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

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

Biomechanical effect of mineral heterogeneity in trabecular bone

Due to daily loading, trabecular bone is subjected to deformations (i.e., strain), which lead to stress in the bone tissue. When stress and/or strain deviate from the normal range, the remodeling process leads to adaptation of the bone architecture and its degree of mineralization to effectively withstand the sustained altered loading. As the apparent mechanical properties of bone are assumed to depend on the degree and distribution of mineralization, the goal of the present study was examine the influences of mineral heterogeneity on the biomechanical properties of trabecular bone in the human mandibular condyle. For this purpose nine right condyles from human dentate mandibles were scanned and evaluated with a microCT system. Cubic regional volumes of interest were defined, and each was transformed into two different types of finite element (FE) models, one homogeneous and one heterogeneous. In the heterogeneous models the element tissue moduli were scaled to the local degree of mineralization, which was determined using microCT. Compression and shear tests were simulated to determine the apparent elastic moduli in both model types. The incorporation of mineralization variation decreased the apparent Young's and shear moduli by maximally 21% in comparison to the homogeneous models. The heterogeneous model apparent moduli correlated significantly with bone volume fraction and degree of mineralization. It was concluded that disregarding mineral heterogeneity may lead to considerable overestimation of apparent elastic moduli in FE models.     

Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations

Background: The mechanical response of patient-specific bone to various load conditions is of major clinical importance in orthopedics. Herein we enhance the methods presented in Yosibash et al. [2007. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. ASME Journal of Biomechanical Engineering 129(3), 297–309.] for the reliable simulations of the human proximal femur by high-order finite elements (FEs) and validate the simulations by experimental observations.

Method of approach: A fresh-frozen human femur was scanned by quantitative computed tomography (QCT) and thereafter loaded (in vitro experiments) by a quasi-static force of up to 1250 N. QCT scans were manipulated to generate a high-order FE bone model with distinct cortical and trabecular regions having inhomogeneous isotropic elastic properties with Young's modulus represented by continuous spatial functions. Sensitivity analyses were performed to quantify parameters that mostly influence the mechanical response. FE results were compared to displacements and strains measured in the experiments.

Results: Young moduli correlated to QCT Hounsfield Units by relations in Keyak and Falkinstein [2003. Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Medical Engineering and Physics 25, 781–787.] were found to provide predictions that match the experimental results closely. Excellent agreement was found for both the displacements and strains. The presented study demonstrates that reliable and validated high-order patient-specific FE simulations of human femurs based on QCT data are achievable for clinical computer-aided decision making.     

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.     

Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

Elucidation of extracellular matrix mechanics from muscle fibers and fiber bundles

The importance of the extracellular matrix (ECM) in muscle is widely recognized, since ECM plays a central role in proper muscle development (Buck and Horwitz, 1987), tissue structural support (Purslow, 2002), and transmission of mechanical signals between fibers and tendon (Huijing, 1999). Since substrate biomechanical properties have been shown to be critical in the biology of tissue development and remodeling (Engler et al., 2006; Gilbert et al., 2010), it is likely that mechanics are critical for ECM to perform its function. Unfortunately, there are almost no data available regarding skeletal muscle ECM viscoelastic properties. This is primarily due to the impossibility of isolating and testing muscle ECM. Therefore, this note presents a new method to quantify viscoelastic ECM modulus by combining tests of single muscle fibers and fiber bundles. Our results demonstrate that ECM is a highly nonlinearly elastic material, while muscle fibers are linearly elastic.     

Three-dimensional strain fields in a uniform osteotomy gap

Stable internal fixation usually results in a unique histological healing pattern which involves direct cortical reconstruction and an absence of periosteal bridging callus. While it has been suggested that longitudinal interfragmentary strain levels control this healing pattern, the complex, multiaxial strain fields in the interfragmentary region are not well understood. Based on an in-vivo study of gap healing in the sheep tibia by Mansmann et al., we used several finite element models of simplified geometry to: explore modeling assumptions on material linearity and deformation kinematics, and examine the strain distribution in a healing fracture gap subjected to known levels of interfragmentary strain. We found that a general nonlinear material, nonlinear geometric analysis is necessary to model an osteotomy gap subjected to a maximum longitudinal strain of 100 percent. The large displacement, large strain conditions which were used in the in-vivo study result in complex, multiaxial strain fields in the gap. Restricting the maximum longitudinal strain to 10 percent allows use of a linear geometric formulation without compromising the numerical results. At this reduced strain level a linear material model can be used to examine the extent of material yielding within a homogeneous osteotomy gap. Severe local strain variations occurred both through the thickness of the gap and radially from the endosteal to periosteal gap surfaces. The bone/gap interface represented a critical plane of high distortional and volumetric change and principal strain magnitudes exceeded the maximum longitudinal strains.     

