Significance Robust and predictive in vitro models of human cardiac tissue function could have transformative impact on our ability to test new drugs and understand cardiac disease. Despite significant effort, the generation of high-fidelity adult-like human cardiac tissue analogs remains challenging. In this paper, we systematically explore the design criteria for pluripotent stem cell-derived engineered cardiac tissue. Parameters such as biomechanical stress during tissue remodeling, input-cell composition, electrical stimulation, and tissue geometry are evaluated. Our results suggest that a specified combination of a 3D matrix-based microenvironment, uniaxial mechanical stress, and mixtures of cardiomyocytes and fibroblasts improves the performance and maturation state of in vitro engineered cardiac tissue.

Mechanical stimulation is known to cause alterations in the behaviour of cells adhering to a substrate. The mechanisms by which forces are transduced into biological responses within the cell remain largely unknown. Since cellular deformation is likely involved, further understanding of the biomechanical origins of alterations in cellular response can be aided by the use of computational models in describing cellular structural behaviour and in determining cellular deformation due to imposed loads of various magnitudes. In this paper, a finite element modelling approach that can describe the biomechanical behaviour of adherent eukaryotic cells is presented. It fuses two previous modelling approaches by incorporating, in an idealised geometry, all cellular components considered structurally significant, i.e. prestressed cytoskeleton, cytoplasm, nucleus and membrane components. The aim is to determine if we can use this model to describe the non-linear structural behaviour of an adherent cell and to determine the contribution of the various cellular components to cellular stability. Results obtained by applying forces (in the picoNewton range) to the model membrane nodes suggest a key role for the cytoskeleton in determining cellular stiffness. The model captures non-linear structural behaviours such as strain hardening and prestress effects (in the region of receptor sites), and variable compliance along the cell surface. The role of the cytoskeleton in stiffening a cell during the process of cell spreading is investigated by applying forces to five increasingly spread cell geometries. Parameter studies reveal that material properties of the cytoplasm (elasticity and compressibility) also have a large influence on cellular stiffness. The computational model of a single cell developed here is proposed as one that is sufficiently complex to capture the non-linear behaviours of the cell response to forces whilst not being so complex that the parameters cannot be specified. The model could be very useful in computing cellular structural behaviour in response to various in vitro mechanical stimuli (e.g. fluid flow, substrate strain), or for use in algorithms that attempt to simulate mechanobiological processes.

A bio-chemo-mechanical model has been used to predict the contractile responses of smooth cells on a bed of micro-posts. Predictions obtained for smooth muscle cells reveal that, by converging onto a single set of parameters, the model captures all of the following responses in a self-consistent manner: (i) the scaling of the force exerted by the cells with the number of posts; (ii) actin distributions within the cells, including the rings of actin around the micro-posts; (iii) the curvature of the cell boundaries between the posts; and (iv) the higher post forces towards the cell periphery. Similar correspondences between predictions and measurements have been demonstrated for fibroblasts and mesenchymal stem cells once the maximum stress exerted by the stress fibre bundles has been recalibrated. Consistent with measurements, the model predicts that the forces exerted by the cells will increase with both increasing post stiffness and cell area (or equivalently, post spacing). In conjunction with previous assessments, these findings suggest that this framework represents an important step towards a complete model for the coupled bio-chemo-mechanical responses of cells.

The Holzapfel-Gasser-Ogden (HGO) model for anisotropic hyperelastic behaviour of collagen fibre reinforced materials was initially developed to describe the elastic properties of arterial tissue, but is now used extensively for modelling a variety of soft biological tissues. Such materials can be regarded as incompressible, and when the incompressibility condition is adopted the strain energy Ψ of the HGO model is a function of one isotropic and two anisotropic deformation invariants. A compressible form (HGO-C model) is widely used in finite element simulations whereby the isotropic part of Ψ is decoupled into volumetric and isochoric parts and the anisotropic part of Ψ is expressed in terms of isochoric invariants. Here, by using three simple deformations (pure dilatation, pure shear and uniaxial stretch), we demonstrate that the compressible HGO-C formulation does not correctly model compressible anisotropic material behaviour, because the anisotropic component of the model is insensitive to volumetric deformation due to the use of isochoric anisotropic invariants. In order to correctly model compressible anisotropic behaviour we present a modified anisotropic (MA) model, whereby the full anisotropic invariants are used, so that a volumetric anisotropic contribution is represented. The MA model correctly predicts an anisotropic response to hydrostatic tensile loading, whereby a sphere deforms into an ellipsoid. It also computes the correct anisotropic stress state for pure shear and uniaxial deformation. To look at more practical appli- cations, we developed a finite element user-defined material subroutine for the simulation of stent deployment in a slightly compressible artery. Significantly higher stress triaxiality and arterial compliance are computed when the full anisotropic invariants are used (MA model) instead of the isochoric form (HGO-C model).Keywords: Anisotropic, Hyperelastic, Incompressibility, Finite element, Artery, Stent Nomenclature I -identity tensor Ψ -Helmholtz free-energy (strain-energy) function Ψ vol -volumetric contribution to the free energy Ψ aniso -anisotropic contribution to the free energy Ψ iso -isotropic contribution to the isochoric free energy Ψ aniso -anisotropic contribution to the isochoric free energy σ -Cauchy stress σ -deviatoric Cauchy stress q -von Mises equivalent stress σ hyd -hydrostatic (pressure) stress F -deformation gradient J -determinant of the deformation gradient; local ratio of volume change C -right Cauchy-Green tensor I 1 -first invariant of C I 4,6 -anisotropic invariants describing the deformation of reinforcing fibres F -isochoric portion of the deformation gradient C -isochoric portion of the right Cauchy-Green deformation tensor I 1 -first invariant of C I 4,6 -isochoric anisotropic invariants a 0i , i = 4, 6 -unit vector aligned with a reinforcing fibre in the reference configuration a i , i = 4, 6 -updated (deformed) fibre direction (= Fa 0i ) κ 0 -isotropic bulk modulus µ 0 -isotropic shear modulus k i , i = 1, 2 -anisotropic material co...

No abstract