after which further beneficial effects of heterogeneity diminished suggesting a possible optimum level of heterogeneity for the bone tissue. The homogeneous models demonstrated limited areas of damage with extensive crack formation. On the other hand, the heterogeneity in the material properties led to increased damage volume and a more variable distribution of damage compared to the homogeneous models. This resulted in uncracked regions which tended to have less damage accumulation preventing extensive crack propagation. The results also showed that the percent osteonal area was inversely correlated with crack volume and more evenly distributed osteons led to a lower amount of crack growth for all levels of material heterogeneity. In summary, this study developed a new computational modeling approach that directly evaluated the influence of heterogeneity in elastic and fracture material properties on fracture resistance of cortical bone. The results established new information that showed the adverse effects of reduced heterogeneity on fracture resistance in cortical bone and demonstrated the nonlinear relationship between heterogeneity and fracture resistance. This new computational modeling approach provides a tool that can be used to improve the understanding of the effects of material level changes due to prolonged BP use on the overall bone fracture behavior. It may also bring additional insight into the causes of unusual fractures, such as AFF and their possible association with long term BP use.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Multiscale contribution of bone tissue material property heterogeneity to trabecular bone mechanical behavior

Heterogeneity of material properties is an important potential contributor to bone fracture resistance because of its putative contribution to toughness, but establishing the contribution of heterogeneity to fracture risk is still in an incipient stage. Experimental studies have demonstrated changes in distributions of compositional and nanomechanical properties with fragility fracture history, disease, and pharmacologic treatment. Computational studies have demonstrated that models with heterogeneous material properties predict apparent stiffness moderately better than homogeneous models and show greater energy dissipation. Collectively, these results suggest that microscale material heterogeneity affects not only microscale mechanics but also structural performance at larger length scales.

Modeling microdamage behavior of cortical bone

Bone is a complex material which exhibits several hierarchical levels of structural organization. At the submicron-scale, the local tissue porosity gives rise to discontinuities in the bone matrix which have been shown to influence damage behavior. Computational tools to model the damage behavior of bone at different length scales are mostly based on finite element (FE) analysis, with a range of algorithms developed for this purpose. Although the local mechanical behavior of bone tissue is influenced by microstructural features such as bone canals and osteocyte lacunae, they are often not considered in FE damage models due to the high computational cost required to simulate across several length scales, i.e., from the loads applied at the organ level down to the stresses and strains around bone canals and osteocyte lacunae. Hence, the aim of the current study was twofold: First, a multilevel FE framework was developed to compute, starting from the loads applied at the whole bone scale, the local mechanical forces acting at the micrometer and submicrometer level. Second, three simple microdamage simulation procedures based on element removal were developed and applied to bone samples at the submicrometer-scale, where cortical microporosity is included. The present microdamage algorithm produced a qualitatively analogous behavior to previous experimental tests based on stepwise mechanical compression combined with in situ synchrotron radiation computed tomography. Our results demonstrate the feasibility of simulating microdamage at a physiologically relevant scale using an image-based meshing technique and multilevel FE analysis; this allows relating microdamage behavior to intracortical bone microstructure.

Development and validation of a distal radius finite element model to simulate impact loading indicative of a forward fall

The purpose of this work was to develop and validate a finite element model of the distal radius to simulate impact loading. Eight-node hexahedral meshes of the bone and impactor components were created. Three separate impact events were simulated by altering the impact velocity assigned to the model projectile (pre-fracture, crack and fracture). Impact forces and maximum and minimum principal strains were calculated and used in the validation process by comparing with previously collected experimental data. Three measures of mesh quality (Jacobians, aspect ratios and orthogonality) and four validation methods (validation metric, error assessment, fracture comparisons and ensemble averages) assessed the model. The element Jacobians, aspect ratios and orthogonality measures ranged from 0.08 to 12, 1.1 to 26 and -70° to 80°, respectively. The force and strain validation metric ranged from 0.10 to 0.54 and 0.35 to 0.67, respectively. The estimated peak axial force was found to be a maximum of 28.5% greater than the experimental (crack) force, and all forces fell within ±2 standard deviation of the mean experimental fracture forces. The predicted strains were found to differ by a mean of 33% across all impact events, and the model was found to accurately predict the location and severity of bone damage. Overall, the model presented here is a valid representation of the distal radius subjected to impact.

Prediction of risk of fracture in the tibia due to altered bone mineral density distribution resulting from disuse: a finite element study

The disuse-related bone loss that results from immobilisation following injury shares characteristics with osteoporosis in post-menopausal women and the aged, with decreases in bone mineral density leading to weakening of the bone and increased risk of fracture. The aim of this study was to use the finite element method to: (i) calculate the mechanical response of the tibia under mechanical load and (ii) estimate of the risk of fracture; comparing between two groups, an able-bodied group and spinal cord injury patients group suffering from varying degrees of bone loss. The tibiae of eight male subjects with chronic spinal cord injury and those of four able-bodied age-matched controls were scanned using multi-slice peripheral quantitative computed tomography. Images were used to develop full three-dimensional models of the tibiae in Mimics (Materialise) and exported into Abaqus (Simulia) for calculation of stress distribution and fracture risk in response to specified loading conditions - compression, bending and torsion. The percentage of elements that exceeded a calculated value of the ultimate stress provided an estimate of the risk of fracture for each subject, which differed between spinal cord injury subjects and their controls. The differences in bone mineral density distribution along the tibia in different subjects resulted in different regions of the bone being at high risk of fracture under set loading conditions, illustrating the benefit of creating individual material distribution models. A predictive tool can be developed based on these models, to enable clinicians to estimate the amount of loading that can be safely allowed onto the skeletal frame of individual patients who suffer from extensive musculoskeletal degeneration (including spinal cord injury, multiple sclerosis and the ageing population). The ultimate aim is to reduce fracture occurrence in these vulnerable groups.

