Showing papers in "Biomechanics and Modeling in Mechanobiology in 2008"

Growth and remodeling in a thick-walled artery model: effects of spatial variations in wall constituents

Abstract: A mathematical model is presented for growth and remodeling of arteries. The model is a thick-walled tube composed of a constrained mixture of smooth muscle cells, elastin and collagen. Material properties and radial and axial distributions of each constituent are prescribed according to previously published data. The analysis includes stress-dependent growth and contractility of the muscle and turnover of collagen fibers. Simulations were conducted for homeostatic conditions and for the temporal response following sudden hypertension. Numerical pressure-radius relations and opening angles (residual stress) show reasonable agreement with published experimental results. In particular, for realistic material and structural properties, the model predicts measured variations in opening angles along the length of the aorta with reasonable accuracy. These results provide a better understanding of the determinants of residual stress in arteries and could lend insight into the importance of constituent distributions in both natural and tissue-engineered blood vessels.

Remodelling of the angular collagen fiber distribution in cardiovascular tissues

Abstract: Understanding collagen fiber remodelling is desired to optimize the mechanical conditioning protocols in tissue-engineering of load-bearing cardiovascular structures. Mathematical models offer strong possibilities to gain insight into the mechanisms and mechanical stimuli involved in these remodelling processes. In this study, a framework is proposed to investigate remodelling of angular collagen fiber distribution in cardiovascular tissues. A structurally based model for collagenous cardiovascular tissues is extended with remodelling laws for the collagen architecture, and the model is subsequently applied to the arterial wall and aortic valve. For the arterial wall, the model predicts the presence of two helically arranged families of collagen fibers. A branching, diverging hammock-type fiber architecture is predicted for the aortic valve. It is expected that the proposed model may be of great potential for the design of improved tissue engineering protocols and may give further insight into the pathophysiology of cardiovascular diseases.

Influence of boundary conditions on computed apparent elastic properties of cancellous bone

Abstract: High-resolution finite element models of trabecular bone can be used to study trabecular structure-function relationships, elasticity, multiaxial strength, and tissue remodelling in more detail than experiments. Beside effects of the model size, scan/analysis resolution, segmentation process, etc., the type of the applied boundary conditions (BCs) have a strong influence on the predicted elastic properties. Appropriate BCs have to be applied on hexahedral digital finite element models in order to obtain effective elastic properties. Homogeneous displacement BCs as proposed by Van Rietbergen et al. (J Biomech 29(12):1653-1657, 1996) lead to "apparent" rather than to "effective" elastic properties. This study provides some answers concerning such differences by comparing various BC types (uniform displacement, mixed BCs, periodic BCs), different volume element definitions (original and mirrored models), and several bone volume fractions (BVTV ranging from 6.5 to 37.6%). First, the mixed BCs formulated by Hazanov (Arch Appl Mech 68(6):385-394, 1998) are theoretically extended to shear loading of a porous media. Second, six human bone samples are analyzed, their orthotropic Young's moduli, shear moduli, and Poisson's ratios computed and compared. It is found that the proposed mixed BCs give exactly the same effective elastic properties as periodic BCs if a periodic and orthotropic micro-structured material is used and thus denoted as "periodicity compatible" mixed uniform BCs (PMUBCs). As bone samples were shown to be nearly orthotropic for volume element side lengths > or =5 mm the proposed mixed BCs turn out to be the best choice because they give again essentially the same overall elastic properties as periodic BCs. For bone samples of smaller dimensions ( < 5 mm) with a strong anisotropy (beyond orthotropy) uniform displacement BCs remain applicable but they can significantly overestimate the effective stiffness.

The role of fabric in the quasi-static compressive mechanical properties of human trabecular bone from various anatomical locations.

