A round-robin finite element analysis of human femur mechanics between seven participating laboratories with experimental validation

[Numerical simulation in musculoskeletal biomechanics : Application perspectives and possibilities]

BACKGROUND

Computational research methods, such as finite element analysis (FEA) and musculoskeletal multi-body simulation (MBS), are important in musculoskeletal biomechanics because they enable a better understanding of the mechanics of the musculoskeletal system, as well as the development and evaluation of orthopaedic implants. These methods are used to analyze clinically relevant issues in various anatomical regions, such as the hip, knee, shoulder joints and spine. Preoperative simulation can improve surgical planning in orthopaedics and predict individual results.

EXAMPLES FROM PRACTICE

In this article, the methods of FE analysis and MBS are explained using two practical examples, and the activities of the "Numerical Simulation" cluster of the "Musculoskeletal Biomechanics Research Network (MSB-NET)" are presented in more detail. An outlook classifies numerical simulation in the age of artificial intelligence and draws attention to the relevance of simulation in the (re)approval of implants.

Corroboration of coupled musculoskeletal model and finite element predictions with in vivo RSA migration of an uncemented acetabular component

While finite element (FE) models have been used extensively in orthopedic studies, validation of their outcome metrics has been limited to comparison against ex vivo testing. The aim of this study was to validate FE model predictions of the initial cup mechanical environment against patient-matched in vivo measurements of acetabular cup migration using radiostereometric analysis (RSA). Tailored musculoskeletal and FE models were developed using a combination of three-dimensional (3D) motion capture data and clinical computerized tomography (CT) scans for a cohort of eight individuals who underwent primary total hip replacement and were prospectively enrolled in an RSA study. FE models were developed to calculate the mean modulus of cancellous bone, composite peak micromotion (CPM), composite peak strain (CPS) and percentage area of bone ingrowth. The RSA cup migration at 3 months was used to corroborate the FE output metrics. Qualitatively, all FE-predicted metrics followed a similar rank order as the in vivo RSA 3D migration data. The two cases with the lowest predicted CPM (<20 µm), lowest CPS (<0.0041), and high bone modulus (>917 MPa) were confirmed to have the lowest in vivo RSA 3D migration (<0.14 mm). The two cases with the largest predicted CPM (>80 µm), larger CPS (>0.0119) and lowest bone modulus (<472 MPa) were confirmed to have the largest in vivo RSA 3D migration (>0.78 mm). This study enabled the first corroboration between tailored musculoskeletal and FE model predictions with in vivo RSA cup migration. Investigation of additional patient-matched CT, gait, and RSA examinations may allow further development and validation of FE models.

Establishment of a Finite Element Model of Normal Nasal Bone and Analysis of Its Biomechanical Characteristics

Nasal bone is a long, paired series of small bones, which is narrow at the top and broad at the bottom, that forms the base of the nasal dorsum. Together with the nasal part of the frontal bone, the frontal process of the maxilla and the middle plate of the ethmoid bone constitute the bone scaffold of the external nose. In this paper, the DICOM image data file was imported into the Mimics software for 3D reconstruction. At the same time, the Geomagic software was used for relevant image processing, and the finite element software ANSYS was used to establish a finite element model to analyze the stress characteristics of the nasomaxillary complex. Results. The maximum principal stress and maximum strain force at the lower segment of nasal bone and the junction of nasal bone and maxilla were relatively large. When the same external force acts on the lower segment of the nasal bone and the angle is 0° (sagittal force), the maximum principal stress and maximum strain force are the smallest. When the angle continues to increase, the maximum principal stress and maximum strain force continue to increase.

