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Mechanical characteristics of hard and soft tissues are central features for the quantitative description of tissue properties. In this study, we present a biphasic 3D-FE-based method to determine the biomechanical properties of sheep stifle joint articular cartilage (load-bearing area of the medial and lateral femur condyle, n = 28) from stress relaxation indentation tests (s = 0.1 mm, t = 180 s). The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. Parameters were determined using the Levenberg-Marquardt-algorithm. Results showed significant differences between the biomechanical parameters of the lateral (n = 11) and medial (n = 17) femur condyle of the sheep stifle joint articular cartilage. R² of the fit results varied between 0.91 and 0.99. Overall values for the Young’s modulus were 1.316 ± 0.778 MPa, for the Poisson’s ratio 0.106 ± 0.088 and for the permeability 0.008 ± 0.004 mm4/Ns. Future work will focus on studying the influence of experimental settings on the results obtained with the biphasic 3D-FE-model.

Mechanical parameters of hard and soft tissues are explicit markers for quantitative tissue characterization. In this study, we present a comparison of biphasic material properties of equine articular cartilage estimated from stress relaxation (ε = 6 %, t = 1000 s) and creep indentation tests (F = 0.1 N, t = 1000 s). A biphasic 3D-FE-based method is used to determine the biomechanical properties of equine articular cartilage. The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. Parameter identification was executed with the Levenberg- Marquardt-algorithm. Additionally, sensitivity analyses of the calculated biomechanical parameters were performed. Results show that the Young’s modulus E has the largest influence and the Poisson’s ratio of ν ≤ 0.1 is rather insensitive. The R² of the fit results varies between 0.882 and 0.974 (creep model) and between 0.695 and 0.930 (relaxation model). The averaged parameters E and k determined from the creep model yield higher values in comparison to the relaxation model. The differences can be traced back to the experimental settings and to the biphasic material model.

Cartilage constructs produced by SFCTtechnology provide promising opportunities to restore cartilage defects. Mechanical parameters of soft tissues are explicit markers for quantitative tissue characterization. In this study, we present a biphasic 3D-FE-based method to determine the biomechanical properties of SFCT from stress relaxation compression tests (ε = 20 %, t = 3400 s) whereby cartilaginous tissue is modeled as a biphasic material with tension-compression nonlinearity (BMTCN). The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. The R² of the fit results varies between 0.970 and 0.983. The Young’s and fiber modulus determined from SFCT are 37-times and 5-times lower than from native articular cartilage, respectively. Permeability, on the other hand, is 11-times higher than from native articular cartilage.

A biphasic computational model of a growing, vascularized glioma within brain tissue was developed to account for unique features of gliomas, including soft surrounding brain tissue, their low stiffness relative to brain tissue, and a lack of draining lymphatics. This model is the first to couple nonlinear tissue deformation with porosity and tissue hydraulic conductivity to study the mechanical interaction of leaky vasculature and solid growth in an embedded glioma. The present model showed that leaky vasculature and elevated interstitial fluid pressure produce tensile stress within the tumor in opposition to the compressive stress produced by tumor growth. This tensile effect was more pronounced in softer tissue and resulted in a compressive stress concentration at the tumor rim that increased when tumor was softer than host. Aside from generating solid stress, fluid pressure-driven tissue deformation decreased the effective stiffness of the tumor while growth increased it, potentially leading to elevated stiffness in the tumor rim. A novel prediction of reduced porosity at the tumor rim was corroborated by direct comparison with estimates from our in vivo imaging studies. Antiangiogenic and radiation therapy were simulated by varying vascular leakiness and tissue hydraulic conductivity. These led to greater solid compression and interstitial pressure in the tumor, respectively, the former of which may promote tumor infiltration of the host. Our findings suggest that vascular leakiness has an important influence on in vivo solid stress, stiffness, and porosity fields in gliomas given their unique mechanical microenvironment. [ABSTRACT FROM AUTHOR]

The mechanical parameters of articular cartilage estimated from indentation tests depend on the constitutive model adopted to analyze the data. In this study, we present a 3D-FE-based method to determine the biomechanical properties of equine articular cartilage from stress relaxation indentation tests (ε = 6 %, t = 1000 s) whereby articular cartilage is modeled as a biphasic material without (BM) and with tension-compression nonlinearity (BMTCN). The FEmodel computation was optimized by exploiting the axial symmetry and mesh resolution. Parameter identification was executed with the Levenberg-Marquardt-algorithm. The R² of the fit results varies between 0.695 and 0.930 for the BMmodel and between 0.877 and 0.958 for the BMTCN-model. The differences of the R² occur from the more exact description of the initial stress relaxation behaviour by the fiber modulus from the BMTCN-model. The fiber modulus defines the collagen matrix of cartilage. Furthermore, for both models the determined values of Young’s modulus and permeability were in the same order of magnitude.

