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Simulation of Cardiac Cell-Seeded Membranes Using the Edge-Based Smoothed FEM

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Shell and Membrane Theories in Mechanics and Biology

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 45))

Abstract

We present an electromechanically coupled Finite Element model for cardiac tissue. It bases on the mechanical model for cardiac tissue of Hunter et al. that we couple to the McAllister-Noble-Tsien electrophysiological model of purkinje fibre cells. The corresponding system of ordinary differential equations is implemented on the level of the constitutive equations in a geometrically and physically nonlinear version of the so-called edge-based smoothed FEM for plates. Mechanical material parameters are determined from our own pressure-deflection experimental setup. The main purpose of the model is to further examine the experimental results not only on mechanical but also on electrophysiological level down to ion channel gates. Moreover, we present first drug treatment simulations and validate the model with respect to the experiments.

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Notes

  1. 1.

    More exactly \(T\) is the tension in case that the muscle is at rest. Including a history of cross-bridge bindings one could establish an integral equation for the computation of \(T\).

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Acknowledgments

The first two authors have partially been financed by the project Cardiakytos and gratefully thank.

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Europe—Investment in our future

The project has been selected from the operational program for NRW in ‘Ziel 2 Regionale Wettbewerbsfähigkeit und Beschäftigung’ 2007–2013 which is co-financed by EFRE.

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Authors and Affiliations

  1. Laboratory of Engineering Mechanics and FEM, Aachen University of Applied Sciences, Goethestraße 1, 52064, Aachen, Germany

    Ralf Frotscher & Hans-Jürgen Raatschen

  2. Laboratory of Medical and Molecular Biology, Institute of Bioengineering, Aachen University of Applied Sciences, Heinrich-Mußmann-Straße 1, 52428, Jülich, Germany

    Matthias Goßmann & Ayşegül Temiz-Artmann

  3. Biomechanics Lab, Institute of Bioengineering, Aachen University of Applied Sciences, Heinrich-Mußmann-Straße 1, 52428, Jülich, Germany

    Ralf Frotscher & Manfred Staat

Authors
  1. Ralf Frotscher
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  2. Matthias Goßmann
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  3. Hans-Jürgen Raatschen
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  4. Ayşegül Temiz-Artmann
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  5. Manfred Staat
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Corresponding author

Correspondence to Manfred Staat .

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Editors and Affiliations

  1. Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany

    Holm Altenbach

  2. Department of Bio- and Nanomechanics, Belarusian State University, Minsk, Belarus

    Gennadi I. Mikhasev

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Frotscher, R., Goßmann, M., Raatschen, HJ., Temiz-Artmann, A., Staat, M. (2015). Simulation of Cardiac Cell-Seeded Membranes Using the Edge-Based Smoothed FEM. In: Altenbach, H., Mikhasev, G. (eds) Shell and Membrane Theories in Mechanics and Biology. Advanced Structured Materials, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-02535-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-02535-3_11

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-02535-3

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