Millions of degrees of freedom are often required to accurately represent the electrophysiology of the myocardium due to the presence of discretization effects. This study seeks to explore the influence of temporal and spatial discretization on the simulation of cardiac electrophysiology in conjunction with changes in modeling choices. Several finite element analyses are performed to examine how discretization affects solution time, conduction velocity and electrical excitation. Discretization effects are considered along with changes in the electrophysiology model and solution approach. Two action potential models are considered: the Aliev‐Panfilov model and the ten Tusscher‐Noble‐Noble‐Panfilov model. The solution approaches consist of two time integration schemes and different treatments for solving the local system of ordinary differential equations. The efficiency and stability of the calculation approaches are demonstrated to be dependent on the action potential model. The dependency of the conduction velocity on the element size and time step is shown to be different for changes in material parameters. Finally, the discrepancies between the wave propagation in coarse and fine meshes are analyzed based on the temporal evolution of the transmembrane potential at a node and its neighboring Gauss points. Insight obtained from this study can be used to suggest new methods to improve the efficiency of simulations in cardiac electrophysiology.
The goal of this manuscript is to demonstrate the feasibility of our recent numerical developments towards predictive computer simulations in cardiology. In contrast to existing weakly coupled and strongly coupled monolithic approaches in the literature, we utilize a fully implicit staggered solution scheme that enables to study the strong excitation-contraction coupling of the heart tissue in the monodomain and the bidomain setting through finite element simulations. On the constitutive level, we employ the recently proposed modified Hill model (CMAME 315; 434-466, 2017) that treats the myocardium as an electro-visco-active material. All the time integrations are evaluated via an implicit backward Euler scheme that ensures unconditional stability. The performance of the framework is demonstrated by means of two clinically relevant and interesting examples. Firstly, basic deformation characteristics of a personalized left ventricle model such as rotation, twist and longitudinal shortening are simulated along with a physiological pressure-volume relation. In addition, the results of the viscoelastic and elastic solutions are compared. In the second example, we simulate a continuously beating virtual biventricle model having dyssynchrony and imitate two different cardiac resynchronization therapy attempts in order to improve the cardiac output. The corresponding electrocardiograms and left ventricle volume-time relations are recorded during the simulation and compared to the healthy case. K E Y W O R D S cardiac resynchronization therapy, finite element analysis, heart electromechanics, left ventricular twist, personalized heart models
This paper presents a seminumerical homogenization framework for porous hyperelastic materials that is open for any hyperelastic microresponse. The conventional analytical homogenization schemes do apply to a limited number of elementary hyperelastic constitutive models. Within this context, we propose a general numerical scheme based on the homogenization of a spherical cavity in an incompressible unit hyperelastic solid sphere, which is denoted as the mesoscopic representative volume element (mRVE). The approach is applicable to any hyperelastic micromechanical response. The deformation field in the sphere is approximated via nonaffine kinematics proposed by Hou and Abeyaratne (JMPS 40:571-592,1992). Symmetric displacement boundary conditions driven by the principal stretches of the deformation gradient are applied on the outer boundary of the mRVE. The macroscopic quantities, eg, stress and moduli expressions, are obtained by analytically derived pointwise geometric transformations. The macroscopic expressions are then computed numerically through quadrature rules applied in the radial and surface directions of the sphere. A three-scale compressible microsphere model is derived from the developed seminumerical homogenization framework where the micro-meso transition is based on the nonaffine microsphere model at every point of the mRVE. The numerical scheme developed for the derivation of macroscopic homogenized stresses and moduli terms as well as the modeling capability of the three-scale microsphere model is investigated through representative boundary value problems. KEYWORDS compressible hyperelasticity, homogenization methods, microsphere model, rubberlike materials INTRODUCTIONPorous polymeric materials exhibiting compressible hyperelastic behavior are common in engineering practice due to their properties, such as higher energy absorption and noise reduction. Despite the abundance of conventional hyperelastic constitutive models treating rubberlike materials incompressible, we lack a rigorous yet relatively simple treatment of this class of materials. The compressible mechanical response of porous elastomers results from preexisting voids introduced deliberately or unintentionally during the production process. The mechanical behavior of porous elastomers is intrinsically related to cavitation, which is attributed to the sudden growth of these preexisting voids under high triaxial stresses. The study of cavitation is particularly interesting since the initiation, growth, and coalescence of voids lead to 412
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