What makes an accurate and reliable subject-specific finite element model? A case study of an elephant femur

Pre-sliding of femoral neck system improves fixation stability in pauwels type III femoral neck fracture: a finite element analysis

BACKGROUND

Femoral neck fractures are a common injury in older adults and their management presents a significant challenge for orthopedic surgeons. The Femoral Neck System (FNS) was recently introduced for the fixation of femur neck fractures. Although neck shortening was reduced with the FNS, the complication rates were not reduced. Thus, improvements to enhance fixation stability should be made for the FNS. We hypothesized that (1) the pre-sliding technique and (2) the use of longer anti-rotation screw would increase fracture stability. This study aimed to determine the change in fracture stability using the pre-sliding technique and long anti-rotation screw in the FNS for fixation of Pauwels type III femoral neck fractures.

METHODS

Finite element models of Pauwels type III femoral neck fracture fixed with pre-sliding FNS and 5-mm longer anti-rotation screw were established. The models were subjected to normal walking load. The material properties of the elements belonging to the bone were mapped by assigning the formulation with the computed tomography Hounsfield unit.

RESULTS

Pauwels type III femoral neck fractures fixed with pre-slided FNS showed better fracture stability, decreasing fracture gap and sliding by 14% and 12%, respectively, under normal walking load. No element of cortical bone in any of the models had an absolute value of principal strain that exceeded 1%. The peak von Mises stress (VMS) of the implants ranged from 260 to 289 MPa, and the highest peak VMS value was 50% lower than the yield strength of the titanium alloy (800 MPa). The longer anti-rotation screw did not affect fracture stability.

CONCLUSIONS

The pre-sliding technique using the FNS showed higher fracture stability than the standard fixation technique for a Pauwels type III femoral neck fracture. The longer anti-rotation screw did not contribute significantly to fixation stability. As this finite element analysis considered the inhomogeneous mechanical property of the bone, it offered equivalent mechanical conditions to investigate the components of interest.

Trajectory of bolt and length of plate in femoral neck system determine the stability of femur neck fracture and risk of subsequent subtrochanteric fracture : a finite element analysis

BACKGROUND

This study aimed to analyze the differences in the stability of fractures, stress distribution around the distal-most screw according to the length of the plate and the trajectory of the bolt in Pauwels type III femoral neck fracture using the femoral neck system (FNS).

METHODS

Finite element models of Pauwels type III femoral neck fractures were established with surgical variations in the trajectory of the bolt (central, inferior, valgus, and varus) and length of the lateral plate (1- and 2-hole plate). The models were subsequently subjected to normal walking and stair-climbing loads.

RESULTS

The screw-holding cortical bone in subtrochanter in the model with a 2-hole plate and the bolt in the inferior trajectory and the models with 1-hole or 2-hole plate and the bolt in valgus trajectory had shown greater maximum principal strain than the models with central or varus trajectories. The gap and sliding distance on the fracture surface were larger with inferior or varus trajectories of the bolt and smaller with the valgus trajectory of the bolt under both loads, compared to those of the central trajectory.

CONCLUSION

For the fixation of Pauwels type III femoral neck fracture, the trajectory of the FNS bolt and the length of the plate affect the mechanical stability of the fracture and the strain of cortical bone around the distal-most screw. The surgical target should stay on the central trajectory of the bolt and the 2-hole plate's mechanical benefits did not exceed the risk.

A novel training-free method for real-time prediction of femoral strain

Surrogate methods for rapid calculation of femoral strain are limited by the scope of the training data. We compared a newly developed training-free method based on the superposition principle (Superposition Principle Method, SPM) and popular surrogate methods for calculating femoral strain during activity. Finite-element calculations of femoral strain, muscle, and joint forces for five different activity types were obtained previously. Multi-linear regression, multivariate adaptive regression splines, and Gaussian process were trained for 50, 100, 200, and 300 random samples generated using Latin Hypercube (LH) and Design of Experiment (DOE) sampling. The SPM method used weighted linear combinations of 173 activity-independent finite-element analyses accounting for each muscle and hip contact force. Across the surrogate methods, we found that 200 DOE samples consistently provided low error (RMSE < 100 µε), with model construction time ranging from 3.8 to 63.3 h and prediction time ranging from 6 to 1236 s per activity. The SPM method provided the lowest error (RMSE = 40 µε), the fastest model construction time (3.2 h) and the second fastest prediction time per activity (36 s) after Multi-linear Regression (6 s). The SPM method will enable large numerical studies of femoral strain and will narrow the gap between bone strain prediction and real-time clinical applications.