Mechanical parameters of hard and soft tissues are explicit markers for quantitative tissue characterization. In this study, we present a biphasic 3D-FE-based method to determine the biomechanical properties of equine articular cartilage from creep indentation tests (F = 0.1 N, t = 1000 s). The FE-model computation was optimized by exploiting the axial symmetry and mesh resolution. Parameter identification was executed with the Levenberg-Marquardt-algorithm. Additionally, sensitivity analyses of the calculated biomechanical parameters were performed. Results show that the Young’s modulus has the largest influence and the Poisson’s ratio of ν ≤ 0.1 is rather insensitive. The R² of the fit results varies between 0.882 and 0.974. The determined values for the Young’s modulus were 0.806 ± 0.093 MPa, the Poisson’s ratio 0.03 ± 0.06 and the permeability 0.012 ± 0.002 mm4/Ns. Future work will deal with mathematical extensions of the biphasic 3D-FE-model.

Biomechanical abnormalities of solid tumours involve stiffening of the tissue and accumulation of mechanical stresses. Both abnormalities affect cancer cell proliferation and invasiveness and thus, play a crucial role in tumour morphology and metastasis. Even though, it has been known for more than two decades that high mechanical stresses reduce cancer cell proliferation rates driving growth towards lowstress regions, most biomechanical models of tumour growth account for isotropic growth. This cannot be valid, however, in tumours that grow within multiple host tissues of different mechanical properties, such as the spine. In these cases, structural heterogeneity would result in anisotropic growth of tumours. To this end, we present a biomechanical, biphasic model for anisotropic growth of spinal tumours. The model that accounts for both the fluid and the solid phase of the tumour was used to predict the evolution of solid stress and interstitial fluid pressure in intramedullary spinal tumours and highlight the differences between isotropic and anisotropic growth. Varying the degree of anisotropy, we found considerable differences in the shape of the tumours, leading to tumours of more realistic ellipsoidal shapes. [ABSTRACT FROM AUTHOR]

An analytical model for a spherical poroelastic tumor embedded in normal poroelastic tissues under creep compression is presented in this paper. The tissue is modeled as a cylindrical sample containing a spherical inclusion having different material properties. Analytical expression for the volumetric strain generated inside the inclusion during creep compression is obtained. Error analysis is carried out by comparing the results from the developed analytical model with corresponding results obtained from an established finite element software for a number of samples with different material properties. The error is found to be below 2.5 % for the samples with a small inclusion and 7 % in the samples with a large inclusion. The analytical solutions reported in this paper can greatly impact elasticity imaging techniques aiming at reconstructing mechanical properties of tumors such as Young's modulus, Poisson's ratio, interstitial permeability and vascular permeability. [ABSTRACT FROM AUTHOR]

Abstract Introduction It is assumed that transverse force physically open maxillary sutures and induce tensile stress that directly stimulates bone formation. However, orthopedic tensile stress is static, which cannot directly stimulate bone formation. We hypothesize that the anabolic response to transverse forces is indirect, the result of inflammation-induced osteoclast activation followed by a transition into osteogenesis. To test our hypothesis, we evaluated tissue, cellular, and molecular responses in the sutures during maxillary expansion. Materials and methods Sprague-Dawley rats (n = 95) were divided into four groups (n = 5 rats/group/time point, except for the expansion group, which did not have a day 0 sample): untreated control (C), sham (S), expansion (Exp), and expansion with nonsteroidal anti-inflammatory medication (Exp + NSAID). Maxillae were collected 0, 1, 3, 7, 14, and 28 days postexpansion for micro–computed tomography, light microscopy, gene expression, protein, and immunohistochemistry analysis. Results Compared with the sham group, the Exp group showed early expression of cytokines in the mid-palatal suture, osteoclast activation, and bone resorption resulting in widening of the suture. Anabolic bone formation was delayed, occurring after this initial catabolic phase. NSAIDs significantly decreased sutural widening, bone formation, and skeletal and dental expansion. During the transition from catabolic to anabolic phase, expression of osteoclast-osteoblast communicator molecules increased significantly. Conclusion Transverse force stimulates two distinct phases in the mid-palatal suture. An early catabolic phase, characterized by inflammation, osteoclast recruitment, and activity, results in bone resorption and sutural widening. Then osteoclasts activate osteoblasts resulting in an anabolic phase, during which the integrity of the skeleton is reestablished. [ABSTRACT FROM AUTHOR]

