Modelling Biological Gel Contraction by Cells: Mechanocellular Formulation and Cell Traction Force Quantification

Traction forces developed by most cell types play a significant role in the spatial organisation of biological tissues. However, due to the complexity of cell-extracellular matrix interactions, these forces are quantitatively difficult to estimate without explicitly considering cell properties and extracellular mechanical matrix responses. Recent experimental devices elaborated for measuring cell traction on extracellular matrix use cell deposits on a piece of gel placed between one fixed and one moving holder. We formulate here a mathematical model describing the dynamic behaviour of the cell-gel medium in such devices. This model is based on a mechanical force balance quantification of the gel visco-elastic response to the traction forces exerted by the diffusing cells. Thus, we theoretically analyzed and simulated the displacement of the free moving boundary of the system under various conditions for cells and gel concentrations. This modelis then used as the theoretical basis of an experimental device where endothelial cells are seeded on a rectangular biogel of fibrin cast between two floating holders, one fixed and the other linked to a force sensor. From a comparison of displacement of the gel moving boundary simulated by the model and the experimental data recorded from the moving holder displacement, the magnitude of the traction forces exerted by the endothelial cell on the fibrin gel was estimated for different experimental situations. Different analytical expressions for the cell traction term are proposed and the corresponding force quantifications are compared to the traction force measurements reported for various kind of cells with the use of similar or different experimental devices. This revised version was published online in June 2006 with corrections to the Cover Date.     

Critical conditions for pattern formation and in vitro tubulogenesis driven by cellular traction fields

In vitro angiogenesis assays have shown that tubulogenesis of endothelial cells within biogels, like collagen or fibrin gels, only appears for a critical range of experimental parameter values. These experiments have enabled us to develop and validate a theoretical model in which mechanical interactions of endothelial cells with extracellular matrix influence both active cell migration--haptotaxis--and cellular traction forces. Depending on the number of cells, cell motility and biogel rheological properties, various 2D endothelial patterns can be generated, from non-connected stripe patterns to fully connected networks, which mimic the spatial organization of capillary structures. The model quantitatively and qualitatively reproduces the range of critical values of cell densities and fibrin concentrations for which these cell networks are experimentally observed. We illustrate how cell motility is associated to the self-enhancement of the local traction fields exerted within the biogel in order to produce a pre-patterning of this matrix and subsequent formation of tubular structures, above critical thresholds corresponding to bifurcation points of the mathematical model. The dynamics of this morphogenetic process is discussed in the light of videomicroscopy time lapse sequences of endothelial cells (EAhy926 line) in fibrin gels. Our modeling approach also explains how the progressive appearance and morphology of the cellular networks are modified by gradients of extracellular matrix thickness.     

Fibronectin matrix polymerization increases tensile strength of model tissue

The composition and organization of the extracellular matrix (ECM) contribute to the mechanical properties of tissues. The polymerization of fibronectin into the ECM increases actin organization and regulates the composition of the ECM. In this study, we examined the ability of cell-dependent fibronectin matrix polymerization to affect the tensile properties of an established tissue model. Our data indicate that fibronectin polymerization increases the ultimate strength and toughness, but not the stiffness, of collagen biogels. A fragment of fibronectin that stimulates mechanical tension generation by cells, but is not incorporated into ECM fibrils, did not increase the tensile properties, suggesting that changes in actin organization in the absence of fibronectin fibril formation are not sufficient to increase tensile strength. The actin cytoskeleton was needed to initiate the fibronectin-induced increases in the mechanical properties. However, once fibronectin-treated collagen biogels were fully contracted, the actin cytoskeleton no longer contributed to the tensile strength. These data indicate that fibronectin polymerization plays a significant role in determining the mechanical strength of collagen biogels and suggest a novel mechanism by which fibronectin can be used to enhance the mechanical performance of artificial tissue constructs.     

Rheological properties of cross-linked hyaluronan-gelatin hydrogels for tissue engineering

Hydrogels that mimic the natural extracellular matrix (ECM) are used in three-dimensional cell culture, cell therapy, and tissue engineering. A semi-synthetic ECM based on cross-linked hyaluronana offers experimental control of both composition and gel stiffness. The mechanical properties of the ECM in part determine the ultimate cell phenotype. We now describe a rheological study of synthetic ECM hydrogels with storage shear moduli that span three orders of magnitude, from 11 to 3 500 Pa, a range important for engineering of soft tissues. The concentration of the chemically modified HA and the cross-linking density were the main determinants of gel stiffness. Increase in the ratio of thiol-modified gelatin reduced gel stiffness by diluting the effective concentration of the HA component.     

