Orientation of orthotropic material properties in a femur FE model: A method based on the principal stresses directions

Biomechanical changes in the proximal femur before and after removal of femoral neck system

BACKGROUND

As an innovative internal fixation system, FNS (femoral neck system) is increasingly being utilized by surgeons for the treatment of femoral neck fractures. At present, there have been numerous finite element analysis experiments studying the immediate stability of FNS and CSS in treating femoral neck fractures. However, there is scarce mechanical analysis available regarding the effects post internal fixation removal. This study aimed to investigate the alterations in mechanical parameters of the proximal femur before and after the removal of FNS (femoral neck system), and to assess potential distinctions in indicators following the extraction of CSS (Cannulated Screws).

METHODS

A proximal femur model was reconstructed using finite element numerical techniques. The models for CSS and FNS were formulated utilizing characteristics and parametric definitions. The internal fixation was combined with a normal proximal femur model to simulate the healing state after fracture surgery. Within the framework of static analysis, consistent stress burdens were applied across the entirety of the models. The total deformation and equivalent stress of the proximal femur were recorded before and after the removal of internal fixation.

RESULTS

Under the standing condition, the total deformation of the model before and after removing CSS was 0.99 mm and 1.10 mm, respectively, indicating an increase of 12%. The total deformation of the model before and after removing FNS was 0.65 mm and 0.76 mm, respectively, indicating an increase of 17%. The equivalent stress for CSS and FNS were 55.21 MPa and 250.67 MPa, respectively. The average equivalent stress on the cross-section of the femoral neck before and after removal of CSS was 7.76 MPa and 6.11 MPa, respectively. The average equivalent stress on the cross-section of the femoral neck before and after removal of FNS was 9.89 MPa and 8.79 MPa, respectively.

CONCLUSIONS

The retention of internal fixation may contribute to improved stability of the proximal femur. However, there still existed risks of stress concentration in internal fixation and stress shielding in the proximal femur. Compared to CSS, the removal of FNS results in larger bone tunnels and insufficient model stability. Further clinical interventions are recommended to address this issue.

Evaluate the effect of bone density variation on stress distribution at the bone-implant interface using numerical analysis

The current study aims to comprehend how different bone densities affect stress distribution at the bone-implant interface. This will help understand the behaviour and help predict success rates of the implant planted in different bone densities. The process of implantation involves the removal of bone from a small portion of the jawbone to replace either a lost tooth or an infected one and an implant is inserted in the cavity made as a result. Now the extent of fixation due to osseointegration is largely dependent on the condition of the bone in terms of the density. Generally, the density of the bone is classified into four categories namely D1, D2, D3, and D4; with D1 being purely cortical and D4 having higher percentage of cancellous bordered by cortical bone. A bone model with a form closely resembling the actual bone was made using 3D CAD software and was meshed using Hyper Mesh. The model was subjected to an oblique load of 120 N at 70° to the vertical to replicate occlusal loading. A finite element static analysis was done using Abaqus software. The stress distribution contours at the bone-implant contact zone were studied closely to understand the changes as a result of the varying density. It was revealed that as the quantity of the cancellous bone increased from D1 to D4 the cortical peak stress levels dropped. The bone density and the corresponding change in the material characteristics was also responsible for the variation in the peak stress and displacement values.

Stress reduction through cortical bone thickening improves bone mechanical behavior in adult female Beclin-1+/- mice

