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

Numerical analysis of hip fracture due to a sideways fall

The primary purpose of this paper is to outline a methodology for evaluating the likelihood of cortical bone fracture in the proximal femur in the event of a sideways fall. The approach includes conducting finite element (FE) analysis in which the cortical bone is treated as an anisotropic material, and the admissibility of the stress field is validated both in tension and compression regime. In assessing the onset of fracture, two methodologies are used, namely the Critical Plane approach and the Microstructure Tensor approach. The former is employed in the tension regime, while the latter governs the conditions at failure in compression. The propagation of localized damage is modeled using a constitutive law with embedded discontinuity (CLED). In this approach, the localized deformation is described by a homogenization procedure in which the average properties of cortical tissue intercepted by a macrocrack are established. The key material properties governing the conditions at failure are specified from a series of independent material tests conducted on cortical bone samples tested at different orientations relative to the loading direction. The numerical analysis deals with simulations of experiments involving the sideways fall, and the results are compared with the experimental data. This includes both the evolution of fracture pattern and the local load-displacement characteristics. The proposed approach is numerically efficient, and the results do not display a pathological mesh-dependency. Also, in contrast to the XFEM approach, the analysis does not require any extra degrees of freedom.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

A novel mechanical parameter to quantify the microarchitecture effect on apparent modulus of trabecular bone: A computational analysis of ineffective bone mass

BACKGROUND

One of the characteristics of osteoporotic bone is the deterioration of trabecular microarchitecture. Previous studies have shown microarchitecture alone can vary the apparent modulus of trabecular bone significantly independent of bone volume fraction (BV/TV) from morphological and topological perspectives. However, modulus is a mechanical quantity and there is a lack of mechanical explanatory parameters. This study aims to propose a novel mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone.

MATERIALS AND METHODS

Fourteen human female cadaveric vertebrae were scanned with a dual-energy X-ray (DXA) equipment followed by a micro-CT (μCT) system at 18 μm isotropic resolution. Four trabecular bone specimens (3.46 × 3.46 × 3.46 mm) were obtained from each vertebral body and converted to voxel-based micro finite element (μFE) models. The apparent modulus (E) of the μFE model was computed using a linear micro finite element analysis (μFEA). The normalized apparent modulus (E*) was computed as E divided by BV/TV. The relationship between E and BV/TV was analyzed by linear, power-law and exponential regressions. Linear regression was performed between E* and BV/TV. Ineffective bone mass (InBM) was defined as the bone mass with a negligible contribution to the load-resistance and represented by elements with von Mises stress less than a certain stress threshold. InBM was quantified as the low von Mises stress ratio (LS_VMR), which is the ratio of the number of InBM elements to the total number of elements in the μFE model. An incremental search technique with coarse and fine search intervals of 10 and 1 MPa, respectively, was adopted to determine the stress threshold for calculating LS_VMR of the μFE model. Correlation between E* and LS_VMR was analyzed using linear and power-law models for each stress threshold. The threshold producing the highest coefficient of determination (R²) in the correlation between E* and LS_VMR was taken as the optimal stress threshold for calculating LS_VMR. Linear regression was performed between E and LS_VMR. Multiple linear regression of E against both BV/TV and LS_VMR was further analyzed.

RESULTS

E significantly (p < .001) correlates to BV/TV whereas E* has no significant (p = .75) correlation with BV/TV. Incremental search suggests 59 MPa to be the optimal stress threshold for calculating LS_VMR. BV/TV alone can explain 59% of the variation in E using power-law regression model (E = 2254.64BV/TV^1.04, R² = 0.59, p < .001). LS_VMR alone can explain 48% of the variation in E using linear regression model (E = 1696.4-1647.1LS_VMR, R² = 0.48, p < .001). With these two predictors taken into consideration, 95% of the variation in E can be explained in a multiple linear regression model (E = 1364.89 + 2184.37BV/TV - 1605.38LS_VMR, adjusted R² = 0.95, p < .001).

CONCLUSION

LS_VMR can be adopted as the mechanical parameter to quantify the microarchitecture effect on the apparent modulus of trabecular bone.

Coupling Musculoskeletal Dynamics and Subject-Specific Finite Element Analysis of Femoral Cortical Bone Failure after Endoprosthetic Knee Replacement

Background and Objective

A common reconstruction procedure after a wide resection of bone tumors around the knee is endoprosthetic knee replacement. The aim of this study was to investigate the characteristics of bone injury of the patient after endoprosthetic knee replacement during walking.

Methods

A subject-specific finite element model of the femur-prosthesis-tibia complex was established via CT scans. To obtain its physiologically realistic loading environments, the musculoskeletal inverse dynamic analysis was implemented. The extracted muscle forces and ground forces were then applied to the finite element model to investigate bone stress distribution at various stages of the gait cycle.

Results

The maximum femur stress of each stage varied from 33.14 MPa to 70.61 MPa in the gait cycle. The stress concentration position with a distance of 267.2 mm to the tibial plateau showed a good agreement with the patient injury data.

Conclusions

Overall results indicated the reasonability of the simulation method to determine loading environments and injury characteristics which the patient experienced with knee endoprosthesis during walking.