Validation of a voxel-based FE method for prediction of the uniaxial apparent modulus of human trabecular bone using macroscopic mechanical tests and nanoindentation

Assessment of the mechanical properties of trabecular bone is of major biological and clinical importance for the investigation of bone diseases, fractures and their treatments. Finite element (FE) methods are getting increasingly popular for quantifying the elastic and failure properties of trabecular bone. In particular, voxel-based FE methods have been previously used to calculate the effective elastic properties of trabecular microstructures. However, in most studies, bone tissue moduli were assumed or back-calculated to match the apparent elastic moduli from experiments, which often lead to surprisingly low values when compared to nanoindentation results. In this study, voxel-based FE analysis of trabecular bone is combined with physical measures of volume fraction, micro-CT (microCT) reconstructions, uniaxial mechanical tests and specimen-specific nanoindentation tests for proper validation of the method. Cylindrical specimens of cancellous bone were extracted from human femurs and their volume fraction determined with Archimede's method. Uniaxial apparent modulus of the specimens was measured with an improved tension-compression testing protocol that minimizes boundary artefacts. Their microCT reconstructions were segmented to match the measured bone volume fraction and used to create full-size voxel models with 30-45 microm element size. For each specimen, linear isotropic elastic material properties were defined based on specific nanoindentation measurements of its embedded bone tissue. Linear FE analyses were finally performed to simulate the uniaxial mechanical tests. Additional parametric analyses were performed to evaluate the potential errors on the predicted apparent modulus arising from variations in segmentation threshold, tissue modulus, and the use of 125-mm(3) cubic sub-regions. The results demonstrate an excellent correspondence between experimental measures and FE predictions of uniaxial apparent modulus. In conclusion, the adopted voxel-based FE approach is found to be a robust method to predict the linear elastic properties of human cancellous bone, provided segmentation of the microCT reconstructions is carefully calibrated, tissue modulus is known a priori and the entire region of interest is included in the analysis.     

Mineral heterogeneity affects predictions of intratrabecular stress and strain

Knowledge of the influence of mineral variations (i.e., mineral heterogeneity) on biomechanical bone behavior at the trabecular level is limited. The aim of this study is to investigate how this material property affects the intratrabecular distributions of stress and strain in human adult trabecular bone. Two different sets of finite element (FE) models of trabecular samples were constructed; tissue stiffness was either scaled to the local degree of mineralization of bone as measured with microCT (heterogeneous) or tissue stiffness was assumed to be homogeneous. The influence of intratrabecular mineral heterogeneity was analyzed by comparing both models. Interesting effects were seen regarding intratrabecular stress and strain distributions. In the homogeneous model, the highest stresses were found at the surface with a significant decrease towards the core. Higher superficial stresses could indicate a higher predicted fracture risk in the trabeculae. In the heterogeneous model this pattern was different. A significant increase in stress with increasing distance from the trabecular surface was found followed by a significant decrease towards the core. This suggests trabecular bending during a compression. In both models a decrease in strain values from surface to core was predicted, which is consistent with trabecular bending. When mineral heterogeneity was taken into account, the predicted intratrabecular patterns of stress and strain are more consistent with the expected biomechanical behavior as based on mineral variations in trabeculae. Our findings indicate that mineral heterogeneity should not be neglected when performing biomechanical studies on topics such as the (long-term or dose dependent) effects of antiresorptive treatments.     