The predictive ability of a QCT-FE model of the proximal femoral stiffness under multiple load cases is strongly influenced by experimental uncertainties

Despite significant improvements in terms of the predictive ability of Quantitative Computed Tomography based Finite Element (QCT-FE) models in estimating femoral strength (fracture load and stiffness), no substantial clinical adoption of this method has taken place to date. Narrowing the wide variability of FE results by standardizing the methodology and validation protocols, as well as reducing the uncertainties in the FEA process have been proposed as routes towards improved reliability. The aim of this study was to: First, validate a QCT-FE model of proximal femoral stiffness in multiple stance load cases, and second, using a parametric approach, determine the influence of select experimental and modeling parameters on the predictive ability of our model. Ten fresh frozen human femoral samples were tested in neutral stance, 15° adducted and 15° abducted load cases. Voxel-based linear-elastic QCT-FE models of the samples were generated to predict the models' stiffness values in all load cases. The base FE models were validated against the experimental results using linear regression. Thirty six deviated models were created using the minimum and maximum values of experiment-based "plausible range" for 18 parameters in 4 categories of embedding, loading, material, and segmentation. The predictive ability of the models were compared in terms of the coefficient of determination (R²) of the linear regression between the measured and predicted stiffness values in all load cases. Our model was capable of capturing 90% of the variation in the experimental stiffness of the samples in neutral stance position (R² = 0.9, concordance correlation coefficient (CCC) = 0.93, percent root mean squared error (RMSE%) = 8.4%, slope and intercept not significantly different from unity and zero, respectively). Embedding and loading categories strongly affected the predictive ability of the models with an average percent difference in R² of 4.36% ± 2.77 and 2.96% ± 1.69 for the stance-neutral load case, respectively. The performance of the models were significantly different in adducted and abducted load cases with their R² dropping to 71% and 70%, respectively. Similarly, off-axes load cases were affected by the parameters differently compared to the neutral load case, with the loading parameter category imposing more than 10% difference on their R², larger than all other categories. We also showed that automatically selecting the best performing plausible value for each parameter and each sample would result in a perfectly linear correlation (R²> 0.99) between the "tuned" model's predicted stiffness and experimental results. Based on our results, high sensitivity of the model performance to experimental parameters requires extra diligence in modeling the embedding geometry and the loading angles since these sources of uncertainty could dwarf the effects of material modeling and image processing parameters. The results of this study could help in improving the robustness of the QCT-FE models of proximal femur by limiting the uncertainties in the experimental and modeling steps.

Age-Related Study and Collision Response of Material Properties of Long Bones in Chinese Pedestrian Lower Limbs

In forensic examination cases, lower limb injuries are common, and pedestrians of different ages suffer different injuries when they are hit by vehicles, especially the injuries to the long bones of the lower limbs. Aging remains a challenging issue for the material properties and injury biomechanical properties of pedestrian lower limb long bones. We analyzed the regression relationship between the age of 50 Chinese pedestrians and the material properties of the lower limb long bones (femur, tibia). We compared them with previous studies to propose a regression model suitable for Chinese human long bone material properties. Through the established Human Active Lower Limb (HALL) model that conforms to the Chinese human anatomy, seven pedestrians’ (20/30/40/50/60/70/80 years old (YO)) lower limbs were parameterized to assign long bone material properties. In the finite element analysis, the Hall model was side-impacted by a family car (FCR) at speeds of 30/40/50/60/70 km/h, respectively. The results showed that an increase in age was negatively correlated with a decrease in the material properties of each long bone. Moreover, with an increase in age, the tolerance limit of long bones gradually decreases, but there will be a limit, and there is no obvious positive correlation with age. During a standing side impact, the stress change in the femur was significantly smaller than that of the tibia, and the stress of the femur and tibia decreased with age. Age is a more significant influencing factor for lower limb injuries. Older pedestrians have a higher risk of lower limb injuries. Forensic experts should pay attention to the critical factor of age when encountering lower limb traffic accident injuries in forensic identification work.

Limit analysis of human proximal femur

A limit analysis numerical approach oriented to predict the peak/collapse load of human proximal femur, under two different loading conditions, is presented. A yield criterion of Tsai-Hu-type, expressed in principal stress space, is used to model the orthotropic bone tissues. A simplified human femur 3D model is envisaged to carry on numerical simulation of in-vitro tests borrowed from the relevant literature and to reproduce their findings. A critical discussion, together with possible future developments, is presented.

