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

Validation and Estimation of Obesity-Induced Intervertebral Disc Degeneration through Subject-Specific Finite Element Modelling of Functional Spinal Units

(1) Background: Intervertebral disc degeneration has been linked to obesity; its potential mechanical effects on the intervertebral disc remain unknown. This study aimed to develop and validate a patient-specific model of L3-L4 vertebrae and then use the model to estimate the impact of increasing body weight on disc degeneration. (2) Methods: A three-dimensional model of the functional spinal unit of L3-L4 vertebrae and its components were developed and validated. Validation was achieved by comparing the range of motions (RoM) and intradiscal pressures with the previous literature. Subsequently, the validated model was loaded according to the body mass index and estimated stress, deformation, and RoM to assess disc degeneration. (3) Results: During validation, L3-L4 RoM and intradiscal pressures: flexion 5.17° and 1.04 MPa, extension 1.54° and 0.22 MPa, lateral bending 3.36° and 0.54 MPa, axial rotation 1.14° and 0.52 MPa, respectively. When investigating the impact of weight on disc degeneration, escalating from normal weight to obesity reveals an increased RoM, by 3.44% during flexion, 22.7% during extension, 29.71% during lateral bending, and 33.2% during axial rotation, respectively. Also, stress and disc deformation elevated with increasing weight across all RoM. (4) Conclusions: The predicted mechanical responses of the developed model closely matched the validation dataset. The validated model predicts disc degeneration under increased weight and could lay the foundation for future recommendations aimed at identifying predictors of lower back pain due to disc degeneration.

Parameter optimization in a finite element mandibular fracture fixation model using the design of experiments approach

Only a few mandibular bone finite element (FE) models have been validated in literature, making it difficult to assess the credibility of the models. In a comparative study between FE models and biomechanical experiments using a synthetic polyamide 12 (PA12) mandible model, we investigate how material properties and boundary conditions affect the FE model's accuracy using the design of experiments approach. Multiple FE parameters, such as contact definitions and the materials' elastic and plastic deformation characteristics, were systematically analyzed for an intact mandibular model and transferred to the fracture fixation model. In a second step, the contact definitions for the titanium screw and implant (S-I), implant and PA12 mandible (I-M), and interfragmentary (IF) PA12 segments were optimized. Comparing simulated deformations (from 0 to -5 mm) and reaction forces (from 10 to 1'415 N) with experimental results showed a strong sensitivity to FE mechanical properties and contact definitions. The results suggest that using the bonded definition for the screw-implant contact of the fracture plate is ineffective. The contact friction parameter set with the highest agreement was identified: titanium screw and implant μ = 0.2, implant and PA12 mandible μ = 0.2, interfragmentary PA12 mandible μ = 0.1. The simulated reaction force (RMSE = 26.60 N) and surface displacement data (RMSE = 0.19 mm) of the FE analysis showed a strong agreement with the experimental biomechanical data. The results were generated through parameter optimization which means that our findings need to be validated in the event of a new dataset with deviating anatomy. Conclusively, the predictive capability of the FE model can be improved by FE model calibration through experimental testing. Validated preoperative quasi-static FE analysis could allow engineers and surgeons to accurately estimate how the implant's choice and placement suit the patient's biomechanical needs.

Prediction of Lung Nodule Progression with an Uncertainty-Aware Hierarchical Probabilistic Network

Predicting whether a lung nodule will grow, remain stable or regress over time, especially early in its follow-up, would help doctors prescribe personalized treatments and better surgical planning. However, the multifactorial nature of lung tumour progression hampers the identification of growth patterns. In this work, we propose a deep hierarchical generative and probabilistic network that, given an initial image of the nodule, predicts whether it will grow, quantifies its future size and provides its expected semantic appearance at a future time. Unlike previous solutions, our approach also estimates the uncertainty in the predictions from the intrinsic noise in medical images and the inter-observer variability in the annotations. The evaluation of this method on an independent test set reported a future tumour growth size mean absolute error of 1.74 mm, a nodule segmentation Dice’s coefficient of 78% and a tumour growth accuracy of 84% on predictions made up to 24 months ahead. Due to the lack of similar methods for providing future lung tumour growth predictions, along with their associated uncertainty, we adapted equivalent deterministic and alternative generative networks (i.e., probabilistic U-Net, Bayesian test dropout and Pix2Pix). Our method outperformed all these methods, corroborating the adequacy of our approach.

