Stress and strain localization in stretched collagenous tissues via a multiscale modelling approach

Mechanobiology of cells in soft collagenous tissues is highly affected by both tissue response at the macroscale and stress/strain localization mechanisms due to features at lower scales. In this paper, the macroscale mechanical behaviour of soft collagenous tissues is modelled by a three-level multiscale approach, based on a multi-step homogenisation technique from nanoscale up to the macroscale. Nanoscale effects, related to both intermolecular cross-links and collagen mechanics, are accounted for, together with geometric nonlinearities at the microscale. Moreover, an effective submodelling procedure is conceived in order to evaluate the local stress and strain fields at the microscale, which is around and within cells. Numerical results, obtained by using an incremental finite element formulation and addressing stretched tendinous tissues, prove consistency and accuracy of the model at both macroscale and microscale, confirming also the effectiveness of the multiscale modelling concept for successfully analysing physiopathological processes in biological tissues.     

Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing

Wound healing is a synchronized cascade of chemical, biological, and mechanical phenomena, which act in concert to restore the damaged tissue. An imbalance between these events can induce painful scarring. Despite intense efforts to decipher the mechanisms of wound healing, the role of mechanics remains poorly understood. Here, we establish a computational systems biology model to identify the chemical, biological, and mechanical mechanisms of scar formation. First, we introduce the generic problem of coupled chemo-bio-mechanics. Then, we introduce the model problem of wound healing in terms of a particular chemical signal, inflammation, a particular biological cell type, fibroblasts, and a particular mechanical model, isotropic hyperelasticity. We explore the cross-talk between chemical, biological, and mechanical signals and show that all three fields have a significant impact on scar formation. Our model is the first step toward rigorous multiscale, multifield modeling in wound healing. Our formulation has the potential to improve effective wound management and optimize treatment on an individualized patient-specific basis.     

Mechanical Boundary Conditions Bias Fibroblast Invasion in a Collagen-Fibrin Wound Model

Because fibroblasts deposit the collagen matrix that determines the mechanical integrity of scar tissue, altering fibroblast invasion could alter wound healing outcomes. Anisotropic mechanical boundary conditions (restraint, stretch, or tension) could affect the rate of fibroblast invasion, but their importance relative to the prototypical drivers of fibroblast infiltration during wound healing—cell and chemokine concentration gradients—is unknown. We tested whether anisotropic mechanical boundary conditions affected the directionality and speed of fibroblasts migrating into a three-dimensional model wound, which could simultaneously expose fibroblasts to mechanical, structural, steric, and chemical guidance cues. We created fibrin-filled slits in fibroblast-populated collagen gels and applied uniaxial mechanical restraint along the short or long axis of the fibrin wounds. Anisotropic mechanical conditions increased the efficiency of fibroblast invasion by guiding fibroblasts without increasing their migration speed. The migration behavior could be modeled as a biased random walk, where the bias due to multiple guidance cues was accounted for in the shape of a displacement orientation probability distribution. Taken together, modeling and experiments suggested an effect of strain anisotropy, rather than strain-induced fiber alignment, on fibroblast invasion.     

Mechanical Boundary Conditions Bias Fibroblast Invasion in a Collagen-Fibrin Wound Model

Because fibroblasts deposit the collagen matrix that determines the mechanical integrity of scar tissue, altering fibroblast invasion could alter wound healing outcomes. Anisotropic mechanical boundary conditions (restraint, stretch, or tension) could affect the rate of fibroblast invasion, but their importance relative to the prototypical drivers of fibroblast infiltration during wound healing—cell and chemokine concentration gradients—is unknown. We tested whether anisotropic mechanical boundary conditions affected the directionality and speed of fibroblasts migrating into a three-dimensional model wound, which could simultaneously expose fibroblasts to mechanical, structural, steric, and chemical guidance cues. We created fibrin-filled slits in fibroblast-populated collagen gels and applied uniaxial mechanical restraint along the short or long axis of the fibrin wounds. Anisotropic mechanical conditions increased the efficiency of fibroblast invasion by guiding fibroblasts without increasing their migration speed. The migration behavior could be modeled as a biased random walk, where the bias due to multiple guidance cues was accounted for in the shape of a displacement orientation probability distribution. Taken together, modeling and experiments suggested an effect of strain anisotropy, rather than strain-induced fiber alignment, on fibroblast invasion.     