Linear stability of viscous fluids flowing through a two-dimensional channel lined with a poroelastic layer which is saturated with the same viscous fluid is numerically studied in this work. Having assumed that the solid matrix of the poroelastics layer obeys the standard linear solid (SLS) model, the basic flow/deformation was obtained for this fluid–solid-interaction (FSI) problem using the “biphasic mixture theory”. The vulnerability of the basic solution so-obtained to infinitesimally-small, normal-mode perturbations was then investigated using a temporal, normal-mode, linear stability analysis. An eigenvalue problem was obtained which was solved numerically using the Chebyshev pseudo-spectral collocation method. The main objective of the present work was to investigate the role played by the inhomogeneity/anisotropy of the poroelastic layer on the critical Reynolds number for the core flow. From the obtained results, we have reached the conclusion that anisotropy has no significant effect on the stability picture of the main flow. The effect of inhomogeneity on the critical Reynolds number, however, was found to be significant and highly dependent on the permeability number being smaller or larger than a threshold. [ABSTRACT FROM AUTHOR]

Abstract Background Research on the biology of orthodontic tooth movement has led to the prevailing compression-tension theory, which divides the response to orthodontic force into two opposing reactions spatially separated: on the compression side, osteoclasts resorb bone to create space for tooth movement, whereas on the tension side, osteoblasts form bone to restore the alveolar bone structure. Methods Here we take a critical look at the literature on how force-induced inflammation, the periodontal ligament, osteoclasts, and osteoblasts contribute to the biological reaction to orthodontic force. We introduce new evidence that supports a novel theory to explain the biology of tooth movement—the Biphasic Theory. Results The Biphasic Theory of Orthodontic Tooth Movement divides tooth movement into the initial Catabolic Phase, during which osteoclasts resorb bone at both compression and tension sites, and the Anabolic Phase, which occurs subsequently to restore alveolar bone to its pretreatment levels. Conclusions The Biphasic Theory of Tooth Movement successfully addresses shortfalls in the Compression-Tension Theory of Tooth Movement, provides clinicians with a better understanding of how orthodontic forces move teeth, and offers new targets for therapies aimed at accelerating tooth movement. Highlights • A critical look at the literature tooth movement biology • Propose a new theory - The Biphasic Theory of Orthodontic Tooth Movement • The theory divides tooth movement two phases • Initial Catabolic Phase, during which osteoclasts resorb bone at both compression • Later Anabolic Phase, which occurs subsequently to restore alveolar bone to its pre-treatment levels [ABSTRACT FROM AUTHOR]

Collagen gels are considered a promising biomaterial for the manufacturing of tissue engineering scaffolds, however, their mechanical properties often need to be improved to enable them to provide enough mechanical support during the course of tissue regeneration process. In this paper, we present a simple self-compression technique for the improvement of the mechanical properties of collagen gels, identified by the fitting of bespoke biphasic finite element models. Radially-confined highly hydrated gels were allowed to self-compress for 18 h, expelling fluid, and which were subsequently subjected to unconfined ramp-hold compression. Gels, initially of 0.2%, 0.3% and 0.4% (w/v) collagen and 13 mm thickness, transformed to 2.9 ± 0.2%, 3.2 ± 0.3% and 3.6 ± 0.1% (w/w) collagen and 0.45 ± 0.06 mm, 0.69 ± 0.04 mm and 0.99 ± 0.07 mm thickness. Young's moduli of the compressed gels did not increase with increasing collagen fibril density, whilst zero-strain hydraulic permeability significantly decreased from 51 to 21 mm 4 /Ns. The work demonstrates that biphasic theory, applied to unconfined compression, is a highly appropriate paradigm to mechanically characterise concentrated collagen gels and that confined compression of highly hydrated gels should be further investigated to enhance gel mechanical performance. [ABSTRACT FROM AUTHOR]

