A Surface-to-Surface Finite Element Algorithm for Large Deformation Frictional Contact in febio

A computational framework to optimize the mechanical behavior of synthetic vascular grafts

The failure of synthetic small-diameter vascular grafts has been attributed to a mismatch in the compliance between the graft and native artery, driving mechanisms that promote thrombosis and neointimal hyperplasia. Additionally, the buckling of grafts results in large deformations that can lead to device failure. Although design features can be added to lessen the buckling potential (e.g., reinforcing coil), the addition is detrimental to decreasing compliance. Herein, we developed a novel finite element (FE) framework to inform vascular graft design by evaluating compliance and resistance to buckling. A batch-processing scheme iterated across the multi-dimensional design parameter space, which included three parameters: coil thickness, modulus, and spacing - generating 100 unique designs. FE models were created for each coil-reinforced graft design to simulate pressurization, axial buckling, and bent buckling, and results were analyzed to quantify compliance, buckling load, and kink radius, respectively. Validation of the FE models demonstrated that model predictions agreed with experimental observations for compliance (r = 0.99), buckling load (r = 0.89), and kink resistance (r = 0.97). Model predictions demonstrated a broad range of values for compliance (1.1-7.9 %/mmHg × 10-2), buckling load (0.28-0.84 N), and kink radius (6-10 mm) across the design parameter space. Subsequently, data for each design parameter combination were optimized (i.e., minimized) to identify candidate graft designs with promising mechanical properties. Our model-directed framework successfully elucidated the complex mechanical determinants of graft performance, established structure-property relationships, and identified vascular graft designs with optimal mechanical properties, potentially improving clinical outcomes by addressing device failure.

Modeling Fatigue Failure of Cartilage and Fibrous Biological Tissues Using Constrained Reactive Mixture Theory

Fatigue failure in biological soft tissues plays a critical role in the etiology of chronic soft tissue injuries and diseases such as osteoarthritis (OA). Understanding failure mechanisms is hindered by the decades-long timescales over which damage takes place. Analyzing the factors contributing to fatigue failure requires the help of validated computational models developed for soft tissues. This study presents a framework for fatigue failure of fibrous biological tissues based on reaction kinetics, where the composition of intact and fatigued material regions can evolve via degradation and breakage over time, in response to energy-based fatigue and damage criteria. Using reactive constrained mixture theory, material region mass fractions are governed by the axiom of mass balance. Progression of fatigue is controlled by an energy-based reaction rate, with user-selected probability functions defining the damage propensity of intact and fatigued material regions. Verification of this reactive theory, which is implemented in the open-source FEBio finite element software, is provided in this study. Validation is also demonstrated against experimental data, showing that predicted damage can be linked to results from biochemical assays. The framework is also applied to study fatigue failure during frictional contact of cartilage. Simulating previous experiments suggests that frictional effects slightly increase fatigue progression, but the main driver is cyclic compressive contact loading. This study demonstrated the ability of theoretical models to complement and extend experimental findings, advancing our understanding of the time progression of fatigue in biological tissues.

What is the most important mechanical factor involved in trapeziometacarpal osteoarthritis development? A sensitivity analysis based on biomechanical modelling

Few studies consider the variability of the model parameters. This study aimed to perform a sensitivity analysis of a trapeziometacarpal joint model, by performing 675 finite element simulations built from the combination of different morphologies, joint passive stiffness, and grip strategies to estimate the joint pressure. Pressure variability was significantly more affected by morphology than grip strategy and joint passive stiffness. The effect of morphology and grip strategy on joint pressure was significant. A significant correlation between the trapezium dorso-volar curvature and the joint pressure was found. Morphology seems more important than the other parameters to estimate joint contact pressure correctly.