Comparison of the biomechanical differences in the occlusal movement of wild-type and BMP9 knockout mice with apical periodontitis

Apical periodontitis is a common clinical disease caused by bacteria; bacterial metabolites can cause an imbalance in bone homeostasis, bone mass reduction, and tooth loss. Bone resorption in apical periodontitis causes a concentration of stress in the tooth and periodontal tissues during occlusion, which aggravates the disease. Emerging evidence indicates that bone morphogenetic protein 9 (BMP9), also known as growth differentiation factor 2(Gdf2), may play an important role in tooth and dentoalveolar development. Herein, we investigated the role of BMP9 in the development of apical periodontitis and its effects on the biomechanics of dentoalveolar bone. Apical periodontitis models were established in five BMP9 knockout (KO) mice and five C57BL/6 WT (wild-type) mice. At baseline and 14, 28, and 42 days after modeling, in vivo micro-computed tomography analysis and three-dimensional (3D) reconstruction were performed to evaluate the apical lesion in each mouse, and confirm that the animal models were successfully established. Finite element analysis (FEA) was performed to study the stress and strain at the alveolar fossa of each mouse under the same vertical and lateral stress. FEA revealed that the stress and strain at the alveolar fossa of each mouse gradually concentrated on the tooth cervix. The stress and strain at the tooth cervix gradually increased with time but were decreased at day 42. Under the same lingual loading, the maximum differences of the stress and strain at the tooth root in KO mice were greater than those in WT mice. Thus, these findings demonstrate that BMP9 could affect the biomechanical response of the alveolar fossa at the tooth root in mice with apical periodontitis. Moreover, the effects of BMP9 on the biomechanical response of the alveolar bone may be site-dependent. Overall, this work contributes to an improved understanding of the pathogenesis of apical periodontitis and may inform the development of new treatment strategies for apical periodontitis.

Designing and in vitro testing of a novel patient-specific total knee prosthesis using the probabilistic approach

In order to prevent failure as well as ensure comfort, patient-specific modelling for prostheses has been gaining interest. However, deterministic analyses have been widely used in the design process without considering any variation/uncertainties related to the design parameters of such prostheses. Therefore, this study aims to compare the performance of patient-specific anatomic Total Knee Arthroplasty (TKA) with off-the-shelf TKA. In the patient-specific model, the femoral condyle curves were considered in the femoral component's inner and outer surface design. The tibial component was designed to completely cover the tibia cutting surface. In vitro experiments were conducted to compare these two models in terms of loosening of the components. A probabilistic approach based on the finite element method was also used to compute the probability of failure of both models. According to the deterministic analysis results, 103.10 and 21.67 MPa von Mises stress values were obtained for the femoral component and cement in the anatomical model, while these values were 175.86 and 25.76 MPa, respectively, for the conventional model. In order to predict loosening damage due to local osteolysis or stress shield, it was determined that the deformation values in the examined cement structures were 15% lower in the anatomical model. According to probabilistic analysis results, it was observed that the probability of encountering an extreme value for the anatomical model is far less than that of the conventional model. This indicates that the anatomical model is safer than the conventional model, considering the failure scenarios in this study.

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.

Establishing the Biofidelity of a Multiphysics Finite Element Model of the Human Heart

PURPOSE

Accelerating development of new therapeutic cardiac devices remains a clinical and technical priority. High-performance computing and the emergence of functional and complex in silico models of human anatomy can be an engine to accelerate the commercialization of innovative, safe, and effective devices.

METHODS

An existing three-dimensional, nonlinear model of a human heart with flow boundary conditions was evaluated. Its muscular tissues were exercised using electrophysiological boundary conditions, creating a dynamic, electro-mechanical simulation of the kinetics of the human heart. Anatomic metrics were selected to characterize the functional biofidelity of the model based on their significance to the design of cardiac devices. The model output was queried through the cardiac cycle and compared to in vivo literature values.

RESULTS

For the kinematics of mitral and aortic valves and curvature of coronary vessels, the model's performance was at or above the 95th percentile range of the in vivo data from large patient cohorts. One exception was the kinematics of the tricuspid valve. The model's mechanical use environment would subject devices to generally conservative use conditions.

CONCLUSIONS

This conservative simulated use environment for heart-based medical devices, and its judicious application in the evaluation of medical devices is justified, but careful interpretation of the results is encouraged.

Alterations in femoral neck strength following pelvic irradiation. A finite element analysis of simulated eccentric forces using bone density data derived from CT

BACKGROUND AND PURPOSE

Radiotherapy is known to produce long-term skeletal complications. We aim to evaluate the biomechanical effect on femoral neck bone from hypothetical eccentric loads on pre- and post-radiotherapy CT-images for patients treated for rectal cancer.