Objectives: To investigate the ploughing mechanism associated with tractional force formation on the temporomandibular joint (TMJ) disc surface.Setting and Sample Population: Ten left TMJ discs were harvested from 6- to 8-month-old male Yorkshire pigs.Materials and Methods: Confined compression tests characterized mechanical TMJ disc properties, which were incorporated into a biphasic finite element model (FEM). The FEM was established to investigate load carriage within the extracellular matrix (ECM) and the ploughing mechanism during tractional force formation by simulating previous in vitro plough experiments.Results: Biphasic mechanical properties were determined in five TMJ disc regions (average±standard deviation for aggregate modulus: 0.077±0.040 MPa; hydraulic permeability: 0.88±0.37×10-3 mm4 /Ns). FE simulation results demonstrated that interstitial fluid pressurization is a dominant loading support mechanism in the TMJ disc. Increased contact load and duration led to increased solid ECM strain and stress within, and increased ploughing force on the surface of the disc.Conclusion: Sustained mechanical loading may play a role in load carriage within the ECM and ploughing force formation during stress-field translation at the condyle-disc interface. This study further elucidated the mechanism of ploughing on tractional force formation and provided a baseline for future analysis of TMJ mechanics, cartilage fatigue and early TMJ degeneration. [ABSTRACT FROM AUTHOR]

Articular cartilage has high water content and biphasic property. The structures of the tissue are inhomogeneous and anisotropic. Furthermore, the mechanical behavior of cartilage shows depth-dependence. Therefore it is necessary to consider not only the average tissue property but also the local one to explain mechanical and functional behavior. Previously, we created two-dimensional biphasic finite element (FE) cartilage tissue models considering the depth-dependence of elastic modulus distribution based on experimental results. As a result, this finding indicates that the depth-dependence of elastic modulus has a remarked influence on the deformed profile. In this study, the effectiveness of collagen fiber network in addition to the depth-dependent elastic modulus of cartilage tissue is evaluated. By creating of cartilage tissue models using axisymmetric biphasic elements and spring elements, we analyzed the unconfined compressive behaviors of articular cartilage specimens and compared the FE analyses to experimental results. Every FE model has depth-dependence of elastic modulus based on our previous formula, while the Poisson's ratio and permeability of solid phase were assumed as constant in literature data. To compare experimental result with finite element analysis (FEA), boundary conditions for FEA were given to correspond to the compression test. As a result, total load capacity and deformed profiles immediately after compression of FEA simulation on eventual model corresponded to experimental results by controlling spring constant. Furthermore, local strain of axial direction in FEA results for eventual model and experimental ones show the same tendency about time-dependent change. Then, we considered intrinsic fluid flow of eventual model.

In temporomandibular joints (TMJs), the cartilage on the condylar head displays a unique ultrastructure with a dense layer of type I collagen in the superficial zone, different from hyaline cartilage in other joints. This study aims to elucidate the roles of this fibrous zone in the mechanical behaviors, particularly lubrication, of TMJ under physiological loading regimes. Mechanical tests on porcine condylar cartilage demonstrated that the superficial and middle-deep zones exhibit tension-compression nonlinearity. The tensile and compressive moduli of the superficial zone are 30.73 ± 12.97 and 0.028 ± 0.016 MPa, respectively, while those for the middle-deep zone are 2.43 ± 1.75 and 0.14 ± 0.09 MPa. A nonlinear finite element model of condylar cartilage was built to simulate sliding of a spherical probe over the articular surface. The presence of the superficial zone significantly promoted interstitial fluid pressurization (IFP) inside the loaded cartilage and reduced the friction force on the surface, compared to the case without the superficial zone. Finite element simulations showed that IFP depends on sliding speed but not normal load, which matches the experimental results. This study revealed the presence of the fibrous zone can significantly reduce the deformation of condylar cartilage under compression and the friction force on its surface during sliding. [ABSTRACT FROM AUTHOR]