Fetus descent simulation with the active uterine contraction during the vaginal delivery: MRI-based evaluation and uncertainty quantification

Finite element models ranging from single to multiscale models have been widely used to gain valuable insights into the physiological delivery process and associated complication scenarios. However, the fetus descent simulation with the active uterine contraction is still challenging for validation and uncertainty quantification issues. The present study performed a fetus descent simulation using the active uterine contraction. Then, simulation outcomes were evaluated using theoretical and in vivo MRI childbirth data. Moreover, parameter uncertainty and propagation were also performed. A maternal pelvis model was developed. The active uterine contraction was modeled using a transversely isotropic Mooney-Rivlin material. Displacement trajectories were compared between simulation, theoretical and in vivo MRI childbirth data. Monte Carlo (M.C) and Polynomial Chaos Expansion (PCE) methods were applied to quantify uncertain parameters and their propagations. Obtained results showed that fetal descent behavior is consistent with the MRI-based observation as well as the theoretical trajectory (curve of Carus). The head downward vertical displacement ranges from 0 to approximately 47 mm. A reduction of 50% in uterine size was observed during the simulation. Three high-sensitive parameters (C 1 , C 2 , Ca 0 ) were also identified. Our study suggested that the use of the active uterine contraction is essential for simulating vaginal delivery but the global parameter sensitivity, parameter uncertainty, and outcome evaluation should be carefully performed. As a perspective, the developed approach could be extrapolated for patient-specific modeling and associated delivery complication simulations to identify risks and potential therapeutic solutions.

The effect of trapeziometacarpal joint passive stiffness on mechanical loadings of cartilages

Hypermobility of the trapeziometacarpal joint is commonly considered to be a potential risk factor for osteoarthritis. Nevertheless, the results remain controversial due to a lack of quantitative validation. The objective of this study was to evaluate the effect of joint laxity on the mechanical loadings of cartilage. A patient-specific finite element model of trapeziometacarpal joint passive stiffness was developed. The joint passive stiffness was modeled by creating linear springs all around the joint. The linear spring stiffness was determined by using an optimization process to fit force-displacement data measured during laxity tests performed on eight healthy volunteers. The estimated passive stiffness parameters were then included in a full thumb finite element simulation of a pinch grip task driven by muscle forces to evaluate the effect on trapeziometacarpal loading. The correlation between stiffness and the loading of cartilage in terms of joint contact pressure and maximum shear strain was analyzed. A significant negative correlation was found between the trapeziometacarpal joint passive stiffness and the contact pressure on trapezium cartilage during the simulated pinch grip task. These results therefore suggest that the hypermobility of the trapeziometacarpal joint could affect the contact pressure on trapezium cartilage and support the existence of an increased risk associated with hypermobility.

A systematic comparison between FEBio and PolyFEM for biomechanical systems

BACKGROUND AND OBJECTIVES

Finite element simulations are widely employed as a non-invasive and cost-effective approach for predicting outcomes in biomechanical simulations. However, traditional finite element software, primarily designed for engineering materials, often encountered limitations in contact detection and enforcement, leading to simulation failure when dealing with complex biomechanical configurations. Currently, a lot of model tuning is required to get physically accurate finite element simulations without failures. This adds significant human interaction to each iteration of a biomechanical model. This study addressed these issues by introducing PolyFEM, a novel finite element solver that guarantees inversion- and intersection-free solutions with completely automatic collision detection. The objective of this research is to validate PolyFEM's capabilities by comparing its results with those obtained from a well-established finite element solver, FEBio.

METHODS

To achieve this goal, five comparison scenarios were formulated to assess and validate PolyFEM's performance. The simulations were reproduced using both PolyFEM and FEBio, and the final results were compared. The five comparison scenarios included: (1) reproducing simulations from the FEBio test suite, consisting of static, dynamic, and contact-driven simulations; (2) replicating simulations from the verification paper published alongside the original release of FEBio; (3) a biomechanically based contact problem; (4) creating a custom simulation involving high-energy collisions between soft materials to highlight the difference in collision methods between the two solvers; and (5) performing biomechanical simulations of biting and quasi-stance.

