A novel approach to estimate trabecular bone anisotropy from stress tensors

The impact of the parameters of the constitutive model on the distribution of strain in the femoral head

The rapid spread of the finite element method has caused that it has become, among other methods, the standard tool for pre-clinical estimates of bone properties. This paper presents an application of this method for the calculation and prediction of strain and stress fields in the femoral head. The aim of the work is to study the influence of the considered anisotropy and heterogeneity of the modeled bone on the mechanical fields during a typical gait cycle. Three material models were tested with different properties of porous bone carried out in literature: a homogeneous isotropic model, a heterogeneous isotropic model, and a heterogeneous anisotropic model. In three cases studied, the elastic properties of the bone were determined basing on the Zysset-Curnier approach. The tensor of elastic constants defining the local properties of porous bone is correlated with a local porosity and a second order fabric tensor describing the bone microstructure. In the calculations, a model of the femoral head generated from high-resolution tomographic scans was used. Experimental data were drawn from publicly available database "Osteoporotic Virtual Physiological Human Project." To realistically reflect the load on the femoral head, main muscles were considered, and their contraction forces were determined based on inverse kinematics. For this purpose, the results from OpenSim packet were used. The simulations demonstrated that differences between the results predicted by these material models are significant. Only the anisotropic model allowed for the plausible distribution of stresses along the main trabecular groups. The outcomes also showed that the precise evaluation of the mechanical fields is critical in the context of bone tissue remodeling under mechanical stimulations.

The Effect on the Fracture Healing following Femoral Neck Shortening after Osteoporotic Femoral Neck Fracture Treated with Internal Fixation: Finite Element Analysis

Objective

To evaluate the stress status of fracture site caused by femoral neck shortening and to analyze the stress of fracture site and the implants from the finite element point of view.

Methods

CT scan data of hip of a normal adult female were collected. Three-dimensional reconstruction MICs and related module function simulation was used to establish the postoperative shortening model of femoral neck fracture with Pauwels angle > 50°, which was treated with cannulated screws. The models were divided into four groups: normal femoral neck, shortening in 2.5 mm, shortening in 7.5 mm, and shortening in 12.5 mm. The finite element analysis software msc.nastran2012 was used, and the data of maximum stress and stress nephogram of fracture site and implants were carried out.

Results

From normal femoral neck to shortening in 12.5 mm of the femoral neck, the maximum tensile stress increased gradually in the fracture site above the cannulated screws while compressive stress decreased gradually in the fracture site below the cannulated screws, and the maximum stress of the cannulated screws increased gradually with obvious stress concentration at the screw holes in the fracture site, and the peak value of stress concentration was about 179 MPa.

Conclusion

The biomechanical environment of the fracture site changed by femoral neck shortening. With the increasing of femoral neck shortening, the stress of the fracture site and implants would be uneven; then, the stability of fracture site would become worse, and the possibility of implant sliding or even breakage would be increased.

Additively manufactured biodegradable porous metals

Partially due to the unavailability of ideal bone substitutes, the treatment of large bony defects remains one of the most important challenges of orthopedic surgery. Additively manufactured (AM) biodegradable porous metals that have emerged since 2018 provide unprecedented opportunities for fulfilling the requirements of an ideal bone implant. First, the multi-scale geometry of these implants can be customized to mimic the human bone in terms of both micro-architecture and mechanical properties. Second, a porous structure with interconnected pores possesses a large surface area, which is favorable for the adhesion and proliferation of cells and, thus, bony ingrowth. Finally, the freeform geometrical design of such biomaterials could be exploited to adjust their biodegradation behavior so as to maintain the structural integrity of the implant during the healing process while ensuring that the implant disappears afterwards, paving the way for full bone regeneration. While the AM biodegradable porous metals that have been studied so far have shown many unique properties as compared to their solid counterparts, the unprecedented degree of flexibility in their geometrical design has not yet been fully exploited to optimize their properties and performance. In order to develop the ideal bone implants, it is important to take advantage of the full potential of AM biodegradable porous metals through detailed and systematic study on their biodegradation behavior, mechanical properties, biocompatibility, and bone regeneration performance. This review paper presents the state of the art in AM biodegradable porous metals and is focused on the effects of material type, processing, geometrical design, and post-AM treatments on the mechanical properties, biodegradation behavior, in vitro biocompatibility, and in vivo bone regeneration performance of AM porous Mg, Fe, and Zn as well as their alloys. We also identify a number of knowledge gaps and the challenges encountered in adopting AM biodegradable porous metals for orthopedic applications and suggest some promising areas for future research.

