Computational cardiology: A modified Hill model to describe the electro-visco-elasticity of the myocardium

Cansız, Barış; Dal, Hüsnü; Kaliske, Michael

doi:10.1016/j.cma.2016.10.009

Cited by 25 publications

(26 citation statements)

References 56 publications

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“…This section is devoted to a brief introduction of the fundamental variables and kinematics describing the electro‐visco‐elastic nature of the cardiac tissue and the coupled field equations governing the deformation and electrophysiology of the myocardium in a bidomain setting. For a detailed discussion, the reader is referred to the recent studies …”

Section: Electromechanical Coupling In Myocardial Tissuementioning

confidence: 99%

“…All the evolution equations are integrated through an implicit Euler scheme. We refer to Cansız et al . for a wide review on the constitutive equations, the evolution equations and their update algorithms.…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…The overall goal of this manuscript is to demonstrate the applicability of our recent numerical developments in terms of finite element analyses of personalized heart models. For this purpose, we focus on two different examples, which are thought to be clinically relevant and interesting.…”

Section: Introductionmentioning

confidence: 99%

“…In the presented simulations, a fully implicit staggered solution scheme in both a monodomain and a bidomain setting is utilized for the strong excitation‐contraction coupling in the myocardial tissue. Unlike most of the existing constitutive models for the contracting myocardial tissue, which disregard the viscous effects, we employ the modified Hill model that enables to incorporate the viscous characteristics of the active myocardium. We have recently tested this constitutive law through various numerical examples and reported that viscosity significantly alters the electromechanical state of the myocardium and should be considered in computer simulations of the heart .…”

Section: Introductionmentioning

confidence: 99%

“…Unlike most of the existing constitutive models for the contracting myocardial tissue, which disregard the viscous effects, we employ the modified Hill model that enables to incorporate the viscous characteristics of the active myocardium. We have recently tested this constitutive law through various numerical examples and reported that viscosity significantly alters the electromechanical state of the myocardium and should be considered in computer simulations of the heart . The electrophysiological characteristics of the myocardium are described by the well‐known phenomenological model of Aliev and Panfilov consisting of two coupled ordinary differential equations (ODEs).…”

Section: Introductionmentioning

confidence: 99%

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Towards predictive computer simulations in cardiology: Finite element analysis of personalized heart models

et al. 2018

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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

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Section: Electromechanical Coupling In Myocardial Tissuementioning

confidence: 99%

Section: Constitutive Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Towards predictive computer simulations in cardiology: Finite element analysis of personalized heart models

et al. 2018

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Fast and reliable reduced‐order models for cardiac electrophysiology

Chellappa,

Cansız,

Feng

et al. 2023

GAMM-Mitteilungen

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Mathematical models of the human heart increasingly play a vital role in understanding the working mechanisms of the heart, both under healthy functioning and during disease. The ultimate aim is to aid medical practitioners diagnose and treat the many ailments affecting the heart. Towards this, modeling cardiac electrophysiology is crucial as the heart's electrical activity underlies the contraction mechanism and the resulting pumping action. Apart from modeling attempts, the pursuit of efficient, reliable, and fast solution algorithms has been of great importance in this context. The governing equations and the constitutive laws describing the electrical activity in the heart are coupled, nonlinear, and involve a fast moving wave front, which is generally solved by the finite element method. The numerical treatment of this complex system as part of a virtual heart model is challenging due to the necessity of fine spatial and temporal resolution of the domain. Therefore, efficient surrogate models are needed to predict the electrical activity in the heart under varying parameters and inputs much faster than the finely resolved models. In this work, we develop an adaptive, projection‐based reduced‐order surrogate model for cardiac electrophysiology. We introduce an a posteriori error estimator that can accurately and efficiently quantify the accuracy of the surrogate model. Using the error estimator, we systematically update our surrogate model through a greedy search of the parameter space. Furthermore, using the error estimator, the parameter search space is dynamically updated such that the most relevant samples get chosen at every iteration. The proposed adaptive surrogate model is tested on three benchmark models to illustrate its efficiency, accuracy, and ability of generalization.

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Finite element modeling of electro‐viscoelasticity in fiber reinforced electro‐active polymers

Kanan

Kaliske

2021

Numerical Meth Engineering

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In this work, aspects considering material modeling of electro-mechanical coupling in fiber reinforced electro-active polymers (EAP) and the corresponding finite element implementation are considered. We propose a constitutive model that takes into account the electro-viscoelastic behavior of the isotropic matrix and the influence of unidirectional fibers on both the hyperelastic response and the viscous behavior of the whole composite. Two distinct existing models that describe the electro-mechanical coupling, are demonstrated and implemented, moreover, a numerical link between both models for three-dimensional continua in terms of tensor calculus, is identified. We propose the extended-tube model for the elastic response with some of its parameters evolving in response to the electric field, in order to fit electro-viscoelastic experiments. Regarding the finite element implementation, in addition to the deformation field and the electric potential, two pairs of field variables are introduced on the element level, to enforce quasi-incompressibility and quasi-inextensibility. It is shown that using the mixed finite element improves the convergence behavior for the simulation of soft EAP with relatively stiff fibers. Moreover, the choice of the model that expresses the nature of the underlying coupling is shown to noticeably affect the degree of simulated actuation in fiber reinforced actuators.

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Computational cardiology: A modified Hill model to describe the electro-visco-elasticity of the myocardium

Cited by 25 publications

References 56 publications

Towards predictive computer simulations in cardiology: Finite element analysis of personalized heart models

Towards predictive computer simulations in cardiology: Finite element analysis of personalized heart models

Fast and reliable reduced‐order models for cardiac electrophysiology

Finite element modeling of electro‐viscoelasticity in fiber reinforced electro‐active polymers

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