Fragility fractures, which are more prevalent in women, may be significantly influenced by autophagy due to altered bone turnover. As an essential mediator of autophagy, Beclin-1 modulates bone homeostasis by regulating osteoclast and chondrocyte differentiation, however, the alteration in the local bone mechanical environment in female Beclin-1+/- mice remains unclear. In this study, our aim is to investigate the biomechanical behavior of femurs from seven-month-old female wild-type (WT) and Beclin-1+/- mice under peak physiological load, using finite element analysis on micro-CT images. Micro-CT imaging analyses revealed femoral cortical thickening in Beclin-1+/- female mice compared to WT. Three-point bending test demonstrated a 63.94% increase in whole-bone strength and a 61.18% increase in stiffness for female Beclin-1+/- murine femurs, indicating improved biomechanical integrity. After conducting finite element analysis, Beclin-1+/- mice exhibited a 26.99% reduction in von Mises stress and a 31.62% reduction in maximum principal strain in the femoral midshaft, as well as a 36.64% decrease of von Mises stress in the distal femurs, compared to WT mice. Subsequently, the strength-safety factor was determined using an empirical formula, revealing that Beclin-1+/- mice exhibited significantly higher minimum safety factors in both the midshaft and distal regions compared to WT mice. In summary, considering the increased response of bone adaptation to mechanical loading in female Beclin-1+/- mice, our findings indicate that increasing cortical bone thickness significantly improves bone biomechanical behavior by effectively reducing stress and strain within the femoral shaft.

Quantitative Load Dependency Analysis of Local Trabecular Bone Microstructure to Understand the Spatial Characteristics in the Synthetic Proximal Femur

Analysis of the dependency of the trabecular structure on loading conditions is essential for understanding and predicting bone structure formation. Although previous studies have investigated the relationship between loads and structural adaptations, there is a need for an in-depth analysis of this relationship based on the bone region and load specifics. In this study, the load dependency of the trabecular bone microstructure for twelve regions of interest (ROIs) in the synthetic proximal femur was quantitatively analyzed to understand the spatial characteristics under seven different loading conditions. To investigate the load dependency, a quantitative measure, called the load dependency score (LDS), was established based on the statistics of the strain energy density (SED) distribution. The results showed that for the global model and epiphysis ROIs, bone microstructures relied on the multiple-loading condition, whereas the structures in the metaphysis depended on single or double loads. These results demonstrate that a given ROI is predominantly dependent on a particular loading condition. The results confirm that the dependency analysis of the load effects for ROIs should be performed both qualitatively and quantitatively.

Cortical bone continuum damage mechanics constitutive model with stress triaxiality criterion to predict fracture initiation and pattern

A primary objective of finite element human body models (HBMs) is to predict response and injury risk in impact scenarios, including cortical bone fracture initiation, fracture pattern, and the potential to simulate post-fracture injury to underlying soft tissues. Current HBMs have been challenged to predict the onset of failure and bone fracture patterns owing to the use of simplified failure criteria. In the present study, a continuum damage mechanics (CDM) model, incorporating observed mechanical response (orthotropy, asymmetry, damage), was coupled to a novel phenomenological effective strain fracture criterion based on stress triaxiality and investigated to predict cortical bone response under different modes of loading. Three loading cases were assessed: a coupon level notched shear test, whole bone femur three-point bending, and whole bone femur axial torsion. The proposed material model and fracture criterion were able to predict both the fracture initiation and location, and the fracture pattern for whole bone and specimen level tests, within the variability of the reported experiments. There was a dependence of fracture threshold on finite element mesh size, where higher mesh density produced similar but more refined fracture patterns compared to coarser meshes. Importantly, the model was functional, accurate, and numerically stable even for relatively coarse mesh sizes used in contemporary HBMs. The proposed model and novel fracture criterion enable prediction of fracture initiation and resulting fracture pattern in cortical bone such that post-fracture response can be investigated in HBMs.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10-20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Limit analysis of human proximal femur

A limit analysis numerical approach oriented to predict the peak/collapse load of human proximal femur, under two different loading conditions, is presented. A yield criterion of Tsai-Hu-type, expressed in principal stress space, is used to model the orthotropic bone tissues. A simplified human femur 3D model is envisaged to carry on numerical simulation of in-vitro tests borrowed from the relevant literature and to reproduce their findings. A critical discussion, together with possible future developments, is presented.