Performance of a Piezoelectric Energy Harvesting System for an Energy-Autonomous Instrumented Total Hip Replacement: Experimental and Numerical Evaluation

Instrumented implants can improve the clinical outcome of total hip replacements (THRs). To overcome the drawbacks of external energy supply and batteries, energy harvesting is a promising approach to power energy-autonomous implants. Therefore, we recently presented a new piezoelectric-based energy harvesting concept for THRs. In this study, the performance of the proposed energy harvesting system was numerically and experimentally investigated. First, we numerically reproduced our previous results for the physiologically based loading situation in a simplified setup. Thereafter, this configuration was experimentally realised by the implantation of a functional model of the energy harvesting concept into an artificial bone segment. Additionally, the piezoelectric element alone was investigated to analyse the predictive power of the numerical model. We measured the generated voltage for a load profile for walking and calculated the power output. The maximum power for the directly loaded piezoelectric element and the functional model were 28.6 and 10.2 µW, respectively. Numerically, 72.7 µW was calculated. The curve progressions were qualitatively in good accordance with the numerical data. The deviations were explained by sensitivity analysis and model simplifications, e.g., material data or lower acting force levels by malalignment and differences between virtual and experimental implantation. The findings verify the feasibility of the proposed energy harvesting concept and form the basis for design optimisations with increased power output.

Prediction of interfragmentary movement in fracture fixation constructs using a combination of finite element modeling and rigid body assumptions

The amount of interfragmentary movement has been identified as a crucial factor for successful fracture healing. The aim of our study was to combine finite element analysis with a rigid body assumption to efficiently predict interfragmentary movement in fixed tibial fractures. The interfragmentary movement in a transverse tibial shaft fracture (AO/OTA type 42-A3) fixed with a locked plating construct was simulated using finite element analysis. In order to assess the contribution of the components on the resulting interfragmentary movement, the tibia, screws and embedding was either simulated deformable or as rigid body. The rigid and the deformable model accurately predicted the interfragmentary movement (R² = 0.99). The axial movement ranged between 0.1 mm and 1.3 mm and shear movements were between 0.2 mm and 0.5 mm. Differences between the two models were smaller than 73 μm (axial) and 46 μm (shear). The rigid body assumption reduced computation time and memory usage by up to 61% and 97%, respectively.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53-0.65, average error of 13-17%). A lower correlation was found for failure load (R2 = 0.21-0.48, average error of 9-15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75-0.80 for stiffness, R2 = 0.55-0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Finite element analysis of bone remodelling with piezoelectric effects using an open-source framework

Bone tissue exhibits piezoelectric properties and thus is capable of transforming mechanical stress into electrical potential. Piezoelectricity has been shown to play a vital role in bone adaptation and remodelling processes. Therefore, to better understand the interplay between mechanical and electrical stimulation during these processes, strain-adaptive bone remodelling models without and with considering the piezoelectric effect were simulated using the Python-based open-source software framework. To discretise numerical attributes, the finite element method (FEM) was used for the spatial variables and an explicit Euler scheme for the temporal derivatives. The predicted bone apparent density distributions were qualitatively and quantitatively evaluated against the radiographic scan of a human proximal femur and the bone apparent density calculated using a bone mineral density (BMD) calibration phantom, respectively. Additionally, the effect of the initial bone density on the resulting predicted density distribution was investigated globally and locally. The simulation results showed that the electrically stimulated bone surface enhanced bone deposition and these are in good agreement with previous findings from the literature. Moreover, mechanical stimuli due to daily physical activities could be supported by therapeutic electrical stimulation to reduce bone loss in case of physical impairment or osteoporosis. The bone remodelling algorithm implemented using an open-source software framework facilitates easy accessibility and reproducibility of finite element analysis made.

Reporting checklist for verification and validation of finite element analysis in orthopedic and trauma biomechanics

Finite element analysis (FEA) has become a fundamental tool for biomechanical investigations in the last decades. Despite several existing initiatives and guidelines for reporting on research methods and results, there are still numerous issues that arise when using computational models in biomechanical investigations. According to our knowledge, these problems and controversies lie mainly in the verification and validation (V&V) process as well as in the set-up and evaluation of FEA. This work aims to introduce a checklist including a report form defining recommendations for FEA in the field of Orthopedic and Trauma (O&T) biomechanics. Therefore, a checklist was elaborated which summarizes and explains the crucial methodologies for the V&V process. In addition, a report form has been developed which contains the most important steps for reporting future FEA. An example of the report form is shown, and a template is provided, which can be used as a uniform basis for future documentation. The future application of the presented report form will show whether serious errors in biomechanical investigations using FEA can be minimized by this checklist. Finally, the credibility of the FEA in the clinical area and the scientific exchange in the community regarding reproducibility and exchangeability can be improved.

