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.

Continuum Growth Mechanics: Reconciling Two Common Frameworks.

The objective of this study was to investigate whether the two most common growth mechanics modeling frameworks, the constrained-mixture growth model and the kinematic growth model, could be reconciled mathematically. The purpose of this effort was to provide practical guidelines for potential users of these modeling frameworks. Results showed that the kinematic growth model is mathematically consistent with a special form of the constrained-mixture growth model, where only one generation of a growing solid exists at any given time, overturning its entire solid mass at each instant of growth in order to adopt the reference configuration dictated by the growth deformation. The thermodynamics of the kinematic growth model, along with the specialized constrained-mixture growth model, requires a cellular supply of chemical energy to allow deposition of solid mass under a stressed state. A back-of-the-envelope calculation shows that the amount of chemical energy required to sustain biological growth under these models is negligibly small, when compared to the amount of energy normally consumed daily by the human body. In conclusion, this study successfully reconciled the two most popular growth theories for biological growth and explained the special circumstances under which the constrained-mixture growth model reduces to the kinematic growth model.

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.

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.

The Problem With National Institute of Standards and Technology Thermodynamics Tables in Continuum Mechanics.

Thermodynamics is a fundamental topic of continuum mechanics and biomechanics, with a wide range of applications to physiological and biological processes. This study addresses two fundamental limitations of current thermodynamic treatments. First, thermodynamics tables distributed online by the U.S. National Institute of Standards and Technology (NIST) report properties of fluids as a function of absolute temperature T and absolute pressure P. These properties include mass density ρ, specific internal energy u, enthalpy h=u+P/ρ, and entropy s. However, formulations of jump conditions across phase boundaries derived from Newton's second law of motion and the first law of thermodynamics employ the gauge pressure p=P-Pr, where Pr is an arbitrarily selected referential absolute pressure. Interchanging p with P is not innocuous as it alters tabulated NIST values for u while keeping h and s unchanged. Using p for functions of state and governing equations solves the problem with using NIST entries for the specific internal energy u in standard thermodynamics tables and analyses of phase transformation in continuum mechanics. Second, constitutive models for the free energy of fluids, such as water and air, are not typically provided in standard thermodynamics treatments. This study proposes a set of constitutive models and validates them against suitably modified NIST data.

Integration of Febio as an Instructional Tool in the Undergraduate Biomechanics Curriculum.

Computer simulations play an important role in a range of biomedical engineering applications. Thus, it is important that biomedical engineering students engage with modeling in their undergraduate education and establish an understanding of its practice. In addition, computational tools enhance active learning and complement standard pedagogical approaches to promote student understanding of course content. Herein, we describe the development and implementation of learning modules for computational modeling and simulation (CM&S) within an undergraduate biomechanics course. We developed four CM&S learning modules that targeted predefined course goals and learning outcomes within the febio studio software. For each module, students were guided through CM&S tutorials and tasked to construct and analyze more advanced models to assess learning and competency and evaluate module effectiveness. Results showed that students demonstrated an increased interest in CM&S through module progression and that modules promoted the understanding of course content. In addition, students exhibited increased understanding and competency in finite element model development and simulation software use. Lastly, it was evident that students recognized the importance of coupling theory, experiments, and modeling and understood the importance of CM&S in biomedical engineering and its broad application. Our findings suggest that integrating well-designed CM&S modules into undergraduate biomedical engineering education holds much promise in supporting student learning experiences and introducing students to modern engineering tools relevant to professional development.

Mechanics of lung cancer: A finite element model shows strain amplification during early tumorigenesis.

