Cohesive finite element modeling of age-related toughness loss in human cortical bone

Although the age-related loss of bone quality has been implicated in bone fragility, a mechanistic understanding of the relationship is necessary for developing diagnostic and treatment modalities in the elderly population at risk of fracture. In this study, a finite element based cohesive zone model is developed and applied to human cortical bone in order to capture the experimentally shown rising crack growth behavior and age-related loss of bone toughness. The cohesive model developed here is based on a traction–crack opening displacement relationship representing the fracture processes in the vicinity of a propagating crack. The traction–displacement curve, defining the cohesive model, is composed of ascending and descending branches that incorporate material softening and nonlinearity. The results obtained indicate that, in contrast to initiation toughness, the finite element simulations of crack growth in compact tension (CT) specimens successfully capture the rising R-curve (propagation toughness) behavior and the age-related loss of bone toughness. In close correspondence with the experimentally observed decrease of 14–15% per decade, the finite element simulation results show a decrease of 13% in the R-curve slope per decade. The success of the simulations is a result of the ability of cohesive models to capture and predict the parameters related to bone fracture by representing the physical processes occurring in the vicinity of a propagating crack. These results illustrate that fracture mechanisms in the process zone control bone toughness and any modification to these would cause age-related toughness loss.     

Effects of intracortical porosity on fracture toughness in aging human bone: a microCT-based cohesive finite element study

The extent to which increased intracortical porosity affects the fracture properties of aging and osteoporotic bone is unknown. Here, we report the development and application of a microcomputed tomography based finite element approach that allows determining the effects of intracortical porosity on bone fracture by blocking all other age-related changes in bone. Previously tested compact tension specimens from human tibiae were scanned using microcomputed tomography and converted to finite element meshes containing three-dimensional cohesive finite elements in the direction of the crack growth. Simulations were run incorporating age-related increase in intracortical porosity but keeping cohesive parameters representing other age-related effects constant. Additional simulations were performed with reduced cohesive parameters. The results showed a 6% decrease in initiation toughness and a 62% decrease in propagation toughness with a 4% increase in porosity. The reduction in toughnesses became even more pronounced when other age-related effects in addition to porosity were introduced. The initiation and propagation toughness decreased by 51% and 83%, respectively, with the combined effect of 4% increase in porosity and decrease in the cohesive properties reflecting other age-related changes in bone. These results show that intracortical porosity is a significant contributor to the fracture toughness of the cortical bone and that the combination of computational modeling with advanced imaging improves the prediction of the fracture properties of the aged and the osteoporotic cortical bone.     

Prognosis of implant longevity in terms of annual bone loss: a methodological finite element study

Dental implant failure is mainly the consequence of bone loss at peri-implant area. It usually begins in crestal bone. Due to this gradual loss, implants cannot withstand functional force without bone overload, which promotes complementary loss. As a result, implant lifetime is significantly decreased. To estimate implant success prognosis, taking into account 0.2 mm annual bone loss for successful implantation, ultimate occlusal forces for the range of commercial cylindrical implants were determined and changes of the force value for each implant due to gradual bone loss were studied. For this purpose, finite element method was applied and von Mises stresses in implant–bone interface under 118.2 N functional occlusal load were calculated. Geometrical models of mandible segment, which corresponded to Type II bone (Lekholm & Zarb classification), were generated from computed tomography images. The models were analyzed both for completely and partially osseointegrated implants (bone loss simulation). The ultimate value of occlusal load, which generated 100 MPa von Mises stresses in the critical point of adjacent bone, was calculated for each implant. To estimate longevity of implants, ultimate occlusal loads were correlated with an experimentally measured 275 N occlusal load (Mericske-Stern & Zarb). These findings generally provide prediction of dental implants success.     

The implant thread as a retention element in cortical bone: the effect of thread size and thread profile: a finite element study

Assuming that high stress peaks in the bone can trigger bone resorption a screw-shaped bone implant should be given such a design that the peak stresses arising in the bone, as a result of a certain load, are minimized. Using idealized assumptions the aim of the study was to analyse the effect of variations of the size and the profile of the thread of an axially loaded, screw-shaped, bone implant upon the magnitude of the stress peaks in cortical bone. The investigation was performed by means of axisymmetric finite element analysis. It was found that the shape of the thread profile has a profound effect upon the magnitude of the stresses in the bone and that very small threads of a favourable profile can be quite effective.     

