Erratum: "A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity" [ASME J. Biomech Eng., 2023, 145(1), p. 011004; DOI: 10.1115/1.4054983].

In this erratum, we correct a mistake in a subcomponent of the numerical algorithm proposed in our recent study for modeling anisotropic reactive nonlinear viscoelasticity (doi:10.1115/1.4054983), for the special case where multiple weak bond families may be recruited with loading. This correction overcomes a nonphysical response noted under uni-axial cyclical loading.

Simulating Cerebral Edema and Ischemia After Traumatic Acute Subdural Hematoma Using Triphasic Swelling Biomechanics.

Poor outcome following traumatic acute subdural hematoma (ASDH) is associated with the severity of the primary injury and secondary injury including cerebral edema and ischemia. However, the underlying secondary injury mechanism contributing to elevated intracranial pressure (ICP) and high mortality rate remains unclear. Cerebral edema occurs in response to the exposure of the intracellular fixed charge density (FCD) after cell death, causing ICP to increase. The increased ICP from swollen tissue compresses blood vessels in adjacent tissue, restricting blood flow and leading to ischemic damage. We hypothesize that the mass occupying effect of ASDH exacerbates the ischemic injury, leading to ICP elevation, which is an indicator of high mortality rate in the clinic. Using FEBio (febio.org) and triphasic swelling biomechanics, this study modeled clinically relevant ASDHs and simulated post-traumatic brain swelling and ischemia to predict ICP. Results showed that common convexity ASDH significantly increased ICP by exacerbating ischemic injury, and surgical removal of the convexity ASDH may control ICP by preventing ischemia progression. However, in cases where the primary injury is very severe, surgical intervention alone may not effectively decrease ICP, as the contribution of the hematoma to the elevated ICP is insignificant. In addition, interhemispheric ASDH, located between the cerebral hemispheres, does not significantly exacerbate ischemia, supporting the conservative surgical management generally recommended for interhemispheric ASDH. The joint effect of the mass occupying effect of the blood clot and resulting ischemia contributes to elevated ICP which may increase mortality. Our novel approach may improve the fidelity of predicting patient outcome after motor vehicle crashes and traumatic brain injuries due to other causes.

Region-Dependent Mechanical Properties of Human Brain Tissue Under Large Deformations Using Inverse Finite Element Modeling.

This study aims to facilitate intracranial simulation of traumatic events by determining the mechanical properties of different anatomical structures of the brain. Our experimental indentation paradigm used fresh, post-operative human tissue, which is highly advantageous in determining mechanical properties without being affected by postmortem time. This study employed an inverse finite element approach coupled with experimental indentation data to characterize mechanical properties of the human hippocampus (CA1, CA3, dentate gyrus), cortex white matter, and cortex grey matter. We determined that an uncoupled viscoelastic Ogden constitutive formulation was most appropriate to represent the mechanical behavior of these different regions of brain. Anatomical regions were significantly different in their mechanical properties. The cortex white matter was stiffer than cortex grey matter, and the CA1 and dentate gyrus were both stiffer than cortex grey matter. Although no sex dependency was observed, there were trends indicating that male brain regions were generally stiffer than corresponding female regions. In addition, there were no statistically significant age dependent differences. This study provides a structure-specific description of fresh human brain tissue mechanical properties, which will be an important step toward explicitly modeling the heterogeneity of brain tissue deformation during TBI through finite element modeling.

Spatial Configurations of 3D Extracellular Matrix Collagen Density and Anisotropy Simultaneously Guide Angiogenesis.

