Optimizing Accuracy of Proximal Femur Elastic Modulus Equations

Prediction of vertebral failure under general loadings of compression, flexion, extension, and side-bending

Bone pathologies such as osteoporosis and metastasis can significantly compromise the load-bearing capacity of the spinal column, increasing the risk of vertebral fractures, some of which may occur during routine physical activities. Currently, there is no clinical tool that accurately assesses the risk of vertebral fractures associated with these activities in osteoporotic and metastatic spines. In this paper, we develop and validate a quantitative computed tomography-based finite element analysis (QCT/FEA) method to predict vertebral fractures under general load conditions that simulate flexion, extension, and side-bending movements, reflecting the body's activities under various scenarios. Initially, QCT/FEA models of cadaveric spine cohorts were developed. The accuracy and verification of the methodology involved comparing the fracture force outcomes to those experimentally observed and measured under pure compression loading scenarios. The findings revealed a strong correlation between experimentally measured failure loads and those estimated computationally (R2 = 0.96, p < 0.001). For the selected vertebral specimens, we examined the effects of four distinct boundary conditions that replicate flexion, extension, left side-bending, and right side-bending loads. The results showed that spine bending load conditions led to over a 62% reduction in failure force outcomes compared to pure compression loading conditions (p ≤ 0.0143). The study also demonstrated asymmetrical strain distribution patterns when the loading condition shifted from pure compression to spine bending, resulting in larger strain values on one side of the bone and consequently reducing the failure load. The results of this study suggest that QCT/FEA can be effectively used to analyze various boundary conditions resembling real-world physical activities, providing a valuable tool for assessing vertebral fracture risks.

Patient-specific bone material modelling can improve the predicted biomechanical outcomes of sacral fracture fixation techniques: A comparative finite element study

OBJECTIVE

To evaluate and compare the biomechanical efficacy of six iliosacral screw fixation techniques for treating unilateral AO Type B2 (Denis Type II) sacral fractures using literature-based and QCT-based bone material properties in finite element (FE) models.

METHODS

Two FE models of the intact pelvis were constructed: the literature-based model (LBM) with bone material properties taken from the literature, and the patient-specific model (PSM) with QCT-derived bone material properties. Unilateral transforaminal sacral fracture was modelled to assess different fixation techniques: iliosacral screw (ISS) at the first sacral vertebra (S1) (ISS1), ISS at the second sacral vertebra (S2) (ISS2), ISS at S1 and S2 (ISS12), transverse iliosacral screws (TISS) at S1 (TISS1), TISS at S2 (TISS2), and TISS at S1 and S2 (TISS12). A 600 N vertical load with both acetabula fixed was applied. Vertical stiffness (VS), relative interfragmentary displacement (RID), and the von Mises stress values in the screws and fracture interface were analysed.

RESULTS

The lowest and highest normalised VS was given by ISS1 and TISS12 techniques for LBM and PSM, with 137 % and 149 %, and 375 % and 472 %, respectively. In comparison with the LBM, the patient-specific bone modelling increased the maximum screw stress values by 19.3, 16.3, 27.8, 2.3, 24.4 and 7.8 % for ISS1, ISS2, ISS12, TISS1, TISS2 and TISS12, respectively. The maximum RID values were between 0.10 mm and 0.47 mm for all fixation techniques in both models. The maximum von Mises stress results on the fracture interface show a substantial difference between the two models, as PSM (mean ± SD of 15.76 ± 8.26 MPa) gave lower stress values for all fixation techniques than LBM (mean ± SD of 28.95 ± 6.91 MPa).

CONCLUSION

The differences in stress distribution underline the importance of considering locally defined bone material properties when investigating internal mechanical parameters. Based on the results, all techniques demonstrated clinically sufficient stability, with TISS12 being superior from a biomechanical standpoint. Both LBM and PSM models indicated a consistent trend in ranking the fixation techniques based on stability. However, long-term clinical trials are recommended to confirm the findings of the study.

Risk modeling of femoral neck fracture based on geometric parameters of the proximal epiphysis

BACKGROUND

Fractures of the proximal femur epiphysis are problematic for state health care because they are associated with severe medical and social problems and high morbidity and mortality rates.

AIM

To model the potential risk of hip fracture via femur geometric parameters.

METHODS

Seventy educational cadaveric femurs from people aged 14 to 80 years, 10 X-ray images from the records of the Human Anatomy Department and 10 X-ray images from the Department of Traumatology, Orthopedics and Disaster Surgery of Sechenov University, were evaluated. The parameters of the fractured bone were measured using images captured with a Canon d60 camera. The projection values of the proximal epiphysis of the cadaveric femurs and geometric parameters of the bones shown in the X-ray images were measured with Autodesk software (AutoCAD 2018). Analysis of the video frames showing bone rotation reveal that the greater trochanter can be inscribed in a parallelepiped, where one of the faces is parallel to the plane of view in the frontal standard projection and is rectangular. The angle of bone rotation obtained by turning the cube corresponded to the angle measured with the second technique. This reliable method of calculating the rotation of the bone relative to the anterior projection was employed in subsequent calculations. The geometric parameters of the femur were measured using X-ray images according to the proposed method.