Early lung cancer lesions develop within a unique microenvironment that undergoes constant cyclic stretch from respiration. While tumor stiffening is an established driver of tumor progression, the contribution of stress and strain to lung cancer is unknown. We developed tissue scale finite element models of lung tissue to test how early lesions alter respiration-induced strain. We found that an early tumor, represented as alveolar filling, amplified the strain experienced in the adjacent alveolar walls. Tumor stiffening further increased the amplitude of the strain in the adjacent alveolar walls and extended the strain amplification deeper into the normal lung. In contrast, the strain experienced in the tumor proper was less than the applied strain, although regions of amplification appeared at the tumor edge. Measurements of the alveolar wall thickness in clinical and mouse model samples of lung adenocarcinoma (LUAD) showed wall thickening adjacent to the tumors, consistent with cellular response to strain. Modeling alveolar wall thickening by encircling the tumor with thickened walls moved the strain amplification radially outward, to the next adjacent alveolus. Simulating iterative thickening in response to amplified strain produced tracks of thickened walls. We observed such tracks in early-stage clinical samples. The tracks were populated with invading tumor cells, suggesting that strain amplification in very early lung lesions could guide pro-invasive remodeling of the tumor microenvironment. The simulation results and tumor measurements suggest that cells at the edge of a lung tumor and in surrounding alveolar walls experience increased strain during respiration that could promote tumor progression.

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.

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.

Matrix anisotropy promotes angiogenesis in a density-dependent manner.

Angiogenesis is necessary for wound healing, tumorigenesis, implant inosculation, and homeostasis. In each situation, matrix structure and mechanics play a role in determining whether new vasculatures can establish transport to new or hypoxic tissues. Neovessel growth and directional guidance are sensitive to three-dimensional (3-D) matrix anisotropy and density, although the individual and integrated roles of these matrix features have not been fully recapitulated in vitro. We developed a tension-based method to align 3-D collagen constructs seeded with microvessel fragments in matrices of three levels of collagen fibril anisotropy and two levels of collagen density. The extent and direction of neovessel growth from the parent microvessel fragments increased with matrix anisotropy and decreased with density. The proangiogenic effects of anisotropy were attenuated at higher matrix densities. We also examined the impact of matrix anisotropy in an experimental model of neovessel invasion across a tissue interface. Matrix density was found to dictate the success of interface crossing, whereas interface curvature and fibril alignment were found to control directional guidance. Our findings indicate that complex configurations of matrix density and alignment can facilitate or complicate the establishment or maintenance of vascular networks in pathological and homeostatic angiogenesis. Furthermore, we extend preexisting methods for tuning collagen anisotropy in thick constructs. This approach addresses gaps in tissue engineering and cell culture by supporting the inclusion of large multicellular structures in prealigned constructs.NEW & NOTEWORTHY Matrix anisotropy and density have a considerable effect on angiogenic vessel growth and directional guidance. However, the current literature relies on 2-D and simplified models of angiogenesis (e.g., tubulogenesis and vasculogenesis). We present a method to align 3-D collagen scaffolds embedded with microvessel fragments to different levels of anisotropy. Neovessel growth increases with anisotropy and decreases with density, which may guide angiogenic neovessels across tissue interfaces such as during implant inosculation and tumorigenesis.

Effects of osteogenic ambulatory mechanical stimulation on early stages of BMP-2 mediated bone repair.

Purpose: Mechanical loading of bone defects through rehabilitation is a promising approach to stimulate repair and reduce nonunion risk; however, little is known about how therapeutic mechanical stimuli modulate early-stage repair before mineralized bone formation. The objective of this study was to investigate the early effects of osteogenic loading on cytokine expression and angiogenesis during the first 3 weeks of BMP-2 mediated segmental bone defect repair.Materials and Methods: A rat model of BMP-2 mediated bone defect repair was subjected to an osteogenic mechanical loading protocol using ambulatory rehabilitation and a compliant, load-sharing fixator with an integrated implantable strain sensor. The effect of fixator load-sharing on local tissue strain, angiogenesis, and cytokine expression was evaluated.Results: Using sensor readings for local measurements of boundary conditions, finite element simulations showed strain became amplified in remaining soft tissue regions between 1 and 3 weeks (Week 3: load-sharing: -1.89 ± 0.35% and load-shielded: -1.38 ± 0.35% vs. Week 1: load-sharing: -1.54 ± 0.17%; load-shielded: -0.76 ± 0.06%). Multivariate analysis of cytokine arrays revealed that load-sharing significantly altered expression profiles in the defect tissue at 2 weeks compared to load-shielded defects. Specifically, loading reduced VEGF (p = 0.052) and increased CXCL5 (LIX) levels. Subsequently, vascular volume in loaded defects was reduced relative to load-shielded defects but similar to intact bone at 3 weeks. Endochondral bone repair was also observed histologically in loaded defects at 3 weeks.Conclusions: Together, these results demonstrate that moderate ambulatory strains previously shown to stimulate bone regeneration significantly alter early angiogenic and cytokine signaling and may promote endochondral ossification.

