Combining specimen-specific finite-element models and optimization in cortical-bone material characterization improves prediction accuracy in three-point bending tests

Elucidation of the radius and ulna fracture mechanisms in toy poodle dogs using finite element analysis

Fractures occurring in the distal radius and ulna of toy breed dogs pose distinctive challenges for veterinary practitioners, requiring specialized treatment approaches primarily based on anatomical features. Finite Element Analysis (FEA) was applied to conduct numerical experiments to determine stress distribution across the bone. This methodology offers an alternative substitute for directly investigating these phenomena in living dog experiments, which could present ethical obstacles. A three-dimensional bone model of the metacarpal, carpal, radius, ulna, and humerus was reconstructed from Computed Tomography (CT) images of the toy poodle and dachshund forelimb. The model was designed to simulate the jumping and landing conditions from a vertical distance of 40 cm to the ground within a limited timeframe. The investigation revealed considerable variations in stress distribution patterns between the radius and ulna of toy poodles and dachshunds, indicating notably elevated stress levels in toy poodles compared to dachshunds. In static and dynamic stress analysis, toy poodles exhibit peak stress levels at the distal radius and ulna. The Von Mises stresses for toy poodles reach 90.07 MPa (static) and 1,090.75 MPa (dynamic) at the radius and 1,677.97 MPa (static) and 1,047.98 MPa (dynamic) at the ulna. Conversely, dachshunds demonstrate lower stress levels for 5.39 MPa (static) and 231.79 MPa (dynamic) at the radius and 390.56 MPa (static) and 513.28 MPa (dynamic) at the ulna. The findings offer valuable insights for modified treatment approaches in managing fractures in toy breed dogs, optimizing care and outcomes.

Comprehensively characterizing heterogeneous and transversely isotropic properties of femur cortical bones

Comprehensive characterization of the transversely isotropic mechanical properties of long bones along both the longitudinal and circumferential gradients is crucial for developing accurate mathematical models and studying bone biomechanics. In addition, mechanical testing to derive elastic, plastic, and failure properties of bones is essential for modeling plastic deformation and failure of bones. To achieve these, we machined a total of 336 cortical specimens, including 168 transverse and 168 longitudinal specimens, from four different quadrants of seven different sections of 3 bovine femurs. We conducted three-point bending tests of these specimens at a loading rate of 0.02 mm/s. Young's modulus, yield stress, tangential modulus, and effective plastic strain for each specimen were derived from correction equations based on classical beam theory. Our statistical analysis reveals that the longitudinal gradient has a significant effect on the Young's modulus, yield stress, and tangential modulus of both longitudinal and transverse specimens, whereas the circumferential gradient significantly influences the Young's modulus, yield stress, and tangential modulus of transverse specimens only. The differences in Young's modulus and yield stress between longitudinal specimens from different sections are greater than 40%, whereas those between transverse specimens are approximately 30%. The Young's modulus and yield stress of transverse specimens in the anterior quadrant were 18.81%/15.46% and 18.34%/14.88% higher than those in the posterior and lateral quadrants, respectively. There is no significant interaction between the longitudinal gradient and the circumferential gradient. Considering the transverse isotropy, it is crucial to consider loading direction when investigating the impact of circumferential gradients in the anterior, lateral, medial, and posterior directions. Our findings indicate that the conventional assumption of homogeneity in simulating the cortical bone of long bones may have limitations, and researchers should consider the anatomical position and loading direction of femur specimens for precise prediction of mechanical responses.

Effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structures: a finite element investigation

BACKGROUND

Running with the appropriate intensity may produce a positive influence on the mechanical properties of cortical bone structure. However, few studies have discussed the effects of different running intensities on the mechanical properties at different levels, especially at the micro-level, because the micromechanical parameters are difficult to measure experimentally.

METHODS

An approach that combines finite element analysis and experimental data was proposed to predict a micromechanical parameter in the rat femoral cortical bone structure, namely, the micro-level failure strain. Based on the previous three-point bending experimental information, fracture simulations were performed on the femur finite element models to predict their failure process under the same bending load, and the micro-level failure strains in tension and compression of these models were back-calculated by fitting the experimental load-displacement curves. Then, the effects of different running intensities on the micro-level failure strain of rat femoral cortical bone structure were investigated.

RESULTS

The micro-level failure strains of the cortical bone structures expressed statistical variations under different running intensities, which indicated that different mechanical stimuli of running had significant influences on the micromechanical properties. The greatest failure strain occurred in the cortical bone structure under low-intensity running, and the lowest failure strain occurred in the structure under high-intensity running.

CONCLUSIONS

Moderate and low-intensity running were effective in enhancing the micromechanical properties, whereas high-intensity running led to the weakening of the micromechanical properties of cortical bone. Based on these, the changing trends in the micromechanical properties were exhibited, and the effects of different running intensities on the fracture performance of rat cortical bone structures could be discussed in combination with the known mechanical parameters at the macro- and nano-levels, which provided the theoretical basis for reducing fracture incidence through running exercise.

