Comparison of cellular strain with applied substrate strain in vitro

Strain magnitudes within tenocytes undergoing substrate tensile strain are not well defined. It was hypothesized that strain magnitudes at the cellular level would reflect those of the applied substrate (equibiaxial or uniaxial) strain. A vacuum-operated device was used to apply equibiaxial or uniaxial tension to a flexible substrate upon which tenocytes were cultured in monolayer. Images of tenocytes labeled with Fura-2, to detect free intracellular calcium ions, and MitoFluor Green, to detect mitochondria, were taken prior to strain and for 20 min during application of static strain. A custom-written, texture correlation program computed strain magnitudes in the cell based on the change in pixel pattern displacements between images of non-strained and strained cells. On average, cellular strain was approximately 37+/-8% and 63+/-11% of the applied equibiaxial and uniaxial substrate strain, respectively. The largest cell strains were detected in cells oriented parallel to the direction of applied uniaxial tensile strain. However, strain magnitudes within a cell were heterogeneous. The variance in strain magnitude within and among tenocytes is dependent on cell orientation, cell stiffness, cytoskeleton organization, subcellular organelles, or placement and type of cell-substrate contacts. Results of the present study indicate that cultured tenocytes experience a moderate fraction of the applied substrate strain.     

Applying controlled non-uniform deformation for in vitro studies of cell mechanobiology

Cells within connective tissues routinely experience a wide range of non-uniform mechanical loads that regulate many cell behaviors. In this study, we developed an experimental system to produce complex strain patterns for the study of strain magnitude, anisotropy, and gradient effects on cells in culture. A standard equibiaxial cell stretching system was modified by affixing glass coverslips (5, 10, or 15 mm diameter) to the center of 35 mm diameter flexible-bottomed culture wells. Ring inserts were utilized to limit applied strain to different levels in each individual well at a given vacuum pressure thus enabling parallel experiments at different strain levels. Deformation fields were measured using high-density mapping for up to 6% applied strain. The addition of the rigid inclusion creates strong circumferential and radial strain gradients, with a continuous range of stretch anisotropy ranging from strip biaxial to equibiaxial strain and radial strains up to 24% near the inclusion. Dermal fibroblasts seeded within our 2D system (5 mm inclusions; 2% applied strain for 2 days at 0.2 Hz) demonstrated the characteristic orientation perpendicular to the direction of principal strain. Dermal fibroblasts seeded within fibrin gels (5 mm inclusions; 6% applied strain for 8 days at 0.2 Hz) oriented themselves similarly and compacted their surrounding matrix to an increasing extent with local strain magnitude. This study verifies how inhomogeneous strain fields can be produced in a tunable and simply constructed system and demonstrates the potential utility for studying gradients with a continuous spectrum of strain magnitudes and anisotropies.     

Molecular dynamics simulations showing 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) membrane mechanoporation damage under different strain paths

Continuum finite element material models used for traumatic brain injury lack local injury parameters necessitating nanoscale mechanical injury mechanisms be incorporated. One such mechanism is membrane mechanoporation, which can occur during physical insults and can be devastating to cells, depending on the level of disruption. The current study investigates the strain state dependence of phospholipid bilayer mechanoporation and failure. Using molecular dynamics, a simplified membrane, consisting of 72 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) phospholipids, was subjected to equibiaxial, 2:1 non-equibiaxial, 4:1 non-equibiaxial, strip biaxial, and uniaxial tensile deformations at a von Mises strain rate of 5.45 × 10⁸ s^?1, resulting in velocities in the range of 1 to 4.6 m·s^?1. A water bridge forming through both phospholipid bilayer leaflets was used to determine structural failure. The stress magnitude, failure strain, headgroup clustering, and damage responses were found to be strain state-dependent. The strain state order of detrimentality in descending order was equibiaxial, 2:1 non-equibiaxial, 4:1 non-equibiaxial, strip biaxial, and uniaxial. The phospholipid bilayer failed at von Mises strains of .46, .47, .53, .77, and 1.67 during these respective strain path simulations. Additionally, a Membrane Failure Limit Diagram (MFLD) was created using the pore nucleation, growth, and failure strains to demonstrate safe and unsafe membrane deformation regions. This MFLD allowed representative equations to be derived to predict membrane failure from in-plane strains. These results provide the basis to implement a more accurate mechano-physiological internal state variable continuum model that captures lower length scale damage and will aid in developing higher fidelity injury models.     