Testing hypotheses for the function of the carnivoran baculum using finite-element analysis

The baculum (os penis) is a mineralized bone within the glans of the mammalian penis and is one of the most morphologically diverse structures in the mammal skeleton. Recent experimental work provides compelling evidence for sexual selection shaping the baculum, yet the functional mechanism by which this occurs remains unknown. Previous studies have tested biomechanical hypotheses for the role of the baculum based on simple metrics such as length and diameter, ignoring the wealth of additional shape complexity present. For the first time, to our knowledge, we apply a computational simulation approach (finite-element analysis; FEA) to quantify the three-dimensional biomechanical performance of carnivoran bacula (n = 74) based upon high-resolution micro-computed tomography scans. We find a marginally significant positive correlation between sexual size dimorphism and baculum stress under compressive loading, counter to the 'vaginal friction' hypothesis of bacula becoming more robust to overcome resistance during initial intromission. However, a highly significant negative relationship exists between intromission duration and baculum stress under dorsoventral bending. Furthermore, additional FEA simulations confirm that the presence of a ventral groove would reduce deformation of the urethra. We take this as evidence in support of the 'prolonged intromission' hypothesis, suggesting the carnivoran baculum has evolved in response to pressures on the duration of copulation and protection of the urethra.

The Tarsometatarsus of the Ostrich Struthio camelus: Anatomy, Bone Densities, and Structural Mechanics

Background

The ostrich Struthio camelus reaches the highest speeds of any extant biped, and has been an extraordinary subject for studies of soft-tissue anatomy and dynamics of locomotion. An elongate tarsometatarsus in adult ostriches contributes to their speed. The internal osteology of the tarsometatarsus, and its mechanical response to forces of running, are potentially revealing about ostrich foot function.

Methods/Principal Findings

Computed tomography (CT) reveals anatomy and bone densities in tarsometatarsi of an adult and a young juvenile ostrich. A finite element (FE) model for the adult was constructed with properties of compact and cancellous bone where these respective tissues predominate in the original specimen. The model was subjected to a quasi-static analysis under the midstance ground reaction and muscular forces of a fast run. Anatomy–Metatarsals are divided proximally and distally and unify around a single internal cavity in most adult tarsometatarsus shafts, but the juvenile retains an internal three-part division of metatarsals throughout the element. The juvenile has a sparsely ossified hypotarsus for insertion of the m. fibularis longus, as part of a proximally separate third metatarsal. Bone is denser in all regions of the adult tarsometatarsus, with cancellous bone concentrated at proximal and distal articulations, and highly dense compact bone throughout the shaft. Biomechanics–FE simulations show stress and strain are much greater at midshaft than at force applications, suggesting that shaft bending is the most important stressor of the tarsometatarsus. Contraction of digital flexors, inducing a posterior force at the TMT distal condyles, likely reduces buildup of tensile stresses in the bone by inducing compression at these locations, and counteracts bending loads. Safety factors are high for von Mises stress, consistent with faster running speeds known for ostriches.

Conclusions/Significance

High safety factors suggest that bone densities and anatomy of the ostrich tarsometatarsus confer strength for selectively critical activities, such as fleeing and kicking predators. Anatomical results and FE modeling of the ostrich tarsometatarsus are a useful baseline for testing the structure’s capabilities and constraints for locomotion, through ontogeny and the full step cycle. With this foundation, future analyses can incorporate behaviorally realistic strain rates and distal joint forces, experimental validation, and proximal elements of the ostrich hind limb.