Indentation testing is widely used to evaluate the mechanical properties of articular cartilage. However, most curve-fitting solutions for indentation analysis require the deformation data of cartilage at the equilibrium state, which often takes the tissue hours to reach. The lengthy testing time reduces the efficiency of indentation, increases the chance of tissue deterioration, and prevents in vivo applications. To overcome these limitations, a novel technique based on principal component analysis (PCA) was developed in this study, which can predict the full indentation creep curve based on the first few minutes' deformation history and the principal components. The accuracy of this technique was confirmed using the indentation data from 40 temporomandibular joint condylar cartilage samples and 17 bovine knee joint samples. The mechanical properties determined by biphasic curve-fitting using predicted and experimental data are in good agreement, with the difference between the two less than 5%. For TMJ and knee cartilages, it is found that any number of full tests beyond eight will not lead to any increase larger than 1% in the accuracy, indicating a low sample number required for prediction. In addition, the principal components of indentation creep curves are consistent for the same type of cartilage tested with identical protocols, but significantly different between two distinct cartilages. Therefore PCA may also represent a new method to compare the mechanical behaviors of different cartilages, as it avoids the assumptions associated with mechanical constitutive models and relies purely on the experimental data. [ABSTRACT FROM AUTHOR]

The cornea is a transparent connective tissue with dual functions of protecting the eye (mechanical properties) and refracting the light (optical properties). Both of these properties are derived from the corneal intricate and pseudo regular extracellular matrix, the stroma. From the mechanics point of view, the corneal extracellular matrix is a hydrated structure composed of collagen fibrils, proteoglycans, and the interstitial fluid. The objective of this study was to investigate compressive biomechanical properties of the cornea using an experimental and numerical framework. The unconfined compression stress- relaxation tests were performed to measure the corneal behavior experimentally and the transversely isotropic biphasic theory was used to analyze the experimental data. It was observed that the behavior of the corneal stroma under stepwise stress-relaxation compression is similar to that of the other soft hydrated tissues and is composed of an immediate stiff response, a transient relaxation phase, and a final steady-state stage. Within the range of deformation considered in this study, maximum and equilibrium reaction stresses were linearly dependent on the compressive strain. The linear transversely isotropic biphasic model curve fitted experimental measurements with the coefficient of determination Tfit²=0.98 + 0.01. The mechanical parameters of the porcine corneal stroma were calculated as a function of the engineering strain. The corneal out-of-plane modulus was almost independent of the compressive strain, the transverse Young's modulus linearly increased with increasing strain, and the permeability coefficient decayed exponentially with increasing strain. The average mechanical parameters under unconfined compression were found to be: the out-of-plane modulus Ez = 5.61 KPa, the transverse Young's modulus Er = 1.33 MPa, and the permeability coefficient Kt = 2.14 × 10-14 m4/N.s. [ABSTRACT FROM AUTHOR]

An elastic-biphasic model for the simulation of the periodontal ligament (PDL) and the adjacent tooth is presented and investigated. The PDL is modelled as a biphasic material following the work of Ehlers and Markert (2001), whereas the tooth is modelled as a linear elastic body. A spatial discretisation scheme is proposed based on mixed finite elements for the spatial discretisation. Due to nonlinearity in the model, a predictor–corrector scheme is employed as a temporal discretisation scheme. In order to validate the PDL model,in vitromeasurements are compared with numerical simulations. The numerical simulations are performed using geometries resulting from micro-CT scanner of the same porcine tooth, which was employed for theinvitromeasurements. [ABSTRACT FROM PUBLISHER]

Abstract: 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). [Copyright &y& Elsevier]

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://mrl.sci.utah.edu/software/febio), 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. [ABSTRACT FROM AUTHOR]