Extracellular matrix (ECM) collagen density and fibril anisotropy are thought to affect the development of new vasculatures during pathologic and homeostatic angiogenesis. Computational simulation is emerging as a tool to investigate the role of matrix structural configurations on cell guidance. However, prior computational models have only considered the orientation of collagen as a model input. Recent experimental evidence indicates that cell guidance is simultaneously influenced by the direction and intensity of alignment (i.e., degree of anisotropy) as well as the local collagen density. The objective of this study was to explore the role of ECM collagen anisotropy and density during sprouting angiogenesis through simulation in the AngioFE and FEBio modeling frameworks. AngioFE is a plugin for FEBio (Finite Elements for Biomechanics) that simulates cell-matrix interactions during sprouting angiogenesis. We extended AngioFE to represent ECM collagen as deformable 3D ellipsoidal fibril distributions (EFDs). The rate and direction of microvessel growth were modified to depend simultaneously on the ECM collagen anisotropy (orientation and degree of anisotropy) and density. The sensitivity of growing neovessels to these stimuli was adjusted so that AngioFE could reproduce the growth and guidance observed in experiments where microvessels were cultured in collagen gels of varying anisotropy and density. We then compared outcomes from simulations using EFDs to simulations that used AngioFE's prior vector field representation of collagen anisotropy. We found that EFD simulations were more accurate than vector field simulations in predicting experimentally observed microvessel guidance. Predictive simulations demonstrated the ability of anisotropy gradients to recruit microvessels across short and long distances relevant to wound healing. Further, simulations predicted that collagen alignment could enable microvessels to overcome dense tissue interfaces such as tumor-associated collagen structures (TACS) found in desmoplasia and tumor-stroma interfaces. This approach can be generalized to other mechanobiological relationships during cell guidance phenomena in computational settings.

Finite Element Implementation of Computational Fluid Dynamics With Reactive Neutral and Charged Solute Transport in FEBio.

The objective of this study was to implement a novel fluid-solutes solver into the open-source finite element software FEBio, that extended available modeling capabilities for biological fluids and fluid-solute mixtures. Using a reactive mixture framework, this solver accommodates diffusion, convection, chemical reactions, electrical charge effects, and external body forces, without requiring stabilization methods that were deemed necessary in previous computational implementations of the convection-diffusion-reaction equation at high Peclet numbers. Verification and validation problems demonstrated the ability of this solver to produce solutions for Peclet numbers as high as 1011, spanning the range of physiological conditions for convection-dominated solute transport. This outcome was facilitated by the use of a formulation that accommodates realistic values for solvent compressibility, and by expressing the solute mass balance such that it properly captured convective transport by the solvent and produced a natural boundary condition of zero diffusive solute flux at outflow boundaries. Since this numerical scheme was not necessarily foolproof, guidelines were included to achieve better outcomes that minimize or eliminate the potential occurrence of numerical artifacts. The fluid-solutes solver presented in this study represents an important and novel advancement in the modeling capabilities for biomechanics and biophysics as it allows modeling of mechanobiological processes via the incorporation of chemical reactions involving neutral or charged solutes within dynamic fluid flow. The incorporation of charged solutes in a reactive framework represents a significant novelty of this solver. This framework also applies to a broader range of nonbiological applications.

The effects of leaflet material properties on the simulated function of regurgitant mitral valves.

Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated (1) the influence of tissue extensibility and (2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.

The Effects of leaflet material properties on the simulated function of regurgitant mitral valves.

Advances in three-dimensional imaging provide the ability to construct and analyze finite element (FE) models to evaluate the biomechanical behavior and function of atrioventricular valves. However, while obtaining patient-specific valve geometry is now possible, non-invasive measurement of patient-specific leaflet material properties remains nearly impossible. Both valve geometry and tissue properties play a significant role in governing valve dynamics, leading to the central question of whether clinically relevant insights can be attained from FE analysis of atrioventricular valves without precise knowledge of tissue properties. As such we investigated 1) the influence of tissue extensibility and 2) the effects of constitutive model parameters and leaflet thickness on simulated valve function and mechanics. We compared metrics of valve function (e.g., leaflet coaptation and regurgitant orifice area) and mechanics (e.g., stress and strain) across one normal and three regurgitant mitral valve (MV) models with common mechanisms of regurgitation (annular dilation, leaflet prolapse, leaflet tethering) of both moderate and severe degree. We developed a novel fully-automated approach to accurately quantify regurgitant orifice areas of complex valve geometries. We found that the relative ordering of the mechanical and functional metrics was maintained across a group of valves using material properties up to 15% softer than the representative adult mitral constitutive model. Our findings suggest that FE simulations can be used to qualitatively compare how differences and alterations in valve structure affect relative atrioventricular valve function even in populations where material properties are not precisely known.

A Numerical Scheme for Anisotropic Reactive Nonlinear Viscoelasticity.