Multiscale strain analysis of tissue equivalents using a custom-designed biaxial testing device

Mechanical signals transferred between a cell and its extracellular matrix play an important role in regulating fundamental cell behavior. To further define the complex mechanical interactions between cells and matrix from a multiscale perspective, a biaxial testing device was designed and built. Finite element analysis was used to optimize the cruciform specimen geometry so that stresses within the central region were concentrated and homogenous while minimizing shear and grip effects. This system was used to apply an equibiaxial loading and unloading regimen to fibroblast-seeded tissue equivalents. Digital image correlation and spot tracking were used to calculate three-dimensional strains and associated strain transfer ratios at macro (construct), meso, matrix (collagen fibril), cell (mitochondria), and nuclear levels. At meso and matrix levels, strains in the 1- and 2-direction were statistically similar throughout the loading-unloading cycle. Interestingly, a significant amplification of cellular and nuclear strains was observed in the direction perpendicular to the cell axis. Findings indicate that strain transfer is dependent upon local anisotropies generated by the cell-matrix force balance. Such multiscale approaches to tissue mechanics will assist in advancement of modern biomechanical theories as well as development and optimization of preconditioning regimens for functional engineered tissue constructs.     

Design and validation of a corneal bioreactor

Mechanical strain is an important signal that influences the behavior and properties of cells in a wide variety of tissues. Physiologically similar mechanical strain can revert cultured cells to a more normal phenotype. Here, we have demonstrated that 3% equibiaxial (EB) and uniaxial strains confer favorable protein expression in cultured rabbit corneal fibroblasts (RCFs), with approximately 35% and 65% reduction in expression of α‐smooth muscle actin (α‐SMA), respectively. We have designed a novel bioreactor that is capable of imparting up to 7% EB strain and up to 6% EB strain using a cornea‐shaped post. Additional features of the bioreactor include the application of shear stress to cells in culture and the ability to image cells using optical coherence microscopy (OCM) without being removed from the system. Biotechnol. Bioeng. 2012; 109: 3189–3198. © 2012 Wiley Periodicals, Inc.     

Combining dynamic stretch and tunable stiffness to probe cell mechanobiology in vitro

Cells have the ability to actively sense their mechanical environment and respond to both substrate stiffness and stretch by altering their adhesion, proliferation, locomotion, morphology, and synthetic profile. In order to elucidate the interrelated effects of different mechanical stimuli on cell phenotype in vitro, we have developed a method for culturing mammalian cells in a two-dimensional environment at a wide range of combined levels of substrate stiffness and dynamic stretch. Polyacrylamide gels were covalently bonded to flexible silicone culture plates and coated with monomeric collagen for cell adhesion. Substrate stiffness was adjusted from relatively soft (G′ = 0.3 kPa) to stiff (G′ = 50 kPa) by altering the ratio of acrylamide to bis-acrylamide, and the silicone membranes were stretched over circular loading posts by applying vacuum pressure to impart near-uniform stretch, as confirmed by strain field analysis. As a demonstration of the system, porcine aortic valve interstitial cells (VIC) and human mesenchymal stem cells (hMSC) were plated on soft and stiff substrates either statically cultured or exposed to 10% equibiaxial or pure uniaxial stretch at 1Hz for 6 hours. In all cases, cell attachment and cell viability were high. On soft substrates, VICs cultured statically exhibit a small rounded morphology, significantly smaller than on stiff substrates (p<0.05). Following equibiaxial cyclic stretch, VICs spread to the extent of cells cultured on stiff substrates, but did not reorient in response to uniaxial stretch to the extent of cells stretched on stiff substrates. hMSCs exhibited a less pronounced response than VICs, likely due to a lower stiffness threshold for spreading on static gels. These preliminary data demonstrate that inhibition of spreading due to a lack of matrix stiffness surrounding a cell may be overcome by externally applied stretch suggesting similar mechanotransduction mechanisms for sensing stiffness and stretch.     

Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues

Structural constitutive models integrate information on tissue composition and structure, avoiding ambiguities in material characterization. However, critical structural information (such as fiber orientation) must be modeled using assumed statistical distributions, with the distribution parameters estimated from fits to the mechanical test data. Thus, full realization of structural approaches continues to be limited without direct quantitative structural information for direct implementation or to validate model predictions. In the present study, fiber orientation information obtained using small angle light scattering (SALS) was directly incorporated into a structural constitutive model based on work by Lanir (J. Biomech., v. 16, pp. 1-12, 1983). Demonstration of the model was performed using existing biaxial mechanical and fiber orientation data for native bovine pericardium (Sacks and Chuong, ABME, v.26, pp. 892-902, 1998). The structural constitutive model accurately predicted the complete measured biaxial mechanical response. An important aspect of this approach is that only a single equibiaxial test to determine the effective fiber stress-strain response and the SALS-derived fiber orientation distribution were required to determine the complete planar biaxial mechanical response. Changes in collagen fiber crimp under equibiaxial strain suggest that, at the meso-scale, fiber deformations follow the global tissue strains. This result supports the assumption of affine strain to estimate the fiber strains. However, future evaluations will have to be performed for tissue subjected to a wider range of strain to more fully validate the current approach.     

A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics

This paper presents a finite element formulation suitable for large-strain modeling of biological tissues and uses this formulation to implement an accurate finite element model for mitral valve leaflet tissue. First, an experimentally derived strain energy function is obtained from literature. This function is implemented in finite elements using the mixed pressure-displacement formulation. A modification is made to aid in maintaining positive definiteness of the stiffness matrix at low strains. The numerical implementation is shown to be accurate in representing the analytical model of material behavior. The mixed formulation is useful for modeling of soft biological tissues in general, and the model presented here is applicable to finite element simulation of mitral valve mechanics.     

Comparison of the linear finite element prediction of deformation and strain of human cancellous bone to 3D digital volume correlation measurements

The mechanical properties of cancellous bone and the biological response of the tissue to mechanical loading are related to deformation and strain in the trabeculae during function. Due to the small size of trabeculae, their motion is difficult to measure. To avoid the need to measure trabecular motions during loading the finite element method has been used to estimate trabecular level mechanical deformation. This analytical approach has been empirically successful in that the analytical models are solvable and their results correlate with the macroscopically measured stiffness and strength of bones. The present work is a direct comparison of finite element predictions to measurements of the deformation and strain at near trabecular level. Using the method of digital volume correlation, we measured the deformation and calculated the strain at a resolution approaching the trabecular level for cancellous bone specimens loaded in uniaxial compression. Smoothed results from linearly elastic finite element models of the same mechanical tests were correlated to the empirical three-dimensional (3D) deformation in the direction of loading with a coefficient of determination as high as 97% and a slope of the prediction near one. However, real deformations in the directions perpendicular to the loading direction were not as well predicted by the analytical models. Our results show, that the finite element modeling of the internal deformation and strain in cancellous bone can be accurate in one direction but that this does not ensure accuracy for all deformations and strains.     

Application of the u-p finite element method to the study of articular cartilage.

The finite element method using the principle of virtual work was applied to the biphasic theory to establish a numerical routine for analyses of articular cartilage behavior. The matrix equations that resulted contained displacements of the solid matrix (mu) and true fluid pressure (p) as the unknown variables at the element nodes. Both small and large strain conditions were considered. The algorithms and computer code for the analysis of two-dimensional plane strain, plane stress, and axially symmetric cases were developed. The u-p finite element numerical procedure demonstrated excellent agreement with available closed-form and numerical solutions for the configurations of confined compression and unconfined compression under small strains, and for confined compression under large strains. The model was also used to examine the behavior of a repaired articular surface. The differences in material properties between the repair tissue and normal cartilage resulted in significant deformation gradients across the repair interface as well as increased fluid efflux from the tissue.     

An improved texture correlation algorithm to measure substrate-cytoskeletal network strain transfer under large compressive strain

Force-induced deformation of tissues is transduced to the cytoskeletal (CSK) network within cells via focal adhesions. Previous studies have characterized transfer of strains of less than 15% from the substrate to the cell, using mitochondria as surrogate markers for CSK deformation. However, it is unclear if intracellular strains determined from mitochondrial displacement accurately reflect CSK network deformation. Furthermore, previous studies have not characterized substrate-CSK network strain transfer for strain magnitudes exceeding 15%, as can occur in vivo and in cell culture studies. Here, we developed and characterized a texture correlation algorithm to address the image distortion problem caused by large strain. We then used this algorithm to characterize large compressive strain (-40%) transfer from the substrate to the CSK in living cells, using fluorescently tagged actin to perform the tracking and both fluorescently tagged actin and talin to make validation measurements. With this approach, we were able to demonstrate explicitly that substrate strain transfers directly to CSK deformation in living cells undergoing large compressive deformation, and that the strain transfer ratios are independent of cell alignment. The tools and approaches developed here enable improved characterization of cell-matrix interactions under large deformation and in doing so, may reveal new insights into mechanotransduction mechanisms in such circumstances.     

