Probabilistic finite element analysis of a craniofacial finite element model

Antibacterial and osteoinductive properties of wollastonite scaffolds impregnated with propolis produced by additive manufacturing

Biocompatible ceramic scaffolds offer a promising approach to address the challenges in bone reconstruction. Wollastonite, well-known for its exceptional biocompatibility, has attracted significant attention in orthopedics and craniofacial fields. However, the antimicrobial properties of wollastonite have contradictory findings, necessitating further research to enhance its antibacterial characteristics. This study aimed to explore a new approach to improve in vitro biological response in terms of antimicrobial activity and cell proliferation by taking advantage of additive manufacturing for the development of scaffolds with complex geometries by 3D printing using propolis-modified wollastonite. The scaffolds were designed with a TPMS (Triply Periodic Minimal Surface) gyroid geometric shape and 3D printed prior to impregnation with propolis extract. The paste formulation was characterized by rheometric measurements, and the presence of propolis was confirmed by FTIR spectroscopy. The scaffolds were comprehensively assessed for their mechanical strength. The biological characterization involved evaluating the antimicrobial effects against Staphylococcus aureus and Staphylococcus epidermidis, employing Minimum Inhibitory Concentration (MIC), Zone of Inhibition (ZOI), and biofilm formation assays. Additionally, SaOs-2 cultures were used to study cell proliferation (Alamar blue assay), and potential osteogenic was tested (von Kossa, Alizarin Red, and ALP stainings) at different time points. Propolis impregnation did not compromise the mechanical properties of the scaffolds, which exhibited values comparable to human trabecular bone. Propolis incorporation conferred antibacterial activity against both Staphylococcus aureus and Staphylococcus epidermidis. The implementation of TPMS gyroid geometry in the scaffold design demonstrated favorable cell proliferation with increased metabolic activity and osteogenic potential after 21 days of cell cultures.

Does the model reflect the system? When two-dimensional biomechanics is not 'good enough'

Models are mathematical representations of systems, processes or phenomena. In biomechanics, finite-element modelling (FEM) can be a powerful tool, allowing biologists to test form-function relationships in silico, replacing or extending results of in vivo experimentation. Although modelling simplifications and assumptions are necessary, as a minimum modelling requirement the results of the simplified model must reflect the biomechanics of the modelled system. In cases where the three-dimensional mechanics of a structure are important determinants of its performance, simplified two-dimensional modelling approaches are likely to produce inaccurate results. The vertebrate mandible is one among many three-dimensional anatomical structures routinely modelled using two-dimensional FE analysis. We thus compare the stress regimes of our published three-dimensional model of the chimpanzee mandible with a published two-dimensional model of the chimpanzee mandible and identify several fundamental differences. We then present a series of two-dimensional and three-dimensional FE modelling experiments that demonstrate how three key modelling parameters, (i) dimensionality, (ii) symmetric geometry, and (iii) constraints, affect deformation and strain regimes of the models. Our results confirm that, in the case of the primate mandible (at least), two-dimensional FEM fails to meet this minimum modelling requirement and should not be used to draw functional, ecological or evolutionary conclusions.

Anthroengineering: an independent interdisciplinary field

In recent decades, funding agencies, institutes and professional bodies have recognized the profound benefits of transdisciplinarity in tackling targeted research questions. However, once questions are answered, the previously abundant support often dissolves. As such, the long-term benefits of these transdisciplinary approaches are never fully achieved. Over the last several decades, the integration of anthropology and engineering through inter- and multidisciplinary work has led to advances in fields such as design, human evolution and medical technologies. The lack of formal recognition, however, of this transdisciplinary approach as a unique entity rather than a useful tool or a subfield makes it difficult for researchers to establish laboratories, secure permanent jobs, fund long-term research programmes and train students in this approach. To facilitate the growth and development and witness the long-term benefits of this approach, we propose the integration of anthropology and engineering be recognized as a new, independent field known as anthroengineering. We present a working definition for anthroengineering and examples of how anthroengineering has been used. We discuss the necessity of recognizing anthroengineering as a unique field and explore potential novel applications. Finally, we discuss the future of anthroengineering, highlighting avenues for moving the field forward.