Bone ingrowth around porous-coated acetabular implant: a three-dimensional finite element study using mechanoregulatory algorithm

Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent on the mechanical environment of the implant–bone structure. The objective of the study is to gain an insight into the tissue differentiation around an acetabular component. A mapping framework has been developed to simulate appropriate mechanical environment in the three-dimensional microscale model, implement the mechanoregulatory tissue differentiation algorithm and subsequently assess spatial distribution of bone ingrowth around an acetabular component, quantitatively. The FE model of implanted pelvis subjected to eight static load cases during a normal walking cycle was first solved. Thereafter, a mapping algorithm has been employed to include the variations in implant–bone relative displacement and host bone material properties from the macroscale FE model of implanted pelvis to the microscale FE model of the beaded implant–bone interface. The evolutionary tissue differentiation was observed in each of the 13 microscale models corresponding to 13 acetabular regions. The total implant–bone relative displacements, averaged over each region of the acetabulum, were found to vary between 10 and 60 \(\upmu \hbox {m}\). Both the linear elastic and biphasic poroelastic models predicted similar mechanoregulatory peri-prosthetic tissue differentiation. Considerable variations in bone ingrowth (13–88 %), interdigitation depth (0.2–0.82 mm) and average tissue Young’s modulus (970–3430 MPa) were predicted around the acetabular cup. A progressive increase in the average Young’s modulus, interdigitation depth and decrease in average radial strains of newly formed tissue layer were also observed. This scheme can be extended to investigate tissue differentiation for different surface texture designs on the implants.     

Correlations between indentation modulus and mineral density in bone-fracture calluses

The mechanical properties of a healing bone fracture depend not only on the geometry of the fracture callus but also on the material properties of the callus tissues. Despite the biomechanical importance of callus tissues in restoring mechanical integrity to the injured bone, little is known about the material properties of these tissues and whether these properties can be estimated non-invasively. This study used nanoindentation to quantify the spatial variations in indentation modulus throughout the fracture callus and correlated the measurements of modulus with measurements of tissue mineral density (TMD) obtained from images from micro-computed tomography (μCT). Fracture calluses were harvested from rats 24 days following creation of a full-thickness, transverse osteotomy in the femoral mid-diaphysis. Calluses were imaged using μCT, and the average TMD and the median grayvalue (X-ray attenuation) of five, pre-defined volumes of interest (VOIs) in each callus were computed. Nanoindentation was then performed at multiple, regularly spaced locations across 150 μm-thick, sagittal sections of the calluses. The indentation modulus ranged from 0.51 to 1680 MPa throughout the callus, with the highest moduli in the center of the fracture gap and the lowest in the periphery of the gap (P < 0.05). TMD was also highest in the center of the gap (P < 0.05). An increasing trend in both modulus and TMD was observed in the regions of the callus adjacent to the periosteal surfaces of the cortex. While no correlation was found between the average indentation modulus in a given VOI and the median grayvalue of that VOI, the average indentation modulus and the average TMD were positively correlated (R = 0.70, P < 0.05). Together, these findings establish the spatial heterogeneity in the mechanical behavior of tissues in fracture calluses and indicate that the indentation modulus of these tissues can be estimated by non-invasive measurements of tissue mineralization.     

Predicting the external formation of callus tissues in oblique bone fractures: idealised and clinical case studies

It is proposed that the external asymmetric formation of callus tissues that forms naturally about an oblique bone fracture can be predicted computationally. We present an analysis of callus formation for two cases of bone fracture healing: idealised and subject-specific oblique bone fractures. Plane strain finite element (FE) models of the oblique fractures were generated to calculate the compressive strain field experienced by the immature callus tissues due to interfragmentary motion. The external formations of the calluses were phenomenologically simulated using an optimisation style algorithm that iteratively removes tissue that experiences low strains from a large domain. The resultant simulated spatial formation of the healing tissues for the two bone fracture cases showed that the calluses tended to form at an angle equivalent to the angle of the oblique fracture line. The computational results qualitatively correlated with the callus formations found in vivo. Consequently, the proposed methods show potential as a means of predicting callus formation in pre-clinical testing.     

Assessment of mechanobiological models for the numerical simulation of tissue differentiation around immediately loaded implants