Simulation of vertebral trabecular bone loss using voxel finite element analysis

Trabecular bone loss in human vertebral bone is characterised by thinning and eventual perforation of the horizontal trabeculae. Concurrently, vertical trabeculae are completely lost with no histological evidence of significant thinning. Such bone loss results in deterioration in apparent modulus and strength of the trabecular core. In this study, a voxel-based finite element program was used to model bone loss in three specimens of human vertebral trabecular bone. Three sets of analyses were completed. In Set 1, strain adaptive resorption was modelled, whereby elements which were subject to the lowest mechanical stimulus (principal strain) were removed. In Set 2, both strain adaptive and microdamage mechanisms of bone resorption were included. Perforation of vertical trabeculae occurred due to microdamage resorption of elements with strains that exceeded a damage threshold. This resulted in collapse of the trabecular network under compression loading for two of the specimens tested. In Set 3, the damage threshold strain was gradually increased as bone loss progressed, resulting in reduced levels of microdamage resorption. This mechanism resulted in trabecular architectures in which vertical trabeculae had been perforated and which exhibited similar apparent modulus properties compared to experimental values reported in the literature. Our results indicate that strain adaptive remodelling alone does not explain the deterioration in mechanical properties that have been observed experimentally. Our results also support the hypothesis that horizontal trabeculae are lost principally by strain adaptive resorption, while vertical trabeculae may be lost due to perforation from microdamage resorption followed by rapid strain adaptive resorption of the remaining unloaded trabeculae.     

Biomechanical study of pediatric human cervical spine: a finite element approach

Although considerable effort has been made to understand the biomechanical behavior of the adult cervical spine, relatively little information is available on the response of the pediatric cervical spine to external forces. Since significant anatomical differences exist between the adult and pediatric cervical spines, distinct biomechanical responses are expected. The present study quantified the biomechanical responses of human pediatric spines by incorporating their unique developmental anatomical features. One-, three-, and six-year-old cervical spines were simulated using the finite element modeling technique, and their responses computed and compared with the adult spine response. The effects of pure overall structural scaling of the adult spine, local component developmental anatomy variations that occur to the actual pediatric spines, and structural scaling combined with local component anatomy variations on the responses of the pediatric spines were studied. Age- and component-related developmental anatomical features included variations in the ossification centers, cartilages, growth plates, vertebral centrum, facet joints, and annular fibers and nucleus pulposus of the intervertebral discs. The flexibility responses of the models were determined under pure compression, pure flexion, pure extension, and varying degrees of combined compression-flexion and compression-extension. The pediatric spine responses obtained with the pure overall (only geometric) scaling of the adult spine indicated that the flexibilities consistently increase in a uniform manner from six- to one-year-old spines under all loading cases. In contrast, incorporation of local anatomic changes specific to the pediatric spines of the three age groups (maintaining the same adult size) not only resulted in considerable increases in flexibilities, but the responses also varied as a function of the age of the pediatric spine and type of external loading. When the geometric scaling effects were added to these spines, the increases in flexibilities were slightly higher; however, the pattern of the responses remained the same as found in the previous approach. These results indicate that inclusion of developmental anatomical changes characteristic of the pediatric spines has more of a predominant effect on biomechanical responses than extrapolating responses of the adult spine based on pure overall geometric scaling.     

Rising crack-growth-resistance behavior in cortical bone: implications for toughness measurements

Fracture mechanics studies have characterized bone's resistance to fracture in terms of critical stress intensity factor and critical strain energy release rate measured at the onset of a fracture crack. This approach, although useful, provide a limited insight into fracture behavior of bone because, unlike classical brittle materials, bone is a microcracking solid that derives its resistance to fracture during the process of crack propagation from microfracture mechanisms occurring behind the advancing crack front. To address this shortfall, a crack propagation-based approach to measure bone toughness is described here and compared with crack initiation approach. Post hoc analyses of data from previously tested bovine and antler cortical bone compact specimens demonstrates that, in contrast to crack initiation approach, the crack propagation approach successfully identifies the superior toughness properties of red deer's antler cortical bone. Propagation-based slope of crack growth resistance curve is, therefore, a more useful parameter to evaluate cortical bone fracture toughness.     

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.     

Experimental validation of finite element predicted bone strain in the human metatarsal

Metatarsal stress fracture is a common injury observed in athletes and military personnel. Mechanical fatigue is believed to play an important role in the etiology of stress fracture, which is highly dependent on the resulting bone strain from the applied load. The purpose of this study was to validate a subject-specific finite element (FE) modeling routine for bone strain prediction in the human metatarsal. Strain gauge measurements were performed on 33 metatarsals from seven human cadaveric feet subject to cantilever bending, and subject-specific FE models were generated from computed tomography images. Material properties for the FE models were assigned using a published density-modulus relationship as well as density-modulus relationships developed from optimization techniques. The optimized relationships were developed with a ‘training set’ of metatarsals (n = 17) and cross-validated with a ‘test set’ (n = 16). The published and optimized density elasticity equations provided FE-predicted strains that were highly correlated with experimental measurements for both the training (r² ≥ 0.95) and test (r² ≥ 0.94) sets; however, the optimized equations reduced the maximum error by 10% to 20% relative to the published equation, and resulted in an X = Y type of relationship between experimental measurements and FE predictions. Using a separate optimized density-modulus equation for trabecular and cortical bone did not improve strain predictions when compared to a single equation that spanned the entire bone density range. We believe that the FE models with optimized material property assignment have a level of accuracy necessary to investigate potential interventions to minimize metatarsal strain in an effort to prevent the occurrence of stress fracture.     