Reactive viscoelasticity is a theoretical framework based on the theory of reactive constrained mixtures that encompasses nonlinear viscoelastic responses. It models a viscoelastic solid as a mixture of strong and weak bonds that maintain the cohesiveness of the molecular constituents of the solid matter. Strong bonds impart the elastic response while weak bonds break and reform into a stress-free state in response to loading. The process of bonds breaking and reforming is modeled as a reaction where loaded bonds are the reactants and bonds reformed into a stress-free state are the products of a reaction. The reaction is triggered by the evolving state of loading. The state of stress in strong bonds is a function of the total strain in the material, whereas the state of stress in weak bonds is based on the state of strain relative to the time that these bonds were reformed. This study introduces two important practical contributions to the reactive nonlinear viscoelasticity framework: (1) normally, the evaluation of the stress tensor involves taking a summation over a continually increasing number of weak bond generations, which is poorly suited for a computational scheme. Therefore, this study presents an effective numerical scheme for evaluating the strain energy density, the Cauchy stress, and spatial elasticity tensors of reactive viscoelastic materials. (2) We provide the conditions for satisfying frame indifference for anisotropic nonlinear viscoelasticity, including for tension-bearing fiber models. Code verifications and model validations against experimental data provide evidence in support of this updated formulation.

Damage Mechanics of Biological Tissues in Relation to Viscoelasticity.

This study examines the theoretical foundations for the damage mechanics of biological tissues in relation to viscoelasticity. Its primary goal is to provide a mechanistic understanding of well-known experimental observations in biomechanics, which show that the ultimate tensile strength of viscoelastic biological tissues typically increases with increasing strain rate. The basic premise of this framework is that tissue damage occurs when strong bonds, such as covalent bonds in the solid matrix of a biological tissue, break in response to loading. This type of failure is described as elastic damage, under the idealizing assumption that strong bonds behave elastically. Viscoelasticity arises from three types of dissipative mechanisms: (1) Friction between molecules of the same species, which is represented by the tissue viscosity. (2) Friction between fluid and solid constituents of a porous medium, which is represented by the tissue hydraulic permeability. (3) Dissipative reactions arising from weak bonds breaking in response to loading, and reforming in a stress-free state, such as hydrogen bonds and other weak electrostatic bonds. When a viscoelastic tissue is subjected to loading, some of that load may be temporarily supported by those frictional and weak bond forces, reducing the amount of load supported by elastic strong bonds and thus, the extent of elastic damage sustained by those bonds. This protective effect depends on the characteristic time response of viscoelastic mechanisms in relation to the loading history. This study formalizes these concepts by presenting general equations that can model the damage mechanics of viscoelastic tissues.

Development of a continuum damage model to predict accumulation of sub-failure damage in tendons.

Many painful and physically debilitating conditions involve sub-failure mechanical damage to seemingly intact connective tissues such as tendons and ligaments. We found that the amount of denatured collagen in rat tail tendon (RTT) fascicles increased over experiments of cyclic loading to a constant load level (creep cyclic fatigue) with fluorescently tagged collagen hybridizing peptides (CHPs) that bind to denatured collagen. To better understand tendon sub-failure damage progression, computational modeling of tendon materials via finite element analysis in FEBio has been conducted. The objective of this project was to develop, implement, and test the ability of a new continuum damage mechanics (CDM) model in FEBio to represent the sub-failure damage behavior seen in our RTT fascicle creep cyclic fatigue experimental data. There appeared to be two distinct mechanisms responsible for the creep cyclic fatigue softening behavior of RTT fascicles over the number of cycles to failure: the preconditioning effect and overall collagen damage. In our finite element (FE) models, the RTT fascicle undamaged elastic constitutive material was composed of a matrix and fibers described by the Coupled Veronda-Westmann and exponential-linear materials. This undamaged elastic material was convolved with a modified CDM model adapted from Balzani et al., in 2012. The novelty of the Balzani damage model is the inclusion of two interrelated mechanisms described as continuous and discontinuous damage. The continuous damage formulation calculates damage accumulation during the loading and reloading of each new cycle, while the discontinuous damage approach accumulates damage from the maximum strain over the loading history to the current time. We modified the Balzani damage model formulations to represent exponential and sigmoidal increases in damage marked by the preconditioning effect and collagen damage in RTT fascicles as functions of continuous and discontinuous damage. The original Balzani damage model was first verified, then the modified CDM model was implemented into FEBio and used to reproduce the sample specific experimental creep cyclic fatigue stress-strain data as well as predict incremental cyclic fatigue. The resulting model will be useful for future experimental and computational studies of damage mechanics to understand tendon pathologies.