Abstract: Osteoporosis leads to an increased risk of bone fracture. While bone density and architecture can be assessed in vivo with increasing accuracy using CT and MRI, their relationship with the critical mechanical properties at various anatomical sites remain unclear. The objective of this study was to quantify the quasi-static compressive mechanical properties of human trabecular bone among different skeletal sites and compare their relationships with bone volume fraction and a measure of microstructural anisotropy called fabric. Over 600 trabecular bone samples from six skeletal sites were assessed by $$\upmu CT$$ and tested in uniaxial compression. Bone volume fraction correlated positively with elastic modulus, yield stress, ultimate stress, and the relationships depended strongly on skeletal site. The account of fabric improved these correlations substantially, especially when the data of all sites were pooled together, but the fabric–mechanical property relationships remained somewhat distinct among the anatomical sites. The study confirms that, beyond volume fraction, fabric plays an important role in determining the mechanical properties of trabecular bone and should be exploited in mechanical analysis of clinically relevant sites of the human skeleton.

On the anisotropy and inhomogeneity of permeability in articular cartilage.

Abstract: Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is “directed” by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.

A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading

Abstract: The importance of fluid-flow-induced shear stress and matrix-induced cell deformation in transmitting the global tendon load into a cellular mechanotransduction response is yet to be determined. A multiscale computational tendon model composed of both matrix and fluid phases was created to examine how global tendon loading may affect fluid-flow-induced shear stresses and membrane strains at the cellular level. The model was then used to develop a quantitative experiment to help understand the roles of membrane strains and fluid-induced shear stresses on the biological response of individual cells. The model was able to predict the global response of tendon to applied strain (stress, fluid exudation), as well as the associated cellular response of increased fluid-flow-induced shear stress with strain rate and matrix-induced cell deformation with strain amplitude. The model analysis, combined with the experimental results, demonstrated that both strain rate and strain amplitude are able to independently alter rat interstitial collagenase gene expression through increases in fluid-flow-induced shear stress and matrix-induced cell deformation, respectively.

Inverse method of stress analysis for cerebral aneurysms.

Abstract: We present a method for predicting the wall stress in a class of cerebral aneurysms. The method hinges on an inverse formulation of the elastostatic equilibrium problem; it takes as the input a deformed configuration and the corresponding pressure, and predicts the wall stress in the given deformed state. For a membrane structure, the inverse formulation possesses a remarkable feature, that is, it can practically determine the wall tension without accurate knowledge of the wall elastic properties. In this paper, we present a finite element formulation for the inverse membrane problem and perform material sensitivity studies on idealized lesions and an image-based cerebral aneurysm model.

Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

Abstract: Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.

Bone ingrowth into a porous coated implant predicted by a mechano-regulatory tissue differentiation algorithm.

Abstract: Bone ingrowth into a porous surface is one of the primary methods for fixation of orthopaedic implants. Improved understanding of bone formation and fixation of these devices should improve their performance and longevity. In this study predictions of bone ingrowth into an implant porous coating were investigated using mechano-reculatory models. The mechano-regulatory tissue differentiation algorithm proposed by Lacroix et al., and a modified version that enforces a tissue differentiation pathway by transitioning from differentiation to bone adaptation were investigated. The modified algorithm resulted in nearly the same behavior as the original algorithm when applied to a fracture-healing model. The algorithms were further compared using micromechanical finite element model of a beaded porous scaffold. Predictions of bone and fibrous tissue formation were compared between the two algorithms and to clinically observed phenomena. Under loading conditions corresponding to a press-fit hip stem, the modified algorithm predicted bone ingrowth into approximately 25% of the pore space, which is similar to that reported in experimental studies, while the original algorithm was unstable. When micromotion at the bone-implant interface was simulated, 20 μm of transverse displacement resulted in soft tissue formation at the bone-implant interface and minimal bone ingrowth. In contrast, 10 and 5 μm of micromotion resulted in bone filling 40% of the pore space and a stable interface, again consistent with clinical and experimental observations.

Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

Abstract: Computational models were used to explore the idea that morphogenesis is regulated, in part, by feedback from mechanical stress according to Beloussov’s hyper-restoration (HR) hypothesis. According to this hypothesis, active tissue responses to stress perturbations tend to restore, but overshoot, the original (target) stress. To capture this behavior, the rate of growth or contraction is assumed to depend on the difference between the current and target stresses. Stress overshoot is obtained by letting the target stress change at a rate proportional to the same stress difference. The feasibility of the HR hypothesis is illustrated by models for stretching of epithelia, cylindrical bending of plates, invagination of cylindrical and spherical shells, and early amphibian development. In each case, an initial perturbation leads to an active mechanical response that changes the form of the tissue. The results show that some morphogenetic processes can be entirely self-driven by HR responses once they are initiated (possibly by genetic activity). Other processes, however, may require secondary mechanisms or perturbations to proceed to completion.

A mathematical model for bone tissue regeneration inside a specific type of scaffold.

Abstract: Bone tissue regeneration using scaffolds is receiving an increasing interest in orthopedic surgery and tissue engineering applications. In this study, we present the geometrical characterization of a specific family of scaffolds based on a face cubic centered (FCC) arrangement of empty pores leading to analytical formulae of porosity and specific surface. The effective behavior of those scaffolds, in terms of mechanical properties and permeability, is evaluated through the asymptotic homogenization theory applied to a representative volume element identified with the unit cell FCC. Bone growth into the scaffold is estimated by means of a phenomenological model that considers a macroscopic effective stress as the mechanical stimulus that regulates bone formation. Cell migration within the scaffold is modeled as a diffusion process based on Fick’s law which allows us to estimate the cell invasion into the scaffold microstructure. The proposed model considers that bone growth velocity is proportional to the concentration of cells and regulated by the mechanical stimulus. This model allows us to explore what happens within the scaffold, the surrounding bone and their interaction. The mathematical model has been numerically implemented and qualitatively compared with previous experimental results found in the literature for a scaffold implanted in the femoral condyle of a rabbit. Specifically, the model predicts around 19 and 23% of bone regeneration for non-grafted and grafted scaffolds, respectively, both with an initial porosity of 76%.

The estimated elastic constants for a single bone osteonal lamella

Abstract: Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the collagen fibril whose diameter is the order of 20 nm. The next structural level is the collagen fiber with a diameter of the order of 80 nm. A lamella is a laminate structure, composed of multiple collagen fibers with embedded minerals and consists of several laminates. The thickness of one laminate in the lamella is approximately 130 nm. All collagen fibers in a laminate in the lamella are oriented in one direction. However, the laminates rotate relative to the adjacent laminates. In this work, all collagen fibers in a lamella are assumed to be aligned in the longitudinal direction. This kind of bone with all collagen fibers aligned in one direction is called a parallel fibered bone. The effective elastic constants for a parallel fibered bone are estimated by assuming periodic substructures. These results provide a database for estimating the anisotropic poroelastic constants of an osteon and also provide a database for building mathematical or computational models in bone micromechanics, such as bone damage mechanics and bone poroelasticity.

Computational modeling of morphogenesis regulated by mechanical feedback.

Abstract: Mechanical forces cause changes in form during embryogenesis and likely play a role in regulating these changes. This paper explores the idea that changes in homeostatic tissue stress (target stress), possibly modulated by genes, drive some morphogenetic processes. Computational models are presented to illustrate how regional variations in target stress can cause a range of complex behaviors involving the bending of epithelia. These models include growth and cytoskeletal contraction regulated by stress-based mechanical feedback. All simulations were carried out using the commercial finite element code ABAQUS, with growth and contraction included by modifying the zero-stress state in the material constitutive relations. Results presented for bending of bilayered beams and invagination of cylindrical and spherical shells provide insight into some of the mechanical aspects that must be considered in studying morphogenetic mechanisms.