Multiscale model predicts tissue-level failure from collagen fiber-level damage

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.     

Metabolic responses induced by compression of chondrocytes in variable-stiffness microenvironments

Cells sense and respond to mechanical loads in a process called mechanotransduction. These processes are disrupted in the chondrocytes of cartilage during joint disease. A key driver of cellular mechanotransduction is the stiffness of the surrounding matrix. Many cells are surrounded by extracellular matrix that allows for tissue mechanical function. Although prior studies demonstrate that extracellular stiffness is important in cell differentiation, morphology and phenotype, it remains largely unknown how a cell’s biological response to cyclical loading varies with changes in surrounding substrate stiffness. Understanding these processes is important for understanding cells that are cyclically loaded during daily in vivo activities (e.g. chondrocytes and walking). This study uses high-performance liquid chromatography – mass spectrometry to identify metabolomic changes in primary chondrocytes under cyclical compression for 0–30 minutes in low- and high-stiffness environments. Metabolomic analysis reveals metabolites and pathways that are sensitive to substrate stiffness, duration of cyclical compression, and a combination of both suggesting changes in extracellular stiffness in vivo alter mechanosensitive signaling. Our results further suggest that cyclical loading minimizes matrix deterioration and increases matrix production in chondrocytes. This study shows the importance of modeling in vivo stiffness with in vitro models to understand cellular mechanotransduction.     

Experimental study and constitutive modeling of the viscoelastic mechanical properties of the human prolapsed vaginal tissue

In this paper, the viscoelastic mechanical properties of vaginal tissue are investigated. Using previous results of the authors on the mechanical properties of biological soft tissues and newly experimental data from uniaxial tension tests, a new model for the viscoelastic mechanical properties of the human vaginal tissue is proposed. The structural model seems to be sufficiently accurate to guarantee its application to prediction of reliable stress distributions, and is suitable for finite element computations. The obtained results may be helpful in the design of surgical procedures with autologous tissue or prostheses.     

Analysis of effects of friction on the deformation behavior of soft tissues in unconfined compression tests

Frictionless specimen/platen contact in unconfined compression tests has traditionally been assumed in determining material properties of soft tissues via an analytical solution. In the present study, the suitability of this assumption was examined using a finite element method. The effect of the specimen/platen friction on the mechanical characteristics of soft tissues in unconfined compression was analyzed based on the published experimental data of three different materials (pigskin, pig brain, and human calcaneal fat). The soft tissues were considered to be nonlinear and viscoelastic; the friction coefficient at the contact interface between the specimens and platens was assumed to vary from 0.0 to 0.5. Our numerical simulations show that the tissue specimens are, due to the specimen/platen friction, not compressed in a uniform stress/strain state, as has been traditionally assumed in analytical analysis. The stress of the specimens obtained with the specimen/platen friction can be greater than those with the frictionless specimen/platen contact by more than 50%, even in well-controlled test conditions.     

Mechanical characterization of anisotropic planar biological soft tissues using large indentation: a computational feasibility study

Traditionally, the complex mechanical behavior of planar soft biological tissues is characterized by (multi)axial tensile testing. While uniaxial tests do not provide sufficient information for a full characterization of the material anisotropy, biaxial tensile tests are difficult to perform and tethering effects limit the analyses to a small central portion of the test sample. In both cases, determination of local mechanical properties is not trivial. Local mechanical characterization may be performed by indentation testing. Conventional indentation tests, however, often assume linear elastic and isotropic material properties, and therefore these tests are of limited use in characterizing the nonlinear, anisotropic material behavior typical for planar soft biological tissues. In this study, a spherical indentation experiment assuming large deformations is proposed. A finite element model of the aortic valve leaflet demonstrates that combining force and deformation gradient data, one single indentation test provides sufficient information to characterize the local material behavior. Parameter estimation is used to fit the computational model to simulated experimental data. The aortic valve leaflet is chosen as a typical example. However, the proposed method is expected to apply for the mechanical characterization of planar soft biological materials in general.     