Subchondral Bone Relative Area and Density in Human Osteoarthritic Femoral Heads Assessed with Micro-CT before and after Mechanical Embedding of the Innovative Multi-Spiked Connecting Scaffold for Resurfacing THA Endoprostheses: A Pilot Study

The multi-spiked connecting scaffold (MSC-Scaffold) prototype is the essential innovation in the fixation of components of resurfacing total hip arthroplasty (THRA) endoprostheses in the subchondral trabecular bone. We conducted the computed micro-tomography (micro-CT) assessment of the subchondral trabecular bone microarchitecture before and after the MSC-Scaffold embedding in femoral heads removed during long-stem endoprosthesis total hip arthroplasty (THA) of different bone densities from 4 patients with hip osteoarthritis (OA). The embedding of the MSC-Scaffold in subchondral trabecular bone causes the change in its relative area (BA/TA, bone area/total area ratio) ranged from 18.2% to 24.7% (translating to the calculated density ρ_B relative change 11.1–14.4%, and the compressive strength S relative change 75.3–122.7%) regardless of its initial density (before the MSC-Scaffold embedding). The densification of the trabecular microarchitecture of subchondral trabecular bone due to the MSC-Scaffold initial embedding gradually decreases with the increasing distance from the apexes of the MSC-Scaffold’s spikes while the spatial extent of this subchondral trabecular bone densification ranged from 1.5 to 2.5 mm (which is about half the height of the MSC-Scaffold’s spikes). It may be suggested, despite the limited number of examined femoral heads, that: (1) the magnitude of the effect of the MSC-Scaffold embedding on subchondral trabecular bone densification may be a factor contributing to the maintenance of the MSC-Scaffold also for decreased initial bone density values, (2) the deeper this effect of the subchondral trabecular bone densification, the better strength of subchondral trabecular bone, and as consequence, the better post-operative embedding of the MSC-Scaffold in the bone should be expected.

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms and assuming isotropic bone material property. The objective of the study is to develop an orthotropic bone remodelling algorithm for evaluation of peri-prosthetic bone adaptation in the uncemented implanted femur. The simulations considered loading conditions from a variety of daily activities. The orthotropic algorithm was tested on 2D and 3D models of the intact femur for verification of predicted results. The predicted orthotropic directionality, based on principal stress directions, was in agreement with the trabecular orientation in a micro-CT data of proximal femur. The validity of the proposed strain-based algorithm was assessed by comparing the predicted results of the orthotropic model with those of the strain-energy-density-based isotropic formulation. Despite agreement in cortical densities [Formula: see text], the isotropic remodelling algorithm tends to predict relatively higher values around the distal tip of the implant as compared to the orthotropic model. Both formulations predicted 4-8% bone resorption in the proximal femur. A linear regression analysis revealed a significant correlation [Formula: see text] between the stresses and strains on the cortex of the proximal femur, predicted by the isotropic and orthotropic formulations. Despite reasonable agreement in peri-prosthetic bone density distributions, the quantitative differences with isotropic model predictions highlight the combined influences of bone orthotropy and mechanical stimulus in the adaptation process.

Influence of a metaphyseal sleeve on the stress-strain state of a bone-tumor implant system in the distal femur: an experimental and finite element analysis

Background

Aseptic loosening of distal femoral tumor implants significantly correlates with the resection length. We designed a new “sleeve” that is specially engaged in the metaphysis at least 5 cm proximal to the knee joint line to preserve as much bone stock as possible. This study investigates the influence of a metaphyseal sleeve on the stress-strain state of a bone tumor implant system in the distal femur.

Methods

Cortex strains in intact and implanted femurs were predicted with finite element (FE) models. Moreover strains were experimentally measured in a cadaveric femur with and without a sleeve and stem under an axial compressive load of 1000 N. The FE models, which were validated by linear regression, were used to investigate the maximal von Mises stress and the implanted-to-intact (ITI) ratios of strain in the femur with single-legged stance loading under immediate postoperative and osseointegration conditions.

Results

Good agreement was noted between the experimental measurements and numerical predictions of the femoral strains (coefficient of determination (R²) ≥ 0.95; root-mean-square error (RMSE%) ≈ 10%). The ITI ratios for the metaphysis were between 13 and 28% and between 10 and 21% under the immediate postoperative and osseointegration conditions, respectively, while the ITI ratios for the posterior and lateral cortices around the tip of the stem were 110% and 119% under the immediate-postoperative condition, respectively, and 114% and 101% under the osseointegration condition, respectively. The maximal von Mises stresses for the implanted femur were 113.8 MPa and 43.41 MPa under the immediate postoperative and osseointegration conditions, which were 284% and 47% higher than those in the intact femur (29.6 MPa), respectively.