MR Imaging of Human Brain Mechanics In Vivo: New Measurements to Facilitate the Development of Computational Models of Brain Injury

Computational models of the brain and its biomechanical response to skull accelerations are important tools for understanding and predicting traumatic brain injuries (TBIs). However, most models have been developed using experimental data collected on animal models and cadaveric specimens, both of which differ from the living human brain. Here we describe efforts to noninvasively measure the biomechanical response of the human brain with MRI-at non-injurious strain levels-and generate data that can be used to develop, calibrate, and evaluate computational brain biomechanics models. Specifically, this paper reports on a project supported by the National Institute of Neurological Disorders and Stroke to comprehensively image brain anatomy and geometry, mechanical properties, and brain deformations that arise from impulsive and harmonic skull loadings. The outcome of this work will be a publicly available dataset ( http://www.nitrc.org/projects/bbir ) that includes measurements on both males and females across an age range from adolescence to older adulthood. This article describes the rationale and approach for this study, the data available, and how these data may be used to develop new computational models and augment existing approaches; it will serve as a reference to researchers interested in using these data.

Uncertainty quantification implementations in human hemodynamic flows

BACKGROUND AND OBJECTIVE

Human hemodynamic modeling is usually influenced by uncertainties occurring from a considerable unavailability of information linked to the boundary conditions and the physical properties used in the numerical models. Calculating the effect of these uncertainties on the numerical findings along the cardiovascular system is a demanding process due to the complexity of the morphology of the body and the area dynamics. To cope with all these difficulties, Uncertainty Quantification (UQ) methods seem to be an ideal tool.

RESULTS

This study focuses on analyzing and summarizing some of the recent research efforts and directions of implementing UQ in human hemodynamic flows by analyzing 139 research papers. Initially, the suitability of applying this approach is analyzed and demonstrated. Then, an overview of the most significant research work in various fields of biomedical hemodynamic engineering is presented. Finally, it is attempted to identify any possible forthcoming directions for research and methodological progress of UQ in biomedical sciences.

CONCLUSION

This review concludes that by finding the best statistical methods and parameters to represent the propagated uncertainties, while achieving a good interpretation of the interaction between input-output, is crucial for implementing UQ in biomedical sciences.

Effects of premature contact in maxillary alveolar bone in rats: relationship between experimental analyses and a micro scale FEA computational simulation study

OBJECTIVE

The aim of the investigation was to evaluate the maxillary alveolar bone morphology, bone architecture, and bone turnover in relation to the mechanical strain distribution in rats with dental premature contact.

MATERIALS AND METHODS

Fifty 2-month-old male Wistar rats were used. The premature contact group (N=40) received a unilateral (right side) resin cementation on the occlusal surface of the upper first molar. The animals were distributed in 4 subgroups according to the periods of euthanasia: 7, 14, 21, and 28 days after cementation (N=10, for each period). For the control group (N=10), the teeth were kept without resin, featuring a normal occlusion. The pieces including the upper first molars, alveolar bone, and periodontal tissue were processed to histological and immunohistochemical evaluation of RANK-L and TRAP protein expression. A three-dimensional bone microarchitecture analysis was performed, where the heads of animals were scanned using microtomography and analyzed using CT-Analyser software (Bruker, Kontich, Belgium). In the computer simulation by finite element analysis, two micro-scaled three-dimensional finite element models of first molar and dentoalveolar tissues were constructed, in representation of control and premature contact groups, using Materialise MIMICS Academic Research v18 (Materialise, Leuven, Belgium). The analysis was set to simulate a maxillary molar biting during the power stroke phase. The total deformation, equivalent strain, and minimum principal strain distribution were calculated.

RESULTS

The expression of RANK-L and TRAP presented higher positive ratio in the 7-day period compared to the control group. The three-dimensional morphometry showed decrease of bone volume in the premature contact, with significant values between the control and the 7-day and 14-day groups (P = 0.007). In FEA, the premature contact model presented a uniform compressive strain distribution in the alveolar bone crest compared to a non-uniform compressive strain distribution in the control model.

CONCLUSIONS

The results from FEA, 3D bone microarchitecture, and histological and immunohistochemical analyses showed that a model with dental traumatic occlusion resulted in changes of alveolar bone mechanobiology and, consequently, its morphology.

