Apparent- and Tissue-Level Yield Behaviors of L4 Vertebral Trabecular Bone and Their Associations with Microarchitectures

Relationship between mechanical and microstructural parameters of rat lumbar spine in different ages

Exploring the relationships between microstructure and mechanical properties of bones may provide effective suggestions for increasing bone strength and reducing osteoporotic fracture. In this research, the tissue-level mechanical parameters, microstructure parameters of cancellous bone, and apparent mechanical parameters of L6 vertebral body were calculated in female SD rats aged 1-, 3-, 5-, 7-, 9-, 11-, 13-, 15-, 16-, and 17-month-old. Data were processed with Kruskal-Wallis test, linear regression and Spearman's rank correlation analysis. Appropriately increasing the plate Tb.N could enhance mechanical properties of bone. Tb.Th and Tb.N were two key factors in determining the tissue-level mechanical properties of cancellous bone. The microstructure could significantly predict mechanical parameters. Our findings may help to further understand the mechanism of osteoporotic fractures.

Effects of continuous subcutaneous insulin infusion on the microstructures, mechanical properties and bone mineral compositions of lumbar spines in type 2 diabetic rats

BACKGROUND

Continuous subcutaneous insulin infusion (CSII) for the treatment of type 2 diabetes (T2D) can improve the structure and strength of femur of rats, but the effect of CSII treatment on the lumbar spine of T2D rats is unknown. The purpose of this study is to investigate the effects of CSII on the microstructure, multi-scale mechanical properties and bone mineral composition of the lumbar spine in T2D rats.

METHODS

Seventy 6-week-old male Sprague-Dawley (SD) rats were divided into two batches, each including Control, T2D, CSII and Placebo groups, and the duration of insulin treatment was 4-week and 8-week, respectively. At the end of the experiment, the rats were sacrificed to take their lumbar spine. Microstructure, bone mineral composition and nanoscopic-mesoscopic-apparentand-macroscopic mechanical properties were evaluated through micro-computed tomography (micro-CT), Raman spectroscopy, nanoindentation test, nonlinear finite element analysis and compression test.

RESULTS

It was found that 4 weeks later, T2D significantly decreased trabecular thickness (Tb.Th), nanoscopic-apparent and partial mesoscopic mechanical parameters of lumbar spine (P < 0.05), and significantly increased bone mineral composition parameters of cortical bone (P < 0.05). It was shown that CSII significantly improved nanoscopic-apparent mechanical parameters (P < 0.05). In addition, 8 weeks later, T2D significantly decreased bone mineral density (BMD), bone volume fraction (BV/TV) and macroscopic mechanical parameters (P < 0.05), and significantly increased bone mineral composition parameters of cancellous bone (P < 0.05). CSII treatment significantly improved partial mesoscopic-macroscopic mechanical parameters and some cortical bone mineral composition parameters (P < 0.05).

CONCLUSIONS

CSII treatment can significantly improve the nanoscopic-mesoscopic-apparent-macroscopic mechanical properties of the lumbar spine in T2D rats, as well as the bone structure and bone mineral composition of the lumbar vertebrae, but it will take longer treatment time to restore the normal level. In addition, T2D and CSII treatment affected bone mineral composition of cortical bone earlier than cancellous bone of lumbar spine in rat. Our study can provide evidence for clinical prevention and treatment of T2D-related bone diseases.

Prediction of fracture initiation and propagation in pelvic bones

The objective is developing an XFEM model that is capable of predicting different types of fracture in the pelvic bone under various loading conditions. Previously published mechanical and failure characteristics of cortical and cancellous tissues were implemented and assigned to an intact pelvic bone with specified cortical and cancellous tissues. Various loading conditions, including combined load directions, were applied to the acetabulum to model different types of fracture (e.g., anterior/posterior wall fracture and transverse fracture) in the pelvic bone. The predicated types of fracture and the maximum force at fracture were compared to those acquired from previously published experimental tests. Anterior/posterior wall fracture and transverse fracture were the most common types of fractures determined in the simulations. The XFEM simulations were able to predict similar fractures to those reported in the experimental tests. The maximum fracture force in the XFEM model was found to be 18.6 kN compared to 8.85 kN reported in the previous experimental tests. The results revealed that different types of fracture in the pelvic bones can be caused by the various loading conditions in unstable high-rate impact loads. Using proper mechanical and failure behaviors of cortical and cancellous tissues, XFEM modeling of pelvic bone is capable of predicting bone fracture. In future work, the XFEM models of cancellous and cortical tissues can be assigned to other bones in human body skeleton so that the failure mechanism in such bones can be investigated.

Prediction of the natural frequencies of different degrees of degenerated human lumbar segments L2-L3 using dynamic finite element analysis

BACKGROUND AND OBJECTIVE

Chronic exposure to resonant environment may cause more serious injuries to human lumbar spine than other vibrations. On the condition that the natural frequency of human lumbar spine is known, excitation frequency from an external vibration source can be optimized to keep away from the natural frequency and thus avoid lumbar resonance. Therefore, this study aimed to present an approach to predict the natural frequency of the human lumbar spine.

