Morphology based anisotropic finite element models of the proximal femur validated with experimental data

Scaphoid numerical simulation of the critical loading until fracture

The numerical study of the scaphoid fracture, although it is relatively unexplored, can be of great clinical interest since it is highly common and can result in temporary or persistent disability. In this manuscript, seven combinations of boundary conditions and contacts between adjacent bones, together with four different loads, simulating real hand movements, are assessed. Three different fracture criteria for bones are employed to study the failure of the scaphoid with the aforementioned combination of interaction conditions. The results offer an interesting view of the accuracy of the possible interaction between adjacent bones. For future calculation, it would be possible to choose a combination of the balance between precision and computational cost savings. This study provides a comprehensive assessment into the modeling of the scaphoid bone and its interactions with adjacent bones. The findings reveal that various choices of interactions can yield similar results, allowing for flexibility in selecting interaction models based on desired accuracy or computational efficiency. Ultimately, this study establishes a foundational understanding for future research on modeling scaphoid motion.

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.

Effect of fall direction on the lower hip fracture risk in athletes with different loading histories: A finite element modeling study in multiple sideways fall configurations

Physical loading makes bones stronger through structural adaptation. Finding effective modes of exercise to improve proximal femur strength has the potential to decrease hip fracture risk. Previous proximal femur finite element (FE) modeling studies have indicated that the loading history comprising impact exercises is associated with substantially higher fracture load. However, those results were limited only to one specified fall direction. It remains thus unclear whether exercise-induced higher fracture load depends on the fall direction. To address this, using magnetic resonance images of proximal femora from 91 female athletes (mean age 24.7 years with >8 years competitive career) and their 20 non-athletic but physically active controls (mean age 23.7 years), proximal femur FE models were created in 12 different sideways fall configurations. The athletes were divided into five groups by typical loading patterns of their sports: high-impact (H-I: 9 triple- and 10 high-jumpers), odd-impact (O-I: 9 soccer and 10 squash players), high-magnitude (H-M: 17 powerlifters), repetitive-impact (R-I: 18 endurance runners), and repetitive non-impact (R-NI: 18 swimmers). Compared to the controls, the FE models showed that the H-I and R-I groups had significantly (p < 0.05) higher fracture loads, 11-17% and 22-28% respectively, in all fall directions while the O-I group had significantly 10-11% higher fracture loads in four fall directions. The H-M and R-NI groups did not show significant benefit in any direction. Also, the analyses of the minimum fall strength (MFS) among these multiple fall configurations confirmed significantly 15%, 11%, and 14% higher MFSs in these impact groups, respectively, compared to the controls. These results suggest that the lower hip fracture risk indicated by higher fracture loads in athletes engaged in high impact or repetitive impact sports is independent of fall direction whereas the lower fracture risk attributed to odd-impact exercise is more modest and specific to the fall direction. Moreover, in concordance with the literature, the present study also confirmed that the fracture risk increases if the impact is imposed on the more posterolateral aspect of the hip. The present results highlight the importance of engaging in the impact exercises to prevent hip fractures and call for retrospective studies to investigate whether specific impact exercise history in adolescence and young adulthood is also associated with lower incidence of hip fractures in later life.

Which experimental procedures influence the apparent proximal femoral stiffness? A parametric study

Background

Experimental validation is the gold standard for the development of FE predictive models of bone. Employing multiple loading directions could improve this process. To capture the correct directional response of a sample, the effect of all influential parameters should be systematically considered. This study aims to determine the impact of common experimental parameters on the proximal femur’s apparent stiffness.

Methods

To that end, a parametric approach was taken to study the effects of: repetition, pre-loading, re-adjustment, re-fixation, storage, and μCT scanning as random sources of uncertainties, and loading direction as the controlled source of variation in both stand and side-fall configurations. Ten fresh-frozen proximal femoral specimens were prepared and tested with a novel setup in three consecutive sets of experiments. The neutral state and 15-degree abduction and adduction angles in both stance and fall configurations were tested for all samples and parameters. The apparent stiffness of the samples was measured using load-displacement data from the testing machine and validated against marker displacement data tracked by DIC cameras.