Non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus

Abstract: The objective of this work was to determine the linear and non-linear viscoelastic behavior of abdominal aortic aneurysm thrombus and to study the changes in mechanical properties throughout the thickness of the thrombus. Samples are gathered from thrombi of seven patients. Linear viscoelastic data from oscillatory shear experiments show that the change of properties throughout the thrombus is different for each thrombus. Furthermore the variations found within one thrombus are of the same order of magnitude as the variation between patients. To study the non-linear regime, stress relaxation experiments are performed. To describe the phenomena observed experimentally, a non-linear multimode model is presented. The parameters for this model are obtained by fitting this model successfully to the experiments. The model cannot only describe the average stress response for all thrombus samples but also the highest and lowest stress responses. To determine the influence on the wall stress of the behavior observed the model proposed needs to implemented in the finite element wall stress analysis.

Myocardial material parameter estimation: a non-homogeneous finite element study from simple shear tests.

Abstract: The passive material properties of myocardium play a major role in diastolic performance of the heart. In particular, the shear behaviour is thought to play an important mechanical role due to the laminar architecture of myocardium. We have previously compared a number of myocardial constitutive relations with the aim to extract their suitability for inverse material parameter estimation. The previous study assumed a homogeneous deformation. In the present study we relaxed the homogeneous assumption by implementing these laws into a finite element environment in order to obtain more realistic measures for the suitability of these laws in both their ability to fit a given set of experimental data, as well as their stability in the finite element environment. In particular, we examined five constitutive laws and compare them on the basis of (i) “goodness of fit”: how well they fit a set of six shear deformation tests, (ii) “determinability”: how well determined the objective function is at the optimal parameter fit, and (iii) “variability”: how well determined the material parameters are over the range of experiments. Furthermore, we compared the FE results with those from the previous study. It was found that the same material law as in the previous study, the orthotropic Fung-type “Costa-Law”, was the most suitable for inverse material parameter estimation for myocardium in simple shear.

Modeling the mechanical consequences of vibratory loading in the vertebral body: microscale effects.

Abstract: Osteoporosis affects nearly 10 million individuals in the United States. Conventional treatments include anti-resorptive drug therapies, but recently, it has been demonstrated that delivering a low magnitude, dynamic stimulus via whole body vibration can have an osteogenic effect without the need for large magnitude strain stimulus. Vibration of the vertebral body induces a range of stimuli that may account for the anabolic response including low magnitude strains, interfacial shear stress due to marrow movement, and blood transport. In order to evaluate the relative importance of these stimuli, we integrated a microstructural model of vertebral cancellous bone with a mixture theory model of the vertebral body. The predicted shear stresses on the surfaces of the trabeculae during vibratory loading are in the range of values considered to be stimulatory and increase with increasing solid volume fraction. Peak volumetric blood flow rates also varied with strain amplitude and frequency, but exhibited little dependence on solid volume fraction. These results suggest that fluid shear stress governs the response of the vertebrae to whole body vibration and that the marrow viscosity is a critical parameter which modulates the shear stress.

The mechanobiological effects of periosteal surface loads

Abstract: We have developed an improved mechanobiological model of bone morphogenesis and functional adaptation that includes the influences of periosteum tension and pressure on bone formation and resorption. Previous models assumed that periosteal and endosteal bone deposition and resorption rates are governed only by the local intracortical daily stress or strain stimulus caused by cyclic loading. The new model incorporates experimental findings that pressures on periosteal surfaces can impede bone formation or induce bone resorption, whereas periosteal tensile strains perpendicular to bone surfaces can impede bone resorption or induce bone formation. We propose that these effects can produce flattened or concave bone surfaces in regions of periosteal pressure and bone ridges in regions of periosteal tension. The model was implemented with computer simulations to illustrate the role of adjacent muscles on the development of the triangular cross-sectional geometry of the rat tibia. The results suggest that intracortical stresses dictate bone size, whereas periosteal pressures may work in combination with intracortical stresses and other mechanobiological factors in the development of local bone cross-sectional shapes.