Compression testing of very soft biological tissues using semi-confined configuration--a word of caution

We analyse semi-confined (i.e. using no-slip boundary conditions) compression experiment of very soft tissue sample using finite element method. We show that the assumption that the planes perpendicular to the direction of the applied force remain plane during the experiments is not satisfied for compression levels lower than previously stated in Miller [2005. Method for testing very soft biological tissues in compression. Journal of Biomechanics 38, 153-158]. Therefore, we recommend that the parameters for constitutive models of very soft tissues be determined by fitting a solution of the finite element models of the experimental set-up to the measurements obtained using semi-confined compression experiments.     

Tensile and compressive properties of healthy and osteoarthritic human articular cartilage

Osteoarthritis (OA) is a disease affecting articular cartilage and the underlying bone, resulting from many biological and mechanical interacting factors which change the extracellular matrix (ECM) and cells and lead to increasing levels of cartilage degeneration, like softening, fibrillation, ulceration and cartilage loss. The early diagnosis of the disease is fundamental to prevent pain, further tissue degeneration and reduce hospital costs. Although morphological modifications can be detected by modern non-invasive diagnostic techniques, they may not be evident in the early stages of OA. The mechanical properties of articular cartilage are related to its composition and structure and are sensitive to even small changes in the ECM that could occur in early OA. The aim of the present study was to compare the mechanical properties of healthy and OA cartilage using a combined experimental-numerical approach. Experimental assessments consisted of step wise confined and unconfined compression and tension stress relaxation tests on disks (for compression) or strips (for tension) of cartilage obtained from human femoral heads discarded from the operating room after total hip replacement. The numerical model was based on the biphasic theory and included the tension-compression non-linearity. Considering OA samples vs normal samples, the static compressive modulus was 55-68% lower, the permeability was 60-80% higher, the dynamic compressive modulus was 59-64% lower, the static tension modulus was 72-83% lower. The model successfully simulated the experimental tests performed on healthy and OA cartilage and was used in combination with the experimental tests to evaluate the role of different ECM components in the mechanical response of normal and OA cartilage.     

Cell adhesion mechanisms and stress relaxation in the mechanics of tumours

Tumour cells usually live in an environment formed by other host cells, extra-cellular matrix and extra-cellular liquid. Cells duplicate, reorganise and deform while binding each other due to adhesion molecules exerting forces of measurable strength. In this paper, a macroscopic mechanical model of solid tumour is investigated which takes such adhesion mechanisms into account. The extracellular matrix is treated as an elastic compressible material, while, in order to define the relationship between stress and strain for the cellular constituents, the deformation gradient is decomposed in a multiplicative way distinguishing the contribution due to growth, to cell rearrangement and to elastic deformation. On the basis of experimental results at a cellular level, it is proposed that at a macroscopic level there exists a yield condition separating the elastic and dissipative regimes. Previously proposed models are obtained as limit cases, e.g. fluid-like models are obtained in the limit of fast cell reorganisation and negligible yield stress. A numerical test case shows that the model is able to account for several complex interactions: how tumour growth can be influenced by stress, how and where it can generate cell reorganisation to release the stress level, how it can lead to capsule formation and compression of the surrounding tissue.     

Extracellular matrix ligand and stiffness modulate immature nucleus pulposus cell-cell interactions

The nucleus pulposus (NP) of the intervertebral disc functions to provide compressive load support in the spine, and contains cells that play a critical role in the generation and maintenance of this tissue. The NP cell population undergoes significant morphological and phenotypic changes during maturation and aging, transitioning from large, vacuolated immature cells arranged in cell clusters to a sparse population of smaller, isolated chondrocyte-like cells. These morphological and organizational changes appear to correlate with the first signs of degenerative changes within the intervertebral disc. The extracellular matrix of the immature NP is a soft, gelatinous material containing multiple laminin isoforms, features that are unique to the NP relative to other regions of the disc and that change with aging and degeneration. Based on this knowledge, we hypothesized that a soft, laminin-rich extracellular matrix environment would promote NP cell-cell interactions and phenotypes similar to those found in immature NP tissues. NP cells were isolated from porcine intervertebral discs and cultured in matrix environments of varying mechanical stiffness that were functionalized with various matrix ligands; cellular responses to periods of culture were assessed using quantitative measures of cell organization and phenotype. Results show that soft (<720 Pa), laminin-containing extracellular matrix substrates promote NP cell morphologies, cell-cell interactions, and proteoglycan production in vitro, and that this behavior is dependent upon both extracellular matrix ligand and substrate mechanical properties. These findings indicate that NP cell organization and phenotype may be highly sensitive to their surrounding extracellular matrix environment.     