A Computational Framework for Atrioventricular Valve Modeling Using Open-Source Software.

Atrioventricular valve regurgitation is a significant cause of morbidity and mortality in patients with acquired and congenital cardiac valve disease. Image-derived computational modeling of atrioventricular valves has advanced substantially over the last decade and holds particular promise to inform valve repair in small and heterogeneous populations, which are less likely to be optimized through empiric clinical application. While an abundance of computational biomechanics studies has investigated mitral and tricuspid valve disease in adults, few studies have investigated its application to vulnerable pediatric and congenital heart populations. Further, to date, investigators have primarily relied upon a series of commercial applications that are neither designed for image-derived modeling of cardiac valves nor freely available to facilitate transparent and reproducible valve science. To address this deficiency, we aimed to build an open-source computational framework for the image-derived biomechanical analysis of atrioventricular valves. In the present work, we integrated an open-source valve modeling platform, SlicerHeart, and an open-source biomechanics finite element modeling software, FEBio, to facilitate image-derived atrioventricular valve model creation and finite element analysis. We present a detailed verification and sensitivity analysis to demonstrate the fidelity of this modeling in application to three-dimensional echocardiography-derived pediatric mitral and tricuspid valve models. Our analyses achieved an excellent agreement with those reported in the literature. As such, this evolving computational framework offers a promising initial foundation for future development and investigation of valve mechanics, in particular collaborative efforts targeting the development of improved repairs for children with congenital heart disease.

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.

Finite Element Implementation of Biphasic-Fluid Structure Interactions in febio.

In biomechanics, solid-fluid mixtures have commonly been used to model the response of hydrated biological tissues. In cartilage mechanics, this type of mixture, where the fluid and solid constituents are both assumed to be intrinsically incompressible, is often called a biphasic material. Various physiological processes involve the interaction of a viscous fluid with a porous-hydrated tissue, as encountered in synovial joint lubrication, cardiovascular mechanics, and respiratory mechanics. The objective of this study was to implement a finite element solver in the open-source software febio that models dynamic interactions between a viscous fluid and a biphasic domain, accommodating finite deformations of both domains as well as fluid exchanges between them. For compatibility with our recent implementation of solvers for computational fluid dynamics (CFD) and fluid-structure interactions (FSI), where the fluid is slightly compressible, this study employs a novel hybrid biphasic formulation where the porous skeleton is intrinsically incompressible but the fluid is also slightly compressible. The resulting biphasic-FSI (BFSI) implementation is verified against published analytical and numerical benchmark problems, as well as novel analytical solutions derived for the purposes of this study. An illustration of this BFSI solver is presented for two-dimensional (2D) airflow through a simulated face mask under five cycles of breathing, showing that masks significantly reduce air dispersion compared to the no-mask control analysis. In addition, we model three-dimensional (3D) blood flow in a bifurcated carotid artery assuming porous arterial walls and verify that mass is conserved across all fluid-permeable boundaries. The successful formulation and implementation of this BFSI solver offers enhanced multiphysics modeling capabilities that are accessible via an open-source software platform.

A Formulation for Fluid-Structure Interactions in febio Using Mixture Theory.

Many physiological systems involve strong interactions between fluids and solids, posing a significant 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, 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 from the FSI literature 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 enhance the multiphysics modeling capabilities in febio relevant to the biomechanics and biophysics communities.

A Plugin Framework for Extending the Simulation Capabilities of FEBio.