A new fracture assessment approach coupling HR-pQCT imaging and fracture mechanics-based finite element modeling

A new fracture assessment approach that combines HR-pQCT imaging with fracture mechanics-based finite element modeling was developed to evaluate distal radius fracture load. Twenty distal radius images obtained from postmenopausal women (fracture, n=10; nonfracture, n=10) were processed to obtain a cortical and a whole bone model for each subject. The geometrical properties of each model were evaluated and the corresponding fracture load was determined under realistic fall conditions using cohesive finite element modeling. The results showed that the whole bone fracture load can be estimated based on the cortical fracture load for nonfracture (R(2)=0.58, p=0.01) and pooled data (R(2)=0.48, p<0.001) but not for the fracture group. The portion of the whole bone fracture load carried by the cortical bone increased with increasing cortical fracture load (R(2)≥0.5, p<0.05) indicating that a more robust cortical bone carries a larger percentage of whole bone fracture load. Cortical thickness was found to be the best predictor of both cortical and whole bone fracture load for all groups (R(2) range: 0.49-0.96, p<0.02) with the exception of fracture group whole bone fracture load showing the predictive capability of cortical geometrical properties in determining whole bone fracture load. Fracture group whole bone fracture load was correlated with trabecular thickness (R(2)=0.4, p<0.05) whereas the nonfracture and the pooled group did not show any correlation with the trabecular parameters. In summary, this study introduced a new modeling approach that coupled HR-pQCT imaging with fracture mechanics-based finite element simulations, incorporated fracture toughness and realistic fall loading conditions in the models, and showed the significant contribution of the cortical compartment to the overall fracture load of bone. Our results provide more insight into the fracture process in bone and may lead to improved fracture load predictions.

Interface micromechanics of transverse sections from retrieved cemented hip reconstructions: an experimental and finite element comparison

In finite element analysis (FEA) models of cemented hip reconstructions, it is crucial to include the cement-bone interface mechanics. Recently, a micromechanical cohesive model was generated which reproduces the behavior of the cement-bone interface. The goal was to investigate whether this cohesive model was directly applicable on a macro level. From transverse sections of retrieved cemented hip reconstructions, two FEA-models were generated. The cement-bone interface was modeled with cohesive elements. A torque was applied and the cement-bone interface micromotions, global stiffness and stem translation were monitored. A sensitivity analysis was performed to investigate whether the cohesive model could be improved. All results were compared with experimental findings. That the original cohesive model resulted in a too compliant macromechanical response; the motions were too large and the global stiffness too small. When the cohesive model was modified, the match with the experimental response improved considerably.

Evaluation of the influence of strain rate on Colles' fracture load

Colles' fracture, a transverse fracture of the distal radius bone, is one of the most frequently observed osteoporotic fractures resulting from low energy or traumatic events, associated with low and high strain rates, respectively. Although experimental studies on Colles' fracture were carried out at various loading rates ranging from static to impact loadings, there is no systematic study in the literature that isolates the influence of strain rate on Colles' fracture load. In order to provide a better understanding of fracture risk, the current study combines experimental material property measurements under varying strain rates with computational modeling and presents new information on the effect of strain rate on Colles' fracture. The simulation results showed that Colles' fracture load decreased with increasing strain rate with a steeper change in lower strain rates. Specifically, strain rate values (0.29s(-1)) associated with controlled falling without fracture corresponded to a 3.7% reduction in the fracture load. On the other hand, the reduction in the fracture load was 34% for strain rate of 3.7s(-1) reported in fracture inducing impact cadaver experiments. Further increase in the strain rate up to 18s(-1) led to an additional 22% reduction. The most drastic reduction in fracture load occurs at strain rates corresponding to the transition from controlled to impact falling. These results are particularly important for the improvement of fracture risk assessment in the elderly because they identify a critical range of loading rates (10-50mm/s) that can dramatically increase the risk of Colles' fracture.

Interaction of microstructure and microcrack growth in cortical bone: a finite element study

Microstructural features including osteons and cement lines are considered to play an important role in determining the crack growth behaviour in cortical bone. This study aims to develop a computational mechanics approach to evaluate microscale fracture mechanisms in bone. In this study, finite element models based on actual human cortical bone images that allow for arbitrary crack growth were utilised to determine the crack propagation behaviour. The simulations varied the cement line and osteon strength and fracture toughness in different bone microstructures to assess the crack propagation trajectory, stress-strain relationship and nonlinear strain energy density. The findings of this study provide additional insight into the individual influence of microstructural features and their properties on crack growth behaviour in bone using a computational approach.

