Model Of Cortical Bone Research Articles

Micromechanics fracture in osteonal cortical bone: A study of the interactions between microcrack propagation, microstructure and the material properties

A two-dimensional micromechanical fibre reinforced composite materials model for osteonal cortical bone is presented. The interstitial bone is modelled as a matrix, the osteons are modelled as fibres, and the cement line is presented as interface tissue. The interaction between osteons and microcracks is evaluated by linear elastic fracture mechanics theory, followed by a determination of the stress intensity factor at the vicinity of the microcrack tips. The results indicate that bone microstructural heterogeneity greatly influences fracture parameters. Furthermore, microstructural morphology and loading conditions affect growth trajectories, the microcrack propagation trajectory deviates from the osteon under tensile loading, and osteon penetration is observed under compressive loads.

P-11 Inelastic Constitutive Modeling of Cortical Bone Taking Account of Anisotropic Damage and Viscoelasticity

P-11 Inelastic Constitutive Modeling of Cortical Bone Taking Account of Anisotropic Damage and Viscoelasticity

Haversian cortical bone model with many radial microcracks: An elastic analytic solution

In this study, the fracture micromechanics of Haversian cortical bone has been considered. To this effect, a two-dimensional micromechanical fibre–ceramic matrix composite tissue materials model has been presented. The interstitial tissue was modeled as a matrix and the osteon was modeled as a fibre, followed by the application of linear elastic fracture mechanics theory. The solution for edge dislocations, in terms of Green's functions, was adopted to formulate a system of singular integral equations for the radial microcracks in the matrix in vicinity of the osteon. The problem was solved for various configurations and the corresponding stress intensity factors were computed. The results of this study indicated that the interaction between microcracks and an osteon was limited to vicinity of the osteon. Furthermore, the effect of microstructure morphology and heterogeneity on the fracture behavior has been established. The interactions between microcracks were also analyzed for various configurations. These selected configurations exhibited the effects of stress amplification and stress shielding.

Detecting and Tracking Changes of Morphologies and Mechanical Characteristics in the Lumbar Vertebrae of OVX Rats Using RP Technique and Micro-FE Method

In the present study, changes of morphologies and mechanical characteristics in the lumbar vertebrae of the ovariectomised (OVX) rats were investigated and analyzed by Finite Element (FE) and Rapid-Prototyped (RP) models based on micro-computed tomography (micro-CT). In previous researches, there were many studies about morphology such as bone mineral density and trabecular microstructure. However, detecting and tracking local changes were few in the trabecular and cortical bone of the lumbar vertebrae for the OVX rats. Experimental and simulated studies were used to investigate mechanical characteristics of the lumbar vertebral bones for the OVX rats. Three dimensional (3D) geometries of the models (RP and FE models), generated from in-vivo micro-CT scan data, were obtained from the 4th lumbar of the OVX rats. Three specimens (whole vertebral, trabecular and cortical bone models) were generated and analyzed in the simulated compression tests. For further verification, the experimental compression test for RP models ‘instead of real bone specimens’ was performed to indirectly validate the results of the simulated compression test for the FE models. The results were similar to those of the compression test simulated by micro-FE analysis. The present study showed the efficiency of the combined method (FE and RP techniques based on in-vivo micro-CT) as a nondestructive evaluation.

Sensitivity of 1‐MHz ultrasound compression and shear waves propagating on cortical bone porosity: A numerical study

The objective of this study was to describe how the porosity of cortical bone affects ultrasound propagation (wavelength: mm scale). The bulk compression and shear velocities were determined for 40 specimens of human radius using finite‐difference computation of transient ultrasound bulk waves in axial and transverse directions. The 3D microstructure of the specimens were obtained using high‐resolution synchrotron radiation micro‐computed tomography (voxel size =10μm). The pores were filled with a nonviscous fluid and the model assumed the bone material to be elastic and transversely isotropic or isotropic. All bulk wave velocities decreased quasi‐linearly with increasing porosity, e.g., typically 28 m/s/%por for the axial compressional wave velocity. For the radial compressional wave velocity, the rate depended on the assumption on the bone material (for isotropy 56 m/s/%por and for transverse isotropy 19 m/s/%por). In case of transversely isotropic bone matrix, cortical bone tended to become more acoustically isotropic when its porosity increases in agreement with previous experimental studies. This study may help to develop more accurate models of cortical bone used to design improved ultrasound devices and to provide guidelines for establishing methods for the ultrasonic determination of bone properties.