RESULTS

We found that PolyFEM was capable of replicating all simulations previously conducted in FEBio. Particularly noteworthy is PolyFEM's superiority in high-energy contact simulations, where FEBio fell short, unable to complete over half of the simulations in Scenario 4. Although some of the simulations required significantly more simulation time in PolyFEM compared to FEBio, it is important to highlight that PolyFEM achieved these results without the need for any additional model tuning or contact declaration.

DISCUSSION

Despite being in the early stages of development, PolyFEM currently provides verified solutions for hyperelastic materials that are consistent with FEBio, both in previously published workflows and novel finite element scenarios. PolyFEM exhibited the ability to tackle challenging biomechanical problems where other solvers fell short, thus offering the potential to enhance the accuracy and realism of future finite element analyses.

Role of lung lobar sliding on parenchymal distortion during breathing

Sliding between lung lobes along lobar fissures is a poorly understood aspect of lung mechanics. The objective of this study was to test the hypothesis that lobar sliding helps reduce distortion in the lung parenchyma during breathing. Finite element models of left lungs with geometries and boundary conditions derived from medical images of human subjects were developed. Effect of lobar sliding was studied by comparing nonlinear finite elastic contact mechanics simulations that allowed and disallowed lobar sliding. Lung parenchymal distortion during simulated breath-holds and tidal breathing was quantified with the model's spatial mean anisotropic deformation index (ADI), a measure of directional preference in volume change that varies spatially in the lung. Models that allowed lobar sliding had significantly lower mean ADI (i.e., lesser parenchymal distortion) than models that disallowed lobar sliding under simulations of both tidal breathing (5.3% median difference, P = 0.008, n = 8) and lung deformation between breath-holds at total lung capacity and functional residual capacity (3.2% median difference, P = 0.03, n = 6). This effect was most pronounced in the lower lobe where lobar sliding reduced parenchymal distortion with statistical significance, but not in the upper lobe. In addition, more lobar sliding was correlated with greater reduction in distortion between sliding and nonsliding models in our study cohorts (Pearson's correlation coefficient of 0.95 for tidal breathing, 0.87 for breath-holds, and 0.91 for the combined dataset). These findings are consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.NEW & NOTEWORTHY The role of lobar sliding in lung mechanics is poorly understood. Delineating this role could help explain how breathing is affected by anatomical differences between subjects such as incomplete and missing lobar fissures. We used computational contact mechanics models of lungs from human subjects to delineate the effect of lobar sliding by comparing simulations that allowed and disallowed sliding. We found evidence consistent with the hypothesis that lung lobar sliding reduces parenchymal distortion during breathing.

Identifiability of soft tissue constitutive parameters from in-vivo macro-indentation

Reliable identification of soft tissue material parameters is frequently required in a variety of applications, particularly for biomechanical simulations using finite element analysis (FEA). However, determining representative constitutive laws and material parameters is challenging and often comprises a bottleneck that hinders the successful implementation of FEA. Soft tissues exhibit a nonlinear response and are commonly modeled using hyperelastic constitutive laws. In-vivo material parameter identification, for which standard mechanical tests (e.g., uniaxial tension and compression) are inapplicable, is commonly achieved using finite macro-indentation test. Due to the lack of analytical solutions, the parameters are commonly identified using inverse FEA (iFEA), in which simulated results and experimental data are iteratively compared. However, determining what data must be collected to accurately identify a unique parameter set remains unclear. This work investigates the sensitivities of two types of measurements: indentation force-depth data (e.g., measured using an instrumented indenter) and full-field surface displacements (e.g., using digital image correlation). To eliminate model fidelity and measurement-related errors, we employed an axisymmetric indentation FE model to produce synthetic data for four 2-parameter hyperelastic constitutive laws: compressible Neo-Hookean, and nearly incompressible Mooney-Rivlin, Ogden, and Ogden-Moerman models. For each constitutive law, we computed the objective functions representing the discrepancies in the reaction force, the surface displacement, and their combination, and visualized them for hundreds of parameter sets, spanning a representative range as found in the literature for the bulk soft tissue complex in human lower limbs. Moreover, we quantified three identifiability metrics, which provided insights into the uniqueness (or lack thereof) and the sensitivities. This approach provides a clear and systematic evaluation of the parameter identifiability, which is independent of the selection of the optimization algorithm and initial guesses required in iFEA. Our analysis indicated that the indenter's force-depth data, despite being commonly used for parameter identification, was insufficient for reliably and accurately identifying both parameters for all the investigated material models and that the surface displacement data improved the parameter identifiability in all cases, although the Mooney-Rivlin parameters remained poorly identifiable. Informed by the results, we then discuss several identification strategies for each constitutive model. Finally, we openly provide the codes used in this study, to allow others to further investigate the indentation problem according to their specifications (e.g., by modifying the geometries, dimensions, mesh, material models, boundary conditions, contact parameters, or objective functions).