Abstract: This study experimentally and numerically investigates the polymer electrolyte fuel cell (PEFC) catalyst layers (CLs) to analyze the coupled pore-fluid diffusion and resultant stress distribution. In the study, effect of nanoporosity on mechanical strength is explored by analyzing the CL structure based on the elastic modulus and the yield strength scaling laws of open-cell foams. A finite element analysis of the CL is performed by adopting the biphasic consolidation theory. The biphasic theory in combination with the transient consolidation principle of a porous body is formulated to account for the variation in the external loading conditions as well as the internal pore pressure. The CLs are observed to have the elastoplastic ionomer matrix and anisotropic nanoporosity, which are responsible for the localized plastic densification on indentation. The indentation behavior of the CLs appears to respond similar to the conventional low-density nanoporous foams leading to the localized nonlinear response of contact stiffness. The mechanical properties were found to be insensitive to the constituents’ (Pt and Carbon) concentration gradation over the CL thickness. In the numerical results, effect of porosity loss on the transport properties is discussed to highlight the importance of estimating the stress levels. It is outlined from the present study that under critical loading conditions, the yield limits of the CL play a crucial role in estimating the extent of transport losses. The effective proton conductivity and oxygen diffusivity losses are dependent on the macroscopic strength of the ionomer and the effective electronic conductivity loss is a function of intrinsic strength of the CL, which is also responsible for the overall durability of the CL. [Copyright &y& Elsevier]

Cartilage material properties are important for understanding joint function and diseases, but can be challenging to obtain. Three biphasic material properties (aggregate modulus, Poisson's ratio and permeability) can be determined using an analytical or finite element model combined with optimisation to find the material properties values that best reproduce an experimental creep curve. The purpose of this study was to develop an easy-to-use resource to determine biphasic cartilage material properties. A Cartilage Interpolant Response Surface was generated from interpolation of finite element simulations of creep indentation tests. Creep indentation tests were performed on five sites across a tibial plateau. A least-squares residual search of the Cartilage Interpolant Response Surface resulted in a best-fit curve for each experimental condition with corresponding material properties. These sites provided a representative range of aggregate moduli (0.48-1.58 MPa), Poisson's ratio (0.00-0.05) and permeability (1.7 × 10- 15-5.4 × 10- 15 m4/N s) values found in human cartilage. The resource is freely available from https://simtk.org/home/va-squish. [ABSTRACT FROM AUTHOR]

The article presents descriptions of the mechanical behaviors of articular cartilage and their correlations with collagen, proteoglycan and water with emphasis on understanding the osmotic effect inside the tissue. According to the author, the articular cartilage is a layer of low-friction, load-bearing soft tissue that overlies the articulating bony ends in diarthrodial joints. He added that the articular cartilage provides the joint with essential biochemical functions such as wear resistance, load bearing and shock absorption. He emphasized that articular cartilage is vital for maintaining joint motion, but can involve in a degenerative disease of joints such as osteoarthritis when it is damaged.

Abstract: Articular cartilage exhibits viscoelasticity in response to mechanical loading that is well described using biphasic or poroelastic continuum models. To date, boundary element methods (BEMs) have not been employed in modeling biphasic tissue mechanics. A three-dimensional direct poroelastic BEM, formulated in the Laplace transform domain, is applied to modeling stress relaxation in cartilage. Macroscopic stress relaxation of a poroelastic cylinder in uni-axial confined compression is simulated and validated against a theoretical solution. Microscopic cell deformation due to poroelastic stress relaxation is also modeled. An extended Laplace inversion method is employed to accurately represent mechanical responses in the time domain. [Copyright &y& Elsevier]

A study was conducted on combinations of preconditioned iterative methods with matrix reordering to solve the linear systems arising from a biphasic velocity-pressure (v-p) finite element formulation used to simulate soft hydrated tissues in the human musculoskeletal system. Krylov subspace methods were tested due to the symmetric indefiniteness of our systems, specifically the generalized minimal residual (GMRES), transpose-free quasi-minimal residual (TFQMR), and biconjugate gradient stabilized (BiCGSTAB) methods. Standard graph reordering techniques were used with incomplete LU (ILU) preconditioning. Performance of the methods was compared on the basis of convergence rate, computing time, and memory requirements. Our results indicate that performance is affected more significantly by the choice of reordering scheme than by the choice of Krylov method. Overall, BiCGSTAB with one-way dissection (OWD) reordering performed best for a test problem representative of a physiological tissue layer. The preferred methods were then used to simulate the contact of the humeral head and glenoid tissue layers in glenohumeral joint of the shoulder, using a penetration-based method to approximate contact. The distribution of pressure and stress fields within the tissues shows significant through-thickness effects and demonstrates the importance of simulating soft hydrated tissues with a biphasic model. [ABSTRACT FROM AUTHOR]