Experimental tests of planar strain theory for predicting bone cross-sectional longitudinal and shear strains

Understanding the diversity of skeletal loading regimes in vertebrate long bones during locomotion has been significantly enhanced by the application of planar strain theory (PST) to in vivo bone strain data. PST is used to model the distribution of longitudinal strains normal to the bone's transverse cross-section and the location of the neutral axis of bending. To our knowledge, the application of this theory to skeletal biomechanics has not been experimentally validated. We evaluated the accuracy of PST using strain measurements from emu tibiotarsi instrumented with four strain gauges and loaded in ex vivo four-point bending. Using measured strains from three-gauge combinations, PST was applied to predict strain values at a fourth gauge's location. Experimentally measured and predicted strain values correlated linearly with a slope near 1.0, suggesting that PST accurately predicts longitudinal strains. Additionally, we assessed the use of PST to extrapolate shear strains to locations on a bone not instrumented with rosette strain gauges. Guineafowl TBTs were instrumented with rosette strain gauges and in vivo longitudinal and shear strains were measured during treadmill running. Individual-specific and sample-mean ratios between measured longitudinal strains from the medial and posterior bone surfaces were used to extrapolate posterior-site shear strain from shear strains measured on the medial surface. Measured and predicted shear strains at the posterior gauge site using either ratio showed trends for a positive correlation between measured and predicted strains, but the correlation did not equal 1.0 and had a non-zero intercept, suggesting that the use of PST should be carefully considered in the context of the goals of the study and the desired precision for the predicted shear strains.

Biomechanical implications of intraspecific shape variation in chimpanzee crania: moving toward an integration of geometric morphometrics and finite element analysis

In a broad range of evolutionary studies, an understanding of intraspecific variation is needed in order to contextualize and interpret the meaning of variation between species. However, mechanical analyses of primate crania using experimental or modeling methods typically encounter logistical constraints that force them to rely on data gathered from only one or a few individuals. This results in a lack of knowledge concerning the mechanical significance of intraspecific shape variation that limits our ability to infer the significance of interspecific differences. This study uses geometric morphometric methods (GM) and finite element analysis (FEA) to examine the biomechanical implications of shape variation in chimpanzee crania, thereby providing a comparative context in which to interpret shape-related mechanical variation between hominin species. Six finite element models (FEMs) of chimpanzee crania were constructed from CT scans following shape-space Principal Component Analysis (PCA) of a matrix of 709 Procrustes coordinates (digitized onto 21 specimens) to identify the individuals at the extremes of the first three principal components. The FEMs were assigned the material properties of bone and were loaded and constrained to simulate maximal bites on the P(3) and M(2) . Resulting strains indicate that intraspecific cranial variation in morphology is associated with quantitatively high levels of variation in strain magnitudes, but qualitatively little variation in the distribution of strain concentrations. Thus, interspecific comparisons should include considerations of the spatial patterning of strains rather than focus only on their magnitudes.

Comparative finite-element analysis: a single computational modelling method can estimate the mechanical properties of porcine and human vertebrae

Significant advances in the functional analysis of musculoskeletal systems require the development of modelling techniques with improved focus, accuracy and validity. This need is particularly visible in the fields, such as palaeontology, where unobservable parameters may lie at the heart of the most interesting research questions, and where models and simulations may provide some of the most innovative solutions. Here, we report on the development of a computational modelling method to generate estimates of the mechanical properties of vertebral bone across two living species, using elderly human and juvenile porcine specimens as cases with very different levels of bone volume fraction and mineralization. This study is presented in two parts; part I presents the computational model development and validation, and part II the virtual loading regime and results. This work paves the way for the future estimation of mechanical properties in fossil mammalian bone.

Effects of densitometry, material mapping and load estimation uncertainties on the accuracy of patient-specific finite-element models of the scapula

Patient-specific biomechanical models including patient-specific finite-element (FE) models are considered potentially important tools for providing personalized healthcare to patients with musculoskeletal diseases. A multi-step procedure is often needed to generate a patient-specific FE model. As all involved steps are associated with certain levels of uncertainty, it is important to study how the uncertainties of individual components propagate to final simulation results. In this study, we considered a specific case of this problem where the uncertainties of the involved steps were known and the aim was to determine the uncertainty of the predicted strain distribution. The effects of uncertainties of three important components of patient-specific models, including bone density, musculoskeletal loads and the parameters of the material mapping relationship on the predicted strain distributions, were studied. It was found that the number of uncertain components and the level of their uncertainty determine the uncertainty of simulation results. The 'average' uncertainty values were found to be relatively small even for high levels of uncertainty in the components of the model. The 'maximum' uncertainty values were, however, quite high and occurred in the areas of the scapula that are of the greatest clinical relevance. In addition, the uncertainty of the simulation result was found to be dependent on the type of movement analysed, with abduction movements presenting consistently lower uncertainty values than flexion movements.