Using a finite element model of the thumb to study Trapeziometacarpal joint contact during lateral pinch

BACKGROUND

Finite element (FE) analysis is widely used in different fields of orthopaedic surgery, however, its application to the trapeziometacarpal joint has been limited due to the small size, complex biconcave-convex joint geometry, and complex musculature. The goal of this study was to improve upon existing models by creating a muscle-driven FE thumb model and use the model to simulate the biomechanical effect of hand therapy exercises and ligament reconstructive surgeries.

METHODS

Bone and cartilage geometry were based on a CT dataset of a subject performing a static lateral pinch task. A previously validated musculoskeletal model was utilized to extract electromyography (EMG)-driven muscle forces. Five ligaments with biomechanical significance were modeled as springs using literature values and attached according to their anatomical landmarks.

FINDINGS

The biomechanical consequence of various interventions was proxied as a change in the maximum cartilage stress. The result shows tightening the dorsal ligament complex (dorsal radial ligament, dorsal central ligament, posterior oblique ligament) is the most effective, achieving a stress reduction of 4.8%. Five exercises used in hand therapies were modeled, among which thenar eminence strengthening showed the most prominent stress reduction of 4.0%. Four ligament reconstructive surgeries were modeled, with Eaton-Littler reconstruction showed the most significant stress reduction of 25.0%.

INTERPRETATION

Among the routinely utilized treatment options for early thumb osteoarthritis, we found that three methods: dorsal ligament imbrication, thenar eminence exercise, and the Eaton-Littler method may confer biomechanical advantages cartilage loading. These advantages align with the clinically observed favorable outcomes.

A Finite Element Algorithm for Large Deformation Biphasic Frictional Contact Between Porous-Permeable Hydrated Soft Tissues

The frictional response of porous and permeable hydrated biological tissues such as articular cartilage is significantly dependent on interstitial fluid pressurization. To model this response, it is common to represent such tissues as biphasic materials, consisting of a binary mixture of a porous solid matrix and an interstitial fluid. However, no computational algorithms currently exist in either commercial or open-source software that can model frictional contact between such materials. Therefore, this study formulates and implements a finite element algorithm for large deformation biphasic frictional contact in the open-source finite element software FEBio. This algorithm relies on a local form of a biphasic friction model that has been previously validated against experiments, and implements the model into our recently-developed surface-to-surface (STS) contact algorithm. Contact constraints, including those specific to pressurized porous media, are enforced with the penalty method regularized with an active-passive augmented Lagrangian scheme. Numerical difficulties specific to challenging finite deformation biphasic contact problems are overcome with novel smoothing schemes for fluid pressures and Lagrange multipliers. Implementation accuracy is verified against semi-analytical solutions for biphasic frictional contact, with extensive validation performed using canonical cartilage friction experiments from prior literature. Essential details of the formulation are provided in this paper, and the source code of this biphasic frictional contact algorithm is made available to the general public.