Relative Impact of Androgen and Estrogen Receptor Activation in the Effects of Androgens on Trabecular and Cortical Bone in Growing Male Mice: A Study in the Androgen Receptor Knockout Mouse Model

The relative importance of AR and ER activation has been studied in pubertal male AR knockout and WT mice after orchidectomy and androgen replacement therapy, either with or without an aromatase inhibitor. AR activation dominates normal trabecular bone development and cortical bone modeling in male mice. Moreover, optimal periosteal bone expansion is only observed in the presence of both AR and ER activation. Androgen receptor (AR)-mediated androgen action has traditionally been considered a key determinant of male skeletal growth. Increasing evidence, however, suggests that estrogens are also essential for normal male bone growth. Therefore, the relative importance of AR-mediated and estrogen receptor (ER)-mediated androgen action after aromatization remains to be clarified. Trabecular and cortical bone was studied in intact or orchidectomized pubertal AR knockout (ARKO) and male wildtype (WT) mice, with or without replacement therapy (3-8 weeks of age). Nonaromatizable (dihydrotestosterone [DHT]) and aromatizable (testosterone [T]) androgens and T plus an aromatase inhibitor (anastrazole) were administered to orchidectomized ARKO and WT mice. Trabecular and cortical bone modeling were evaluated by static and dynamic histomorphometry, respectively. AR inactivation or orchidectomy induced a similar degree of trabecular bone loss (-68% and -71%, respectively). Both DHT and T prevented orchidectomy-induced bone loss in WT mice but not in ARKO mice. Administration of an aromatase inhibitor did not affect T action on trabecular bone. AR inactivation and orchidectomy had similar negative effects on cortical thickness (-13% and -8%, respectively) and periosteal bone formation (-50% and -26%, respectively). In orchidectomized WT mice, both DHT and T were found to stimulate periosteal bone formation and, as a result, to increase cortical thickness. In contrast, the periosteum of ARKO mice remained unresponsive to either DHT or T. Interestingly, administration of an aromatase inhibitor partly reduced T action on periosteal bone formation in orchidectomized WT mice (-34% versus orchidectomized WT mice on T), but not in ARKO mice. This effect was associated with a significant decrease in serum IGF-I (-21% versus orchidectomized WT mice on T). These findings suggest a major role for AR activation in normal development of trabecular bone and periosteal bone growth in male mice. Moreover, optimal stimulation of periosteal growth is only obtained in the presence of both AR and ER activation.

Metabolic Derangements in the Insulin‐Resistant Heart

To investigate whether controlled early loading enhances peri-implant bone mass and bone-to-implant contact. Low-frequency stimulation (3 Hz) and varying force amplitudes, causing varying strains, were applied in three guinea-pig series. Three series of guinea-pigs received percutaneous TiO(2)-blasted implants in both tibiae. One week after implant installation, one implant was stimulated with a sinusoidally varying bending moment while the contra-lateral implant served as an unloaded control. Force amplitudes of 0.5, 1 and 2 N were applied on a 20-mm-long cantilever, resulting in strains of 133, 267 and 533 muepsilon, respectively, measured by a strain gauge bonded on the surface of the tibial bone at 1.3 mm from the implant's distal surface. Implant stability was followed by means of resonance frequency analysis. Bone-to-implant contact and bone mass [BM (%) bone occupied area fraction] were analysed histomorphometrically. A significant positive effect on the difference in bone mass at the stimulated vs. at the control side was observed in the distal half peri-implant marrow cavity for early mechanical stimulation at a frequency of 3 Hz (P<0.0001). An optimum was reached for the applied load, which causes a strain of approximately 267 muepsilon 1.3 mm from the implant. Implant stability gradually increased in time; no significant effect of early stimulation could be measured. The effect of early controlled mechanical stimulation on the peri-implant bone, in this cortical bone model, is strongly dependent on force amplitude/strain at low-frequency stimulation.