MATERIAL AND METHODS

Pre- and post-radiotherapy CT-images of rectal cancer from 10 patients were selected randomly. The cortical and trabecular bone was segmented by hand. The biomechanical simulations of 4 eccentric loads and one load aligned with the femoral neck axis were completed using finite element analysis (FEA) in both pre- and post-patient models.

RESULTS

A comparative statistical study was completed of pre- and post-radiotherapy patient models of stress and displacement factors. Significant differences were found in eccentric loads in both factors. Natural load has a significant difference in stress, but no differences were found for displacements. The absolute difference in eccentric load applied to the anterior area location on the same patient implies from 5.3% to 40.5% of the stress yield values reported in previous studies.

CONCLUSIONS

Loads applied to the anterior area of the femoral head must be considered in fracture simulations because the percentage of yield stress of pre- and post-irradiated bones shows a significant biomechanical change.

Validated Finite Element Models of Premolars: A Scoping Review

Finite element (FE) models are widely used to investigate the biomechanics of reconstructed premolars. However, parameter identification is a complex step because experimental validation cannot always be conducted. The aim of this study was to collect the experimentally validated FE models of premolars, extract their parameters, and discuss trends. A systematic review was performed following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. Records were identified in three electronic databases (MEDLINE [PubMed], Scopus, The Cochrane Library) by two independent reviewers. Twenty-seven parameters dealing with failure criteria, model construction, material laws, boundary conditions, and model validation were extracted from the included articles. From 1306 records, 214 were selected for eligibility and entirely read. Among them, 19 studies were included. A heterogeneity was observed for several parameters associated with failure criteria and model construction. Elasticity, linearity, and isotropy were more often chosen for dental and periodontal tissues with a Young’s modulus mostly set at 18–18.6 GPa for dentine. Loading was mainly simulated by an axial force, and FE models were mostly validated by in vitro tests evaluating tooth strains, but different conditions about experiment type, sample size, and tooth status (intact or restored) were reported. In conclusion, material laws identified herein could be applied to future premolar FE models. However, further investigations such as sensitivity analysis are required for several parameters to clarify their indication.

Validation and Improvement of a Bicycle Crank Arm Based in Numerical Simulation and Uncertainty Quantification

In this study, a finite element model of a bicycle crank arm are compared to experimental results. The structural integrity of the crank arm was analyzed in a universal dynamic test bench. The instrumentation used has allowed us to know the fatigue behavior of the component tested. For this, the prototype was instrumented with three rectangular strain gauge rosettes bonded in areas where failure was expected. With the measurements made by strain gauges and the forces registers from the load cell used, it has been possible to determine the state of the stresses for different loads and boundary conditions, which has subsequently been compared with a finite element model. The simulations show a good agreement with the experimental results, when the potential sources of uncertainties are considered in the validation process. This analysis allowed us to improve the original design, reducing its weight by 15%. The study allows us to identify the manufacturing process that requires the best metrological control to avoid premature crank failure. Finally, the numerical fatigue analysis carried out allows us to conclude that the new crank arm can satisfy the structural performance demanded by the international bicycle standard. Additionally, it can be suggested to the standard to include the verification that no permanent deformations have occurred in the crank arm during the fatigue test. It has been observed that, in some cases this bicycle component fulfils the minimum safety requirements, but presents areas with plastic strains, which if not taken into account can increase the risk of injury for the cyclist due to unexpected failure of the component.

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.

Systems biology: perspectives on multiscale modeling in research on endocrine-related cancers

Drawing on concepts from experimental biology, computer science, informatics, mathematics and statistics, systems biologists integrate data across diverse platforms and scales of time and space to create computational and mathematical models of the integrative, holistic functions of living systems. Endocrine-related cancers are well suited to study from a systems perspective because of the signaling complexities arising from the roles of growth factors, hormones and their receptors as critical regulators of cancer cell biology and from the interactions among cancer cells, normal cells and signaling molecules in the tumor microenvironment. Moreover, growth factors, hormones and their receptors are often effective targets for therapeutic intervention, such as estrogen biosynthesis, estrogen receptors or HER2 in breast cancer and androgen receptors in prostate cancer. Given the complexity underlying the molecular control networks in these cancers, a simple, intuitive understanding of how endocrine-related cancers respond to therapeutic protocols has proved incomplete and unsatisfactory. Systems biology offers an alternative paradigm for understanding these cancers and their treatment. To correctly interpret the results of systems-based studies requires some knowledge of how in silico models are built, and how they are used to describe a system and to predict the effects of perturbations on system function. In this review, we provide a general perspective on the field of cancer systems biology, and we explore some of the advantages, limitations and pitfalls associated with using predictive multiscale modeling to study endocrine-related cancers.

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.