Assessment of the viscoelastic mechanical properties of the porcine optic nerve head using micromechanical testing and finite element modeling

Optic nerve head (ONH) biomechanics is centrally involved in the pathogenesis of glaucoma, a blinding ocular condition often characterized by elevation and fluctuation of the intraocular pressure and resulting loads on the ONH. Further, tissue viscoelasticity is expected to strongly influence the mechanical response of the ONH to mechanical loading, yet the viscoelastic mechanical properties of the ONH remain unknown. To determine these properties, we conducted micromechanical testing on porcine ONH tissue samples, coupled with finite element modeling based on a mixture model consisting of a biphasic material with a viscoelastic solid matrix. Our results provide a detailed description of the viscoelastic properties of the porcine ONH at each of its four anatomical quadrants (i.e., nasal, superior, temporal, and inferior). We showed that the ONH's viscoelastic mechanical response can be explained by a dual mechanism of fluid flow and solid matrix viscoelasticity, as is common in other soft tissues. We obtained porcine ONH properties as follows: matrix Young's modulus E=1.895[1.056,2.391] kPa (median [min., max.]), Poisson's ratio ν=0.142[0.060,0.312], kinetic time-constant τ=214[89,921] sec, and hydraulic permeability k=3.854×10^-1[3.457×10^-2,9.994×10^-1] mm⁴/(N.sec). These values can be used to design and fabricate physiologically appropriate ex vivo test environments (e.g., 3D cell culture) to further understand glaucoma pathophysiology. STATEMENT OF SIGNIFICANCE: Optic nerve head (ONH) biomechanics is an important aspect of the pathogenesis of glaucoma, the leading cause of irreversible blindness. The ONH experiences time-varying loads, yet the viscoelastic behavior of this tissue has not been characterized. Here, we measure the time-dependent response of the ONH in porcine eyes and use mechanical modeling to provide time-dependent mechanical properties of the ONH. This information allows us to identify time-varying stimuli in vivo which have timescales matching the characteristic response times of the ONH, and can also be used to design and fabricate ex vivo 3D cultures to study glaucoma pathophysiology in a physiologically relevant environment, enabling the discovery of new generations of glaucoma medications focusing on neuroprotection.

On the use of constrained reactive mixtures of solids to model finite deformation isothermal elastoplasticity and elastoplastic damage mechanics

This study presents a framework for plasticity and elastoplastic damage mechanics by treating materials as reactive solids whose internal composition evolves in response to applied loading. Using the framework of constrained reactive mixtures, plastic deformation is accounted for by allowing loaded bonds within the material to break and reform in a stressed state. Bonds which break and reform represent a new generation with a new reference configuration, which is time-invariant and provided by constitutive assumption. The constitutive relation for the reference configuration of each generation may depend on the selection of a suitable yield measure. The choice of this measure and the resulting plastic flow conditions are constrained by the Clausius-Duhem inequality. We show that this framework remains consistent with classical plasticity approaches and principles. Verification of this reactive plasticity framework, which is implemented in the open source FEBio finite element software (febio.org), is performed against standard 2D and 3D benchmark problems. Damage is incorporated into this reactive framework by allowing loaded bonds to break permanently according to a suitable damage measure, where broken bonds can no longer store free energy. Validation is also demonstrated against experimental data for problems involving plasticity and plastic damage. This study demonstrates that it is possible to formulate simple elastoplasticity and elastoplastic damage models within a consistent framework which uses measures of material mass composition as theoretically observable state variables. This theoretical frame can be expanded in scope to account for more complex behaviors.

