Cardiac myocytes are the fundamental cells composing the heart muscle. The propagation of electric signals and chemical quantities through them is responsible for their nonlinear contraction and dilatation. In this study, a theoretical model and a finite element formulation are proposed for the simulation of adhesive contact interactions between myocytes across the so-called gap junctions. A multi-field interface constitutive law is proposed for their description, integrating the adhesive and contact mechanical response with their electrophysiological behavior. From the computational point of view, the initial and boundary value problem is formulated as a structure-structure interaction problem, which leads to a straightforward implementation amenable for parallel computations. Numerical tests are conducted on different couples of myocytes, characterized by different shapes related to their stages of growth, capturing the experimental response. The proposed framework is expected to have impact on the understanding how imperfect mechano-transduction could lead to emergent pathological responses.is still unchallenged due to the high computational and modeling complexities, relevant contributions regard finite element procedures for the theoretical description of single cell contractility responses under different environmental stimuli [26,27,28,29,30] or whole reconstructed heart geometries for selected pathological states [31]. In order to incorporate dominant mechanisms occurring at different scales within a constitutive framework for the cardiac tissue, microstructural properties have to be properly described, including mechano-regulated interactions occurring among tissue constituents. Though our modeling refers to the cell micro-scale, we assume a continuum approach [30]. Experimental evidences on single cell contractility showed that forces are induced where no visible stress fibers are present, thus implying that a much finer scale is responsible for the observed phenomena and therefore continuum level considerations can be adopted [27,32,33,34].Structural and physical properties of contact myocytes, in particular, will be the main object of this study. Intercellular communication between excitable contractile cells concentrates at the intercaleted discs and concerns with microscopic electrical conductance, metabolic and mechanical coupling [35]. A schematic representation of two-dimensional cardiomyocytes contact problems is provided in Fig. 1(a). The interface constitutive model concerns (i) voltage-dependent GJs ruling the electrical conductance for membrane voltage propagation, and (ii) adhesive and contact membrane interfaces dictating mechanical stress localization across adjacent cells. In addition, localized focal adhesions are described via appropriate boundary conditions. The problem at hand deserves an accurate cellular mechanical description in which structural heterogeneities, appropriate constitutive relations, and active dynamics are the three key factors to be formalized within a generalized ...

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Introduction -Distant spreading of primary lesions is modulated by the vascular dynamics of circulating tumor cells (CTCs) and their ability to establish metastatic niches. While the mechanisms regulating CTC homing in specific tissues are yet to be elucidated, it is well documented that CTCs possess different size, biological properties and deformability.Methods -A computational model is presented to predict the vascular transport and adhesion of CTCs in whole blood. A Lattice-Boltzmann method, which is employed to solve the Navier-Stokes equation for the plasma flow, is coupled with an Immersed Boundary Method. Results -The vascular dynamics of a CTC is assessed in large and small microcapillaries. The CTC shear modulus k ctc is varied returning CTCs that are stiffer, softer and equally deformable as compared to RBCs. In large microcapillaries, soft CTCs behave similarly to RBCs and move away from the vessel walls; whereas rigid CTCs are pushed laterally by the fast moving RBCs and interact with the vessel walls. Three adhesion behaviors are observed -firm adhesion, rolling and crawling over the vessel walls -depending on the CTC stiffness. On the contrary, in small microcapillaries, rigid CTCs are pushed downstream by a compact train of RBCs and cannot establish any firm interaction with the vessel walls; whereas soft CTCs are squeezed between the vessel wall and the RBC train and rapidly establish firm adhesion. Concluisons -These findings document the relevance of cell deformability in CTC vascular adhesion and provide insights on the mechanisms regulating metastasis formation in different vascular districts. arXiv:1907.09284v1 [cond-mat.soft]

We present a partitioned algorithm aimed at extending the capabilities of existing solvers for the simulation of coupled advection-di↵usion-reaction systems and incompressible, viscous flow. The space discretization of the governing equations is based on mixed finite element methods defined on unstructured meshes, whereas the time integration hinges on an operator splitting strategy that exploits the di↵er-ences in scales between the reaction, advection, and di↵usion processes, considering the global system as a number of sequentially linked sets of partial di↵erential, and algebraic equations. The flow solver presents the advantage that all unknowns in the system (here vorticity, velocity, and pressure) can be fully decoupled and thus turn the overall scheme very attractive from the computational perspective. The robustness of the proposed method is illustrated with a series of numerical tests in 2D and 3D, relevant in the modelling of bacterial bioconvection and Boussinesq systems.

This paper focuses on the relation between Gibbs and Markov random fields, one instance of the close relation between abstract and applied mathematics so often stressed by Lucio Russo in his scientific work. We start by proving a more explicit version, based on spin products, of the Hammersley-Clifford theorem, a classic result which identifies Gibbs and Markov fields under finite energy. Then we argue that the celebrated counterexample of Moussouris, intended to show that there is no complete coincidence between Markov and Gibbs random fields in the presence of hard-core constraints, is not really such. In fact, the notion of a constrained Gibbs random field used in the example and in the subsequent literature makes the unnatural assumption that the constraints are infinite energy Gibbs interactions on the same graph. Here we consider the more natural extended version of the equivalence problem, in which constraints are more generally based on a possibly larger graph, and solve it. The bearing of the more natural approach is shown by considering identifiability of discrete random fields from support, conditional independencies and corresponding moments. In fact, by means of our previous results, we show identifiability for a large class of problems, and also examples with no identifiability. Various open questions surface along the way. Personal acknowledgment. One of us (Gandolfi) learned about the theory of Gibbs and Markov random fields from Lucio Russo in a course based on [Ruelle 1978]. He is indebted to Lucio for his inspirational lectures and for many other things, such as an interest in percolation theory and statistical physics, a deep conviction of the close relation between abstract and applied mathematics, and an involvement in questions about the history of science. This paper focuses on one instance of this close association between abstract and applied mathematics, namely the relation between Gibbs and Markov random fields; in spite of the great number of studies and applications of these models, this relationship has not been appropriately investigated in the literature.