CLINICAL RELEVANCE

These results could be applied in dental treatment planning bringing biological and mechanical feedback to provide an effective mechanism to obtain physiological bone loss responses. Furthermore, this association between experimental and computational analyses will be important to figure out the alveolar bone response to mechanical stimulation in different clinical conditions.

Evaluation of Stress Distribution of Four Different Fixation Systems at High- and Low-Level Subcondylar Fractures on a Nonhomogenous Finite Element Model

PURPOSE

The aim of the present study was to provide insight into a suitable fixation system for subcondylar fractures located at different levels.

MATERIALS AND METHODS

High and low subcondylar fractures were simulated on a nonhomogenous mandibular model, and rhombic, trapezoid, and lambda plates and 2 miniplates were used for fixation. The stress in the bone and displacement of the fracture site were measured using finite element analysis.

RESULTS

For both high and low subcondylar fractures, the lowest von Mises stress was measured in the rhombic plate system. For high subcondylar fractures, the highest tension in the cortical bone was measured in the trapezoid plate system, and the highest compression was measured in the rhombic plate system. For low subcondylar fractures, the highest tension in the bone was measured in the rhombic system and the highest compression was measured in the trapezoid system. In both high and low subcondylar fracture models, the least displacement amount was measured in the 2-plate system.

CONCLUSIONS

The results of the present study have shown that the rhombic plate system might be the proper choice for high subcondylar fractures and the 2-plate system might provide better results for low subcondylar fractures.

Influence of population variability in ligament material properties on the mechanical behavior of ankle: a computational investigation

Biomechanical behavior of ankle ligaments varies among individuals, with the underlying mechanism at multiple scales remaining unquantified. The present probabilistic study investigated how population variability in ligament material properties would influence the joint mechanics. A previously developed finite element ankle model with parametric ligament properties was used. Taking the typical external rotation as example loading scenario, joint stability of the investigated population was consistently shared by specific ligaments within a narrow tolerance range, i.e. 62.8 ± 8.2 Nm under 36.1 ± 5.7° foot rotation. In parallel, the inherent material variability significantly alters the consequent injury patterns. Three most vulnerable ligaments and the consequent rupture sequences were identified, with the structural weak spot and the following progressive stability loss dominated by the relative stiffness among ligaments. This study demonstrated the feasibility of biofidelic models in investigating individual difference at the material level, and emphasized the importance of probabilistic description of individual difference when identifying the injury mechanism of a broad spectrum.

Stochastic analysis of a heterogeneous micro-finite element model of a mouse tibia

Finite element (FE) analysis can be used to predict bone mechanical environments that can be used for many important applications, such as the understanding of bone mechano-regulation mechanisms. However, when defining the FE models, uncertainty in bone material properties may lead to marked variations in the predicted mechanical environment. The aim of this study is to investigate the influence of uncertainty in bone material property on the mechanical environment of bone. A heterogeneous FE model of a mouse tibia was created from micro computed tomography images. Axial compression loading was applied, and all possible bone density-modulus relationships were considered through stochastic analysis. The 1st and 3rd principal strains (ε₁ and ε₃) and the strain energy density (SED) were quantified in the tibial volume of interest (VOI). The bounds of ε₁, ε₃, and SED were determined by the bounds of the density-modulus relationship; the bone mechanical environment (ε₁, ε₃, and SED) and the bone density-modulus relationship exhibit the same trend of change; the relative percentage differences caused by bone material uncertainty are up to 28%, 28%, and 21% for ε₁, ε₃, and SED, respectively. These data provide guidelines on the adoption of bone density-modulus relationship in heterogeneous FE models.

Computational Evaluation of Cochlear Implant Surgery Outcomes Accounting for Uncertainty and Parameter Variability