Finite element modeling of 3D human mesenchymal stem cell-seeded collagen matrices exposed to tensile strain

The use of human mesenchymal stem cells (hMSCs) in tissue engineering is attractive due to their ability to extensively self-replicate and differentiate into a multitude of cell lineages. It has been experimentally established that hMSCs are influenced by chemical and mechanical signals. However, the combined chemical and mechanical in vitro culture conditions that lead to functional tissue require greater understanding. In this study, finite element models were created to evaluate the local loading conditions on bone marrow-derived hMSCs seeded in three-dimensional collagen matrices exposed to cyclic tensile strain. Mechanical property and geometry data used in the models were obtained experimentally from a previous study in our laboratory and from mechanical testing. Eight finite element models were created to simulate three-dimensional hMSC-seeded collagen matrices exposed to different levels of cyclic tensile strain (10% and 12%), culture media (complete growth and osteogenic differentiating), and durations of culture (7 and 14 days). Through finite element analysis, it was determined that globally applied uniaxial tensile strains of 10% and 12% resulted in local strains up to 18.3% and 21.8%, respectively. Model results were also compared to experimental studies in an attempt to explain observed differences between hMSC response to 10% and 12% cyclic tensile strain.     

Using digital image correlation to determine bone surface strains during loading and after adaptation of the mouse tibia

Previous models of cortical bone adaptation, in which loading is imposed on the bone, have estimated the strains in the tissue using strain gauges, analytical beam theory, or finite element analysis. We used digital image correlation (DIC), tracing a speckle pattern on the surface of the bone during loading, to determine surface strains in a murine tibia during compressive loading through the knee joint. We examined whether these surface strains in the mouse tibia are modified following two weeks of load-induced adaptation by comparison with contralateral controls. Results indicated non-uniform strain patterns with isolated areas of high strain (0.5%), particularly on the medial side. Strain measurements were reproducible (standard deviation of the error 0.03%), similar between specimens, and in agreement with strain gauge measurements (between 0.1 and 0.2% strain). After structural adaptation, strains were more uniform across the tibial surface, particularly on the medial side where peak strains were reduced from 0.5% to 0.3%. Because DIC determines local strains over the entire surface, it will provide a better understanding of how strain stimulus influences the bone response during adaptation.     

13C Metabolic Flux Analysis of acetate conversion to lipids by Yarrowia lipolytica

Volatile fatty acids (VFAs) are an inexpensive and renewable carbon source that can be generated from gas fermentation and anaerobic digestion of fermentable wastes. The oleaginous yeast Yarrowia lipolytica is a promising biocatalyst that can utilize VFAs and convert them into triacylglycerides (TAGs). However, currently there is limited knowledge on the metabolism of Y. lipolytica when cultured on VFAs. To develop a better understanding, we used acetate as the sole carbon source to culture two strains, a control strain and a previously engineered strain for lipid overaccumulation. For both strains, metabolism during the growth phase and lipid production phase were investigated by metabolic flux analysis using two parallel sodium acetate tracers. The resolved flux distributions demonstrate that the glyoxylate shunt pathway is constantly active and the flux through gluconeogenesis varies depending on strain and phase. In particular, by regulating the activities of malate transport and pyruvate kinase, the cells divert only a portion of the glyoxylate shunt flux required to satisfy the needs for anaplerotic reactions and NADPH production through gluconeogenesis and the oxidative pentose phosphate pathway (PPP). Excess flux flows back to the tricarboxylic acid (TCA) cycle for energy production. As with the case of glucose as the substrate, the primary source for lipogenic NADPH is derived from the oxidative PPP.     