Correlation of Bone Material Model Using Voxel Mesh and Parametric Optimization

The authors present an algorithm for determining the stiffness of the bone tissue for individual ranges of bone density. The paper begins with the preparation and appropriate mechanical processing of samples from the bovine femur and their imaging using computed tomography and then processing DICOM files in the MIMICS system. During the processing of DICOM files, particular emphasis was placed on defining basic planes along the sides of the samples, which improved the representation of sample geometry in the models. The MIMICS system transformed DICOM images into voxel models from which the whole bone FE model was built in the next step. A single voxel represents the averaged density of the real sample in a very small finite volume. In the numerical model, it is represented by the HEX8 element, which is a cube. All voxels were divided into groups that were assigned average equivalent densities. Then, the previously prepared samples were loaded to failure in a three-point bending test. The force waveforms as a function of the deflection of samples were obtained, based on which the global stiffness of the entire sample was determined. To determine the stiffness of each averaged voxel density value, the authors used advanced optimization analyses, during which numerical analyses were carried out simultaneously, independently mapping six experimental tests. Ultimately, the use of genetic algorithms made it possible to select a set of stiffness parameters for which the error of mapping the global stiffness for all samples was the smallest. The discrepancies obtained were less than 5%, which the authors considered satisfactory by the authors for such a heterogeneous medium and for samples collected from different parts of the bone. Finally, the determined data were validated for the sample that was not involved in the correlation of material parameters. The stiffness was 7% lower than in the experimental test.

Is the 0.2%-Strain-Offset Approach Appropriate for Calculating the Yield Stress of Cortical Bone?

The 0.2% strain offset approach is mostly used to calculate the yield stress and serves as an efficient method for cross-lab comparisons of measured material properties. However, it is difficult to accurately determine the yield of the bone. Especially when computational models require accurate material parameters, clarification of the yield point is needed. We tested 24 cortical specimens harvested from six bovine femora in three-point bending mode, and 11 bovine femoral cortical specimens in the tensile mode. The Young's modulus and yield stress for each specimen derived from the specimen-specific finite element (FE) optimization method was regarded as the most ideal constitutive parameter. Then, the strain offset optimization method was used to find the strain offset closest to the ideal yield stress for the 24 specimens. The results showed that the 0 strain offsets underestimated (- 25%) the yield stress in bending and tensile tests, while the 0.2% strain offsets overestimated the yield stress (+ 65%) in three-point bending tests. Instead, the yield stress determined by 0.007 and 0.05% strain offset for bending and tensile loading respectively, can effectively characterize the biomechanical responses of the bone, thereby helping to build an accurate FE model.

Influence of bone defect position and span in 3-point bending tests: experimental and finite element analysis

Three-point bending test is the most common mechanical test used for quantifying the biomechanical quality of bone tissue and bone healing in small animals. However, there is a lack of standardization for evaluation of bone repair by cortical perforation. The aim of this study was to determine the influence of bone defect position in the proximal metaphysis of rat tibias during load application and different span configuration on the three-point bending test outcomes. Cortical defects with 1.6 mm diameter were created at a standardized location on the medial surface of 60 tibias of male Wistar rats. The animals were euthanized 7 days after surgery. Five specimens were used to create 3D models for finite element analysis using high-resolution micro-CT images. Two spans (6 and 10mm) and three positions of the bone defect in relation to the load application (upward, frontal and downward) were evaluated experimentally (n = 10) and in finite element analysis (n = 5). Maximum load (N) and stiffness (N/mm) were statistically analyzed with 2-way ANOVA and Tukey test (α = 0.05). The results demonstrated that span and orientation of the bone defect significantly influenced the fracture pattern, stress distribution and force versus displacement relation. Therefore, reliable outcome can be achieved creating the bone defect at 8 mm from the extremity of the proximal epiphysis; placing a 10 mm distance span and downward facing defect position to allow a better distribution of stress and more fracture patterns that reached the bone defect target area with less intra-group variability.

Biomechanical properties enhancement of gamma radiation-sterilized cortical bone using antioxidants

Gamma radiation sterilization is the method used by the majority of tissue banks to reduce disease transmission from infected donors to recipients through bone allografts. However, many studies have reported that gamma radiation impairs the structural and mechanical properties of bone via formation of free radicals, the effect of which could be reduced using free radical scavengers. The aim of this study is to examine the radioprotective role of hydroxytyrosol (HT) and alpha lipoic acid (ALA) on the mechanical properties of gamma-sterilized cortical bone of bovine femur, using three-point bending and microhardness tests. Specimens of bovine femurs were soaked in ALA and HT for 3 and 7 days, respectively, before being exposed to 35-kGy gamma radiation. In unirradiated samples, both HT and ALA pre-treatment improved the cortical bone bending plastic properties (maximum bending stress, maximum bending strain, and toughness) without affecting microhardness. Irradiation resulted in a drastic reduction of the plastic properties and an increased microhardness. ALA treatment before irradiation alleviated the aforementioned reductions in maximum bending stress, maximum bending strain, and toughness. In addition, under ALA treatment, the microhardness was not increased after irradiation. For HT treatment, similar effects were found. In conclusion, the results indicate that HT and ALA can be used before irradiation to enhance the mechanical properties of gamma-sterilized bone allografts.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.