Biomechanical behaviour of cancellous bone on patellofemoral arthroplasty with Journey prosthesis: a finite element study

Isolated patellofemoral (PF) arthritis of the knee is a common cause of anterior knee pain and disability. Patellofemoral arthroplasty (PFA) is a bone conserving solution for patients with PF degeneration. Failure mechanisms of PFA include growing tibiofemoral arthritis and loosening of components. The implant loosening can be associated with bone resorption or fatigue-failure of bone by overload. This research work aims at determining the structural effects of the implantation of PF prosthesis Journey PFJ (Smith & Nephew, Inc., Memphis, TN, USA) on femoral cancellous bone. For this purpose, the finite element method is considered to perform computational simulations for different conditions, such as well-fixed and loosening scenarios. From the global results obtained, in the well-fixed scenario, a decrease in strain on cancellous bone was noticed, which can be related to bone resorption. In the loosening scenario, when the cement layer becomes inefficient, a significant increase in cancellous bone strain was observed, which can be associated with bone fatigue-failure.These strain changes suggest a weakness of the femur after PFA.     

Hand bone loss as an outcome measure in established rheumatoid arthritis: 2-year observational study comparing cortical and total bone loss

The aim of this 2-year longitudinal observational study was to explore hand bone loss as a disease outcome measure in established rheumatoid arthritis (RA).     

Subchondral bone microarchitecture and failure mechanism under compression: A finite element study

Subchondral bone (SCB) microdamage is commonly observed in traumatic joint injuries and has been strongly associated with post-traumatic osteoarthritis (PTOA). Knowledge of the three-dimensional stress and strain distribution within the SCB tissue helps to understand the mechanism of SCB failure, and may lead to an improved understanding of mechanisms of PTOA initiation, prevention and treatment. In this study, we used high-resolution micro-computed tomography (µCT)-based finite element (FE) modelling of cartilage-bone to evaluate the failure mechanism and the locations of SCB tissue at high-risk of initial failure under compression. The µCT images of five cartilage-bone specimens with an average SCB thickness of 1.23 ± 0.20 mm were used to develop five µCT-based FE models. The FE models were analysed under axial compressions of approximately 30 MPa applied to the cartilage surface while the bone edges were constrained. Strain and stress-based failure criteria were then applied to evaluate the failure mechanism of the SCB tissue under excessive compression through articular cartilage. µCT-based FE models predicted two locations in the SCB at high-risk of initial failure: (1) the interface of the calcified-uncalcified cartilage due to excessive tension, and (2) the trabecular bone beneath the subchondral plate due to excessive compression. µCT-based FE models of cartilage-bone enabled us to quantify the distribution of the applied compression which was transferred through the articular cartilage to its underlying SCB, and to investigate the mechanism and the mode of SCB tissue failure. Ultimately, the results will help to understand the mechanism of injury formation in relation to PTOA.     

Long-term study of bone remodelling after femoral stem: a comparison between dexa and finite element simulation

A hip replacement with a cemented or cementless femoral stem produces an effect on the bone called adaptive remodelling, attributable to mechanical and biological factors. The objective of all of cementless prostheses designs has been to achieve a perfect transfer of loads in order to avoid stress-shielding, which produces an osteopenia. In order to quantify this, the long term and mass-produced study with dual energy X-ray absorptiometry (DEXA) is necessary. Finite element (FE) simulation makes possible the explanation of the biomechanical changes which are produced in the femur after stem implantation. The good correlation obtained between the results of the FE simulation and the densitometric study allow, on one hand, to explain from the point of view of biomechanical performance the changes observed in bone density in the long-term, where it is clear that these are due to a different transfer of load in the implanted model compared to the healthy femur; on the other hand, it validates the simulation model, in a way that it can be used in different conditions and at different time periods, to carry out a sufficiently precise prediction of the evolution of the bone density from the biomechanical behaviour in the interaction between the prosthesis and femur.     