Heat Production by 3 Implant Drill Systems After Repeated Drilling and Sterilization

The goal was to measure heat generated in bone by 3 implant drill systems after repeated drilling and sterilization. Temperature was measured with thermocouple technology in vitro using the bovine femoral cortical bone model. Intermittent drilling was accomplished at a constant 2.4-kg load and drill speed of 2,500 rpm. External irrigation at 40 mL/min with normal saline was used. Three implant drill systems-system A (triple twist drills with a relief angle), system B (triple twist drills without a relief angle), and system C (double twist drills with a relief angle)-were evaluated and heat was measured at the final drill in the drilling sequence (4.0 mm or 4.2 mm) at a depth of 15 mm. Thermocouples were placed 0.5 mm from the osteotomy at a depth of 15 mm. Heat measurements were recorded out to 25 uses. Results showed temperature increased with multiple uses. System A and C drills had temperature measurements that were below 47 degrees C, even after 25 uses. System B drills had temperatures that exceeded 47 degrees C from the initial use. Light microscopy showed little drill wear even after 25 uses. Drill geometry plays a major role in heat production and may explain the increased temperature readings seen in system B. These drills lack relief angles and have the smallest clearance angles of the 3 systems. It also has fewer drills in its drilling sequence compared with systems A and C. This study shows that temperatures increase when drills are used multiple times. Systems A and C had acceptable temperature measurements out to 25 uses. System B drills showed significantly higher heat production with little visual signs of wear.

Multi-Scale Modeling of Human Cortical Bone: Aging and Failure Studies

ABSTRACTA multi-scale analysis for unit cells of human cortical bone is presented. Two studies are conducted: the first study concerns the effect of aging over the structural and mechanical properties of human cortical bone; the second study is devoted to the failure mechanism and the development of cracks in cortical bone under various loading conditions. Experiments are conducted on human specimen of different ages in order to measure relevant geometrical and mechanical parameters and obtain microscopic data that will be injected into finite element models. First a continuum FEM model will compute macroscopic information that will be validated through comparison with the experimental measurements. For the failure mechanism study, an XFEM model will be developed in order to allow the growth of multiple cracks until complete failure of the cell. An elastic-damage criterion will be used in order to place the initial cracks in maximum strain locations. To follow the global response of the cell, the stress intensity factors are computed at each crack tip and a load parameter is adjusted so that the stress intensity factors remain at the critical value. In the case of competitive crack tips, a stability analysis is performed by computing the second derivative of the potential energy for each crack. Fatigue loading will be also investigated. The discretization utilizes the eXtended Finite Element Method and requires no remeshing as the cracks grow. The crack geometries are arbitrary with respect to the mesh, and are described by a vector level set. Special boundary conditions and the algorithm for detecting crack bridging and crack entering Haversian canals which allows the cracks to grow until maximum failure and/or percolation is presented.

An elastic plastic damage constitutive model for cortical bone with distinct tension and compression damage variables

An elastic plastic damage constitutive model for cortical bone with distinct tension and compression damage variables