Corrosion fatigue behavior of additively manufactured biodegradable porous zinc

Additively manufactured (AM) biodegradable porous zinc exhibits great potential as a promising bone-substituting biomaterial. However, there is no information whatsoever available regarding its corrosion fatigue behavior. In this study, we used direct metal printing to fabricate topologically ordered biodegradable porous zinc based on a diamond unit cell. We compared the compression-compression fatigue behavior of AM porous zinc in air and in revised simulated body fluid (r-SBF). The fatigue strength of AM porous zinc was high in air (i.e., 70% of its yield strength) and even higher in r-SBF (i.e., 80% of its yield strength). The high value of the relative fatigue strength in air could be attributed to the good ductility of pure zinc itself. The formation of corrosion products around the strut junctions might explain the higher fatigue strength of AM zinc in r-SBF. Furthermore, we compared the fatigue behavior of a uniform design of the AM porous zinc with a functionally graded design. The functionally graded structure exhibited higher relative fatigue strengths than the uniform structure. The inspection of the fatigue crack distribution revealed that the functionally graded design controlled the sequence of crack initiation, which occurred early in the thicker struts and moved towards the thinner struts over time. The theoretical fatigue life models suggest that optimizing the functionally graded structure could be used as an effective means to improve the fatigue life of AM porous zinc. In conclusion, the favorable fatigue behavior of AM porous zinc further highlights its potential as a promising bone-substituting biomaterial. STATEMENT OF SIGNIFICANCE: Additively manufactured (AM) biodegradable porous zinc exhibits great potential for the treatment of large bony defects. However, there is no information available regarding its corrosion fatigue behavior. Here, we compared the fatigue behavior of AM porous zinc in air and in revised simulated body fluid (r-SBF). The fatigue strength of AM porous Zn was even higher in r-SBF than in air, which were attributed to the formation of corrosion products. Furthermore, we found that the functionally graded structure controlled the sequence of crack initiation in differently sized struts and exhibited higher relative fatigue strengths than the uniform structure, suggesting that optimizing the functionally graded structure could be an effective means to improve the fatigue life of AM porous Zn.

Additively manufactured functionally graded biodegradable porous iron

Additively manufactured (AM) functionally graded porous metallic biomaterials offer unique opportunities to satisfy the contradictory design requirements of an ideal bone substitute. However, no functionally graded porous structures have ever been 3D-printed from biodegradable metals, even though biodegradability is crucial both for full tissue regeneration and for the prevention of implant-associated infections in the long term. Here, we present the first ever report on AM functionally graded biodegradable porous metallic biomaterials. We made use of a diamond unit cell for the topological design of four different types of porous structures including two functionally graded structures and two reference uniform structures. Specimens were then fabricated from pure iron powder using selective laser melting (SLM), followed by experimental and computational analyses of their permeability, dynamic biodegradation behavior, mechanical properties, and cytocompatibility. It was found that the topological design with functional gradients controlled the fluid flow, mass transport properties and biodegradation behavior of the AM porous iron specimens, as up to 4-fold variations in permeability and up to 3-fold variations in biodegradation rate were observed for the different experimental groups. After 4 weeks of in vitro biodegradation, the AM porous scaffolds lost 5-16% of their weight. This falls into the desired range of biodegradation rates for bone substitution and confirms our hypothesis that topological design could indeed accelerate the biodegradation of otherwise slowly degrading metals, like iron. Even after 4 weeks of biodegradation, the mechanical properties of the specimens (i.e., E = 0.5-2.1 GPa, σ_y = 8-48 MPa) remained within the range of the values reported for trabecular bone. Design-dependent cell viability did not differ from gold standard controls for up to 48 h. This study clearly shows the great potential of AM functionally graded porous iron as a bone substituting material. Moreover, we demonstrate that complex topological design permits the control of mechanical properties, degradation behavior of AM porous metallic biomaterials. STATEMENT OF SIGNIFICANCE: No functionally graded porous structures have ever been 3D-printed from biodegradable metals, even though biodegradability is crucial both for full tissue regeneration and for the prevention of implant-associated infections in the long term. Here, we present the first report on 3D-printed functionally graded biodegradable porous metallic biomaterials. Our results suggest that topological design in general, and functional gradients in particular can be used as an important tool for adjusting the biodegradation behavior of AM porous metallic biomaterials. The biodegradation rate and mass transport properties of AM porous iron can be increased while maintaining the bone-mimicking mechanical properties of these biomaterials. The observations reported here underline the importance of proper topological design in the development of AM porous biodegradable metals.