Nowadays, there is a growing consensus on the impact of mechanical loading on bone biology. A bone chamber provides a mechanically isolated in vivo environment in which the influence of different parameters on the tissue response around loaded implants can be investigated. This also provides data to assess the feasibility of different mechanobiological models that mathematically describe the mechanoregulation of tissue differentiation. Before comparing numerical results to animal experimental results, it is necessary to investigate the influence of the different model parameters on the outcome of the simulations. A 2D finite element model of the tissue inside the bone chamber was created. The differentiation models developed by Prendergast, et al. ["Biophysical stimuli on cells during tissue differentiation at implant interfaces", Journal of Biomechanics, 30(6), (1997), 539-548], Huiskes et al. ["A biomechanical regulatory model for periprosthetic fibrous-tissue differentiation", Journal of Material Science: Materials in Medicine, 8 (1997) 785-788] and by Claes and Heigele ["Magnitudes of local stress and strain along bony surfaces predict the course and type of fracture healing", Journal of Biomechanics, 32(3), (1999) 255-266] were implemented and integrated in the finite element code. The fluid component in the first model has an important effect on the predicted differentiation patterns. It has a direct effect on the predicted degree of maturation of bone and a substantial indirect effect on the simulated deformations and hence the predicted phenotypes of the tissue in the chamber. Finally, the presence of fluid also causes time-dependent behavior. Both models lead to qualitative and quantitative differences in predicted differentiation patterns. Because of the different nature of the tissue phenotypes used to describe the differentiation processes, it is however hard to compare both models in terms of their validity.     

The spatio-temporal arrangement of different tissues during bone healing as a result of simple mechanobiological rules

During secondary bone healing, different tissue types are formed within the fracture callus depending on the local mechanical and biological environment. Our aim was to understand the temporal succession of these tissue patterns for a normal bone healing progression by means of a basic mechanobiological model. The experimental data stemmed from an extensive, previously published animal experiment on sheep with a 3?mm tibial osteotomy. Using recent experimental data, the development of the hard callus was modelled as a porous material with increasing stiffness and decreasing porosity. A basic phenomenological model was employed with a small number of simulation parameters, which allowed comprehensive parameter studies. The model distinguished between the formation of new bone via endochondral and intramembranous ossification. To evaluate the outcome of the computer simulations, the tissue images of the simulations were compared with experimentally derived tissue images for a normal healing progression in sheep. Parameter studies of the threshold values for the regulation of tissue formation were performed, and the source of the biological stimulation (comprising e.g. stem cells) was varied. It was found that the formation of the hard callus could be reproduced in silico for a wide range of threshold values. However, the bridging of the fracture gap by cartilage on the periosteal side was observed only (i) for a rather specific choice of the threshold values for tissue differentiation and (ii) when assuming a strong source of biological stimulation at the periosteum.     

Substrate Stiffness and Oxygen as Regulators of Stem Cell Differentiation during Skeletal Tissue Regeneration: A Mechanobiological Model

Extrinsic mechanical signals have been implicated as key regulators of mesenchymal stem cell (MSC) differentiation. It has been possible to test different hypotheses for mechano-regulated MSC differentiation by attempting to simulate regenerative events such as bone fracture repair, where repeatable spatial and temporal patterns of tissue differentiation occur. More recently, in vitro studies have identified other environmental cues such as substrate stiffness and oxygen tension as key regulators of MSC differentiation; however it remains unclear if and how such cues determine stem cell fate in vivo. As part of this study, a computational model was developed to test the hypothesis that substrate stiffness and oxygen tension regulate stem cell differentiation during fracture healing. Rather than assuming mechanical signals act directly on stem cells to determine their differentiation pathway, it is postulated that they act indirectly to regulate angiogenesis and hence partially determine the local oxygen environment within a regenerating tissue. Chondrogenesis of MSCs was hypothesized to occur in low oxygen regions, while in well vascularised regions of the regenerating tissue a soft local substrate was hypothesised to facilitate adipogenesis while a stiff substrate facilitated osteogenesis. Predictions from the model were compared to both experimental data and to predictions of a well established computational mechanobiological model where tissue differentiation is assumed to be regulated directly by the local mechanical environment. The model predicted all the major events of fracture repair, including cartilaginous bridging, endosteal and periosteal bony bridging and bone remodelling. It therefore provides support for the hypothesis that substrate stiffness and oxygen play a key role in regulating MSC fate during regenerative events such as fracture healing.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

Effect of boundary conditions,impact loading and hydraulic stiffening on femoral fracture strength