The FEBio software suite is a set of software tools for nonlinear finite element analysis in biomechanics and biophysics. FEBio employs mixture theory to account for the multiconstituent nature of biological materials, integrating the field equations for irreversible thermodynamics, solid mechanics, fluid mechanics, mass transport with reactive species, and electrokinetics. This communication describes the development and application of a new "plugin" framework for FEBio. Plugins are dynamically linked libraries that allow users to add new features and to couple FEBio with other domain-specific software applications without modifying the source code directly. The governing equations and simulation capabilities of FEBio are reviewed. The implementation, structure, use, and application of the plugin framework are detailed. Several example plugins are described in detail to illustrate how plugins enrich, extend, and leverage existing capabilities in FEBio, including applications to deformable image registration, constitutive modeling of biological tissues, coupling to an external software package that simulates angiogenesis using a discrete computational model, and a nonlinear reaction-diffusion solver. The plugin feature facilitates dissemination of new simulation methods, reproduction of published results, and coupling of FEBio with other domain-specific simulation approaches such as compartmental modeling, agent-based modeling, and rigid-body dynamics. We anticipate that the new plugin framework will greatly expand the range of applications for the FEBio software suite and thus its impact.

Three-dimensional femoral head coverage in the standing position represents that measured in vivo during gait.

Individuals with over- or under-covered hips may develop hip osteoarthritis. Femoral head coverage is typically evaluated using radiographs, and/or computed tomography (CT) or magnetic resonance images obtained supine. Yet, these static assessments of coverage may not provide accurate information regarding the dynamic, three-dimensional (3-D) relationship between the femoral head and acetabulum. The objectives of this study were to: (1) quantify total and regional 3-D femoral head coverage in a standing position and during gait, and (2) quantify the relationship between 3-D femoral head coverage in standing to that measured during gait. The kinematic position of the hip during standing and gait was measured in vivo for 11 asymptomatic morphologically normal subjects using dual fluoroscopy and model-based tracking of 3-D CT models. Percent coverage in the standing position and during gait was measured overall and on a regional basis (anterior, superior, posterior, inferior). Coverage in standing was correlated with that measured during gait. For total coverage, very little change in coverage occurred during gait (range: 35.0-36.7%; mean: 36.2%). Coverage at each time point of gait strongly correlated with coverage during standing (r = 0.929-0.989). The regions thought to play an important role in weight bearing (i.e. anterior, superior, posterior) were significantly correlated with coverage in standing during the stance phase. Our results suggest that coverage measured in a standing position is a good surrogate for coverage measured during gait. Clin. Anat. 31:1177-1183, 2018. © 2018 Wiley Periodicals, Inc.

Finite Element Formulation of Multiphasic Shell Elements for Cell Mechanics Analyses in FEBio.

With the recent implementation of multiphasic materials in the open-source finite element (FE) software FEBio (febio.org), 3D models of cells embedded within the tissue may now be analyzed, accounting for porous solid matrix deformation, transport of interstitial fluid and solutes, membrane potential, and reactions. The cell membrane is a critical component in cell models, which selectively regulates the transport of fluid and solutes in the presence of large concentration and electric potential gradients, while also facilitating the transport of various proteins. The cell membrane is much thinner than the cell; therefore, in an FE environment, shell elements formulated as 2D surfaces in 3D space would be preferred for modeling the cell membrane, for the convenience of mesh generation from image-based data, especially for convoluted membranes. However, multiphasic shell elements are yet to be developed in the FE literature and commercial FE software. This study presents a novel formulation of multiphasic shell elements and its implementation in FEBio. The shell model includes front- and back-face nodal degrees of freedom for the solid displacement, effective fluid pressure and effective solute concentrations, and a linear interpolation of these variables across the shell thickness. This formulation was verified against classical models of cell physiology and validated against reported experimental measurements in chondrocytes. This implementation of passive transport of fluid and solutes across multiphasic membranes makes it possible to model the biomechanics of isolated cells or cells embedded in their extracellular matrix, accounting for solvent and solute transport.

Hip chondrolabral mechanics during activities of daily living: Role of the labrum and interstitial fluid pressurization.

Osteoarthritis of the hip can result from mechanical factors, which can be studied using finite element (FE) analysis. FE studies of the hip often assume there is no significant loss of fluid pressurization in the articular cartilage during simulated activities and approximate the material as incompressible and elastic. This study examined the conditions under which interstitial fluid load support remains sustained during physiological motions, as well as the role of the labrum in maintaining fluid load support and the effect of its presence on the solid phase of the surrounding cartilage. We found that dynamic motions of gait and squatting maintained consistent fluid load support between cycles, while static single-leg stance experienced slight fluid depressurization with significant reduction of solid phase stress and strain. Presence of the labrum did not significantly influence fluid load support within the articular cartilage, but prevented deformation at the cartilage edge, leading to lower stress and strain conditions in the cartilage. A morphologically accurate representation of collagen fibril orientation through the thickness of the articular cartilage was not necessary to predict fluid load support. However, comparison with simplified fibril reinforcement underscored the physiological importance. The results of this study demonstrate that an elastic incompressible material approximation is reasonable for modeling a limited number of cyclic motions of gait and squatting without significant loss of accuracy, but is not appropriate for static motions or numerous repeated motions. Additionally, effects seen from removal of the labrum motivate evaluation of labral reattachment strategies in the context of labral repair.

