SCIENTIFIC COMPUTING AND IMAGING INSTITUTE
at the University of Utah

Understanding the mechanical behaviour of chondrocytes as a result of cartilage tissue mechanics has significant implications for both evaluation of mechanobiological function and to elaborate on damage mechanisms. A common procedure for prediction of chondrocyte mechanics (and of cell mechanics in general) relies on a computational post-processing approach where tissue-level deformations drive cell-level models. Potential loss of information in this numerical coupling approach may cause erroneous cellular-scale results, particularly during multiphysics analysis of cartilage. The goal of this study was to evaluate the capacity of first- and second-order data passing to predict chondrocyte mechanics by analysing cartilage deformations obtained for varying complexity of loading scenarios. A tissue-scale model with a sub-region incorporating representation of chondron size and distribution served as control. The post-processing approach first required solution of a homogeneous tissue-level model, results of which were used to drive a separate cell-level model (same characteristics as the sub-region of control model). The first-order data passing appeared to be adequate for simplified loading of the cartilage and for a subset of cell deformation metrics, for example, change in aspect ratio. The second-order data passing scheme was more accurate, particularly when asymmetric permeability of the tissue boundaries was considered. Yet, the method exhibited limitations for predictions of instantaneous metrics related to the fluid phase, for example, mass exchange rate. Nonetheless, employing higher order data exchange schemes may be necessary to understand the biphasic mechanics of cells under lifelike tissue loading states for the whole time history of the simulation.

A finite element formulation of neutral solute transport across a contact interface between deformable porous media is implemented and validated against analytical solutions. By reducing the integral statements of external virtual work on the two contacting surfaces into a single contact integral, the algorithm automatically enforces continuity of solute molar flux across the contact interface, whereas continuity of the effective solute concentration (a measure of the solute mechano-chemical potential) is achieved using a penalty method. This novel formulation facilitates the analysis of problems in biomechanics where the transport of metabolites across contact interfaces of deformable tissues may be of interest. This contact algorithm is the first to address solute transport across deformable interfaces, and is made available in the public domain, open-source finite element code FEBio (http://www.febio.org).

Keywords: FEBio, Finite element modeling, Contact mechanics, Solute transport, Porous media, Biphasic theory

Objective
During neovascularization, the end result is a new functional microcirculation composed of a network of mature microvessels with specific topologies. Although much is known concerning the mechanisms underlying the initiation of angiogenesis, it remains unclear how the final architecture of microcirculatory beds is regulated. To begin to address this, we determined the impact of angiogenic neovessel prepatterning on the final microvascular network topology using a model of implant neovascularization.

Methods and Results
We used 3D direct-write bioprinting or physical constraints in a manner permitting postangiogenesis vascular remodeling and adaptation to pattern angiogenic microvascular precursors (neovessels formed from isolated microvessel segments) in 3D collagen gels before implantation and subsequent network formation. Neovasculatures prepatterned into parallel arrays formed functional networks after 4 weeks postimplantation but lost the prepatterned architecture. However, maintenance of uniaxial physical constraints during postangiogenesis remodeling of the implanted neovasculatures produced networks with aligned microvessels, as well as an altered proportional distribution of arterioles, capillaries, and venules.

Conclusion
Here we show that network topology resulting from implanted microvessel precursors is independent from prepatterning of precursors but can be influenced by a patterning stimulus involving tissue deformation during postangiogenesis remodeling and maturation.

Articular cartilage experiences significant mechanical loads during daily activities. Healthy cartilage provides the capacity for load bearing and regulates the mechanobiological processes for tissue development, maintenance, and repair. Experimental studies at multiple scales have provided a fundamental understanding of macroscopic mechanical function, evaluation of the micromechanical environment of chondrocytes, and the foundations for mechanobiological response. In addition, computational models of cartilage have offered a concise description of experimental data at many spatial levels under healthy and diseased conditions, and have served to generate hypotheses for the mechanical and biological function. Further, modeling and simulation provides a platform for predictive risk assessment, management of dysfunction, as well as a means to relate multiple spatial scales. Simulation-based investigation of cartilage comes with many challenges including both the computational burden and often insufficient availability of data for model development and validation. This review outlines recent modeling and simulation approaches to understand cartilage function from a mechanical systems perspective, and illustrates pathways to associate mechanics with biological function. Computational representations at single scales are provided from the body down to the microstructure, along with attempts to explore multiscale mechanisms of load sharing that dictate the mechanical environment of the cartilage and chondrocytes.