Renal cell carcinoma: handling and treatment

The quality of samples and of pre-analytical steps are crucial in all biological tests, this is dramatically true in proteomics analysis. In renal cell carcinoma preparation for two-dimensional gel electrophoresis the time elapsed between sample collection and treatment, and the heterogeneity of tissues are considered in order to obtain high quality and reproducibility of spots. The mechanical dissection and cell separation by magnetic beads coated with anti-Ber and EP4 antibodies to minimize the contamination of nonepithelial cells are described.     

Changes in proteoglycan synthesis of chondrocytes in articular cartilage are associated with the time-dependent changes in their mechanical environment

Explant loading experiments were conducted to investigate the effect of load duration on proteoglycan synthesis. A compressive load of 0.1 MPa applied for 10 min was found to stimulate proteoglycan synthesis, while the same load applied for 20 h suppressed synthesis. This bimodal response suggests that the cells are responding to different mechanical stimuli as time progresses. A theoretical model has therefore been developed to describe the mechanical environment perceived by cells within soft hydrated tissues (e.g. articular cartilage) while the tissue is being loaded. The cells are modeled, using the biphasic theory, as fluid-solid inclusions embedded in and attached to a biphasic extracellular matrix of distinct material properties. A method of solution is developed which is valid for any axisymmetric loading configuration, provided that the cell radius, a, is small relative to the tissue height, h (i.e. h/a 1). A closed-form analytical solution for this inclusion problem is then presented for the confined compression configuration. Results from this model show that the mechanical environment in and around the cells is time dependent and inhomogeneous, and can be significantly influenced by differences in properties between the cell and the extracellular matrix.     

Validation of theoretical framework explaining active solute uptake in dynamically loaded porous media

Solute transport in biological tissues is a fundamental process necessary for cell metabolism. In connective soft tissues, such as articular cartilage, cells are embedded within a dense extracellular matrix that hinders the transport of solutes. However, according to a recent theoretical study (Mauck et al., 2003, J. Biomech. Eng. 125, 602–614), the convective motion of a dynamically loaded porous solid matrix can also impart momentum to solutes, pumping them into the tissue and giving rise to concentrations which exceed those achived under passive diffusion alone. In this study, the theoretical predictions of this model are verified against experimental measurements. The mechanical and transport properties of an agarose–dextran model system were characterized from independent measurements and substituted into the theory to predict solute uptake or desorption under dynamic mechanical loading for various agarose concentrations and dextran molecular weights, as well as different boundary and initial conditions. In every tested case, agreement was observed between experiments and theoretical predictions as assessed by coefficients of determination ranging from R²=0.61 to 0.95. These results provide strong support for the hypothesis that dynamic loading of a deformable porous tissue can produce active transport of solutes via a pumping mechanisms mediated by momentum exchange between the solute and solid matrix.     

Methodology to determine failure characteristics of planar soft tissues using a dynamic tensile test

Predicting the injury risk in automotive collisions requires accurate knowledge of human tissues, more particularly their mechanical properties under dynamic loadings. The present methodology aims to determine the failure characteristics of planar soft tissues such as skin, hollow organs and large vessel walls. This consists of a dynamic tensile test, which implies high-testing velocities close to those in automotive collisions. To proceed, I-shaped tissue samples are subjected to dynamic tensile tests using a customized tensile device based on the drop test principle. Data acquisition has especially been adapted to heterogeneous and soft biological tissues given that standard measurement systems (considered to be global) have been completed with a non-contact and full-field strain measurement (considered to be local). This local measurement technique, called the Image Correlation Method (ICM) provides an accurate strain analysis by revealing strain concentrations and avoids damaging the tissue. The methodology has first been applied to human forehead skin and can be further expanded to other planar soft tissues. The failure characteristics for the skin in terms of ultimate stress are 3 MPa +/- 1.5 MPa. The ultimate global longitudinal strains are equal to 9.5%+/-1.9% (Green-Lagrange strain), which contrasts with the ultimate local longitudinal strain values of 24.0%+/-5.3% (Green-Lagrange strain). This difference is a consequence of the tissue heterogeneity, clearly illustrated by the heterogeneous distribution of the local strain field. All data will assist in developing the tissue constitutive law that will be implemented in finite element models.