METHODS

Four poroelastic finite element models of human L2-L3 spinal motion segments with different degrees of degeneration were established. Dynamic finite element analyses of these models during 1 h of vibration were then conducted. The mechanical parameters of these models under vibrations at different excitation frequencies were predicted. The excitation frequencies that resulted in the greatest changes in the lumbar mechanical parameters were identified as the natural frequencies of the established L2-L3 spinal motion segments.

RESULTS

Simulation results showed that the natural frequencies of the healthy and mildly degenerated L2-L3 spinal motion segments, moderately degenerated L2-L3 spinal motion segments, and seriously degenerated L2-L3 spinal motion segments were in the range of 5-7, 3-5, and 1-3 Hz, respectively.

CONCLUSIONS

The predicted results indicated that the natural frequencies of the human L2-L3 spinal motion segments gradually decreased with the severity of degeneration. These phenomena may be related to changes in the lumbar structures and materials because of degeneration. This study provided a feasible method to predict the lumbar natural frequencies for different populations, which may be helpful in optimizing external vibration sources to avoid lumbar resonance.

Prediction of mechanical properties of trabecular bone in patients with type 2 diabetes using damage based finite element method

Type-2 diabetic (T2D) and osteoporosis (OP) suffered patients are more prone to fragile fracture though the nature of alteration in areal bone mineral density (aBMD) in these two cases are completely different. Therefore, it becomes crucial to compare the effect of T2D and OP on alteration in mechanical and structural properties of femoral trabecular bone. This study investigated the effect of T2D, OP, and osteopenia on bone structural and mechanical properties using micro-CT, nanoindentation and compression test. Further, a nanoscale finite element model (FEM) was developed to predict the cause of alteration in mechanical properties. Finally, a damage-based FEM was proposed to predict the pathological related alteration of bone's mechanical response. The obtained results demonstrated that the T2D group had lower volume fraction (-18.25%, p = 0.023), young's modulus (-23.47%, p = 0.124), apparent modulus (-37.15%, p = 0.02), and toughness (-40%, p = 0.001) than the osteoporosis group. The damage-based FE results were found in good agreement with the compression experiment results for all three pathological conditions. Also, nanoscale FEM results demonstrated that the elastic and failure properties of mineralised collagen fibril decreases with increase in crystal size. This study reveals that T2D patients are more prone to fragile fracture in comparison to OP and osteopenia patients. Also, the proposed damage-based FEM can help to predict the risk of fragility fracture for different pathological conditions.

High-Performance Computing Comparison of Implicit and Explicit Nonlinear Finite Element Simulations of Trabecular Bone

BACKGROUND AND OBJECTIVE

Finite element models built from micro-computed tomography scans have become a powerful tool to investigate the mechanical properties of trabecular bone. There are two types of solving algorithms in the finite element method: implicit and explicit. Both of these methods have been utilized to study the trabecular bone. However, an investigation comparing the results obtained using the implicit and explicit solvers is lacking. Thus, in this paper, we contrast implicit and explicit procedures by analyzing trabecular bone samples as a case study.

METHODS

Micro-computed tomography-based finite element analysis of trabecular bone under a direct quasi-static compression was done using implicit and explicit methods. The differences in the predictions of mechanical properties and computational time of the two methods were studied using high-performance computing.

RESULTS

Our findings indicate that the results using implicit and explicit solvers are well comparable, given that similar problem set up is carefully utilized. Also, the parallel scalability of the two methods was similar, while the explicit solver performed about five times faster than the implicit method. Along with faster performance, the explicit method utilized significantly less memory for the analysis, which shows another benefit of using an explicit solver for this case study.

CONCLUSIONS

The comparison of the implicit and explicit methods for the simulation of trabecular bone samples should be highly valuable to the bone modeling community and researchers studying complex cellular and architectured materials.

Idealized conductance: A new method to evaluate stiffness of trabecular bone

Stiffness is an important parameter to evaluate the condition of trabecular bone in biomechanical and clinical research. Microstructural parameters are commonly used to evaluate stiffness, but the accuracy needs to be improved. In this study, the electrical conductance of trabecular bone was calculated based on an idealized condition: trabeculae were electrically conductive and isotropy, other constituents in the trabecular bone were not considered in the simulation. The idealized conductance was calculated to evaluate the stiffness of trabecular bone, and the accuracy was compared with microstructural parameters. Twenty-one cubic trabecular cubes (5 × 5 × 5 mm³ ) from three femoral heads were investigated. Microstructural parameters were measured through Micro-CT scanning. Nominal elastic modulus (E) and idealized conductance (G) of trabecular cubes were measured through micro-finite element analysis. Bone volume fraction (BV/TV) is the major microstructural parameter that determine the stiffness of trabecular bone. The correlation coefficient between BV/TV and E along three directions were 0.815 (X-axis), 0.729 (Y-axis) and 0.914 (Z-axis). The correlation between G and E were stronger (X-axis: r = 0.986, Y-axis: r = 0.986, Z-axis: r = 0.991). A regression model combining different microstructural parameters was built to evaluate stiffness, but the correlation between them were not significantly improved (X-axis: r = 0.831, Y-axis: r = 0.807, Z-axis: r = 0.905). Compared with microstructural parameters, idealized conductance was a better parameter to evaluate stiffness of trabecular bone.