Tools for studying and modulating (cardiac muscle) cell mechanics and mechanosensing across the scales

Cardiomyocytes generate force for the contraction of the heart to pump blood into the lungs and body. At the same time, they are exquisitely tuned to the mechanical environment and react to e.g. changes in cell and extracellular matrix stiffness or altered stretching due to reduced ejection fraction in heart disease, by adapting their cytoskeleton, force generation and cell mechanics. Both mechanical sensing and cell mechanical adaptations are multiscale processes. Receptor interactions with the extracellular matrix at the nanoscale will lead to clustering of receptors and modification of the cytoskeleton. This in turn alters mechanosensing, force generation, cell and nuclear stiffness and viscoelasticity at the microscale. Further, this affects cell shape, orientation, maturation and tissue integration at the microscale to macroscale. A variety of tools have been developed and adapted to measure cardiomyocyte receptor-ligand interactions and forces or mechanics at the different ranges, resulting in a wealth of new information about cardiomyocyte mechanobiology. Here, we take stock at the different tools for exploring cardiomyocyte mechanosensing and cell mechanics at the different scales from the nanoscale to microscale and macroscale.     

Cells Actively Stiffen Fibrin Networks by Generating Contractile Stress

During wound healing and angiogenesis, fibrin serves as a provisional extracellular matrix. We use a model system of fibroblasts embedded in fibrin gels to study how cell-mediated contraction may influence the macroscopic mechanical properties of their extracellular matrix during such processes. We demonstrate by macroscopic shear rheology that the cells increase the elastic modulus of the fibrin gels. Microscopy observations show that this stiffening sets in when the cells spread and apply traction forces on the fibrin fibers. We further show that the stiffening response mimics the effect of an external stress applied by mechanical shear. We propose that stiffening is a consequence of active myosin-driven cell contraction, which provokes a nonlinear elastic response of the fibrin matrix. Cell-induced stiffening is limited to a factor 3 even though fibrin gels can in principle stiffen much more before breaking. We discuss this observation in light of recent models of fibrin gel elasticity, and conclude that the fibroblasts pull out floppy modes, such as thermal bending undulations, from the fibrin network, but do not axially stretch the fibers. Our findings are relevant for understanding the role of matrix contraction by cells during wound healing and cancer development, and may provide design parameters for materials to guide morphogenesis in tissue engineering.     

Cells Actively Stiffen Fibrin Networks by Generating Contractile Stress

During wound healing and angiogenesis, fibrin serves as a provisional extracellular matrix. We use a model system of fibroblasts embedded in fibrin gels to study how cell-mediated contraction may influence the macroscopic mechanical properties of their extracellular matrix during such processes. We demonstrate by macroscopic shear rheology that the cells increase the elastic modulus of the fibrin gels. Microscopy observations show that this stiffening sets in when the cells spread and apply traction forces on the fibrin fibers. We further show that the stiffening response mimics the effect of an external stress applied by mechanical shear. We propose that stiffening is a consequence of active myosin-driven cell contraction, which provokes a nonlinear elastic response of the fibrin matrix. Cell-induced stiffening is limited to a factor 3 even though fibrin gels can in principle stiffen much more before breaking. We discuss this observation in light of recent models of fibrin gel elasticity, and conclude that the fibroblasts pull out floppy modes, such as thermal bending undulations, from the fibrin network, but do not axially stretch the fibers. Our findings are relevant for understanding the role of matrix contraction by cells during wound healing and cancer development, and may provide design parameters for materials to guide morphogenesis in tissue engineering.     

Transfer of macroscale tissue strain to microscale cell regions in the deformed meniscus

Cells within fibrocartilaginous tissues, including chondrocytes and fibroblasts of the meniscus, ligament, and tendon, regulate cell biosynthesis in response to local mechanical stimuli. The processes by which an applied mechanical load is transferred through the extracellular matrix to the environment of a cell are not fully understood. To better understand the role of mechanics in controlling cell phenotype and biosynthetic activity, this study was conducted to measure strain at different length scales in tissue of the fibrocartilaginous meniscus of the knee joint, and to define a quantitative parameter that describes the strain transferred from the far-field tissue to a microenvironment surrounding a cell. Experiments were performed to apply a controlled uniaxial tensile deformation to explants of porcine meniscus containing live cells. Using texture correlation analyses of confocal microscopy images, two-dimensional Lagrangian and principal strains were measured at length scales representative of the tissue (macroscale) and microenvironment in the region of a cell (microscale) to yield a strain transfer ratio as a measure of median microscale to macroscale strain. The data demonstrate that principal strains at the microscale are coupled to and amplified from macroscale principal strains for a majority of cell microenvironments located across diverse microstructural regions, with average strain transfer ratios of 1.6 and 2.9 for the maximum and minimum principal strains, respectively. Lagrangian strain components calculated along the experimental axes of applied deformations exhibited considerable spatial heterogeneity and intersample variability, and suggest the existence of both strain amplification and attenuation. This feature is consistent with an in-plane rotation of the principal strain axes relative to the experimental axes at the microscale that may result from fiber sliding, fiber twisting, and fiber-matrix interactions that are believed to be important for regulating deformation in other fibrocartilaginous tissues. The findings for consistent amplification of macroscale to microscale principal strains suggest a coordinated pattern of strain transfer from applied deformation to the microscale environment of a cell that is largely independent of these microstructural features in the fibrocartilaginous meniscus.     