Conclusions

This study reveals that a metaphyseal sleeve may cause stress shielding relative to the intact femur, especially in the distal metaphysis. Stress concentrations might mainly occur in the posterior cortex around the tip of the stem. However, stress concentrations may not be accompanied by periprosthetic fracture under the single-legged stance condition.

Anisotropic computational modelling of bony structures from CT data: An almost automatic procedure

BACKGROUND AND OBJECTIVE

The use of modelling techniques that combine CT data and bone tissue micromechanics is spreading in computational biomechanics. Finite Element models show great potential in surgical planning of intervention and in prediction of stress and strain fields through a non-invasive method. The main challenge pertains to the reliable characterization of bone mechanical behaviour. An almost automatic procedure is here defined, which provides computational models of bony structures considering the actual anisotropy of bone tissue response. The innovative aspect resides on the automatic detection of the directions of anisotropy as the eigenvectors of a three-dimensional distribution matrix of HU values.

METHODS

The procedure combines CT data and micromechanics modelling techniques. Regarding a specific location, the procedure reports both the orthotropic elastic constants, by the analysis of the local HU value, and the anisotropic material directions, by the analysis of the HU values distribution around the specific location.

RESULTS

The procedure returns the distribution of bone tissue orthotropic elasticity tensor. The procedure proves to correctly respect the differentiation between cortical and trabecular bone. Principal directions show to be consistent with experimental data from ultrasound measurements. Regarding the material mapping from voxel to FE model, the developed strategies show to be reliable, leading to marginal errors (lower than 10%) for most of CT voxels (more than 90%). The computational analyses of typical structural loading conditions lead to strain values that are comparable with results from strain gauges experimentations. The development and the exploitation of FE models of different bony structures allow assessing the reliability of the procedure for cortical bone.

CONCLUSIONS

The results highlight the potentialities of the procedure in providing accurate patient-specific biomechanical models of bony structures starting from CT data. The accuracy and the automatism of the procedure are important factors for the development of real time clinical tools. The main limitations of this work remain the not fully automatism and the reliability assessment, which is based mainly on cortical bone regions only.

The effect of rotational degree and routine activity on the risk of collapse in transtrochanteric rotational osteotomy for osteonecrosis of the femoral head-a finite element analysis

To explore the mechanical mechanism and provide preoperative planning basis for transtrochanteric rotational osteotomy (TRO) procedure, a joint-preserving procedure for osteonecrosis of the femoral head. Eleven TRO finite element femurs with the most common types of necrosis were analyzed under multi-loading conditions. Thereafter, we made a comprehensive evaluation by considering the anatomy characters, daily activities, and risk indicators contain necrosis expansion trend, necrotic blood supply pressure, and the risk of fracture. The risk of fracture (ROF) is the lowest when standing on feet and increases gradually during normal walking and walking upstairs and downstairs. Compared with posterior rotation, rotating forward keeps more elements at low risk. Additionally, the correlation analysis shows it has a strong negative correlation (R² = 0.834) with the average modulus of the roof. TRO finally decreased the stress and energy effectively. However, the stress and strain energy arise when rotated posteriorly less than 120°. The comprehensive evaluation observed that rotating forward 90°could reduce the total risks to 64%. TRO is an effective technique to prevent collapse. For the anterior and superior large necrosis, we recommend to rotate forward 60° to 90° (more efficient) or backward 180°. The methodology followed in this study could provide accurate and personalize preoperative planning.

Graphical Abstract

Comparative Study of Femur Bone Having Different Boundary Conditions and Bone Structure Using Finite Element Method

Background:

Femur bone is an important part in human which basically gives stability and support to carry out all day to day activities. It carries loads from upper body to lower abdomen.

Objective:

In this work, the femur having composite structure with cortical, cancellous and bone marrow cavity is bisected from condyle region with respect to 25%, 50% and 75% of its height. There is considerable difference in the region chosen for fixing all degrees of freedom in the analysis of femur.