Postfailure modulus strongly affects microcracking and mechanical property change in human iliac cancellous bone: a study using a 2D nonlinear finite element method

A two-dimensional (2D) finite element (FE) method was used to estimate the ability of bone tissue to sustain damage as a function of postfailure modulus. Briefly, 2D nonlinear compact-tension FE models were created from quantitative back-scattered electron images taken of human iliac crest bone specimens. The effects of different postfailure moduli on predicted microcrack propagation were examined. The 2D FE models were used as surrogates for real bone tissues. The crack number was larger in models with higher postfailure modulus, while mean crack length and area were smaller in these models. The rate of stiffness reduction was greater in the models with lower postfailure modulus. Hence, the current results supported the hypothesis that hard tissue postfailure properties have strong effects on bone microdamage morphology and the rate of change in apparent mechanical properties.     

A finite element study of mechanical stimuli in scaffolds for bone tissue engineering

Mechanical stimuli are one of the factors that affect cell proliferation and differentiation in the process of bone tissue regeneration. Knowledge on the specific deformation sensed by cells at a microscopic level when mechanical loads are applied is still missing in the development of biomaterials for bone tissue engineering. The objective of this study was to analyze the behavior of the mechanical stimuli within some calcium phosphate-based scaffolds in terms of stress and strain distributions in the solid material phase and fluid velocity, fluid pressure and fluid shear stress distributions in the pores filled of fluid, by means of micro computed tomographed (CT)-based finite element (FE) models. Two samples of porous materials, one of calcium phosphate-based cement and another of biodegradable glass, were used. Compressive loads equivalent to 0.5% of compression applied to the solid material phase and interstitial fluid flows with inlet velocities of 1, 10 and 100 microm/s applied to the interconnected pores were simulated, changing also the inlet side and the viscosity of the medium. Similar strain distributions for both materials were found, with compressive and tensile strain maximal values of 1.6% and 0.6%, respectively. Mean values were consistent with the applied deformation. When 10 microm/s of inlet fluid velocity and 1.45 Pas viscosity, maximal values of fluid velocity were 12.76 mm/s for CaP cement and 14.87 mm/s for glass. Mean values were consistent with the inlet ones applied, and mean values of shear stress were around 5 x 10(-5)Pa. Variations on inlet fluid velocity and fluid viscosity produce proportional and independent changes in fluid velocity, fluid shear stress and fluid pressure. This study has shown how mechanical loads and fluid flow applied on the scaffolds cause different levels of mechanical stimuli within the samples according to the morphology of the materials.     

The mechanical influence of bone spicules in the osteochondral junction: A finite element modelling study

Biomechanics and Modeling in Mechanobiology - While much has been done to study how cartilage responds to mechanical loading, as well as modelling such responses, arguably less has been...     

The role of estrogen receptor-beta, in the early age-related bone gain and later age-related bone loss in female mice

The molecular and cellular mechanism of estrogen action in skeletal tissue remains unclear. The purpose of this study was to understand the role of estrogen receptor-beta, (ERbeta) on cortical and cancellous bone during growth and aging by comparing the bone phenotype of 6- and 13-month-old female mice with or without ERbeta. Groups of 11-14 wild-type (WT) controls and ERbeta knockout (BERKO) female mice were necropsied at 6 and 13 months of age. At both ages, BERKO mice did not differ significantly from WT controls in uterine weight and uterine epithelial thickness, indicating that ERbeta does not regulate the growth of uterine tissue. Femoral length increased significantly by 5.5% at 6 months of age in BERKO mice compared with WT controls. At 6 months of age, peripheral quantitative computerized tomography (pQCT) analysis of the distal femoral metaphysis (DFM) and femoral shafts showed that BERKO mice had significantly higher cortical bone content and periosteal circumference as compared with WT controls at both sites. In contrast to the findings in cortical bone, at 6 months of age, there was no difference between BERKO and WT mice in trabecular density, trabecular bone volume (TBV), or formation and resorption indices at the DFM. In 13-month-old WT mice, TBV (-41%), trabecular density (-27%) and cortical thickness decreased significantly. while marrow cavity and endocortical circumference increased significantly compared with 6-month-old WT mice. These age-related decreases in cancellous and endocortical bone did not occur in BERKO mice. At 13 months of age, BERKO mice had significantly higher total, trabecular and cortical bone, while having significantly lower bone resorption, bone formation and bone turnover in DFM compared with WT mice. These results indicate that deleting ERbeta protected against age-related bone loss in both the cancellous and endocortical compartments by decreasing bone resorption and bone turnover in aged female mice. These data demonstrate that in female mice, ERbeta plays a role in inhibiting periosteal bone formation, longitudinal and radial bone growth during the growth period, while it plays a role in stimulating bone resorption, bone turnover and bone loss on cancellous and endocortical bone surfaces during the aging process.