The study of single cell mechanics offers a valuable tool for understanding cellular milieus. Specific knowledge of chondrocyte biomechanics could lead to elucidation of disease etiologies and the biomechanical factors most critical to stimulating regenerative processes in articular cartilage. Recent studies in our laboratory have suggested that it may be acceptable to approximate the shape of a single chondrocyte as a disc. This geometry is easily utilized for generating models of unconfined compression. In this study, three continuum mechanics models of increasing complexity were formulated and used to fit unconfined compression creep data. Creep curves were obtained from middle/deep zone chondrocytes (n=15) and separately fit using the three continuum models. The linear elastic solid model yielded a Young''s modulus of 2.55±0.85 kPa. The viscoelastic model (adapted from the Kelvin model) generated an instantaneous modulus of 2.47±0.85 kPa, a relaxed modulus of 1.48±0.35 kPa, and an apparent viscosity of 1.92±1.80 kPa-s. Finally, a linear biphasic model produced an aggregate modulus of 2.58±0.87 kPa, a permeability of 2.57×10-12±3.09 m4/N-s, and a Poisson''s ratio of 0.069±0.021. The results of this study demonstrate that similar values for the cell modulus can be obtained from three models of increasing complexity. The elastic model provides an easy method for determining the cell modulus, however, the viscoelastic and biphasic models generate additional material properties that are important for characterizing the transient response of compressed chondrocytes. [Copyright &y& Elsevier]

Mixture models have been successfully used to describe the response of articular cartilage to various loading conditions. Mow et al. (J. Biomech. Eng. 102 (1980) 73) formulated a biphasic mixture model of articular cartilage where the collagen–proteoglycan matrix is modeled as an intrinsically incompressible porous-permeable solid matrix, and the interstitial fluid is modeled as an incompressible fluid. Lai et al. (J. Biomech. Eng. 113 (1991) 245) proposed a triphasic model of articular cartilage as an extension of their biphasic theory, where negatively charged proteoglycans are modeled to be fixed to the solid matrix, and monovalent ions in the interstitial fluid are modeled as additional fluid phases. Since both models co-exist in the cartilage literature, it is useful to show how the measured properties of articular cartilage (the confined and unconfined compressive and tensile moduli, the compressive and tensile Poisson''s ratios, and the shear modulus) relate to both theories. In this study, closed-form expressions are presented that relate biphasic and triphasic material properties in tension, compression and shear. These expressions are then compared to experimental findings in the literature to provide greater insight into the measured properties of articular cartilage as a function of bathing solutions salt concentrations and proteoglycan fixed-charge density. [Copyright &y& Elsevier]

Under physiological conditions of loading, articular cartilage is subjected to both compressive strains, normal to the articular surface, and tensile strains, tangential to the articular surface. Previous studies have shown that articular cartilage exhibits a much higher modulus in tension than in compression, and theoretical analyses have suggested that this tension–compression nonlinearity enhances the magnitude of interstitial fluid pressurization during loading in unconfined compression, above a theoretical threshold of 33% of the average applied stress. The first hypothesis of this experimental study is that the peak fluid load support in unconfined compression is significantly greater than the 33% theoretical limit predicted for porous permeable tissues modeled with equal moduli in tension and compression. The second hypothesis is that the peak fluid load support is higher at the articular surface side of the tissue samples than near the deep zone, because the disparity between the tensile and compressive moduli is greater at the surface zone. Ten human cartilage samples from six patellofemoral joints, and 10 bovine cartilage specimens from three calf patellofemoral joints were tested in unconfined compression. The peak fluid load support was measured at 79±11% and 69±15% at the articular surface and deep zone of human cartilage, respectively, and at 94±4% and 71±8% at the articular surface and deep zone of bovine calf cartilage, respectively. Statistical analyses confirmed both hypotheses of this study. These experimental results suggest that the tension–compression nonlinearity of cartilage is an essential functional property of the tissue which makes interstitial fluid pressurization the dominant mechanism of load support in articular cartilage. [Copyright &y& Elsevier]