Patient specific quantitative CT (QCT) imaging data together with the finite element (FE) method may provide an accurate prediction of a patient's femoral strength and fracture risk. Although numerous FE models investigating femoral fracture strength have been published, there is little consent on the effect of boundary conditions, dynamic loading and hydraulic strengthening due to intra-medullary pressure on the predicted fracture strength. We developed a QCT-derived FE model of a proximal femur that included node-specific modulus assigned based on the local bone density. The effect of three commonly used boundary conditions published in literature were investigated by comparing the resulting strain field due to an applied fracture load. The models were also augmented with viscoelastic material properties and subject to a realistic impact load profile to determine the effect of dynamic loads on the strain field. Finally, the effect of hydraulic strengthening was investigated by including node specific permeability and performing a coupled pore diffusion and stress analysis of the FE model. Results showed that all boundary conditions yield the same strain field patterns, but peak strains were 22% lower and fracture load was 18% higher when loaded at the greater trochanter than when loaded at the femoral head. Comparison of the dynamic models showed that material viscoelasticity was important, but inertial effects (vibration and shock) were not. Finally, pore pressure changes did not cause significant hydraulic strengthening of bone under fall impact loading.     

Evaluation of residual stresses due to bone callus growth: a computational study

Mechanical environment in callus is determinant for the evolution of bone healing. However, recent mechanobiological computational works have underestimated the effect that growth exerts on the mechanical environment of callus. In the present work, we computationally evaluate the significance of growth-induced stresses, commonly called residual stresses, in callus. We construct a mechanobiological model of a callus in the metatarsus of a sheep in two different stages: one week and four weeks after fracture. The magnitude of stresses generated during callus growth is compared with the magnitude of stresses when only external loads are applied to the callus. We predict that residual stresses are relevant in some areas, mainly located at the periosteal side far from the fracture gap. Therefore, the inclusion of these residual stresses could represent a significant impact on the callus growth and predict a different evolution of biological processes occurring during bone healing.     

Nanoindentation measurements of biomechanical properties in mature and newly formed bone tissue surrounding an implant

The characterization of the biomechanical properties of newly formed bone tissue around implants is important to understand the osseointegration process. The objective of this study is to investigate the evolution of the hardness and indentation modulus of newly formed bone tissue as a function of healing time. To do so, a nanoindentation device is employed following a multimodality approach using histological analysis. Coin-shaped implants were placed in vivo at a distance of 200 μm from the cortical bone surface, leading to an initially empty cavity of 200 μm * 4.4 mm. Three New Zealand White rabbits were sacrificed after 4, 7, and 13 weeks of healing time. The bone samples were embedded and analyzed using histological analyses, allowing to distinguish mature and newly formed bone tissue. The bone mechanical properties were then measured in mature and newly formed bone tissue. The results are within the range of hardness and apparent Young's modulus values reported in previous literature. One-way ANOVA test revealed a significant effect of healing time on the indentation modulus (p < 0.001, F = 111.24) and hardness (p < 0.02, F = 3.47) of bone tissue. A Tukey-Kramer analysis revealed that the biomechanical properties of newly formed bone tissue (4 weeks) were significantly different from those of mature bone tissue. The comparison with the results obtained in Mathieu et al. (2011, "Micro-Brillouin Scattering Measurements in Mature and Newly Formed Bone Tissue Surrounding an Implant," J. Biomech. Eng., 133, 021006). shows that bone mass density increases by approximately 13.5% between newly formed bone (7 weeks) and mature bone tissue.     

Validation of subject-specific automated p-FE analysis of the proximal femur

Background: The use of subject-specific finite element (FE) models in clinical practice requires a high level of automation and validation. In Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699] a novel method for generating high-order finite element (p-FE) models from CT scans was presented and validated by experimental observations on two fresh frozen femurs (harvested from a 30 year old male and 21 year old female). Herein, we substantiate the validation process by enlarging the experimental database (54 year old female femur), improving the method and examine its robustness under different CT scan conditions.Approach: A fresh frozen femur of a 54 year old female was scanned under two different environments: in air and immersed in water (dry and wet CT). Thereafter, the proximal femur was quasi-statically loaded in vitro by a 1000 N load. The two QCT scans were manipulated to generate p-FE models that mimic the experimental conditions. We compared p-FE displacements and strains of the wet CT model to the dry CT model and to the experimental results. In addition, the material assignment strategy was reinvestigated. The inhomogeneous Young's modulus was represented in the FE model using two different methods, directly extracted from the CT data and using continuous spatial functions as in Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699].Results: Excellent agreement between dry and wet FE models was found for both displacements and strains, i.e. the method is insensitive to CT conditions and may be used in vivo. Good agreement was also found between FE results and experimental observations. The spatial functions representing Young's modulus are local and do not influence strains and displacements prediction. Finally, the p-FE results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer-aided decision making.