Finite Element Framework for Computational Fluid Dynamics in FEBio.

The mechanics of biological fluids is an important topic in biomechanics, often requiring the use of computational tools to analyze problems with realistic geometries and material properties. This study describes the formulation and implementation of a finite element framework for computational fluid dynamics (CFD) in FEBio, a free software designed to meet the computational needs of the biomechanics and biophysics communities. This formulation models nearly incompressible flow with a compressible isothermal formulation that uses a physically realistic value for the fluid bulk modulus. It employs fluid velocity and dilatation as essential variables: The virtual work integral enforces the balance of linear momentum and the kinematic constraint between fluid velocity and dilatation, while fluid density varies with dilatation as prescribed by the axiom of mass balance. Using this approach, equal-order interpolations may be used for both essential variables over each element, contrary to traditional mixed formulations that must explicitly satisfy the inf-sup condition. The formulation accommodates Newtonian and non-Newtonian viscous responses as well as inviscid fluids. The efficiency of numerical solutions is enhanced using Broyden's quasi-Newton method. The results of finite element simulations were verified using well-documented benchmark problems as well as comparisons with other free and commercial codes. These analyses demonstrated that the novel formulation introduced in FEBio could successfully reproduce the results of other codes. The analogy between this CFD formulation and standard finite element formulations for solid mechanics makes it suitable for future extension to fluid-structure interactions (FSIs).

Perspectives on Sharing Models and Related Resources in Computational Biomechanics Research.

The role of computational modeling for biomechanics research and related clinical care will be increasingly prominent. The biomechanics community has been developing computational models routinely for exploration of the mechanics and mechanobiology of diverse biological structures. As a result, a large array of models, data, and discipline-specific simulation software has emerged to support endeavors in computational biomechanics. Sharing computational models and related data and simulation software has first become a utilitarian interest, and now, it is a necessity. Exchange of models, in support of knowledge exchange provided by scholarly publishing, has important implications. Specifically, model sharing can facilitate assessment of reproducibility in computational biomechanics and can provide an opportunity for repurposing and reuse, and a venue for medical training. The community's desire to investigate biological and biomechanical phenomena crossing multiple systems, scales, and physical domains, also motivates sharing of modeling resources as blending of models developed by domain experts will be a required step for comprehensive simulation studies as well as the enhancement of their rigor and reproducibility. The goal of this paper is to understand current perspectives in the biomechanics community for the sharing of computational models and related resources. Opinions on opportunities, challenges, and pathways to model sharing, particularly as part of the scholarly publishing workflow, were sought. A group of journal editors and a handful of investigators active in computational biomechanics were approached to collect short opinion pieces as a part of a larger effort of the IEEE EMBS Computational Biology and the Physiome Technical Committee to address model reproducibility through publications. A synthesis of these opinion pieces indicates that the community recognizes the necessity and usefulness of model sharing. There is a strong will to facilitate model sharing, and there are corresponding initiatives by the scientific journals. Outside the publishing enterprise, infrastructure to facilitate model sharing in biomechanics exists, and simulation software developers are interested in accommodating the community's needs for sharing of modeling resources. Encouragement for the use of standardized markups, concerns related to quality assurance, acknowledgement of increased burden, and importance of stewardship of resources are noted. In the short-term, it is advisable that the community builds upon recent strategies and experiments with new pathways for continued demonstration of model sharing, its promotion, and its utility. Nonetheless, the need for a long-term strategy to unify approaches in sharing computational models and related resources is acknowledged. Development of a sustainable platform supported by a culture of open model sharing will likely evolve through continued and inclusive discussions bringing all stakeholders at the table, e.g., by possibly establishing a consortium.