Cochlear implantation (CI) is a complex surgical procedure that restores hearing in patients with severe deafness. The successful outcome of the implanted device relies on a group of factors, some of them unpredictable or difficult to control. Uncertainties on the electrode array position and the electrical properties of the bone make it difficult to accurately compute the current propagation delivered by the implant and the resulting neural activation. In this context, we use uncertainty quantification methods to explore how these uncertainties propagate through all the stages of CI computational simulations. To this end, we employ an automatic framework, encompassing from the finite element generation of CI models to the assessment of the neural response induced by the implant stimulation. To estimate the confidence intervals of the simulated neural response, we propose two approaches. First, we encode the variability of the cochlear morphology among the population through a statistical shape model. This allows us to generate a population of virtual patients using Monte Carlo sampling and to assign to each of them a set of parameter values according to a statistical distribution. The framework is implemented and parallelized in a High Throughput Computing environment that enables to maximize the available computing resources. Secondly, we perform a patient-specific study to evaluate the computed neural response to seek the optimal post-implantation stimulus levels. Considering a single cochlear morphology, the uncertainty in tissue electrical resistivity and surgical insertion parameters is propagated using the Probabilistic Collocation method, which reduces the number of samples to evaluate. Results show that bone resistivity has the highest influence on CI outcomes. In conjunction with the variability of the cochlear length, worst outcomes are obtained for small cochleae with high resistivity values. However, the effect of the surgical insertion length on the CI outcomes could not be clearly observed, since its impact may be concealed by the other considered parameters. Whereas the Monte Carlo approach implies a high computational cost, Probabilistic Collocation presents a suitable trade-off between precision and computational time. Results suggest that the proposed framework has a great potential to help in both surgical planning decisions and in the audiological setting process.

A novel soft tissue prediction methodology for orthognathic surgery based on probabilistic finite element modelling

Repositioning of the maxilla in orthognathic surgery is carried out for functional and aesthetic purposes. Pre-surgical planning tools can predict 3D facial appearance by computing the response of the soft tissue to the changes to the underlying skeleton. The clinical use of commercial prediction software remains controversial, likely due to the deterministic nature of these computational predictions. A novel probabilistic finite element model (FEM) for the prediction of postoperative facial soft tissues is proposed in this paper. A probabilistic FEM was developed and validated on a cohort of eight patients who underwent maxillary repositioning and had pre- and postoperative cone beam computed tomography (CBCT) scans taken. Firstly, a variables correlation assessed various modelling parameters. Secondly, a design of experiments (DOE) provided a range of potential outcomes based on uniformly distributed input parameters, followed by an optimisation. Lastly, the second DOE iteration provided optimised predictions with a probability range. A range of 3D predictions was obtained using the probabilistic FEM and validated using reconstructed soft tissue surfaces from the postoperative CBCT data. The predictions in the nose and upper lip areas accurately include the true postoperative position, whereas the prediction under-estimates the position of the cheeks and lower lip. A probabilistic FEM has been developed and validated for the prediction of the facial appearance following orthognathic surgery. This method shows how inaccuracies in the modelling and uncertainties in executing surgical planning influence the soft tissue prediction and it provides a range of predictions including a minimum and maximum, which may be helpful for patients in understanding the impact of surgery on the face.

Young's Modulus and Load Complexity: Modeling Their Effects on Proximal Femur Strain

Finite element analysis (FEA) is a powerful tool for evaluating questions of functional morphology, but the application of FEA to extant or extinct creatures is a non-trivial task. Three categories of input data are needed to appropriately implement FEA: geometry, material properties, and boundary conditions. Geometric data are relatively easily obtained from imaging techniques, but often material properties and boundary conditions must be estimated. Here we conduct sensitivity analyses of the effect of the choice of Young's Modulus for elements representing trabecular bone and muscle loading complexity on the proximal femur using a finite element mesh of a modern human femur. We found that finite element meshes that used a Young's Modulus between 500 and 1,500 MPa best matched experimental strains. Loading scenarios that approximated the insertion sites of hip musculature produced strain patterns in the region of the greater trochanter that were different from scenarios that grouped muscle forces to the superior greater trochanter, with changes in strain values of 40% or more for 20% of elements. The femoral head, neck, and proximal shaft were less affected (e.g. approximately 50% of elements changed by 10% or less) by changes in the location of application of muscle forces. From our sensitivity analysis, we recommend the use of a Young's Modulus for the trabecular elements of 1,000 MPa for the proximal femur (range 500-1,500 MPa) and that the muscular loading complexity be dependent on whether or not strains in the greater trochanter are the focus of the analytical question. Anat Rec, 301:1189-1202, 2018. © 2018 Wiley Periodicals, Inc.