Interstitial fluid flow in the osteon with spatial gradients of mechanical properties: a finite element study

Abstract: Bone remodelling is the process that maintains bone structure and strength through adaptation of bone tissue mechanical properties to applied loads. Bone can be modelled as a porous deformable material whose pores are filled with cells, organic material and interstitial fluid. Fluid flow is believed to play a role in the mechanotransduction of signals for bone remodelling. In this work, an osteon, the elementary unit of cortical bone, is idealized as a hollow cylinder made of a deformable porous matrix saturated with an interstitial fluid. We use Biot’s poroelasticity theory to model the mechanical behaviour of bone tissue taking into account transverse isotropic mechanical properties. A finite element poroelastic model is developed in the COMSOL Multiphysics software. Elasticity equations and Darcy’s law are implemented in this software; they are coupled through the introduction of an interaction term to obtain poroelasticity equations. Using numerical simulations, the investigation of the effect of spatial gradients of permeability or Poisson’s ratio is performed. Results are discussed for their implication on fluid flow in osteons: (i) a permeability gradient affects more the fluid pressure than the velocity profile; (ii) focusing on the fluid flow, the key element of loading is the strain rate; (iii) a Poisson’s ratio gradient affects both fluid pressure and fluid velocity. The influence of textural and mechanical properties of bone on mechanotransduction signals for bone remodelling is also discussed.

Prediction of extracellular matrix stiffness in engineered heart valve tissues based on nonwoven scaffolds

Abstract: The in vitro development of tissue engineered heart valves (TEHV) exhibiting appropriate structural and mechanical characteristics remains a significant challenge. An important step yet to be addressed is establishing the relationship between scaffold and extracellular matrix (ECM) mechanical properties. In the present study, a composite beam model accounting for nonwoven scaffold-ECM coupling and the transmural collagen concentration distribution was developed, and utilized to retrospectively estimate the ECM effective stiffness in TEHV specimens incubated under static and cyclic flexure conditions (Engelmayr Jr et~al. in Biomaterials 26(2):175-187 2005). The ECM effective stiffness was expressed as the product of the local collagen concentration and the collagen specific stiffness (i.e., stiffness/concentration), and was related to the overall TEHV effective stiffness via an empirically determined scaffold-ECM coupling parameter and measured transmural collagen concentration distributions. The scaffold-ECM coupling parameter was determined by flexural mechanical testing of polyacrylamide gels (i.e., ECM analogs) of variable stiffness and associated scaffold-polyacrylamide gel composites (i.e., engineered tissue analogs). The transmural collagen concentration distributions were quantified from fluorescence micrographs of picro-sirius red stained TEHV sections. As suggested by a previous structural model of the nonwoven scaffold (Engelmayr Jr and Sacks in J Biomech Eng 128(4):610-622, 2006), nonwoven scaffold-ECM composites did not follow a traditional rule of mixtures. The present study provided further evidence that the primary mode of reinforcement in nonwoven scaffold-ECM composites is an increase in the number fiber-fiber bonds with a concomitant increase in the effective stiffness of the spring-like fiber segments. Simulations of potential ECM deposition scenarios using the current model indicated that the present approach is sensitive to the specific time course of tissue deposition, and is thus very suitable for studies of ECM formation in engineered heart valve tissues.

Part II: Fibroblasts preferentially migrate in the direction of principal strain.

Abstract: A growing body of evidence suggests that the sensory information from the cytoskeleton and integrins may be responsible for guiding migration during mechano- and haptotaxis. However, the dual function of these subcellular structures as mechano-sensors and -actuators is only partially understood. Using a new cell chamber described in the preceding companion paper (Ref to part I, Raeber et al. 2007a) we investigated the migration response of adhesion-dependent fibroblasts embedded 3-dimensionally within synthetic protease-sensitive poly(ethylene glycol) hydrogels to stepwise and cyclic mechanical loads. To that end, we developed a spatially and temporally resolved migration analysis technique capable of providing estimates of statistical cell migration parameters along and perpendicular to the main strain direction. Fibroblasts reoriented themselves in the direction of principal strain, increased their proteolytic migration activity and moved preferentially parallel to the principal strain axis. These results point to a possible correlation between planes of iso-strain and migration direction.