Results

Among the sources of uncertainties, only the storage cycle affected the proximal femoral apparent stiffness significantly. The random effects of setup manipulation and intermittent μCT scanning were negligible. The 15^∘ deviation in loading direction had a significant effect comparable in size to that of switching the loading configuration from neutral stance to neutral side-fall.

Conclusion

According to these results, comparisons between the stiffness of the samples under various loading scenarios can be made if there are no storage intervals between the different load cases on the same samples. These outcomes could be used as guidance in defining a highly repeatable and multi-directional experimental validation study protocol.

Real-time replication of three-dimensional and time-varying physiological loading cycles for bone and implant testing: A novel protocol demonstrated for the proximal human femur while walking

In vitro real-time replication of three-dimensional, time-varying load profiles acting on human bones during physical activity can advance bone and implant testing protocols. This study aimed to develop a novel protocol for applying the three-dimensional, time-varying hip contact force while walking to a human femur specimen. The target force profile was obtained from the literature. A proximal femur from an elderly female donor was instrumented using ten rosette strain gages and tested using a custom-made hexapod robot. A load-control algorithm determined the robot position generating the target force at low frequency (0.0004 Hz). Five cycles of the robot position were played back at five intermediate frequencies up to real-time (0.04, 0.08, 0.16, 0.4, and 0.8 Hz). The hip reaction force, the length of the actuators (position), and cortical strains were compared. The error in the load-control force was 0.3 ± 4.2 N (mean ± SD). The last three force, position, and strain cycles varied by less than 1.1% for every frequency analyzed. Across frequencies, the force increased by 28% at 0.8 Hz as a logarithmic function of frequency (R² = 0.98). The position and strain error linearly increased with frequency up to 0.4 Hz. The median position error and the interquartile range of the strain error reached 15% and 13% at 0.8 Hz. Changes of force and cortical strain at increasing frequencies were linearly related (R² = 0.99). Therefore, the protocol developed can provide repeatable three-dimensional time-varying load profiles, although the comparison of the specimen deformation obtained across frequencies should be considered with care, particularly in the higher frequency range. This information supports the design of dynamic tests of bone and implants.

Bone Density Micro-CT Assessment during Embedding of the Innovative Multi-Spiked Connecting Scaffold in Periarticular Bone to Elaborate a Validated Numerical Model for Designing Biomimetic Fixation of Resurfacing Endoprostheses

Our team has been working for some time on designing a new kind of biomimetic fixation of resurfacing endoprostheses, in which the innovative multi-spiked connecting scaffold (MSC-Scaffold) that mimics the natural interface between articular cartilage and periarticular trabecular bone in human joints is the crucial element. This work aimed to develop a numerical model enabling the design of the considered joint replacement implant that would reflect the mechanics of interacting biomaterials. Thus, quantitative micro-CT analysis of density distribution in bone material during the embedding of MSC-Scaffold in periarticular bone was applied. The performed numerical studies and corresponding mechanical tests revealed, under the embedded MSC-Scaffold, the bone material densification affecting its mechanical properties. On the basis of these findings, the built numerical model was modified by applying a simulated insert of densified bone material. This modification led to a strong correlation between the re-simulation and experimental results (FVU = 0.02). The biomimetism of the MSC-Scaffold prototype that provided physiological load transfer from implant to bone was confirmed based on the Huber–von Mises–Hencky (HMH) stress maps obtained with the validated finite element (FE) model of the problem. The micro-CT bone density assessment performed during the embedding of the MSC-Scaffold prototype in periarticular bone provides insight into the mechanical behaviour of the investigated implant-bone system and validates the numerical model that can be used for the design of material and geometric features of a new kind of resurfacing endoprostheses fixation.

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.