Biomechanical implications of cortical elastic properties of the macaque mandible

Knowledge of the variation in the elastic properties of mandibular cortical bone is essential for modeling bone function. Our aim was to characterize the elastic properties of rhesus macaque mandibular cortical bone and compare these to the elastic properties from mandibles of dentate humans and baboons. Thirty cylindrical samples were harvested from each of six adult female rhesus monkey mandibles. Assuming orthotropy, axes of maximum stiffness in the plane of the cortical plate were derived from ultrasound velocity measurements. Further velocity measurements with longitudinal and transverse ultrasonic transducers along with measurements of bone density were used to compute three-dimensional cortical elastic properties using equations based on Hooke's law. Results showed regional variations in the elastic properties of macaque mandibular cortical bone that have both similarities and differences with that of humans and baboons. So far, the biological and structural basis of these differences is poorly understood.

Analysis of Uncertainty and Variability in Finite Element Computational Models for Biomedical Engineering: Characterization and Propagation

Computational modeling has become a powerful tool in biomedical engineering thanks to its potential to simulate coupled systems. However, real parameters are usually not accurately known, and variability is inherent in living organisms. To cope with this, probabilistic tools, statistical analysis and stochastic approaches have been used. This article aims to review the analysis of uncertainty and variability in the context of finite element modeling in biomedical engineering. Characterization techniques and propagation methods are presented, as well as examples of their applications in biomedical finite element simulations. Uncertainty propagation methods, both non-intrusive and intrusive, are described. Finally, pros and cons of the different approaches and their use in the scientific community are presented. This leads us to identify future directions for research and methodological development of uncertainty modeling in biomedical engineering.

Validation experiments on finite element models of an ostrich (Struthio camelus) cranium

The first finite element (FE) validation of a complete avian cranium was performed on an extant palaeognath, the ostrich (Struthio camelus). Ex-vivo strains were collected from the cranial bone and rhamphotheca. These experimental strains were then compared to convergence tested, specimen-specific finite element (FE) models. The FE models contained segmented cortical and trabecular bone, sutures and the keratinous rhamphotheca as identified from micro-CT scan data. Each of these individual materials was assigned isotropic material properties either from the literature or from nanoindentation, and the FE models compared to the ex-vivo results. The FE models generally replicate the location of peak strains and reflect the correct mode of deformation in the rostral region. The models are too stiff in regions of experimentally recorded high strain and too elastic in regions of low experimentally recorded low strain. The mode of deformation in the low strain neurocranial region is not replicated by the FE models, and although the models replicate strain orientations to within 10° in some regions, in most regions the correlation is not strong. Cranial sutures, as has previously been found in other taxa, are important for modifying both strain magnitude and strain patterns across the entire skull, but especially between opposing the sutural junctions. Experimentally, we find that the strains on the surface of the rhamphotheca are much lower than those found on nearby bone. The FE models produce much higher principal strains despite similar strain ratios across the entirety of the rhamphotheca. This study emphasises the importance of attempting to validate FE models, modelling sutures and rhamphothecae in birds, and shows that whilst location of peak strain and patterns of deformation can be modelled, replicating experimental data in digital models of avian crania remains problematic.

Validity and sensitivity of a human cranial finite element model: implications for comparative studies of biting performance

Finite element analysis (FEA) is a modelling technique increasingly used in anatomical studies investigating skeletal form and function. In the case of the cranium this approach has been applied to both living and fossil taxa to (for example) investigate how form relates to function or infer diet or behaviour. However, FE models of complex musculoskeletal structures always rely on simplified representations because it is impossible completely to image and represent every detail of skeletal morphology, variations in material properties and the complexities of loading at all spatial and temporal scales. The effects of necessary simplifications merit investigation. To this end, this study focuses on one aspect, model geometry, which is particularly pertinent to fossil material where taphonomic processes often destroy the finer details of anatomy or in models built from clinical CTs where the resolution is limited and anatomical details are lost. We manipulated the details of a finite element (FE) model of an adult human male cranium and examined the impact on model performance. First, using digital speckle interferometry, we directly measured strains from the infraorbital region and frontal process of the maxilla of the physical cranium under simplified loading conditions, simulating incisor biting. These measured strains were then compared with predicted values from FE models with simplified geometries that included modifications to model resolution, and how cancellous bone and the thin bones of the circum-nasal and maxillary regions were represented. Distributions of regions of relatively high and low principal strains and principal strain vector magnitudes and directions, predicted by the most detailed FE model, are generally similar to those achieved in vitro. Representing cancellous bone as solid cortical bone lowers strain magnitudes substantially but the mode of deformation of the FE model is relatively constant. In contrast, omitting thin plates of bone in the circum-nasal region affects both mode and magnitude of deformation. Our findings provide a useful frame of reference with regard to the effects of simplifications on the performance of FE models of the cranium and call for caution in the interpretation and comparison of FEA results.