Validation of distal radius failure load predictions by homogenized- and micro-finite element analyses based on second-generation high-resolution peripheral quantitative CT images

This study developed a well-standardized and reproducible approach for micro-finite element (mFE) and homogenized-FE (hFE) analyses that can accurately predict the distal radius failure load using either mFE or hFE models when using the approaches and parameters developed in this study.

INTRODUCTION

Micro-FE analyses based on high-resolution peripheral quantitative CT (HR-pQCT) images are frequently used to predict distal radius failure load. With the introduction of a second-generation HR-pQCT device, however, the default modelling approach no longer provides accurate results. The aim of this study was to develop a well-standardized and reproducible approach for mFE and hFE analyses that can provide precise and accurate results for distal radius failure load predictions based on second-generation HR-pQCT images.

METHODS

Second-generation HR-pQCT was used to scan the distal 20-mm section of 22 cadaver radii. The sections were excised and mechanically tested afterwards. For these sections, mFE and hFE models were made that were used to identify required material parameters by comparing predicted and measured results. Using these parameters, the models were cropped to represent the 10-mm region recommended for clinical studies to test their performance for failure load prediction.

RESULTS

After identification of material parameters, the measured failure load of the 20-mm segments was in good agreement with the results of mFE models (R² = 0.969, slope = 1.035) and hFE models (R² = 0.966, slope = 0.890). When the models were restricted to the clinical region, mFE still accurately predicted the measured failure load (R² = 0.955, slope = 1.021), while hFE predictions were precise but tended to overpredict the failure load (R² = 0.952, slope = 0.780).

CONCLUSIONS

It was concluded that it is possible to accurately predict the distal radius failure load using either mFE or hFE models when using the approaches and parameters developed in this study.

The Role of the Size and Location of the Tumors and of the Vertebral Anatomy in Determining the Structural Stability of the Metastatically Involved Spine: a Finite Element Study

Vertebral fractures associated with the loss of structural integrity of neoplastic vertebrae are common, and determined to the deterioration of the bone quality in the lesion area. The prediction of the fracture risk in metastatically involved spines can guide in deciding if preventive solutions, such as medical prophylaxis, bracing, or surgery are indicated for the patient. In this study, finite element models of 22 thoracolumbar vertebrae were built based on CT scans of three spines, covering a wide spectrum of possible clinical scenarios in terms of age, bone quality and degenerative features, taking into account the local material properties of bone tissue. Simulations were performed in order to investigate the effect of the size and location of the tumoral lesion, the bone quality and the vertebral level in determining the structural stability of the neoplastic vertebrae. Tumors with random size and positions were added to the models, for a total of 660 simulations in which a compressive load was simulated. Results highlighted the fundamental role of the tumor size, whereas the other parameters had a lower, but non-negligible impact on the axial collapse of the vertebra, the vertebral bulge in the transverse plane and the canal narrowing under the application of the load. All the considered parameters are radiologically measurable, and can therefore be translated in a straightforward way to the clinical practice to support decisions about preventive treatment of metastatic fractures.