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.

Denosumab improves density and strength parameters as measured by QCT of the radius in postmenopausal women with low bone mineral density

BACKGROUND

Bone strength is determined by both cortical and trabecular bone compartments and can be evaluated radiologically through measurement of bone density and geometry. Quantitative computed tomography (QCT) separately assesses cortical and trabecular bone reliably at various sites, including the distal radius where there is a gradation of cortical and trabecular bone. We evaluated the effect of denosumab, a fully human monoclonal antibody that inhibits RANK ligand, on distal radius QCT in women with low bone mass to assess the impact of this novel therapy separately on trabecular and cortical bone.

METHODS

Postmenopausal women (n=332) with spine areal bone mineral density (BMD) T-scores between -1.0 and -2.5 received denosumab 60 mg or placebo every 6 months during the 24-month study. QCT measurements along the distal radius were made using a whole-body computed tomography scanner and were used to determine the percentage change from baseline in volumetric BMD; volumetric bone mineral content (BMC); cortical thickness; volume; circumference; and density-weighted polar moment of inertia (PMI), a derived index of bone strength.

RESULTS

Denosumab treatment significantly increased total BMD and BMC along the radius (proximal, distal, and ultradistal sections). At 24 months, the ultradistal region had the greatest percentage increase in total BMD (4.7% [95% CI, 3.6-5.7]; P<0.001) and total BMC (5.7% [95% CI, 4.8-6.6]; P<0.001) over placebo. When cortical and trabecular bone at the proximal and distal regions were separately assessed, cortical bone had significant (P<0.001) increases in BMD, BMC, and thickness, and trabecular bone had a significant increase in BMD relative to placebo (P<0.05). Bone strength, estimated by density-weighted PMI, significantly increased compared with placebo after 6 months of treatment, with the largest percentage increase occurring at 24 months in the ultradistal region (6.6% [95% CI, 5.6-7.6]; P<0.0001).

CONCLUSIONS

QCT measurements demonstrated that denosumab significantly increased BMD, BMC, and PMI along the radius over 24 months. Additionally, denosumab prevented the decrease in QCT-measured cortical thickness observed in the placebo group. These data extend the evidence from previous dual-energy X-ray absorptiometry studies for a positive effect of denosumab on both the cortical and trabecular bone compartments and propose a possible mechanism for the reduction in fracture risk achieved with denosumab therapy.

Multiscale modelling and nonlinear finite element analysis as clinical tools for the assessment of fracture risk

The risk of osteoporotic fractures is currently estimated based on an assessment of bone mass as measured by dual-energy X-ray absorptiometry. However, patient-specific finite element (FE) simulations that include information from multiple scales have the potential to allow more accurate prognosis. In the past, FE models of bone were limited either in resolution or to the linearization of the mechanical behaviour. Now, nonlinear, high-resolution simulations including the bone microstructure have been made possible by recent advances in simulation methods, computer infrastructure and imaging, allowing the implementation of multiscale modelling schemes. For example, the mechanical loads generated in the musculoskeletal system define the boundary conditions for organ-level, continuum-based FE models, whose nonlinear material properties are derived from microstructural information. Similarly microstructure models include tissue-level information such as the dynamic behaviour of collagen by modifying the model's constitutive law. This multiscale approach to modelling the mechanics of bone allows a more accurate characterization of bone fracture behaviour. Furthermore, such models could also include the effects of ageing, osteoporosis and drug treatment. Here we present the current state of the art for multiscale modelling and assess its potential to better predict an individual's risk of fracture in a clinical setting.

Can deterministic mechanical size effects contribute to fracture and microdamage accumulation in trabecular bone?

Failure of bone under monotonic and cyclic loading is related to the bone mineral density, the quality of the bone matrix, and the evolution of microcracks. The theory of linear elastic fracture mechanics has commonly been applied to describe fracture in bone. Evidence is presented that bone failure can be described through a non-linear theory of fracture. Thereby, deterministic size effects are introduced. Concepts of a non-linear theory are applied to discern how the interaction among bone matrix constituents (collagen and mineral), microcrack characteristics, and trabecular architecture can create distinctively differences in the fracture resistance at the bone tissue level. The non-linear model is applied to interpret pre-clinical data concerning the effects of anti-osteoporotic agents on bone properties. The results show that bisphosphonate (BP) treatments that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is reduced. Selective estrogen receptor modulators (SERMs) that suppress bone remodeling will change trabecular bone in ways such that the size of the failure process zone relative to the trabecular thickness is increased. The consequences of these changes are reflected in bone mechanical response and predictions are consistent with experimental observations in the animal model which show that BP treatment is associated with more brittle fracture and microcracks without altering the average length of the cracks, whereas SERM treatments lead to a more ductile fracture and mainly increase crack length with a smaller increase in microcrack density. The model suggests that BPs may be more effective in cases in which bone mass is very low, whereas SERMS may be more effective when milder osteoporotic symptoms are present.