Predicting population level hip fracture risk: a novel hierarchical model incorporating probabilistic approaches and factor of risk principles

Fall-related hip fractures are a major public health issue. While individual-level risk assessment tools exist, population-level predictive models could catalyze innovation in large-scale interventions. This study presents a hierarchical probabilistic model that predicts population-level hip fracture risk based on Factor of Risk (FOR) principles. Model validation demonstrated that FOR output aligned with a published dataset categorized by sex and hip fracture status. The model predicted normalized FOR for 100000 individuals simulating the Canadian older-adult population. Predicted hip fracture risk was higher for females (by an average of 38%), and increased with age (by15% per decade). Potential applications are discussed.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

Anisotropic computational modelling of bony structures from CT data: An almost automatic procedure

BACKGROUND AND OBJECTIVE

The use of modelling techniques that combine CT data and bone tissue micromechanics is spreading in computational biomechanics. Finite Element models show great potential in surgical planning of intervention and in prediction of stress and strain fields through a non-invasive method. The main challenge pertains to the reliable characterization of bone mechanical behaviour. An almost automatic procedure is here defined, which provides computational models of bony structures considering the actual anisotropy of bone tissue response. The innovative aspect resides on the automatic detection of the directions of anisotropy as the eigenvectors of a three-dimensional distribution matrix of HU values.

METHODS

The procedure combines CT data and micromechanics modelling techniques. Regarding a specific location, the procedure reports both the orthotropic elastic constants, by the analysis of the local HU value, and the anisotropic material directions, by the analysis of the HU values distribution around the specific location.

RESULTS

The procedure returns the distribution of bone tissue orthotropic elasticity tensor. The procedure proves to correctly respect the differentiation between cortical and trabecular bone. Principal directions show to be consistent with experimental data from ultrasound measurements. Regarding the material mapping from voxel to FE model, the developed strategies show to be reliable, leading to marginal errors (lower than 10%) for most of CT voxels (more than 90%). The computational analyses of typical structural loading conditions lead to strain values that are comparable with results from strain gauges experimentations. The development and the exploitation of FE models of different bony structures allow assessing the reliability of the procedure for cortical bone.

CONCLUSIONS

The results highlight the potentialities of the procedure in providing accurate patient-specific biomechanical models of bony structures starting from CT data. The accuracy and the automatism of the procedure are important factors for the development of real time clinical tools. The main limitations of this work remain the not fully automatism and the reliability assessment, which is based mainly on cortical bone regions only.

An exclusion approach for addressing partial volume artifacts with quantititive computed tomography-based finite element modeling of the proximal tibia

INTRODUCTION

Quantitative computed tomography based finite element modeling (QCT-FE) has potential to clarify the role of subchondral bone stiffness in osteoarthritis. The limited spatial resolution of clinical QCT systems, however, results in partial volume (PV) artifacts and low contrast between cortical and trabecular bone, which adversely affects the accuracy of QCT-FE models. The objective of this research was to evaluate the agreement between stiffness predictions offered by QCT-FE models of proximal tibial subchondral bone (constructed with and without a new voxel-exclusion algorithm) with experimentally-derived local subchondral bone structural stiffness.

METHODS

Thirteen proximal tibial compartments were obtained and imaged using QCT. Two types of QCT-FE models were developed: (1) standard model, which employed the standard procedure for QCT-FE modeling; and (2) "voxel exclusion (VE)" model, which addressed PV artifacts by excluding low density voxels during the material mapping stage of construction. We assessed agreement between QCT-FE stiffness estimates (using standard and VE approaches) with experimental stiffness by reporting predicted variance from linear regression and mean bias with 95% Limits of Agreement (LOA).

RESULTS

The standard and VE models explained 81% and 84% of the variance in experimentally measured stiffness, respectively. The standard model showed a mean bias of -268 N/mm (LOA -1210 to 679 N/mm); the VE model showed a mean bias of +59 N/mm (LOA -762 to 910 N/mm).