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.

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.

How Does Chondrolabral Damage and Labral Repair Influence the Mechanics of the Hip in the Setting of Cam Morphology? A Finite-Element Modeling Study.

BACKGROUND: Individuals with cam morphology are prone to chondrolabral injuries that may progress to osteoarthritis. The mechanical factors responsible for the initiation and progression of chondrolabral injuries in these individuals are not well understood. Additionally, although labral repair is commonly performed during surgical correction of cam morphology, the isolated mechanical effect of labral repair on the labrum and surrounding cartilage is unknown. QUESTION/PURPOSES: Using a volunteer-specific finite-element analysis, we asked: (1) How does cam morphology create a deleterious mechanical environment for articular cartilage (as evaluated by shear stress, tensile strain, contact pressure, and fluid pressure) that could increase the risk of cartilage damage compared with a radiographically normal hip? (2) How does chondrolabral damage, specifically delamination, delamination with rupture of the chondrolabral junction, and the presence of a chondral defect, alter the mechanical environment around the damage? (3) How does labral repair affect the mechanical environment in the context of the aforementioned chondrolabral damage scenarios? METHODS: The mechanical conditions of a representative hip with normal bony morphology (characterized by an alpha angle of 37°) and one with cam morphology (characterized by an alpha angle of 78°) were evaluated using finite-element models that included volunteer-specific anatomy and kinematics. The bone, cartilage, and labrum geometry for the hip models were collected from two volunteers matched by age (25 years with cam morphology and 23 years with normal morphology), BMI (both 24 kg/m2), and sex (both male). Volunteer-specific kinematics for gait were used to drive the finite-element models in combination with joint reaction forces. Constitutive material models were assigned to the cartilage and labrum, which simulate a physiologically realistic material response, including the time-dependent response from fluid flow through the cartilage, and spatially varied response from collagen fibril reinforcement. For the cam hip, three models were created to represent chondrolabral damage conditions: (1) "delamination," with the acetabular cartilage separated from the bone in one region; (2) "delamination with chondrolabral junction (CLJ) rupture," which includes separation of the cartilage from the labrum tissue; and (3) a full-thickness chondral defect, referred to throughout as "defect," where the acetabular cartilage has degraded so there is a void. Each of the three conditions was modeled with a labral tear and with the labrum repaired. The size and location of the damage conditions simulated in the cartilage and labrum were attained from reported clinical prevalence of the location of these injuries. For each damage condition, the contact area, contact pressure, tensile strain, shear stress, and fluid pressure were predicted during gait and compared. RESULTS: The cartilage in the hip with cam morphology experienced higher stresses and strains than the normal hip. The peak level of tensile strain (25%) and shear stress (11 MPa) experienced by the cam hip may exceed stable conditions and initiate damage or degradation. The cam hip with simulated damage experienced more evenly distributed contact pressure than the intact cam hip, as well as decreased tensile strain, shear stress, and fluid pressure. The peak levels of tensile strain (15% to 16%) and shear stress (2.5 to 2.7 MPa) for cam hips with simulated damage may be at stable magnitudes. Labral repair only marginally affected the overall stress and strain within the cartilage, but it increased local tensile strain in the cartilage near the chondrolabral junction in the hip with delamination and increased the peak tensile strain and shear stress on the labrum. CONCLUSION: This finite-element modeling pilot study suggests that cam morphology may predispose hip articular cartilage to injury because of high shear stress; however, the presence of simulated damage distributed the loading more evenly and the magnitude of stress and strain decreased throughout the cartilage. The locations of the peak values also shifted posteriorly. Additionally, in hips with cam morphology, isolated labral repair in the hip with a delamination injury increased localized strain in the cartilage near the chondrolabral junction. CLINICAL RELEVANCE: In a hip with cam morphology, labral repair alone may not protect the cartilage from damage because of mechanical overload during the low-flexion, weightbearing positions experienced during gait. The predicted findings of redistribution of stress and strain from damage in the cam hip may, in some cases, relieve disposition to damage progression. Additional studies should include volunteers with varied acetabular morphology, such as borderline dysplasia with cam morphology or pincer deformity, to analyze the effect on the conclusions presented in the current study. Further, future studies should evaluate the combined effects of osteochondroplasty and chondrolabral treatment.