The objective of this study was to experimentally verify the well-accepted but untested hypothesis that cartilage interstitial fluid pressurizes variously under the action of an applied cyclical stress in confined compression over a range of loading frequencies, contributing significantly to the cartilage dynamic stiffness. Eighteen bovine cartilage cylindrical samples were tested under load control using a porous indenter in a confined compression chamber fitted with a microchip pressure transducer at its bottom. Over a static stress of 130 kPa, a cyclical stress of amplitude 33 kPa was applied with the indenter at frequencies ranging from 0.0001 to 0.1 Hz. The cartilage interstitial fluid pressure and deformation were measured simultaneously as a function of time. The displacement response at the lowest tested frequency was curvefitted in the time domain to determine the linear biphasic material properties, HA=0.70±0.10 MPa and k0=2.4 × 10-16±0.64 × 10-16m4/Ns. These properties were employed in the biphasic theory to predict the interstitial fluid pressure response and compare it to experiment, resulting in nonlinear coefficients of determination ranging from r2=0.89 ± 0.15 to 0.96±0.03 depending on frequency. It was found for the samples of this study that above a characteristic frequency of 0.00044 Hz, the magnitude and phase of fluid pressurization matched the applied stress, reducing the tissue strain at the impermeable bottom surface to nearly zero. The findings of this study verify the hypothesis that cartilage dynamic stiffness derives primarily from flow-dependent viscoelasticity as predicted by the linear biphasic theory; they demonstrate experimentally the significance of interstitial fluid pressurization as the fundamental mechanism of cartilage load support over a wide range of frequencies. © 2000 Biomedical Engineering Society. PAC00: 8719Rr [ABSTRACT FROM AUTHOR]

A finite element model of the human head by linear biphasic theory is developed to study the dynamic response of the human head to impact. Intracranial tissues are modelled as a binary mixture, i.e. the fluid and solid phases. To validate the biphasic finite element formulation, the result of the numerical analysis of a one-dimensional wave propagation problem is compared with that of analytic solution. The permeabilities of the subarachnoid space and brain which may reproduce the same coup and contre-coup CSF (cerebral spinal fluid) pressures from the monophasic model are searched in the specified range of skull permeability. Then the intracranial pressure distributions from the biphasic model for the frontal impact are compared with those from the monophasic model. In general, the biphasic model produces a more injurious intracranial pressure distribution than the monophasic model. The pressure distribution from the biphasic model shows a little higher contre-coup pressure in the frontal lobe than in the occipital region. This finding is in agreement with those clinical findings that contre-coup injuries are more frequently found in the frontal lobe. Another numerical simulation is conducted to characterize the effect of the volume ratios between two phases in the skull and subarachnoid space. From the results, it can be seen that the variation of the volume ratio in the subarachnoid space affects the intracranial pressure distribution of the lateral part while the variation in the skull does not. [ABSTRACT FROM AUTHOR]

In the present paper, we review the current state-of-the-art in asymptotic modeling of articular contact. Particular attention has been given to the knee joint contact mechanics with a special emphasis on implications drawn from the asymptotic models, including average characteristics for articular cartilage layer. By listing a number of complicating effects such as transverse anisotropy, non-homogeneity, variable thickness, nonlinear deformations, shear loading, and bone deformation, which may be accounted for by asymptotic modeling, some unsolved problems and directions for future research are also discussed.

Indentation testing is widely used to evaluate the mechanical properties of articular cartilage. However, most curve-fitting solutions for indentation analysis require the deformation data of cartilage at the equilibrium state, which often takes the tissue hours to reach. The lengthy testing time reduces the efficiency of indentation, increases the chance of tissue deterioration, and prevents in vivo applications. To overcome these limitations, a novel technique based on principal component analysis (PCA) was developed in this study, which can predict the full indentation creep curve based on the first few minutes' deformation history and the principal components. The accuracy of this technique was confirmed using the indentation data from 40 temporomandibular joint condylar cartilage samples and 17 bovine knee joint samples. The mechanical properties determined by biphasic curve-fitting using predicted and experimental data are in good agreement, with the difference between the two less than 5%. For TMJ and knee cartilages, it is found that any number of full tests beyond eight will not lead to any increase larger than 1% in the accuracy, indicating a low sample number required for prediction. In addition, the principal components of indentation creep curves are consistent for the same type of cartilage tested with identical protocols, but significantly different between two distinct cartilages. Therefore PCA may also represent a new method to compare the mechanical behaviors of different cartilages, as it avoids the assumptions associated with mechanical constitutive models and relies purely on the experimental data., (Copyright © 2014 Elsevier Ltd. All rights reserved.)