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

Geometry Regulates Traction Stresses in Adherent Cells

Cells generate mechanical stresses via the action of myosin motors on the actin cytoskeleton. Although the molecular origin of force generation is well understood, we currently lack an understanding of the regulation of force transmission at cellular length scales. Here, using 3T3 fibroblasts, we experimentally decouple the effects of substrate stiffness, focal adhesion density, and cell morphology to show that the total amount of work a cell does against the substrate to which it is adhered is regulated by the cell spread area alone. Surprisingly, the number of focal adhesions and the substrate stiffness have little effect on regulating the work done on the substrate by the cell. For a given spread area, the local curvature along the cell edge regulates the distribution and magnitude of traction stresses to maintain a constant strain energy. A physical model of the adherent cell as a contractile gel under a uniform boundary tension and mechanically coupled to an elastic substrate quantitatively captures the spatial distribution and magnitude of traction stresses. With a single choice of parameters, this model accurately predicts the cell’s mechanical output over a wide range of cell geometries.     

IDH2 deficiency impairs cutaneous wound healing via ROS-dependent apoptosis

Dermal fibroblasts are mesenchymal cells found between the skin epidermis and subcutaneous tissue that play a pivotal role in cutaneous wound healing by synthesizing fibronectin (a component of the extracellular matrix), secreting angiogenesis factors, and generating strong contractile forces. In wound healing, low concentrations of reactive oxygen species (ROS) are essential in combating invading microorganisms and in cell-survival signaling. However, excessive ROS production impairs fibroblasts. Mitochondrial NADP⁺-dependent isocitrate dehydrogenase (IDH2) is a key enzyme that regulates the mitochondrial redox balance and reduces oxidative stress-induced cell injury through the generation of NADPH. In the present study, the downregulation of IDH2 expression resulted in an increase in cell apoptosis in mouse skin through ROS-dependent ATM-mediated p53 signaling. IDH2 deficiency also delayed cutaneous wound healing in mice and impaired dermal fibroblast function. Furthermore, pretreatment with the mitochondria-targeted antioxidant mito-TEMPO alleviated the apoptosis induced by IDH2 deficiency both in vitro and in vivo. Together, our findings highlight the role of IDH2 in cutaneous wound healing in association with mitochondrial ROS.     

Versatile and inexpensive Hall-Effect force sensor for mechanical characterization of soft biological materials

Mismatch of hierarchical structure and mechanical properties between tissue-engineered implants and native tissue may result in signal cues that negatively impact repair and remodeling. With bottom-up tissue engineering approaches, designing tissue components with proper microscale mechanical properties is crucial to achieve necessary macroscale properties in the final implant. However, characterizing microscale mechanical properties is challenging, and current methods do not provide the versatility and sensitivity required to measure these fragile, soft biological materials. Here, we developed a novel, highly sensitive Hall-Effect based force sensor that is capable of measuring mechanical properties of biological materials over wide force ranges (μN to N), allowing its use at all steps in layer-by-layer fabrication of engineered tissues. The force sensor design can be easily customized to measure specific force ranges, while remaining easy to fabricate using inexpensive, commercial materials. Although we used the force sensor to characterize mechanics of single-layer cell sheets and silk fibers, the design can be easily adapted for different applications spanning larger force ranges (>N). This platform is thus a novel, versatile, and practical tool for mechanically characterizing biological and biomimetic materials.     