Methods:

The CT scans are taken, and 3D model is developed using MIMICS. The developed model is used for static structural analysis by varying the load from 500N to 3000N.

Results:

The findings for 25% bisected femur model report difference in directional deformation less than 5% for loads 2000N and less. In the study comparing fully solid bone and the composite bone, the total deformation obtained for a complete solid bone was 3.5 mm which was 18.7% less than that determined for the composite bone.

Conclusion:

The standardization for fixing the bone is developed. And it is required to fix the distal end always with considering full femur bone.

Statistical analysis of the inter-individual variations of the bone shape, volume fraction and fabric and their correlations in the proximal femur

Including structural information of trabecular bone improves the prediction of bone strength and fracture risk. However, this information is available in clinical CT scans, only for peripheral bones. We hypothesized that a correlation exists between the shape of the bone, its volume fraction (BV/TV) and fabric, which could be characterized using statistical modeling. High-resolution peripheral computed tomography (HR-pQCT) images of 73 proximal femurs were used to build a combined statistical model of shape, BV/TV and fabric. The model was based on correspondence established by image registration and by morphing of a finite element mesh describing the spatial distribution of the bone properties. Results showed no correlation between the distribution of bone shape, BV/TV and fabric. Only the first mode of variation associated with density and orientation showed a strong relationship (R²>0.8). In addition, the model showed that the anisotropic information of the proximal femur does not vary significantly in a population of healthy, osteoporotic and osteopenic samples. In our dataset, the average anisotropy of the population was able to provide a close approximation of the patient-specific anisotropy. These results were confirmed by homogenized finite element (hFE) analyses, which showed that the biomechanical behavior of the proximal femur was not significantly different when the average anisotropic information of the population was used instead of patient-specific fabric extracted from HR-pQCT. Based on these findings, it can be assumed that the fabric information of the proximal femur follows a similar structure in an elderly population of healthy, osteopenic and osteoporotic proximal femurs.

Accounting for spatial variation of trabecular anisotropy with subject-specific finite element modeling moderately improves predictions of local subchondral bone stiffness at the proximal tibia

INTRODUCTION

Previously, a finite element (FE) model of the proximal tibia was developed and validated against experimentally measured local subchondral stiffness. This model indicated modest predictions of stiffness (R²=0.77, normalized root mean squared error (RMSE%)=16.6%). Trabecular bone though was modeled with isotropic material properties despite its orthotropic anisotropy. The objective of this study was to identify the anisotropic FE modeling approach which best predicted (with largest explained variance and least amount of error) local subchondral bone stiffness at the proximal tibia.

METHODS

Local stiffness was measured at the subchondral surface of 13 medial/lateral tibial compartments using in situ macro indentation testing. An FE model of each specimen was generated assuming uniform anisotropy with 14 different combinations of cortical- and tibial-specific density-modulus relationships taken from the literature. Two FE models of each specimen were also generated which accounted for the spatial variation of trabecular bone anisotropy directly from clinical CT images using grey-level structure tensor and Cowin's fabric-elasticity equations. Stiffness was calculated using FE and compared to measured stiffness in terms of R² and RMSE%.

RESULTS

The uniform anisotropic FE model explained 53-74% of the measured stiffness variance, with RMSE% ranging from 12.4 to 245.3%. The models which accounted for spatial variation of trabecular bone anisotropy predicted 76-79% of the variance in stiffness with RMSE% being 11.2-11.5%.

CONCLUSIONS

Of the 16 evaluated finite element models in this study, the combination of Synder and Schneider (for cortical bone) and Cowin's fabric-elasticity equations (for trabecular bone) best predicted local subchondral bone stiffness.