A biomechanical model of mammographic compressions.

Abstract: A number of biomechanical models have been proposed to improve nonrigid registration techniques for multimodal breast image alignment. A deformable breast model may also be useful for overcoming difficulties in interpreting 2D X-ray projections (mammograms) of 3D volumes (breast tissues). If a deformable model could accurately predict the shape changes that breasts undergo during mammography, then the model could serve to localize suspicious masses (visible in mammograms) in the unloaded state, or in any other deformed state required for further investigations (such as biopsy or other medical imaging modalities). In this paper, we present a validation study that was conducted in order to develop a biomechanical model based on the well-established theory of continuum mechanics (finite elasticity theory with contact mechanics) and demonstrate its use for this application. Experimental studies using gel phantoms were conducted to test the accuracy in predicting mammographic-like deformations. The material properties of the gel phantom were estimated using a nonlinear optimization process, which minimized the errors between the experimental and the model-predicted surface data by adjusting the parameter associated with the neo-Hookean constitutive relation. Two compressions (the equivalent of cranio-caudal and medio-lateral mammograms) were performed on the phantom, and the corresponding deformations were recorded using a MRI scanner. Finite element simulations were performed to mimic the experiments using the estimated material properties with appropriate boundary conditions. The simulation results matched the experimental recordings of the deformed phantom, with a sub-millimeter root-mean-square error for each compression state. Having now validated our finite element model of breast compression, the next stage is to apply the model to clinical images.

An estimate of anisotropic poroelastic constants of an osteon.

Abstract: The anisotropic poroelastic constants of an osteon are estimated by micromechanical analysis. Two extreme cases are examined, the drained and the undrained elastic constants. The drained elastic constants are the porous medium’s effective elastic constants when the fluid in the pores easily escapes and the pore fluid can sustain no pore pressure. The undrained elastic constants are the porous medium’s effective elastic constants when the medium is fully saturated with pore fluid and the fluid cannot escape. The drained and undrained elastic constants at the lacunar and canalicular porosity tissue levels are estimated by using an effective moduli model consisting of the periodic distribution of ellipsoidal cavities. These estimated anisotropic poroelastic constants provide a database for the development of an accurate anisotropic poroelastic model of an osteon.

Regulation of immature cartilage growth by IGF-I, TGF-β1, BMP-7, and PDGF-AB: role of metabolic balance between fixed charge and collagen network

Abstract: Cartilage growth may involve alterations in the balance between the swelling tendency of proteoglycans and the restraining function of the collagen network. Growth factors, including IGF-I, TGF-β1, BMP-7, and PDGF-AB, regulate chondrocyte metabolism and, consequently, may regulate cartilage growth. Immature bovine articular cartilage explants from the superficial and middle zones were incubated for 13 days in basal medium or medium supplemented with serum, IGF-I, TGF-β1, BMP-7, or PDGF-AB. Variations in tissue size, accumulation of proteoglycan and collagen, and tensile properties were assessed. The inclusion of serum, IGF-I, or BMP-7 resulted in expansive tissue growth, stimulation of proteoglycan deposition but not of collagen, and a diminution of tensile integrity. The regulation of cartilage metabolism by TGF-β1 resulted in tissue homeostasis, with maintenance of size, composition, and function. Incubation in basal medium or with PDGF-AB resulted in small volumetric and compositional changes, but a marked decrease in tensile integrity. These results demonstrate that the phenotype of cartilage growth, and the associated balance between proteoglycan content and integrity of the collagen network, is regulated differentially by certain growth factors.