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.

Stress and strain distribution in femoral heads for hip resurfacing arthroplasty with different materials: A finite element analysis

Femoral bone loss due to stress and strain shielding is a common problem in hip resurfacing arthroplasty (HRA), which arises from the different stiffness of implant materials and the adjacent bone. Usually, the implants used in HRA are made of cobalt-chromium alloy (CoCr). As a novel concept, implants may also be made of ceramics, whose stiffness exceeds that of the adjacent bone by a multiple. Therefore, this computational study aimed to evaluate whether poly (ether-ether-ketone) (PEEK) or a hybrid material with a PEEK body and ceramic surface made of alumina toughened zirconia (ATZ) might be more suitable implant alternatives for HRA, as they can avoid stress and strain shielding. A reconstructed model of a human femur with an HRA implant was simulated, whereby the material of the HRA was varied between CoCr, ATZ, zirconia toughened alumina (ZTA), PEEK, and a hybrid PEEK-ATZ material. The implant fixation method also varied (cemented or cementless). The simulated models were compared with an intact model to analyze stress and strain distribution in the femoral head and neck. The strain distribution was evaluated at a total of 30,344 (cemented HRA) and 63,531 (uncemented HRA) nodes in the femoral head and neck region and divided into different strain regions (<400 µm/m: atrophy; 400-3000 μm/m: bone preserving and building; 3000-20,000 μm/m: yielding and >20,000 μm/m fracture). In addition, the mechanical stability of the implants was evaluated. When the material of the HRA implant was simulated as metal or ceramic while evaluating the strains, it was seen that around 22-26% of the analyzed nodes in the femoral head and neck were in an atrophic region, 47-51% were in a preserving or building region, and 27-28% were in a yielding region. In the case of PEEK implant, less than 0.5% of the analyzed nodes were in an atrophic region, 66-69% in a preserving or building region, and 31-34% in a yielding region. The fixation technique also had a small influence. When a hybrid HRA was simulated, the strains at the analyzed nodes depended on the thickness of the ceramic material. In conclusion, the material of the HRA implant was crucial in terms of stress and strain distribution in the adjacent bone. HRA made of PEEK or a hybrid material leads to decisively reduced stress and strain alteration compared to stiffer materials such as CoCr, ATZ, and ZTA. This confirms the potential for reduction in stress and strain shielding in the femoral head with the use of a hybrid material with a PEEK body for HRA.

The Application of Digital Volume Correlation (DVC) to Evaluate Strain Predictions Generated by Finite Element Models of the Osteoarthritic Humeral Head

Continuum-level finite element models (FEMs) of the humerus offer the ability to evaluate joint replacement designs preclinically; however, experimental validation of these models is critical to ensure accuracy. The objective of the current study was to quantify experimental full-field strain magnitudes within osteoarthritic (OA) humeral heads by combining mechanical loading with volumetric microCT imaging and digital volume correlation (DVC). The experimental data was used to evaluate the accuracy of corresponding FEMs. Six OA humeral head osteotomies were harvested from patients being treated with total shoulder arthroplasty and mechanical testing was performed within a microCT scanner. MicroCT images (33.5 µm isotropic voxels) were obtained in a pre- and post-loaded state and BoneDVC was used to quantify full-field experimental strains (≈ 1 mm nodal spacing, accuracy = 351 µstrain, precision = 518 µstrain). Continuum-level FEMs with two types of boundary conditions (BCs) were simulated: DVC-driven and force-driven. Accuracy of the FEMs was found to be sensitive to the BC simulated with better agreement found with the use of DVC-driven BCs (slope = 0.83, r² = 0.80) compared to force-driven BCs (slope = 0.22, r² = 0.12). This study quantified mechanical strain distributions within OA trabecular bone and demonstrated the importance of BCs to ensure the accuracy of predictions generated by corresponding FEMs.