Re-evaluating the toughness of human cortical bone

Data for fracture in human humeral cortical bone are re-analyzed to assess the validity for this material of linear-elastic fracture mechanics (LEFM), which is the standard method of analyzing toughness and one basis for analyzing clinical data relating to bone quality. A nonlinear fracture model, which is based on representing the damage zone in the bone by a cohesive model, is calibrated against a number of sets of test data for normal (not diseased or aged) human cortical bone taken from cadavers. The data consist of load vs. load-point displacement measurements from standard compact–tension fracture tests. Conventional LEFM is unable to account for the shape of the load–displacement curves, but the nonlinear model overcomes this deficiency. Calibration of the nonlinear model against one data curve leads to predictions of the peak load and the displacement to peak load for two other data curves that are, for this limited test set, more accurate than those made using LEFM. Furthermore, prior observations of damage mechanisms in bone are incompatible with the modeling assumption of LEFM that all nonlinearity is confined to a zone much smaller than the specimen and the crack length. The predictions of the cohesive model and the prior observations concur that the length of the nonlinear zone in human cortical bone varies in the range 3–10 mm, which is comparable to or larger than naturally-occurring bones and the specimens used to test them. We infer that LEFM is not an accurate model for cortical bone. The fracture toughness of bone deduced via LEFM from test data will not generally be a material constant, but will take different values for different crack lengths and test configurations. The accuracy of using LEFM or single-parameter fracture toughness for analyzing the significance of data from clinical studies is called into question. The nonlinear cohesive zone model is proposed to be a more accurate model of bone and the traction-displacement or cohesive law is hypothesized to be a material property. The cohesive law contains a more complete representation of the mechanics of material failure than the single-parameter fracture toughness and may therefore provide a superior measure of bone quality, e.g., for assessing the efficacy of therapy for osteoporosis.

Prediction of Cortical Bone Elastic Constants by a Two-Level Micromechanical Model Using a Generalized Self-Consistent Method

A two-level micromechanical model of cortical bone based on a generalized self-consistent method was developed to take into consideration the transversely isotropic elasticity of many microstructural features in cortical bone, including Haversian canals, resorption cavities, and osteonal and interstitial lamellae. In the first level, a single osteon was modeled as a two-phase composite such that Haversian canals were represented by elongated pores while the surrounding osteonal lamellae were considered as matrix. In the second level, osteons and resorption cavities were modeled as multiple inclusions while interstitial lamellae were regarded as matrix. The predictions of cortical bone elasticity from this two-level micromechanical model were mostly in agreement with experimental data for the dependence of transversely isotropic elasticity of human femoral cortical bone on porosity. However, variation in cortical bone elastic constants was greater in experimental data than in model predictions. This could be attributed to variations in the elastic properties of microstructural features in cortical bone. The present micromechanical model of cortical bone will be useful in understanding the contribution of cortical bone porosity to femoral neck fractures.

A fatigue microcrack alters fluid velocities in a computational model of interstitial fluid flow in cortical bone

Targeted remodeling is activated by fatigue microcracks and plays an important role in maintaining bone integrity. It is widely believed that fluid flow-induced shear stress plays a major role in modulating the mechanotransduction process. Therefore, it is likely that fluid flow-induced shear stress plays a major role in the initiation of the repair of fatigue damage. Since no in vivo measurements of fluid flow within bone exist, computational and mathematical models must be employed to investigate the fluid flow field and the shear stress occurring within cortical bone. We developed a computational fluid dynamic model of cortical bone to examine the effect of a fatigue microcrack on the fluid flow field. Our results indicate that there are alterations in the fluid flow field as far as 150 μm away from the crack, and that at distances farther than this, the fluid flow field is similar to the fluid flow field of intact bone. Through the crack and immediately above and below it, the fluid velocity is higher, while at the lateral edges it is lower than that calculated for the intact model, with a maximum change of 29%. Our results suggest that the presence of a fatigue microcrack can alter the shear stress in regions near the crack. These alterations in shear stress have the potential to significantly alter mechanotransduction and may play a role in the initiation of the repair of fatigue microcracks.

Theoretical Accuracy of Model-Based Shape Matching for Measuring Natural Knee Kinematics with Single-Plane Fluoroscopy