RESULTS

The geometric parameters of 70 femurs were analyzed, and correlation coefficients were calculated. Our measurement results were compared with those reported by other authors. The potential influence of femur geometry on force distribution in the proximal epiphysis of the femur was described, and a 2-dimensional model of the femur epiphysis associated with minimal neck fracture risk was provided. The assessment of the geometric parameters of the femoral epiphysis indicated the greatest risk of a varus fracture of the neck if the angle of the minimal resistance zone (AMRZ) index > 24° and the neck-shaft angle (NSA) < 127.5°. In contrast, the minimum risk was observed at AMRZ < 14° and NSA > 128.87°.

CONCLUSION

The proposed method provides the potential femur neck fracture risk based on geometric parameters.

Single-level subject-specific finite element model can predict fracture outcomes in three-level spine segments under different loading rates

Osteoporosis-related vertebral compression fracture can occur under normal physiological activities. Bone metastasis is another source of vertebral fracture. Different loading rates, either high-energy traumas such as falls or low-energy traumas under normal physiological activities, can result in different fracture outcomes. The aim of the current study was to develop a quantitative computed tomography-based finite element analysis (QCT/FEA) technique for single vertebral bodies to predict fracture strength of three-level spine segments. Developed QCT/FEA technique was also used to characterize vertebral elastic moduli at two loading rates of 5 mm/min, representing a physiologic loading condition, and 12000 mm/min, representing a high-energy trauma. To this end, a cohort of human spine segments divided into three groups of intact, defect, and augmented were mechanically tested to fracture; then, experimental stiffness and fracture strength values were measured. Outcomes of this study showed no significant difference between the elastic modulus equations at the two testing speeds. Areal bone mineral density measured by dual x-ray absorptiometry (DXA/BMD) explained only 53% variability (R² = 0.53) in fracture strength outcomes. However, QCT/FEA could explain 70% of the variability (R² = 0.70) in experimentally measured fracture strength values. Adding disk degeneration grading, testing speed, and sex to QCT/FEA-estimated fracture strength values further increased the performance of our statistical model by 14% (adjusted R² of 0.84 between the prediction and experimental fracture forces). In summary, our results indicated that a single-vertebra model, which is computationally less expensive and more time efficient, is capable of estimating fracture outcomes with acceptable performance (range: 70-84%).

Evaluation of experimental, analytical, and computational methods to determine long-bone bending stiffness

Methods used to evaluate bone mechanical properties vary widely depending on the motivation and environment of individual researchers, clinicians, and industries. Further, the innate complexity of bone makes validation of each method difficult. Thus, the purpose of the present research was to quantify methodological error of the most common methods used to predict long-bone bending stiffness, more specifically, flexural rigidity (EI). Functional testing of a bi-material porcine bone surrogate, developed in a previous study, was conducted under four-point bending test conditions. The bone surrogate was imaged using computed tomography (CT) with an isotropic voxel resolution of 0.625 mm. Digital image correlation (DIC) of the bone surrogate was used to quantify the methodological error between experimental, analytical, and computational methods used to calculate EI. These methods include the application of Euler Bernoulli beam theory to mechanical testing and DIC data; the product of the bone surrogate composite bending modulus and second area moment of inertia; and finite element analysis (FEA) using computer-aided design (CAD) and CT-based geometric models. The methodological errors of each method were then compared. The results of this study determined that CAD-based FEA was the most accurate determinant of bone EI, with less than five percent difference in EI to that of the DIC and consistent reproducibility of the measured displacements for each load increment. CT-based FEA was most accurate for axial strains. Analytical calculations overestimated EI and mechanical testing was the least accurate, grossly underestimating flexural rigidity of long-bones.

Numerical investigation of mechanical behavior of human femoral diaphysis in normal and defective geometry: experimental evaluation

Failure and major reoperation after internal fixation (IF) in mature femoral bones are common and proper selection of fixation method may reduce the rate of reoperations. Investigating the mechanical behavior of the human femoral diaphysis, this article studies effect of mechanical properties and geometry of the bone on selection of IF method. To this aim, we calculated the bone mineral density in human femurs, and then, using computed tomography scan, we obtained geometry and nonhomogeneous properties of the bone. Finite element (FE) models of osteotomised femurs were reinforced using four types of screws with a locking compression plate (LCP). We performed buckling and 4-point bending simulations, and results of these simulations represent critical buckling loads, maximum von Mises stresses, and strains around the screws and the central defect. To evaluate FE analysis, we employed the compressive experiments and compared load vs. displacement curves with FE results. Results corresponding to intact, osteotomised, and reinforced states are compared together, and the effect of cortical and unicortical screws in LCPs is studied. The FE results showed that application of identical prophylactic IF for two persons with identical injuries in the same conditions bring quite inverse results. As a consequence, evaluation of osteoporosis, elastic modulus, and morphometric data are required before fixation and screw selection. Besides, for short diaphysis, unicortical screws have maximum strengthening factor in bending. While for long samples, these types of screws can be the worst option, application of cortical screws results to maximum strength in comparison with other types.