Mechanical properties of anterior malleolar ligament from experimental measurement and material modeling analysis

Abstract: In this paper, mechanical properties of the anterior malleolar ligament (AML) of human middle ear were studied through the uniaxial tensile, stress relaxation and failure tests. The digital image correlation (DIC) method was used to assess the boundary effect in experiments and calculate the strain on specimens. The constitutive behavior of the AML was described by a transversely isotropic hyperelastic model which consists of a first-order Ogden model augmented by a I(4)-type reinforcing term. The material parameters of the model were estimated and the viscoelasticity of the AML was illustrated by hysteresis phenomena and stress relaxation function. The mechanical strength of the AML was obtained through the failure test and the mean ultimate stress and stretch ratio were measured as 1.05 MPa and 1.51, respectively. Finally, a linear Young's modulus-stress relationship of the AML was derived based on constitutive equation of the AML within a stress range of 0-0.5 MPa.

Contribution of the extracellular matrix to the viscoelastic behavior of the urinary bladder wall.

Abstract: We previously reported that when the stress relaxation response of urinary bladder wall (UBW) tissue was analyzed using a single continuous reduced relaxation func- tion (RRF), we observed non-uniformly distributed, time- dependent residuals (Ann Biomed Eng 32(10):1409-1419, 2004). We concluded that the single relaxation spectrum was inadequate and that a new viscoelastic model for bladder wall was necessary. In the present study, we report a new approach composed of independent RRFs for smooth mus- cle and the extracellular matrix components (ECM), con- nected through a stress-dependent recruitment function. In order to determine the RRF for the ECM component, biax- ial stress relaxation experiments were first performed on decellularized extracellular matrix network of the bladder obtained from normal and spinal cord injured rats. While it was assumed that smooth muscle followed a single spectrum RRF, modeling the UBW ECM required a dual-Gaussian spectrum. Experimental results revealed that the ECM stress relaxation response was insensitive to the initial stress level. Thus, the average ECM RRF parameters were determined by fitting the average stress relaxation data. The resulting stress relaxation behavior of whole bladder tissue was mod- eled by combining the ECM RRF with the RRF for the smooth muscle component using an exponential recruitment function representing the recruitment of collagen fibers at higher stress levels. In summary, the present study demon- strated, for the first time, that stress relaxation response of bladder tissue can be better modeled when divided into the contributions of the extracellular matrix and smooth muscle components. This modeling approach is suitable for predic- tion of mechanical behaviors of the urinary bladder and other organs that exhibit rapid tissue remodeling (i.e., smooth mus- cle hypertrophy and altered ECM synthesis) under various pathological conditions.

Multilevel finite element modeling for the prediction of local cellular deformation in bone.

Abstract: The underlying mechanisms by which bone cells respond to mechanical stimuli or how mechanical loads act on osteocytes housed in lacunae in bone are not well understood. In this study, a multilevel finite element (FE) approach is applied to predict local cell deformations in bone tissue. The local structure of the matrix dictates the local mechanical environment of an osteocyte. Cell deformations are predicted from detailed linear FE analysis of the microstructure, consisting of an arrangement of cells embedded in bone matrix material. This work has related the loads applied to a whole femur during the stance phase of the gait cycle to the strain of a single lacuna and of canaliculi. The predicted bone matrix strains around osteocyte lacunae and canaliculi were nonuniform and differed significantly from the macroscopically measured strains. Peak stresses and strains in the walls of the lacuna were up to six times those in the bulk extracellular matrix. Significant strain concentrations were observed at sites where the process meets the cell body.

A theoretically-motivated biaxial tissue culture system with intravital microscopy.