Quantification of knee motion under dynamic, in vivo loaded conditions is necessary to understand how knee kinematics influence joint injury, disease, and rehabilitation. Though recent studies have measured three-dimensional knee kinematics by matching geometric bone models to single-plane fluoroscopic images, factors limiting the accuracy of this approach have not been thoroughly investigated. This study used a three-step computational approach to evaluate theoretical accuracy limitations due to the shape matching process alone. First, cortical bone models of the femur tibia/fibula, and patella were created from CT data. Next, synthetic (i.e., computer generated) fluoroscopic images were created by ray tracing the bone models in known poses. Finally, an automated matching algorithm utilizing edge detection methods was developed to align flat-shaded bone models to the synthetic images. Accuracy of the recovered pose parameters was assessed in terms of measurement bias and precision. Under these ideal conditions where other sources of error were eliminated, tibiofemoral poses were within 2 mm for sagittal plane translations and 1.5 deg for all rotations while patellofemoral poses were within 2 mm and 3 deg. However, statistically significant bias was found in most relative pose parameters. Bias disappeared and precision improved by a factor of two when the synthetic images were regenerated using flat shading (i.e., sharp bone edges) instead of ray tracing (i.e., attenuated bone edges). Analysis of absolute pose parameter errors revealed that the automated matching algorithm systematically pushed the flat-shaded bone models too far into the image plane to match the attenuated edges of the synthetic ray-traced images. These results suggest that biased edge detection is the primary factor limiting the theoretical accuracy of this single-plane shape matching procedure.

Modeling Deformation-Induced Fluid Flow in Cortical Bone?s Canalicular?Lacunar System

To explore the potential role that load-induced fluid flow plays as a mechano-transduction mechanism in bone adaptation, a lacunar-canalicular scale bone poroelasticity model is developed and implemented. The model uses micromechanics to homogenize the pericanalicular bone matrix, a system of straight circular cylinders in the bone matrix through which bone fluids can flow, as a locally anisotropic poroelastic medium. In this work, a simplified two-dimensional model of a periodic array of lacunae and their surrounding systems of canaliculi is used to quantify local fluid flow characteristics in the vicinity of a single lacuna. When the cortical bone model is loaded, microscale stress, and strain concentrations occur in the vicinity of individual lacunae and give rise to microscale spatial variations in the pore fluid pressure field. Furthermore, loading of the bone matrix containing canaliculi generates fluid pressures in the contained fluids. Consequently, loading of cortical bone induces fluid flow in the canaliculi and exchange of fluid between canaliculi and lacunae. For realistic bone morphology parameters, and a range of loading frequencies, fluid pressures and fluid-solid drag forces in the canalicular bone are computed and the associated energy dissipation in the models compared to that measured in physical in vitro experiments on human cortical bone. The proposed model indicates that deformation-induced fluid pressures in the lacunar-canalicular system have relaxation times on the order of milliseconds as opposed to the much shorter times (hundredths of milliseconds) associated with deformation-induced pressures in the Haversian system.

Hydraulic Strengthening Affects the Stiffness and Strength of Cortical Bone

A nonlinear, interstitial fluid flow constitutive model for cortical bone was developed to study the strain-rate dependency of cortical bone apparent modulus (Ea). Nine representative volume element (RVE) structural models of cortical bone spanning an effective pore volume fraction P range of 1-40% were examined. Dynamic loading conditions were used to study the fluid flow contribution or hydraulic strengthening (HS) effect on Ea for each RVE model. The model indicated that there is an upper and lower asymptotic bound of strain-rate (10(+/-3) sec(-1)) above or below which there are no further HS effects on Ea. At certain strain-rates (10(-1) to 10(0) sec(-1)) variations in cortical bone porosity had little or no influence on Ea. At lower and higher frequencies, the loss tangent, hence the magnitude of viscoelastic effects is greater. For strain-rates less than 10(-1) sec(-1), lower porosity RVE models were always stiffer than higher porosity RVE models. A generalized power law model is proposed to account for the fact that HS in cortical bone exhibits an upper and lower asymptotic bound and is bi-modal in terms of strain-rate.

Inelastic Constitutive Modelling of Cortical Bone Taking Account of Anisotropy and Damage

An anisotropic inelastic constitutive model of cortical bone was formulated to predict deformation and failure behavior in traffic accidents or falling by utilizing the framework of viscoplasticity and damage mechanics. The model can represent characteristic features of cortical bone, such as anisotropic elastic coefficients with strain rate dependency, viscoplasticity with strength anisotropy as well as strength asymmetry of tension and compression. The damage evolution equation also enables us to predict bone failure with rate dependency. Experimental data of uniaxial compressive or tensile loading tests of human cortical bone at various strain rates were used to validate the proposed model. Predicted stress-strain curves and failure points agreed well with those of experimental data at wide range of strain rates. This shows the present model can be used to predict bone failure in various impact simulations of traffic accidents or falling.