Microstructural and mechanical evaluations of region segmentation methods in classifications of osteonecrosis

Measuring the location of necrotic lesions is necessary to diagnosis of osteonecrosis. Different region segmentation methods of the femoral head were proposed to quantitatively measure necrotic lesions including Japanese Investigation Committee for Avascular Necrosis (JIC) classification and China-Japan Friendship Hospital (CJFH) classification. Biomechanical methods could bring important information to evaluate the reasonability of these classifications. In this study, microstructural and mechanical properties of trabecular bone were quantitatively analyzed according to the region segmentation methods described in these classifications. Microstructural parameters of trabecular bone were analyzed based on micro-CT scanning. Mechanical properties were measured through Nanoindentation and micro-finite element analysis. It was found that microstructural and mechanical properties of trabecular bone in the middle region was more adaptive to load bearing than the medial and lateral regions according to the CJFH classification; lesions in the middle region could bring more changes to microstructure and stress distribution. According to JIC classification, differences of microstructural and mechanical properties among the three regions were not significant. Biomechanical characteristics of trabecular bones could be better distinguished with CJFH classification.

An Equivalent Constitutive Model of Cancellous Bone With Fracture Prediction

To simulate the mechanical and fracture behaviors of cancellous bone in three anatomical directions and to develop an equivalent constitutive model. Microscale extended finite element method (XFEM) models of a cancellous specimen were developed with mechanical behaviors in three anatomical directions. An appropriate abaqus macroscale model replicated the behavior observed in the microscale models. The parameters were defined based on the intermediate bone material properties in the anatomical directions and assigned to an equivalent nonporous specimen of the same size. The equivalent model capability was analyzed by comparing the micro- and macromodels. The hysteresis graphs of the microscale model show that the modulus is the same in loading and unloading; similar to the metal plasticity models. The strength and failure strains in each anatomical direction are higher in compression than in tension. The microscale models exhibited an orthotropic behavior. Appropriate parameters of the cast iron plasticity model were chosen to generate macroscale models that are capable of replicating the observed microscale behavior of cancellous bone. Cancellous bone is an orthotropic material that can be simulated using a cast iron plasticity model. This model is capable of replicating the microscale behavior in finite element (FE) analysis simulations without the need for individual trabecula, leading to a reduction in computational resources without sacrificing model accuracy. Also, XFEM of cancellous bone compared to traditional finite element method proves to be a valuable tool to predict and model the fractures in the bone specimen.

Prediction of failure in cancellous bone using extended finite element method

The objective of our study is to develop extended finite element method models of cancellous bone specimens that are capable of accurately predicting the onset and propagation of cracks under mechanical loading. In order to do so, previously published three-point bending test results of a single trabecula were replicated using two different extended finite element method approaches, namely, elastic-plastic-fracture and elastic-fracture that considered different configurations of the elasto-plastic properties of bone from which the best approach to fit the experimental data was identified. The behavior of a single trabecula was then used in 2D extended finite element method models to quantify the strength of the trabecular tissue of the forearm along three perpendicular anatomical axes. The results revealed that the elastic-plastic-fracture model better represented the experimental data in the model of a single trabecula. Considering the 2D trabecular specimens, the elastic fracture model predicted higher strength than the elastic-plastic-fracture model and there was no difference in stiffness between the two models. In general, the specimens exhibited higher failure strain and more ductile behavior in compression than in tension. In addition, strength and stiffness were found to be higher in tension than compression on average. It can be concluded that with proper parameters, extended finite element method is capable of simulating the ductile behavior of cancellous bone. The models are able to quantify the tensile strength of trabecular tissue in the various anatomical directions reporting an increased strength in the longitudinal direction of forearm cancellous bone tissue. Extended finite element method of cancellous bone proves to be a valuable tool to predict the mechanical characteristics of cancellous bones as a function of the microstructure.

Investigation and Feasibility of Combined 3D Printed Thermoplastic Filament and Polymeric Foam to Simulate the Cortiocancellous Interface of Human Vertebrae

Disorders of the spine are among the most common indications for neurosurgical and orthopedic surgical interventions. Spinal fixation in the form of pedicle screw placement is a common form of instrumentation method in the lower cervical, thoracic, and lumbar spine. A vital principle to understand for the safe and accurate placement of pedicle screws is the palpable difference between the cortical and cancellous bone, both of which have different material properties and compositions. Probing and palpation of the hard cortical bone, also known as the “ventral lamina”, covering the neural elements of the spinal canal during screw placement provides manual feedback to the surgeon, indicating an impending breach if continued directional force is applied. Generally, this practice is learned at the expense of patients in live operating room scenarios. Currently, there is a paucity of human vertebra simulation designs that have been validated based on the in vivo ultrastructure and physical properties of human cortical and cancellous bone. In this study, we examined the feasibility of combining three-dimensionally printed thermoplastic polymers with polymeric foam to replicate both the vertebral corticocancellous interface and surface anatomy for procedural education.

Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.