Abstract: Many cell types produce, remodel, and degrade extracellular matrix in response to diverse stimuli, including mechanical loads Much is known about the molecular biology and biochemistry of the deposition and degradation of collagen, the primary structural constituent of the extracellular matrix in many tissues, yet there has been little modeling of the associated mechanobiology For example, we do not have quantitative descriptions, or rules, for the kinetics of collagen turnover as a function of altered mechanical loading and we do not know what governs the orientation and pre-stretch at which new fibers are incorporated within extant tissue In this paper, we use a constrained mixture theory for growth and remodeling of planar soft tissues to motivate a new experimental approach for investigating competing hypotheses on, for example, how new collagen is aligned by synthetic cells In particular, because stress and strain fields can be homogeneous in a central region of a biaxially tested tissue, and because biaxial testing admits diverse protocols wherein equal stresses can be imposed in the presence of unequal strains or stresses can be maintained in the absence of strain, we report simulations that illustrate the potential utility of biaxial culture studies Finally, we describe the associated design of a computer-controlled system that allows intravital microscopic quantification of collagen density, orientation, and cross-linking at various stages during the adaptation of a native tissue or the development of a tissue engineered equivalent, each subjected to well controlled biaxial loads

Stress-modulated remodeling of a non-homogeneous body

Abstract: Many soft tissues, and arteries in primis, exhibit residual stress after unloading, a characteristic related to the ability to self-organize their own constituents (cells and extracellular matrix proteins). This behavior can be theoretically predicted in a continuum mechanics framework assuming that the body self- remodels toward a homeostatic stress state. Open questions concern the characteristics of a stationary grown state, as dictated by the mechanical properties of the material and by the specific external load. In this paper, we illustrate a mathematical framework and we perform numerical simulations for the remodeling of a two-dimensional (axisymmetric) nonlinear elastic cylinder. In particular, we address the stress-modulated remodeling of the cylinder wall when local variations in the mechanical properties of the material occur. Our main result is that, as in one spatial dimension, the tendency of the system to homeostasis generates, thanks to the remodeling process, a residual stress that homogenizes the tension in the body under load. Possible physiological implications of this result are discussed in the final section.

Three-dimensional simulation of anisotropic cell-driven collagen gel compaction

Abstract: Tissue equivalents (TEs), formed by entrapping cells in a collagen gel, are an important model system for studying cell behavior. We have previously (Barocas and Tranquillo in J Biomech Eng 117:161–170, 1997a) developed an anisotropic biphasic theory of TE mechanics, which comprises five coupled partial differential equations describing interaction among cells and collagen fibers in the TE. The model equations, previously solved in one or two dimensions, were solved in three dimensions using an adaptive finite-element platform. The model was applied to three systems: a rectangular isometric cell traction assay, an otherwise- acellular gel containing two islands of cells, and an idealized tissue-engineered cardiac valve leaflet. In the first two cases, published experimental data were available for comparison, and the model results were consistent with the experimental observations. Fibers and cells aligned in the fixed direction in the isometric assay, and a region of strong fiber alignment arose between the two cell islands. For the valve problem, the alignment predicted by the model was generally similar to that observed experimentally, but an asymmetry in the experiment was not captured by the model.

Mechanics of mesenchymal contribution to clefting force in branching morphogenesis.

Abstract: Branching morphogenesis is ubiquitous and may involve several different mechanisms. Glandular morphogenesis is affected by growth, cell rearrangements, changes in the basal lamina, changes in the stromal ECM, changes in cell–cell and cell–ECM adhesions, mesenchymal contractility, and possibly other mechanisms. We have developed a 3D model of the mechanics of clefting, focusing in this paper solely on the potential role of mesenchyme-generated traction forces. The tissue mechanics are assumed to be those of fluids, and the hypothesized traction forces are modeled as advected by the deformations which they generate. We find that mesenchymal traction forces are sufficient to generate a cleft of the correct size and morphology, in the correct time frame. We find that viscosity of the tissues affects the time course of morphogenesis, and also affects the resulting form of the organ. Morphology is also strongly dependent on the initial distribution of contractility. We suggest an in vitro method of examining the role of mesenchyme in branching morphogenesis.