Background and purpose
Acetabular retroversion may result in anterior acetabular over-coverage and posterior deficiency. It is unclear how standard radiographic measures of retroversion relate to measurements from 3D models, generated from volumetric CT data. We sought to: (1) compare 2D radiographic measurements between patients with acetabular retroversion and normal control subjects, (2) compare 3D measurements of total and regional femoral head coverage between patients and controls, and (3) quantify relationships between radiographic measurements of acetabular retroversion to total and regional coverage of the femoral head.

Patients and methods
For 16 patients and 18 controls we measured the extrusion index, crossover ratio, acetabular angle, acetabular index, lateral center edge angle, and a new measurement termed the "posterior wall distance". 3D femoral coverage was determined from volumetric CT data using objectively defined acetabular rim projections, head-neck junctions, and 4 anatomic regions. For radiographic measurements, intra-observer and inter-observer reliabilities were evaluated and associations between 2D radiographic and 3D model-based measures were determined.

Results
Compared to control subjects, patients with acetabular retroversion had a negative posterior wall distance, increased extrusion index, and smaller lateral center edge angle. Differences in the acetabular index between groups approached statistical significance. The acetabular angle was similar between groups. Acetabular retroversion was associated with a slight but statistically significant increase in anterior acetabular coverage, especially in the anterolateral region. Retroverted hips had substantially less posterior coverage, especially in the posterolateral region.

Interpretation
We found that a number of 2D radiographic measures of acetabular morphology were correlated with 3D model-based measures of total and regional femoral head coverage. These correlations may be used to assist in the diagnosis of retroversion and for preoperative planning.

Our objectives were to determine cartilage contact stress during walking, stair climbing, and descending stairs in a well-defined group of normal volunteers and to assess variations in contact stress and area among subjects and across loading scenarios. Ten volunteers without history of hip pain or disease with normal lateral center-edge angle and acetabular index were selected. Computed tomography imaging with contrast was performed on one hip. Bone and cartilage surfaces were segmented from volumetric image data, and subject-specific finite element models were constructed and analyzed using a validated protocol. Acetabular contact stress and area were determined for seven activities. Peak stress ranged from 7.52 ± 2.11 MPa for heel-strike during walking (233% BW) to 8.66 ± 3.01 MPa for heel-strike during descending stairs (261% BW). Average contact area across all activities was 34% of the surface area of the acetabular cartilage. The distribution of contact stress was highly non-uniform, and more variability occurred among subjects for a given activity than among activities for a single subject. The magnitude and area of contact stress were consistent between activities, although inter-activity shifts in contact pattern were found as the direction of loading changed. Relatively small incongruencies between the femoral and acetabular cartilage had a large effect on the contact stresses. These effects tended to persist across all simulated activities. These results demonstrate the diversity and trends in cartilage contact stress in healthy hips during activities of daily living and provide a basis for future comparisons between normal and pathologic hips.

Keywords: hip, finite element, biomechanics, cartilage contact stresses, cartilage pressure

In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://febio.org/), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.

Biological soft tissues and cells may be subjected to mechanical as well as chemical (osmotic) loading under their natural physiological environment or various experimental conditions. The interaction of mechanical and chemical effects may be very significant under some of these conditions, yet the highly nonlinear nature of the set of governing equations describing these mechanisms poses a challenge for the modeling of such phenomena. This study formulated and implemented a finite element algorithm for analyzing mechanochemical events in neutral deformable porous media under finite deformation. The algorithm employed the framework of mixture theory to model the porous permeable solid matrix and interstitial fluid, where the fluid consists of a mixture of solvent and solute. A special emphasis was placed on solute-solid matrix interactions, such as solute exclusion from a fraction of the matrix pore space (solubility) and frictional momentum exchange that produces solute hindrance and pumping under certain dynamic loading conditions. The finite element formulation implemented full coupling of mechanical and chemical effects, providing a framework where material properties and response functions may depend on solid matrix strain as well as solute concentration. The implementation was validated using selected canonical problems for which analytical or alternative numerical solutions exist. This finite element code includes a number of unique features that enhance the modeling of mechanochemical phenomena in biological tissues. The code is available in the public domain, open source finite element program FEBio (http://mrl.sci.utah.edu/software). [DOI: 10.1115/1.4004810]