A novel registration-based methodology for prediction of trabecular bone fabric from clinical QCT: A comprehensive analysis

Osteoporosis leads to hip fractures in aging populations and is diagnosed by modern medical imaging techniques such as quantitative computed tomography (QCT). Hip fracture sites involve trabecular bone, whose strength is determined by volume fraction and orientation, known as fabric. However, bone fabric cannot be reliably assessed in clinical QCT images of proximal femur. Accordingly, we propose a novel registration-based estimation of bone fabric designed to preserve tensor properties of bone fabric and to map bone fabric by a global and local decomposition of the gradient of a non-rigid image registration transformation. Furthermore, no comprehensive analysis on the critical components of this methodology has been previously conducted. Hence, the aim of this work was to identify the best registration-based strategy to assign bone fabric to the QCT image of a patient’s proximal femur. The normalized correlation coefficient and curvature-based regularization were used for image-based registration and the Frobenius norm of the stretch tensor of the local gradient was selected to quantify the distance among the proximal femora in the population. Based on this distance, closest, farthest and mean femora with a distinction of sex were chosen as alternative atlases to evaluate their influence on bone fabric prediction. Second, we analyzed different tensor mapping schemes for bone fabric prediction: identity, rotation-only, rotation and stretch tensor. Third, we investigated the use of a population average fabric atlas. A leave one out (LOO) evaluation study was performed with a dual QCT and HR-pQCT database of 36 pairs of human femora. The quality of the fabric prediction was assessed with three metrics, the tensor norm (TN) error, the degree of anisotropy (DA) error and the angular deviation of the principal tensor direction (PTD). The closest femur atlas (CTP) with a full rotation (CR) for fabric mapping delivered the best results with a TN error of 7.3 ± 0.9%, a DA error of 6.6 ± 1.3% and a PTD error of 25 ± 2°. The closest to the population mean femur atlas (MTP) using the same mapping scheme yielded only slightly higher errors than CTP for substantially less computing efforts. The population average fabric atlas yielded substantially higher errors than the MTP with the CR mapping scheme. Accounting for sex did not bring any significant improvements. The identified fabric mapping methodology will be exploited in patient-specific QCT-based finite element analysis of the proximal femur to improve the prediction of hip fracture risk.

A novel in silico method to quantify primary stability of screws in trabecular bone

Insufficient primary stability of screws in bone leads to screw loosening and failure. Unlike conventional continuum finite-element models, micro-CT based finite-element analysis (micro-FE) is capable of capturing the patient-specific bone micro-architecture, providing accurate estimates of bone stiffness. However, such in silico models for screws in bone highly overestimate the apparent stiffness. We hypothesized that a more accurate prediction of primary implant stability of screws in bone is possible by considering insertion-related bone damage. We assessed two different screw types and loading scenarios in 20 trabecular bone specimens extracted from 12 cadaveric human femoral heads (N = 5 for each case). In the micro-FE model, we predicted specimen-specific Young's moduli of the peri-implant bone damage region based on morphometric parameters such that the apparent stiffness of each in silico model matched the experimentally measured stiffness of the corresponding in vitro specimen as closely as possible. The standard micro-FE models assuming perfectly intact peri-implant bone overestimated the stiffness by over 330%. The consideration of insertion related damaged peri-implant bone corrected the mean absolute percentage error down to 11.4% for both loading scenarios and screw types. Cross-validation revealed a mean absolute percentage error of 14.2%. We present the validation of a novel micro-FE modeling technique to quantify the apparent stiffness of screws in trabecular bone. While the standard micro-FE model overestimated the bone-implant stiffness, the consideration of insertion-related bone damage was crucial for an accurate stiffness prediction. This approach provides an important step toward more accurate specimen-specific micro-FE models. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2415-2424, 2017.

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.

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

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.

Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphology-elasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography (μCT) reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae, and iliac crest were analyzed. Their morphology was assessed via 25 variables and their stiffness tensor (CFE) was computed from six independent load cases using micro finite element (μFE) analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multiple linear regression model of the dependent variable CFE. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of CFE(r(2) adj  = 0.889), especially in combination with fabric anisotropy (r(2) adj  = 0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (r(2) adj  = 0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric anisotropy further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric anisotropy are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and postelastic properties.