Plastic adherent stromal cells from the bone marrow of commonly used strains of inbred mice: variations in yield, growth, and differentiation

Bone marrow stroma contains a unique cell population, referred to as marrow stromal cells (MSCs), capable of differentiating along multiple mesenchymal cell lineages. A standard liquid culture system has been developed to isolate MSCs from whole marrow by their adherence to plastic wherein the cells grow as clonal populations derived from a single precursor termed the colony-forming-unit fibroblast (CFU-F). Using this liquid culture system, we demonstrate that the relative abundance of MSCs in the bone marrow of five commonly used inbred strains of mice varies as much as 10-fold, and that the cells also exhibit markedly disparate levels of alkaline phosphatase expression, an early marker of osteoblast differentiation. For each strain examined, the method of isolating MSCs by plastic adherence yields a heterogeneous cell population. These plastic adherent cells also exhibit widely varying growth kinetics between the different strains. Importantly, of three inbred strains commonly used to prepare transgenic mice that we examined, only cells derived from FVB/N marrow readily expand in culture. Further analysis of cultures derived from FVB/N marrow showed that most plastic adherent cells express CD11b and CD45, epitopes of lymphohematopoietic cells. The later consists of both pre-B-cell progenitors, granulocytic and monocytic precursors, and macrophages. However, a subpopulation of the MSCs appear to represent bona fide mesenchymal progenitors, as cells can be induced to differentiate into osteoblasts and adipocytes after exposure to dexamethasone and into myoblasts after exposure to amphotericin B. Our results point to significant strain differences in the properties of MSCs and indicate that standard methods cannot be applied to murine bone marrow to isolate relatively pure populations of MSCs.     

Fiber kinematics of small intestinal submucosa under biaxial and uniaxial stretch

Improving our understanding of the design requirements of biologically derived collagenous scaffolds is necessary for their effective use in tissue reconstruction. In the present study, the collagen fiber kinematics of small intestinal submucosa (SIS) was quantified using small angle light scattering (SALS) while the specimen was subjected to prescribed uniaxial or biaxial strain paths. A modified biaxial stretching device based on Billiar and Sacks (J. Biomech., 30, pp. 753-7, 1997) was used, with a real-time analysis of the fiber kinematics made possible due to the natural translucency of SIS. Results indicated that the angular distribution of collagen fibers in specimens subjected to 10% equibiaxial strain was not significantly different from the initial unloaded condition, regardless of the loading path (p=0.31). Both 10% strip biaxial stretch and uniaxial stretches of greater than 5% in the preferred fiber direction led to an increase in the collagen fiber alignment along the same direction, while 10% strip biaxial stretch in the cross preferred fiber direction led to a broadening of the distribution. While an affine deformation model accurately predicted the experimental findings for a biaxial strain state, uniaxial stretch paths were not accurately predicted. Nonaffine structural models will be necessary to fully predict the fiber kinematics under large uniaxial strains in SIS.     

Development of a transient large strain contact method for biological heart valve simulations

A new 2D method to implement transient contact using Comsol Multiphysics (finite element analysis software that enables multiphysics simulations) is described, which is based on Hertzian contact. This method is compared to the existing (default) contact method that does not enable real transient simulations, but instead performs steady-state solutions where time is a constant. The two types of contact modelling have been applied to simple 2D biological heart valve models, undergoing strains in the region of 10% under 20 kPa pressure (applied over 0.3 s). Both the methods predicted comparable stress patterns, locations of peak stresses, deformations and directions of principal stress. The default contact method predicted slightly greater contact stresses, but spreads over a shorter surface length than the new contact method. The default contact method is useful for contact systems with little transient dependency, due to ease of use. However, where transient conditions are important the new contact method is preferred.     

Selection of strains for shiitake production in axenic substrate

Shiitake mushroom consumption is increasing in Brazil. In addition to the implementation of new production methods, it is also important to increase productivity, quality and reduce production costs. In this study, six commercial Lentinula edodes strains were characterized for genetic diversity (rep-PCR analysis) and mushroom production (yield, number and weight of individual mushrooms) using different substrates and cultural conditions. All strains showed genetic differences by repetitive element palindromic based-polymerase chain reaction (rep-PCR). The richest substrate resulted in the greatest production under both environmental conditions. Strains LE4 and LE6 produced the majority of their mushrooms earlier than the other strains. The highest number of mushrooms was observed in the LE6 strain while the highest weights of individual mushrooms were observed in the LE4 strain. Controlled environmental conditions resulted in superior production for all strains, except for LE4, which had empirically greater yield in the semi-controlled environmental condition.