Estimation of mass apparent density and Young's modulus of femoral neck-head region

The purpose of this study is to estimate mass apparent density and Young's modulus to investigate biomechanical properties of the proximal femur bone. In this study eleven specimens of sheep femur bone having age between 1-1.25 years and human femur bone having age between 14 and 81years are used. In the present study, the first technique attempts to estimate the density from the image-based Hounsfield unit which is obtained directly from a computed tomography image. The modulus of elasticity is estimated from density-elasticity relation which is available in the literature. Another technique is used to develop a correlation between computed apparent density and greyscale based coefficient obtained by material mapping method using commercial Simpleware ScanIP software. Estimated mean deviation in apparent mass density and Young's modulus is 4.34% and 4.69% in sheep bone and 4.35% and 4.94% in human bone respectively. It is found that apparent density and Young's modulus obtained shows close agreement with values reported in the literature. Moreover, the study attempts to build up a new material model between human and sheep for orthopaedics clinical trials and research in Indian context. In addition, it is also observed that bone mass density of sheep is 1.60 times human. This method can also be useful to study and analyse biomechanical properties of the human femur bone.

Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

Despite evidence of the biomechanical role of cortical bone, current state of the art finite element models of the proximal femur built from clinical CT data lack a subject-specific representation of the bone cortex. Our main research hypothesis is that the subject-specific modelling of cortical bone layer from CT images, through a deconvolution procedure known as Cortical Bone Mapping (CBM, validated for cortical thickness and density estimates) can improve the accuracy of CT-based FE models of the proximal femur, currently limited by partial volume artefacts. Our secondary hypothesis is that a careful choice of cortical-specific density-elasticity relationship may improve model accuracy. We therefore: (i) implemented a procedure to include subject-specific CBM estimates of both cortical thickness and density in CT-based FE models. (ii) defined alternative models that included CBM estimates and featured a cortical-specific or an independently optimised density-elasticity relationship. (iii) tested our hypotheses in terms of elastic strain estimates and failure load and location prediction, by comparing with a published cohort of 14 femurs, where strain and strength in stance and fall loading configuration were experimentally measured, and estimated through reference FE models that did not explicitly model the cortical compartment. Our findings support the main hypothesis: an explicit modelling of the proximal femur cortical bone layer including CBM estimates of cortical bone thickness and density increased the FE strains prediction, mostly by reducing peak errors (average error reduced by 30%, maximum error and 95th percentile of error distribution halved) and especially when focusing on the femoral neck locations (all error metrics at least halved). We instead rejected the secondary hypothesis: changes in cortical density-elasticity relationship could not improve validation performances. From these improved baseline strain estimates, further work is needed to achieve accurate strength predictions, as models incorporating cortical thickness and density produced worse estimates of failure load and equivalent estimates of failure location when compared to reference models. In summary, we recommend including local estimates of cortical thickness and density in FE models to estimate bone strains in physiological conditions, and especially when designing exercise studies to promote bone strength.

Effect of metastatic lesion size and location on the load-bearing capacity of vertebrae using an optimized ash density-modulus equation

About 1.8 million new cancer cases are estimated in the US in 2019 from which 50-85% might metastasize to the thoracic and lumbar spines. Subject-specific quantitative computed tomography-based finite element analysis (QCT/FEA) is a promising used tool to predict vertebral fracture properties. The aims of this study were twofold: First, to develop an optimized equation for the elastic modulus accounting for all input parameters in FE modeling of fracture properties. Second, to assess the effect of lesion size and location on the predicted fracture loads. An inverse QCT/FEA method was implemented to determine optimal coefficients for the modulus equation as a function of ash density. Lesions of 16 and 20 mm were then virtually located at the center, off-centered, anterior, and posterior regions of the vertebrae. A total of 6426 QCT/FEA models were run to optimize the coefficients and evaluate the effect of lesions on fracture properties. QCT/FEA predicted stiffness showed high correlations (50%) with the experimentally measured values. Compared to a 16 mm lesion size, a 20 mm lesion had a reduction in failure load of 55%, 57%, 52%, and 44% at the center, off-centered, anterior cortex, and pedicle, respectively (p < 0.001). Lesions affecting mostly trabecular bone showed the largest reduction in predicted failure loads (about 55%), and females presented weaker outcomes than males. An optimal elastic modulus equation resulted in accurate vertebral stiffness predictions. A deterioration of the trabecular bone due to the presence of a lesion highly affected the predicted fracture loads, and this reduction was significantly higher in females compared to males.