title: Mathematical modelling of active contraction in isolated cardiomyocytes.
abstract: We investigate the interaction of intracellular calcium spatio-temporal variations with the self-sustained contractions in cardiac myocytes. A consistent mathematical model is presented considering a hyperelastic description of the passive mechanical properties of the cell, combined with an active-strain framework to explain the active shortening of myocytes and its coupling with cytosolic and sarcoplasmic calcium dynamics. A finite element method based on a Taylor-Hood discretization is employed to approximate the nonlinear elasticity equations, whereas the calcium concentration and mechanical activation variables are discretized by piecewise linear finite elements. Several numerical tests illustrate the ability of the model in predicting key experimentally established characteristics including: (i) calcium propagation patterns and contractility, (ii) the influence of boundary conditions and cell shape on the onset of structural and active anisotropy and (iii) the high localized stress distributions at the focal adhesions. Besides, they also highlight the potential of the method in elucidating some important subcellular mechanisms affecting, e.g. cardiac repolarization.
authors.affiliation: CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland ricardo.ruiz@epfl.ch.
authors.forename: Ricardo
authors.initials: R
authors.lastname: Ruiz-Baier
authors.affiliation: Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, I-00128 Rome, Italy.
authors.forename: Alessio
authors.initials: A
authors.lastname: Gizzi
authors.affiliation: CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
authors.forename: Simone
authors.initials: S
authors.lastname: Rossi
authors.affiliation: Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, I-00128 Rome, Italy.
authors.forename: Christian
authors.initials: C
authors.lastname: Cherubini
authors.affiliation: CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.
authors.forename: Aymen
authors.initials: A
authors.lastname: Laadhari
authors.affiliation: Nonlinear Physics and Mathematical Modeling Laboratory, University Campus Bio-Medico of Rome, I-00128 Rome, Italy.
authors.forename: Simonetta
authors.initials: S
authors.lastname: Filippi
authors.affiliation: CMCS-MATHICSE-SB, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, SwitzerlandMOX - Politecnico de Milano, piazza Leonardo da Vinci 32, 20133 Milano, Italy.
authors.forename: Alfio
authors.initials: A
authors.lastname: Quarteroni
mesh_terms: D002118:Calcium / Q000502:physiology; D003198:Computer Simulation; D020342:Finite Element Analysis; D006321:Heart / Q000502:physiology*; D006801:Humans; D008955:Models, Cardiovascular; D009200:Myocardial Contraction / Q000502:physiology*; D032383:Myocytes, Cardiac / Q000166:cytology / Q000502:physiology*; D013816:Thermodynamics
chemical_list: D002118:Calcium
keywords: active-strain contraction; calcium propagation; cardiomyocyte modelling; coupled multiphysics; finite element formulation; nonlinear elasticity