The anterior-inferior glenohumeral capsule is the primary passive stabilizer to the glenohumeral joint during anterior dislocation. Physical examinations following dislocation are crucial for proper diagnosis of capsule pathology; however,they are not standardized for joint position which may lead to misdiagnoses and poor outcomes. To suggest joint positions for physical examinations where the stability provided by the capsule may be consistent among patients, the objective of this study was to evaluate the distribution of maximum principal strain on the anterior-inferior capsule using two validated subject-specific finite element models of the glenohumeral joint at clinically relevant joint positions. The joint positions with 25 N anterior load applied at 60° of glenohumeral abduction and 10°, 20°, 30° and 40° of external rotation resulted in distributions of strain that were similar between shoulders(r²≥0.7). Furthermore, those positions with 20-40° of external rotation resulted in capsule strains on the glenoid side of the anterior band of the inferior glenohumeral ligament that were significantly greater than in all other capsule regions. These findings suggest that anterior stability provided by the anterior-inferior capsule may be consistent among subjects at joint positions with 60° of glenohumeral abduction and a mid-range (20-40°) of external rotation, and that the glenoid side has the greatest contribution to stability at these joint positions. Therefore, it may be possible to establish standard joint positions for physical examinations that clinicians can use to effectively diagnose pathology in the anterior-inferior capsule following dislocation and lead to improved outcomes.

Instability is a significant concern in total hip arthroplasty (THA), particularly when there is structural compromise of the capsule due to pre-existing pathology or due to necessities of surgical approach. An experimentally grounded fiber-direction-based finite element model of the hip capsule was developed, and was integrated with an established three-dimensional model of impingement/dislocation. Model validity was established by close similarity to results from a cadaveric experiment in a servohydraulic hip simulator. Parametric computational runs explored effects of graded levels of capsule thickness, of regional detachment from the capsule's femoral or acetabular insertions, of surgical incisions of capsule substance, and of capsule defect repairs. Depending strongly upon the specific site, localized capsule defects caused varying degrees of construct stability compromise, with several specific situations involving over 60\% decrement in dislocation resistance. Construct stability was returned substantially toward intact-capsule levels following well-conceived repairs, although the suture sites involved were often at substantial risk of failure. These parametric model results underscore the importance of retaining or robustly repairing capsular structures in THA, in order to maximize overall construct stability. © 2011 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 29:1642–1648, 2011

The relatively high incidence of labral tears among patients presenting with hip pain suggests that the acetabular labrum is often subjected to injurious loading in vivo. However, it is unclear whether the labrum participates in load transfer across the joint during activities of daily living. This study examined the role of the acetabular labrum in load transfer for hips with normal acetabular geometry and acetabular dysplasia using subject-specific finite element analysis. Models were generated from volumetric CT data and analyzed with and without the labrum during activities of daily living. The labrum in the dysplastic model supported 4–11\% of the total load transferred across the joint, while the labrum in the normal model supported only 1–2\% of the total load. Despite the increased load transferred to the acetabular cartilage in simulations without the labrum, there were minimal differences in cartilage contact stresses. This was because the load supported by the cartilage correlated with the cartilage contact area. A higher percentage of load was transferred to the labrum in the dysplastic model because the femoral head achieved equilibrium near the lateral edge of the acetabulum. The results of this study suggest that the labrum plays a larger role in load transfer and joint stability in hips with acetabular dysplasia than in hips with normal acetabular geometry.

Finite element simulations in computational biomechanics commonly require the discretization of extremely complicated geometries. Creating meshes for these complex geometries can be very difficult and time consuming using hexahedral elements. Automatic meshing algorithms exist for tetrahedral elements, but these elements often have numerical problems that discourage their use in complex finite element models. To overcome these problems we have implemented a stabilized, nodally-integrated tetrahedral element formulation in FEBio, our in-house developed finite element code, allowing researchers to use linear tetrahedral elements in their models and still obtain accurate solutions. In addition to facilitating automatic mesh generation, this also allows researchers to use mesh refinement algorithms which are fairly well developed for tetrahedral elements but not so much for hexahedral elements. In this document, the implementation of the stabilized, nodallyintegrated, tetrahedral element, named the \"UT4 element\", is described. Two slightly different variations of the nodally integrated tetrahedral element are considered. In one variation the entire virtual work is stabilized and in the other one the stabilization is only applied to the isochoric part of the virtual work. The implementation of both formulations has been verified and the convergence behavior illustrated using the patch test and three verification problems. Also, a model from our laboratory with very complex geometry is discretized and analyzed using the UT4 element to show its utility for a problem from the biomechanics literature. The convergence behavior of the UT4 element does vary depending on problem, tetrahedral mesh structure and choice of formulation parameters, but the results from the verification problems should assure analysts that a converged solution using the UT4 element can be obtained that is more accurate than the solution from a classical linear tetrahedral formulation.

Keywords: MRL

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ∼0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.

Keywords: mrl