INTERPRETATION

The VE model explained more variance in subchondral bone stiffness with less bias. Our findings indicate that the VE method has potential to improve QCT-FE models of bone affected by PV artifacts.

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.

Numerical modelling of hip fracture patterns in human femur

BACKGROUND AND OBJECTIVE

Hip fracture morphology is an important factor determining the ulterior surgical repair and treatment, because of the dependence of the treatment on fracture morphology. Although numerical modelling can be a valuable tool for fracture prediction, the simulation of femur fracture is not simple due to the complexity of bone architecture and the numerical techniques required for simulation of crack propagation. Numerical models assuming homogeneous fracture mechanical properties commonly fail in the prediction of fracture patterns. This paper focuses on the prediction of femur fracture based on the development of a finite element model able to simulate the generation of long crack paths.

METHODS

The finite element model developed in this work demonstrates the capability of predicting fracture patterns under stance loading configuration, allowing the distinction between the main fracture paths: intracapsular and extracapsular fractures. It is worth noting the prediction of different fracture patterns for the same loading conditions, as observed during experimental tests.

RESULTS AND CONCLUSIONS

The internal distribution of bone mineral density and femur geometry strongly influences the femur fracture morphology and fracture load. Experimental fracture paths have been analysed by means of micro-computed tomography allowing the comparison of predicted and experimental crack surfaces, confirming the good accuracy of the numerical model.

Experimental mechanical strain measurement of tissues

Strain, an important biomechanical factor, occurs at different scales from molecules and cells to tissues and organs in physiological conditions. Under mechanical strain, the strength of tissues and their micro- and nanocomponents, the structure, proliferation, differentiation and apoptosis of cells and even the cytokines expressed by cells probably shift. Thus, the measurement of mechanical strain (i.e., relative displacement or deformation) is critical to understand functional changes in tissues, and to elucidate basic relationships between mechanical loading and tissue response. In the last decades, a great number of methods have been developed and applied to measure the deformations and mechanical strains in tissues comprising bone, tendon, ligament, muscle and brain as well as blood vessels. In this article, we have reviewed the mechanical strain measurement from six aspects: electro-based, light-based, ultrasound-based, magnetic resonance-based and computed tomography-based techniques, and the texture correlation-based image processing method. The review may help solving the problems of experimental and mechanical strain measurement of tissues under different measurement environments.

A comparison of density-modulus relationships used in finite element modeling of the shoulder

Subject- and site-specific modeling techniques greatly improve the accuracy of computational models derived from clinical-resolution quantitative computed tomography (QCT) data. The majority of shoulder finite element (FE) studies use density-modulus relationships developed for alternative anatomical locations. As such, the objectives of this study were to compare the six most commonly used density-modulus relationships in shoulder finite element (FE) studies. To achieve this, ninety-eight (98) virtual trabecular bone cores were extracted from uCT scans of scapulae from 14 cadaveric specimens (7 male; 7 female). Homogeneous tissue moduli of 20 GPa, and heterogeneous tissue moduli scaled by CT-intensity were considered. Micro finite element models (µ-FEMs) of each virtual core were compressively loaded to 0.5% apparent strain and apparent strain energy density (SED_app) was collected. Each uCT virtual core was then co-registered to clinical QCT images, QCT-FEMs created, and each of the 6 density-modulus relationships applied (6 × 98 = 588 QCT-FEMs). The loading and boundary conditions were replicated and SED_app was collected and compared to µ-FEM SED_app. When a homogeneous tissue modulus was considered in the µ-FEMs, SED_app was best predicted in QCT-FEMs with the density-modulus relationship developed from pooled anatomical locations (QCT-FEM SED_app = 0.979µ-FEM SED_app + 0.0066, r² = 0.933). A different density-modulus relationship best predicted SED_app (QCT-FEM SED_app = 1.014µ-FEM SED_app + 0.0034, r² = 0.935) when a heterogeneous tissue modulus was considered. This study compared density-modulus relationships used in shoulder FE studies using an independent computational methodology for comparing these relationships.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.