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.

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.

Which Two-dimensional Radiographic Measurements of Cam Femoroacetabular Impingement Best Describe the Three-dimensional Shape of the Proximal Femur?

BACKGROUND: Many two-dimensional (2-D) radiographic views are used to help diagnose cam femoroacetabular impingement (FAI), but there is little consensus as to which view or combination of views is most effective at visualizing the magnitude and extent of the cam lesion (ie, severity). Previous studies have used a single image from a sequence of CT or MR images to serve as a reference standard with which to evaluate the ability of 2-D radiographic views and associated measurements to describe the severity of the cam lesion. However, single images from CT or MRI data may fail to capture the apex of the cam lesion. Thus, it may be more appropriate to use measurements of three-dimensional (3-D) surface reconstructions from CT or MRI data to serve as an anatomic reference standard when evaluating radiographic views and associated measurements used in the diagnosis of cam FAI. QUESTIONS/PURPOSES: The purpose of this study was to use digitally reconstructed radiographs and 3-D statistical shape modeling to (1) determine the correlation between 2-D radiographic measurements of cam FAI and 3-D metrics of proximal femoral shape; and 2) identify the combination of radiographic measurements from plain film projections that were most effective at predicting the 3-D shape of the proximal femur. METHODS: This study leveraged previously acquired CT images of the femur from a convenience sample of 37 patients (34 males; mean age, 27 years, range, 16-47 years; mean body mass index [BMI], 24.6 kg/m, range, 19.0-30.2 kg/m) diagnosed with cam FAI imaged between February 2005 and January 2016. Patients were diagnosed with cam FAI based on a culmination of clinical examinations, history of hip pain, and imaging findings. The control group consisted of 59 morphologically normal control participants (36 males; mean age, 29 years, range, 15-55 years; mean BMI, 24.4 kg/m, range, 16.3-38.6 kg/m) imaged between April 2008 and September 2014. Of these controls, 30 were cadaveric femurs and 29 were living participants. All controls were screened for evidence of femoral deformities using radiographs. In addition, living control participants had no history of hip pain or previous surgery to the hip or lower limbs. CT images were acquired for each participant and the surface of the proximal femur was segmented and reconstructed. Surfaces were input to our statistical shape modeling pipeline, which objectively calculated 3-D shape scores that described the overall shape of the entire proximal femur and of the region of the femur where the cam lesion is typically located. Digital reconstructions for eight plain film views (AP, Meyer lateral, 45° Dunn, modified 45° Dunn, frog-leg lateral, Espié frog-leg, 90° Dunn, and cross-table lateral) were generated from CT data. For each view, measurements of the α angle and head-neck offset were obtained by two researchers (intraobserver correlation coefficients of 0.80-0.94 for the α angle and 0.42-0.80 for the head-neck offset measurements). The relationships between radiographic measurements from each view and the 3-D shape scores (for the entire proximal femur and for the region specific to the cam lesion) were assessed with linear correlation. Additionally, partial least squares regression was used to determine which combination of views and measurements was the most effective at predicting 3-D shape scores. RESULTS: Three-dimensional shape scores were most strongly correlated with α angle on the cross-table view when considering the entire proximal femur (r = -0.568; p < 0.001) and on the Meyer lateral view when considering the region of the cam lesion (r = -0.669; p < 0.001). Partial least squares regression demonstrated that measurements from the Meyer lateral and 90° Dunn radiographs produced the optimized regression model for predicting shape scores for the proximal femur (R = 0.405, root mean squared error of prediction [RMSEP] = 1.549) and the region of the cam lesion (R = 0.525, RMSEP = 1.150). Interestingly, views with larger differences in the α angle and head-neck offset between control and cam FAI groups did not have the strongest correlations with 3-D shape. CONCLUSIONS: Considered together, radiographic measurements from the Meyer lateral and 90° Dunn views provided the most effective predictions of 3-D shape of the proximal femur and the region of the cam lesion as determined using shape modeling metrics. CLINICAL RELEVANCE: Our results suggest that clinicians should consider using the Meyer lateral and 90° Dunn views to evaluate patients in whom cam FAI is suspected. However, the α angle and head-neck offset measurements from these and other plain film views could describe no more than half of the overall variation in the shape of the proximal femur and cam lesion. Thus, caution should be exercised when evaluating femoral head anatomy using the α angle and head-neck offset measurements from plain film radiographs. Given these findings, we believe there is merit in pursuing research that aims to develop the framework necessary to integrate statistical shape modeling into clinical evaluation, because this could aid in the diagnosis of cam FAI.