Multiscale characterization and micromechanical modeling of crop stem materials

An essential prerequisite for the efficient biomechanical tailoring of crops is to accurately relate mechanical behavior to compositional and morphological properties across different length scales. In this article, we develop a multiscale approach to predict macroscale stiffness and strength properties of crop stem materials from their hierarchical microstructure. We first discuss the experimental multiscale characterization based on microimaging (micro-CT, light microscopy, transmission electron microscopy) and chemical analysis, with a particular focus on oat stems. We then derive in detail a general micromechanics-based model of macroscale stiffness and strength. We specify our model for oats and validate it against a series of bending experiments that we conducted with oat stem samples. In the context of biomechanical tailoring, we demonstrate that our model can predict the effects of genetic modifications of microscale composition and morphology on macroscale mechanical properties of thale cress that is available in the literature.

     

Consistent trilayer biomechanical modeling of aortic valve leaflet tissue

Aortic valve tissue exhibits highly nonlinear, anisotropic, and heterogeneous material behavior due to its complex microstructure. A thorough understanding of these characteristics permits us to develop numerical models that can shed insight on the function of the aortic valve in health and disease. Herein, we take a closer look at consistently capturing the observed physical response of aortic valve tissue in a continuum mechanics framework. Such a treatment is the first step in developing comprehensive multiscale and multiphysics models.We highlight two important aspects of aortic valve tissue behavior: the role of the collagen fiber microstructure and the native prestressing. We propose a model that captures these two features as well as the heterogeneous layer-scale topology of the tissue. We find the model can reproduce the experimentally observed multiscale mechanical behavior in a manner that provides intuition on the underlying mechanics.     

A Combined In Vitro Imaging and Multi-Scale Modeling System for Studying the Role of Cell Matrix Interactions in Cutaneous Wound Healing

Many cell types remodel the extracellular matrix of the tissues they inhabit in response to a wide range of environmental stimuli, including mechanical cues. Such is the case in dermal wound healing, where fibroblast migrate into and remodel the provisional fibrin matrix in a complex manner that depends in part on the local mechanical environment and the evolving multi-scale mechanical interactions of the system. In this study, we report on the development of an image-based multi-scale mechanical model that predicts the short-term (24 hours), structural reorganization of a fibrin gel by fibroblasts. These predictive models are based on an in vitro experimental system where clusters of fibroblasts (i.e., explants) were spatially arranged into a triangular geometry onto the surface of fibrin gels that were subjected to either Fixed or Free in-plane mechanical constraints. Experimentally, regional differences in short-term structural remodeling and cell migration were observed for the two gel boundary conditions. A pilot experiment indicated that these small differences in the short-term remodeling of the fibrin gel translate into substantial differences in long-term (4 weeks) remodeling, particularly in terms of collagen production. The multi-scale models were able to predict some regional differences in remodeling and qualitatively similar reorganization patterns for the two boundary conditions. However, other aspects of the model, such as the magnitudes and rates of deformation of gel, did not match the experiments. These discrepancies between model and experiment provide fertile ground for challenging model assumptions and devising new experiments to enhance our understanding of how this multi-scale system functions. These efforts will ultimately improve the predictions of the remodeling process, particularly as it relates to dermal wound healing and the reduction of patient scarring. Such models could be used to recommend patient-specific mechanical-based treatment dependent on parameters such as wound geometry, location, age, and health.     

Mechanical properties of a mature biofilm from a wastewater system: from microscale to macroscale level

A fundamental understanding of biofilm mechanical stability is critical in order to describe detachment and develop biofouling control strategies. It is thus important to characterise the elastic deformation and flow behaviour of the biofilm under different modes of applied force. In this study, the mechanical properties of a mature wastewater biofilm were investigated with methods including macroscale compression and microscale indentation using atomic force microscopy (AFM). The mature biofilm was found to be mechanically isotropic at the macroscale level as its mechanical properties did not depend on the scales and modes of loading. However, the biofilm showed a tendency for mechanical inhomogeneity at the microscale level as indentation progressed deeper into the matrix. Moreover, it was observed that the adhesion force had a significant influence on the elastic properties of the biofilm at the surface, subjected to microscale tensile loading. These results are expected to inform a damage-based model for biofilm detachment.     

Reconstruction of the connective tissue as a result of transplantation of fibrins dermal equivalent to the wounds of experimental animals

We analyzed the effectiveness of wound healing in rats after application of the dermal equivalent (DE) based on fibrin with dermal fibroblasts. Histological studies of newly formed dermis biopsy samples selected during its recovery in the model wound in laboratory animals have shown a positive effect of DE on wound healing. It was found a significant increase in the area of collagen fibers, in the number of prekapillaries, capillaries and postcapillaries in the granulation tissue after application of DE compared with the control group, suggesting a more intense repair.