More than one way of being a moa: differences in leg bone robustness map divergent evolutionary trajectories in Dinornithidae and Emeidae (Dinornithiformes)

The extinct moa of New Zealand included three families (Megalapterygidae; Dinornithidae; Emeidae) of flightless palaeognath bird, ranging in mass from <15 kg to >200 kg. They are perceived to have evolved extremely robust leg bones, yet current estimates of body mass have very wide confidence intervals. Without reliable estimators of mass, the extent to which dinornithid and emeid hindlimbs were more robust than modern species remains unclear. Using the convex hull volumetric-based method on CT-scanned skeletons, we estimate the mass of a female Dinornis robustus (Dinornithidae) at 196 kg (range 155–245 kg) and of a female Pachyornis australis (Emeidae) as 50 kg (range 33–68 kg). Finite element analysis of CT-scanned femora and tibiotarsi of two moa and six species of modern palaeognath showed that P. australis experienced the lowest values for stress under all loading conditions, confirming it to be highly robust. In contrast, stress values in the femur of D. robustus were similar to those of modern flightless birds, whereas the tibiotarsus experienced the highest level of stress of any palaeognath. We consider that these two families of Dinornithiformes diverged in their biomechanical responses to selection for robustness and mobility, and exaggerated hindlimb strength was not the only successful evolutionary pathway.

Beware the black box: investigating the sensitivity of FEA simulations to modelling factors in comparative biomechanics

Finite element analysis (FEA) is a computational technique of growing popularity in the field of comparative biomechanics, and is an easily accessible platform for form-function analyses of biological structures. However, its rapid evolution in recent years from a novel approach to common practice demands some scrutiny in regards to the validity of results and the appropriateness of assumptions inherent in setting up simulations. Both validation and sensitivity analyses remain unexplored in many comparative analyses, and assumptions considered to be ‘reasonable’ are often assumed to have little influence on the results and their interpretation.

Here we report an extensive sensitivity analysis where high resolution finite element (FE) models of mandibles from seven species of crocodile were analysed under loads typical for comparative analysis: biting, shaking, and twisting. Simulations explored the effect on both the absolute response and the interspecies pattern of results to variations in commonly used input parameters. Our sensitivity analysis focuses on assumptions relating to the selection of material properties (heterogeneous or homogeneous), scaling (standardising volume, surface area, or length), tooth position (front, mid, or back tooth engagement), and linear load case (type of loading for each feeding type).

Our findings show that in a comparative context, FE models are far less sensitive to the selection of material property values and scaling to either volume or surface area than they are to those assumptions relating to the functional aspects of the simulation, such as tooth position and linear load case. Results show a complex interaction between simulation assumptions, depending on the combination of assumptions and the overall shape of each specimen. Keeping assumptions consistent between models in an analysis does not ensure that results can be generalised beyond the specific set of assumptions used. Logically, different comparative datasets would also be sensitive to identical simulation assumptions; hence, modelling assumptions should undergo rigorous selection. The accuracy of input data is paramount, and simulations should focus on taking biological context into account. Ideally, validation of simulations should be addressed; however, where validation is impossible or unfeasible, sensitivity analyses should be performed to identify which assumptions have the greatest influence upon the results.