Biomechanical Role of Bone Anisotropy Estimated on Clinical CT Scans by Image Registration

Image-based modeling is a popular approach to perform patient-specific biomechanical simulations. Accurate modeling is critical for orthopedic application to evaluate implant design and surgical planning. It has been shown that bone strength can be estimated from the bone mineral density (BMD) and trabecular bone architecture. However, these findings cannot be directly and fully transferred to patient-specific modeling since only BMD can be derived from clinical CT. Therefore, the objective of this study was to propose a method to predict the trabecular bone structure using a µCT atlas and an image registration technique. The approach has been evaluated on femurs and patellae under physiological loading. The displacement and ultimate force for femurs loaded in stance position were predicted with an error of 2.5% and 3.7%, respectively, while predictions obtained with an isotropic material resulted in errors of 7.3% and 6.9%. Similar results were obtained for the patella, where the strain predicted using the registration approach resulted in an improved mean squared error compared to the isotropic model. We conclude that the registration of anisotropic information from of a single template bone enables more accurate patient-specific simulations from clinical image datasets than isotropic model.

The influence of bone density and anisotropy in finite element models of distal radius fracture osteosynthesis: Evaluations and comparison to experiments

Continuum-level finite element (FE) models can be used to analyze and improve osteosynthesis procedures for distal radius fractures (DRF) from a biomechanical point of view. However, previous models oversimplified the bone material and lacked thorough experimental validation. The goal of this study was to assess the influence of local bone density and anisotropy in FE models of DRF osteosynthesis for predictions of axial stiffness, implant plate stresses, and screw loads. Experiments and FE analysis were conducted in 25 fresh frozen cadaveric radii with DRFs treated by volar locking plate osteosynthesis. Specimen specific geometries were captured using clinical quantitative CT (QCT) scans of the prepared samples. Local bone material properties were computed based on high resolution CT (HR-pQCT) scans of the intact radii. The axial stiffness and individual screw loads were evaluated in FE models, with (1) orthotropic inhomogeneous (OrthoInhom), (2) isotropic inhomogeneous (IsoInhom), and (3) isotropic homogeneous (IsoHom) bone material and compared to the experimental axial stiffness and screw-plate interface failures. FE simulated and experimental axial stiffness correlated significantly (p<0.0001) for all three model types. The coefficient of determination was similar for OrthoInhom (R(2)=0.807) and IsoInhom (R(2)=0.816) models but considerably lower for IsoHom models (R(2)=0.500). The peak screw loads were in qualitative agreement with experimental screw-plate interface failure. Individual loads and implant plate stresses of IsoHom models differed significantly (p<0.05) from OrthoInhom and IsoInhom models. In conclusion, including local bone density in FE models of DRF osteosynthesis is essential whereas local bone anisotropy hardly effects the models׳ predictive abilities.

Full-Field Strain Measurement During Mechanical Testing of the Human Femur at Physiologically Relevant Strain Rates

Understanding the mechanical properties of human femora is of great importance for the development of a reliable fracture criterion aimed at assessing fracture risk. Earlier ex vivo studies have been conducted by measuring strains on a limited set of locations using strain gauges (SGs). Digital image correlation (DIC) could instead be used to reconstruct the full-field strain pattern over the surface of the femur. The objective of this study was to measure the full-field strain response of cadaver femora tested at a physiological strain rate up to fracture in a configuration resembling single stance. The three cadaver femora were cleaned from soft tissues, and a white background paint was applied with a random black speckle pattern over the anterior surface. The mechanical tests were conducted up to fracture at a constant displacement rate of 15 mm/s, and two cameras recorded the event at 3000 frames per second. DIC was performed to retrieve the full-field displacement map, from which strains were derived. A low-pass filter was applied over the measured displacements before the crack opened in order to reduce the noise level. The noise levels were assessed using a dedicated control plate. Conversely, no filtering was applied at the frames close to fracture to get the maximum resolution. The specimens showed a linear behavior of the principal strains with respect to the applied force up to fracture. The strain rate was comparable to the values available in literature from in vivo measurements during daily activities. The cracks opened and fully propagated in less than 1 ms, and small regions with high values of the major principal strains could be spotted just a few frames before the crack opened. This corroborates the hypothesis of a strain-driven fracture mechanism in human bone. The data represent a comprehensive collection of full-field strains, both at physiological load levels and up to fracture. About 10,000 points were tracked on each bone, providing superior spatial resolution compared to ∼15 measurements typically collected using SGs. These experimental data collection can be further used for validation of numerical models, and for experimental verification of bone constitutive laws and fracture criteria.

Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=-0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.