Three-dimensional simulations of ultrasonic axial transmission velocity measurement on cortical bone models.

The ultrasonic axial transmission technique, used to assess cortical shells of long bones, is investigated using numerical simulations based on a three-dimensional (3D) finite difference code. We focus our interest on the effects of 3D cortical bone geometry (curvature, cortical thickness), anisotropy, and microporosity on speed of sound (SOS) measurements for different frequencies in the MHz range. We first show that SOS values measured on tubular cortical shells are identical to those measured on cortical plates of equal thickness. Anisotropy of cortical bone is then shown to have a major impact on SOS measurement as a function of cortical thickness. The range of SOS values measured on anisotropic bone is half the range found when bone is considered isotropic. Dependence of thickness occurs for cortical shell thinner than 0.5 x lambda(bone) in anisotropic bone (lambda(bone): wavelength in bone), whereas it occurs for cortical shell thinner than lambda(bone) when anisotropy is neglected. Sensitivity of SOS along the bone axis to intracortical microporosity is shown to be approximately -20 m s(-1) per percent of porosity. Using homogenized porous bone, we finally show that the cortical depth that contributes to lateral wave SOS measurement is approximately 1-1.5 mm for frequencies ranging from 500 kHz to 2 MHz under classical in vivo measurement conditions.

The dependence of transversely isotropic elasticity of human femoral cortical bone on porosity

The objective of this study was to examine the dependence of the elastic properties of cortical bone as a transversely isotropic material on its porosity. The longitudinal Young's modulus, transverse Young's modulus, longitudinal shear modulus, transverse shear modulus, and longitudinal Poisson's ratio of cortical bone were determined from eighteen groups of longitudinal and transverse specimens using tensile and torsional tests on a servo-hydraulic material testing system. These cylindrical waisted specimens of cortical bone were harvested from the middle diaphysis of three pairs of human femora. The porosity of these specimens was assessed by means of histology. Our study demonstrated that the longitudinal Young's and shear moduli of human femoral cortical bone were significantly ( p<0.01) negatively correlated with the porosity of cortical bone. Conversely, the elastic properties in the transverse direction did not have statistically significant correlations with the porosity of cortical bone. As a result, the transverse elastic properties of cortical bone were less sensitive to changes in porosity than those in the longitudinal direction. Additionally, the anisotropic ratios of cortical bone elasticity were found to be significantly ( p<0.01) negatively correlated with its porosity, indicating that cortical bone tended to become more isotropic when its porosity increased. These results may help a number of researchers develop more accurate micromechanics models of cortical bone.

The effects of intravenous pamidronate on the bone tissue of children and adolescents with osteogenesis imperfecta.

Cyclical pamidronate infusions increase bone mass in children suffering from osteogenesis imperfecta. The histological basis for these effects remains unknown. Therefore, we compared parameters of iliac bone histomorphometry from 45 patients before and after 2.4 +/- 0.6 years of pamidronate treatment (age at the time of the first biopsy, 1.4-17.5 years; 23 girls). Although biopsy size did not change significantly (P = 0.30), cortical width increased by 88%. Cancellous bone volume increased by 46%. This was due to a higher trabecular number, whereas trabecular thickness remained stable. Bone surface-based indicators of cancellous bone remodeling decreased by 26-75%. There was no evidence for a mineralization defect in any of the patients. These results suggest that, in the growing skeleton, pamidronate has a twofold effect. In remodeling, bone resorption and formation are coupled and consequently both processes are inhibited. However, osteoclasts and osteoblasts are active on different surfaces (and are thus uncoupled) during modeling of cortical bone. Therefore resorption is selectively targeted, and continuing bone formation can increase cortical width.