Is Beak Morphology in Darwin's Finches Tuned to Loading Demands?

One of nature's premier illustrations of adaptive evolution concerns the tight correspondence in birds between beak morphology and feeding behavior. In seed-crushing birds, beaks have been suggested to evolve at least in part to avoid fracture. Yet, we know little about mechanical relationships between beak shape, stress dissipation, and fracture avoidance. This study tests these relationships for Darwin's finches, a clade of birds renowned for their diversity in beak form and function. We obtained anatomical data from micro-CT scans and dissections, which in turn informed the construction of finite element models of the bony beak and rhamphotheca. Our models offer two new insights. First, engineering safety factors are found to range between 1 and 2.5 under natural loading conditions, with the lowest safety factors being observed in species with the highest bite forces. Second, size-scaled finite element (FE) models reveal a correspondence between inferred beak loading profiles and observed feeding strategies (e.g. edge-crushing versus tip-biting), with safety factors decreasing for base-crushers biting at the beak tip. Additionally, we identify significant correlations between safety factors, keratin thickness at bite locations, and beak aspect ratio (depth versus length). These lines of evidence together suggest that beak shape indeed evolves to resist feeding forces.

Automated generation of tissue-specific three-dimensional finite element meshes containing ellipsoidal cellular inclusions

Finite element analysis provides a means of describing cellular mechanics in tissue, which can be useful in understanding and predicting physiological and pathological changes. Many prior studies have been limited to simulations of models containing single cells, which may not accurately describe the influence of mechanical interactions between cells. It is desirable to generate models that more accurately reflect the cellular organisation in tissue in order to evaluate the mechanical function of cells. However, as the model geometry becomes more complicated, manual model generation can become laborious. This can be prohibitive if a large number of distinct cell-scale models are required, for example, in multiscale modelling or probabilistic analysis. Therefore, a method was developed to automatically generate tissue-specific cellular models of arbitrary complexity, with minimal user intervention. This was achieved through a set of scripts, which are capable of generating both sample-specific models, with explicitly defined geometry, and tissue-specific models, with geometry derived implicitly from normal statistical distributions. Models are meshed with tetrahedral (TET) elements of variable size to sufficiently discretise model geometries at different spatial scales while reducing model complexity. The ability of TET meshes to appropriately simulate the biphasic mechanical response of a single-cell model is established against that of a corresponding hexahedral mesh for an illustrative use case. To further demonstrate the flexibility of this tool, an explicit model was developed from three-dimensional confocal laser scanning image data, and a set of models were generated from a statistical cellular distribution of the articular femoral cartilage. The tools presented herein are free and openly accessible to the community at large.

Finite element analysis of a femur to deconstruct the paradox of bone curvature

Most long limb bones in terrestrial mammals exhibit a longitudinal curvature and have been found to be loaded in bending. Bone curvature poses a paradox in terms of the mechanical function of limb bones, for many believe the curvature in these bones increases bending stress, potentially reducing the bone's load carrying capacity (i.e., its mechanical strength). The aim of this study is to investigate the role of longitudinal bone curvature in the design of limb bones. In particular, it has been hypothesized that bone curvature results in a trade-off between the bone's mechanical strength and its bending predictability. We employed finite element analysis (FEA) of abstract and realistic human femora to address this issue. Geometrically simplified human femur models with different curvatures were developed and analyzed with a commercial FEA tool to examine how curvature affects the bone's bending predictability and load carrying capacity. Results were post-processed to yield probability density functions (PDFs) describing the circumferential location of maximum equivalent stress for various curvatures in order to assess bending predictability. To validate our findings, a finite element model was built from a CT scan of a real human femur and compared to the simplified femur model. We found general agreement in trends but some quantitative differences most likely due to the geometric differences between the digitally reconstructed and the simplified finite element models. As hypothesized by others, our results support the hypothesis that bone curvature can increase bending predictability, but at the expense of bone strength.