Exercise Early and Often: Effects of Physical Activity and Exercise on Women's Bone Health

In 2011 over 1.7 million people were hospitalized because of a fragility fracture, and direct costs associated with osteoporosis treatment exceeded 70 billion dollars in the United States. Failure to reach and maintain optimal peak bone mass during adulthood is a critical factor in determining fragility fracture risk later in life. Physical activity is a widely accessible, low cost, and highly modifiable contributor to bone health. Exercise is especially effective during adolescence, a time period when nearly 50% of peak adult bone mass is gained. Here, we review the evidence linking exercise and physical activity to bone health in women. Bone structure and quality will be discussed, especially in the context of clinical diagnosis of osteoporosis. We review the mechanisms governing bone metabolism in the context of physical activity and exercise. Questions such as, when during life is exercise most effective, and what specific types of exercises improve bone health, are addressed. Finally, we discuss some emerging areas of research on this topic, and summarize areas of need and opportunity.

Micro-Finite Element analysis will overestimate the compressive stiffness of fractured cancellous bone

Recently, micro-Finite Element (micro-FE) analysis based on High Resolution peripheral Quantitative CT (HRpQCT) images was introduced to quantify the state of fracture healing (de Jong et al., 2014). That study suggested that the direct post-fracture stiffness may be overestimated by micro-FE. The aim of this study was to investigate this further by measuring the loss in stiffness of cancellous bone samples under compressive loading and to compare this with predictions based on micro-FE analyses and bone microstructural and fracture morphology. Sixty porcine trabecular cores were micro-CT scanned and tested in compression before and after inducing a fracture in 4 different manners. The loss in stiffness as measured in the experiment was compared to that calculated from micro-FE analysis. Additionally, bone morphology parameters and fracture thickness were calculated. The experimentally measured loss in stiffness ranged from 37% to 80%. The losses calculated from the micro-FE analyses were lower and ranged from 36% to 61%, while in one case an increase in stiffness was calculated. For 2 of the 4 experiments, the results of the experiment and micro-FE analyses were significantly different. Only for very smooth fractures good agreement was obtained between FE and experimental results. The loss in stiffness did not correlate with any investigated bone morphology parameter or the thickness of the fracture region. It was concluded that micro-FE analysis can severely overestimate the stiffness of fractured bone depending on the type of fracture, but in the case of smooth fractures good estimates are possible.

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

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

Specimen-specific vertebral fracture modeling: a feasibility study using the extended finite element method

Osteoporotic vertebral body fractures are an increasing clinical problem among the aging population. Specimen-specific finite element models, derived from quantitative computed tomography (QCT), have the potential to more accurately predict failure loads in the vertebra. Additionally, the use of extended finite element modeling (X-FEM) allows for a detailed analysis of crack initiation and propagation in various materials. Our aim was to study the feasibility of QCT/X-FEM analysis to predict fracture properties of vertebral bodies. Three cadaveric specimens were obtained, and the L3 vertebrae were excised. The vertebrae were CT scanned to develop computational models and mechanically tested in compression to measure failure load, stiffness and to observe crack location. One vertebra was used for calibration of the material properties from experimental results and CT gray-scale values. The two additional specimens were used to assess the model prediction. The resulting QCT/X-FEM model of the specimen used for calibration had 2 and 4% errors in stiffness and failure load, respectively, compared with the experiment. The predicted failure loads of the additional two vertebrae were larger by about 41-44% when compared to the measured values, while the stiffness differed by 129 and 40%. The predicted fracture patterns matched fairly well with the visually observed experimental cracks. Our feasibility study indicated that the QCT/X-FEM method used to predict vertebral compression fractures is a promising tool to consider in future applications for improving vertebral fracture risk prediction in the elderly.

A survey of micro-finite element analysis for clinical assessment of bone strength: the first decade

Micro-Finite Element (micro-FE) analysis is now widely used in biomedical research as a tool to derive bone mechanical properties as they relate to its microstructure. With the development of in vivo high-resolution peripheral quantitative CT (HR-pQCT) scanners, it can now be applied to analyze bone in-vivo in the peripheral skeleton. In this survey, the results of several experimental and clinical studies are summarized that addressed the feasibility of this approach to predict bone strength in-vivo. Specific questions that will be addressed are: how accurate are strength predictions based on micro-FE; how reproducible are the results; and, is it a better predictor of bone fracture risk than DXA based measures? Based on results of experimental studies, it is first concluded that micro-FE based on HR-pQCT images can accurately predict the strength of the distal radius during a fall on the outstretched hand using either linear elastic analysis, implementing a 'Pistoia criterion' or similar criterion in combination with an 'effective' Young's modulus or using non-linear analyses. When evaluating results of clinical reproducibility studies, it is concluded that for single-center studies, errors at the radius are less than 4.4% and 3.7% and at the tibia less than 3.6% and 2.3% for stiffness and strength, respectively. In multicenter trials, however, these errors can be increased by some 1.8% and 1.4% for stiffness and strength, respectively. Finally, based on the results of large cohort studies, it is concluded that micro-FE calculated stiffness better separates cases from controls than bone density parameters for subjects with fragility fractures at any site, but not for subjects with only radius fractures. In this latter case, however, combinations of micro-FE derived parameters can significantly improve the separation.