Isolated focal cartilage and labral defects in patients with femoroacetabular impingement syndrome may represent new, unique injury patterns.

PURPOSE: Develop a framework to quantify the size, location and severity of femoral and acetabular-sided cartilage and labral damage observed in patients undergoing hip arthroscopy, and generate a database of individual defect parameters to facilitate future research and treatment efforts. METHODS: The size, location, and severity of cartilage and labral damage were prospectively collected using a custom, standardized post-operative template for 100 consecutive patients with femoroacetabular impingement syndrome. Chondrolabral junction damage, isolated intrasubstance labral damage, isolated acetabular cartilage damage and femoral cartilage damage were quantified and recorded using a combination of Beck and ICRS criteria. Radiographic measurements including alpha angle, head-neck offset, lateral centre edge angle and acetabular index were calculated and compared to the aforementioned chondral data using a multivariable logistic regression model and adjusted odd's ratio. Reliability among measurements were assessed using the kappa statistic and intraclass coefficients were used to evaluate continuous variables. RESULTS: Damage to the acetabular cartilage originating at the chondrolabral junction was the most common finding in 97 hips (97%) and was usually accompanied by labral damage in 65 hips (65%). The width (p = 0.003) and clock-face length (p = 0.016) of the damaged region both increased alpha angle on anteroposterior films. 10% of hips had femoral cartilage damage while only 2 (2%) of hips had isolated defects to either the acetabular cartilage or labrum. The adjusted odds of severe cartilage (p = 0.022) and labral damage (p = 0.046) increased with radiographic cam deformity but was not related to radiographic measures of acetabular coverage. CONCLUSIONS: Damage at the chondrolabral junction was very common in this hip arthroscopy cohort, while isolated defects to the acetabular cartilage or labrum were rare. These data demonstrate that the severity of cam morphology, quantified through radiographic measurements, is a primary predictor of location and severity of chondral and labral damage and focal chondral defects may represent a unique subset of patients that deserve further study. LEVEL OF EVIDENCE: IV.