Total Knee Replacement: Subject-Specific Modeling, Finite Element Analysis, and Evaluation of Dynamic Activities

This study presents a semi-automatic framework to create subject-specific total knee replacement finite element models, which can be used to analyze locomotion patterns and evaluate knee dynamics. In recent years, much scientific attention was attracted to pre-clinical optimization of customized total knee replacement operations through computational modeling to minimize post-operational adverse effects. However, the time-consuming and laborious process of developing a subject-specific finite element model poses an obstacle to the latter. One of this work's main goals is to automate the finite element model development process, which speeds up the proposed framework and makes it viable for practical applications. This pipeline's reliability was ratified by developing and validating a subject-specific total knee replacement model based on the 6th SimTK Grand Challenge data set. The model was validated by analyzing contact pressures on the tibial insert in relation to the patient's gait and analysis of tibial contact forces, which were found to be in accordance with the ones provided by the Grand Challenge data set. Subsequently, a sensitivity analysis was carried out to assess the influence of modeling choices on tibial insert's contact pressures and determine possible uncertainties on the models produced by the framework. Parameters, such as the position of ligament origin points, ligament stiffness, reference strain, and implant-bone alignment were used for the sensitivity study. Notably, it was found that changes in the alignment of the femoral component in reference to the knee bones significantly affect the load distribution at the tibiofemoral joint, with an increase of 206.48% to be observed at contact pressures during 5° internal rotation. Overall, the models produced by this pipeline can be further used to optimize and personalize surgery by evaluating the best surgical parameters in a simulated manner before the actual surgery.

Helical fibrillar microstructure of tendon using serial block-face scanning electron microscopy and a mechanical model for interfibrillar load transfer

Tendon's hierarchical structure allows for load transfer between its fibrillar elements at multiple length scales. Tendon microstructure is particularly important, because it includes the cells and their surrounding collagen fibrils, where mechanical interactions can have potentially important physiological and pathological contributions. However, the three-dimensional (3D) microstructure and the mechanisms of load transfer in that length scale are not known. It has been postulated that interfibrillar matrix shear or direct load transfer via the fusion/branching of small fibrils are responsible for load transfer, but the significance of these mechanisms is still unclear. Alternatively, the helical fibrils that occur at the microstructural scale in tendon may also mediate load transfer; however, these structures are not well studied due to the lack of a three-dimensional visualization of tendon microstructure. In this study, we used serial block-face scanning electron microscopy to investigate the 3D microstructure of fibrils in rat tail tendon. We found that tendon fibrils have a complex architecture with many helically wrapped fibrils. We studied the mechanical implications of these helical structures using finite-element modelling and found that frictional contact between helical fibrils can induce load transfer even in the absence of matrix bonding or fibril fusion/branching. This study is significant in that it provides a three-dimensional view of the tendon microstructure and suggests friction between helically wrapped fibrils as a mechanism for load transfer, which is an important aspect of tendon biomechanics.

Editors' Choice Papers for 2018

No abstract.

A Formulation for Fluid Structure-Interactions in FEBio Using Mixture Theory

Many physiological systems involve strong interactions between fluids and solids, posing a signicant challenge when modeling biomechanics. The objective of this study was to implement a fluid-structure interaction (FSI) solver in the free, open-source finite element code FEBio (febio.org), that combined the existing solid mechanics and rigid body dynamics solver with a recently-developed computational fluid dynamics (CFD) solver. A novel Galerkin-based finite element FSI formulation was introduced based on mixture theory, where the FSI domain was described as a mixture of fluid and solid constituents that have distinct motions. The mesh was defined on the solid domain, specialized to have zero mass, negligible stiffness and zero frictional interactions with the fluid, whereas the fluid was modeled as isothermal and compressible. The mixture framework provided the foundation for evaluating material time derivatives in a material frame for the solid and in a spatial frame for the fluid. Similar to our recently reported CFD solver, our FSI formulation did not require stabilization methods to achieve good convergence, producing a compact set of equations and code implementation. The code was successfully verified against benchmark problems and an analytical solution for squeeze-film lubrication. It was validated against experimental measurements of the flow rate in a peristaltic pump, and illustrated using non-Newtonian blood flow through a bifurcated carotid artery with a thick arterial wall. The successful formulation and implementation of this FSI solver enhances the multiphysics modeling capabilities in FEBio relevant to the biomechanics and biophysics communities.