Finite element modelling versus classic beam theory: comparing methods for stress estimation in a morphologically diverse sample of vertebrate long bones

Classic beam theory is frequently used in biomechanics to model the stress behaviour of vertebrate long bones, particularly when creating intraspecific scaling models. Although methodologically straightforward, classic beam theory requires complex irregular bones to be approximated as slender beams, and the errors associated with simplifying complex organic structures to such an extent are unknown. Alternative approaches, such as finite element analysis (FEA), while much more time-consuming to perform, require no such assumptions. This study compares the results obtained using classic beam theory with those from FEA to quantify the beam theory errors and to provide recommendations about when a full FEA is essential for reasonable biomechanical predictions. High-resolution computed tomographic scans of eight vertebrate long bones were used to calculate diaphyseal stress owing to various loading regimes. Under compression, FEA values of minimum principal stress (σ(min)) were on average 142 per cent (±28% s.e.) larger than those predicted by beam theory, with deviation between the two models correlated to shaft curvature (two-tailed p = 0.03, r(2) = 0.56). Under bending, FEA values of maximum principal stress (σ(max)) and beam theory values differed on average by 12 per cent (±4% s.e.), with deviation between the models significantly correlated to cross-sectional asymmetry at midshaft (two-tailed p = 0.02, r(2) = 0.62). In torsion, assuming maximum stress values occurred at the location of minimum cortical thickness brought beam theory and FEA values closest in line, and in this case FEA values of τ(torsion) were on average 14 per cent (±5% s.e.) higher than beam theory. Therefore, FEA is the preferred modelling solution when estimates of absolute diaphyseal stress are required, although values calculated by beam theory for bending may be acceptable in some situations.

A sensitivity analysis to the role of the fronto-parietal suture in Lacerta bilineata: a preliminary finite element study

Cranial sutures are sites of bone growth and development but micromovements at these sites may distribute the load across the skull more evenly. Computational studies have incorporated sutures into finite element (FE) models to assess various hypotheses related to their function. However, less attention has been paid to the sensitivity of the FE results to the shape, size, and stiffness of the modeled sutures. Here, we assessed the sensitivity of the strain predictions to the aforementioned parameters in several models of fronto-parietal (FP) suture in Lacerta bilineata. For the purpose of this study, simplifications were made in relation to modeling the bone properties and the skull loading. Results highlighted that modeling the FP as either an interdigitated suture or a simplified butt suture, did not reduce the strain distribution in the FP region. Sensitivity tests showed that similar patterns of strain distribution can be obtained regardless of the size of the suture, or assigned stiffness, yet the exact magnitudes of strains are highly sensitive to these parameters. This study raises the question whether the morphogenesis of epidermic scales in the FP region in the Lacertidae is related to high strain fields in this region, because of micromovement in the FP suture.

Determination and validation of the elastic moduli of small and complex biological samples: bone and keratin in bird beaks

In recent years, there has been a surge in the development of finite-element (FE) models aimed at testing biological hypotheses. For example, recent modelling efforts suggested that the beak in Darwin's finches probably evolved in response to fracture avoidance. However, knowledge of the material properties of the structures involved is crucial for any model. For many biological structures, these data are not available and may be difficult to obtain experimentally given the complex nature of biological structures. Beaks are interesting as they appear to be highly optimized in some cases. In order to understand the biomechanics of this small and complex structure, we have been developing FE models that take into account the bilayered structure of the beak consisting of bone and keratin. Here, we present the results of efforts related to the determination and validation of the elastic modulus of bone and keratin in bird beaks. The elastic moduli of fresh and dried samples were obtained using a novel double-indentation technique and through an inverse analysis. A bending experiment is used for the inverse analysis and the validation of the measurements. The out-of-plane displacements during loading are measured using digital speckle pattern interferometry.

Virtual experiments, physical validation: dental morphology at the intersection of experiment and theory

Computational models such as finite-element analysis offer biologists a means of exploring the structural mechanics of biological systems that cannot be directly observed. Validated against experimental data, a model can be manipulated to perform virtual experiments, testing variables that are hard to control in physical experiments. The relationship between tooth form and the ability to break down prey is key to understanding the evolution of dentition. Recent experimental work has quantified how tooth shape promotes fracture in biological materials. We present a validated finite-element model derived from physical compression experiments. The model shows close agreement with strain patterns observed in photoelastic test materials and reaction forces measured during these experiments. We use the model to measure strain energy within the test material when different tooth shapes are used. Results show that notched blades deform materials for less strain energy cost than straight blades, giving insights into the energetic relationship between tooth form and prey materials. We identify a hypothetical 'optimal' blade angle that minimizes strain energy costs and test alternative prey materials via virtual experiments. Using experimental data and computational models offers an integrative approach to understand the mechanics of tooth morphology.