Numerical modeling of the cardiac tissue via an isogeometric collocation approach
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In-vitro replicas of the human heart recapitulating several relevant features are becoming an alternative to more classical animal models [1]. However, their diffusion is limited by the high cost of the assay design, since it mainly relies on a trial-and-error approach. To provide a numerical tool for design such a kind of electro-mecanical devices constituted by cardiac tissue, we develop an isogeometric approach based on a collocation method. In particular, a solver for the Monodomain equation is proposed [2] and extended to the immersed framework [3] to simplify the geometrical modeling. Finally, coupled electro-mechanics is addressed as well [4]. Numerical tests illustrate the main aspects of the proposed approach. [1] MacQueen, Luke A., et al. A tissue-engineered scale model of the heart ventricle. Nature biomedical engineering, 2.12: 930-941, 2018. [2] Torre, Michele, et al. "An efficient isogeometric collocation approach to cardiac electrophysiology." Computer Methods in Applied Mechanics and Engineering 393 (2022): 114782. [3] Torre, Michele, et al. "Immersed isogeometric analysis based on a hybrid collocation/finite cell method." Computer Methods in Applied Mechanics and Engineering 405 (2023): 115856. [4] Torre, Michele, et al. "Isogeometric mixed collocation of nearly-incompressible electromechanics in finite deformations for cardiac muscle simulations." Computer Methods in Applied Mechanics and Engineering 411 (2023): 116055.