Computational modeling of electrochemical coupling: A novel finite element approach towards ionic models for cardiac electrophysiology

Date

2011-01-01

Author

Wong, Jonathan
Göktepe, Serdar
Kuhl, Ellen

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

163
views

0
downloads

We propose a novel, efficient finite element solution technique to simulate the electrochemical response of excitable cardiac tissue. We apply a global-local split in which the membrane potential of the electrical problem is introduced globally as a nodal degree of freedom, while the state variables of the chemical problem are treated locally as internal variables on the integration point level. This particular discretization is efficient and highly modular since different cardiac cell models can be incorporated in a straightforward way through only minor local modifications on the constitutive level. Here, we derive the underlying algorithmic framework for a recently proposed ionic model for human ventricular cardiomyocytes, and demonstrate its integration into an existing nonlinear finite element infrastructure. To ensure unconditional algorithmic stability, we apply an implicit backward Euler scheme to discretize the evolution equations for both the electrical potential and the chemical state variables in time. To increase robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme and illustrate the consistent linearization of the weak form of the excitation problem. This particular solution strategy allows us to apply an adaptive time stepping scheme, which automatically generates small time steps during the rapid upstroke, and large time steps during the plateau, the repolarization, and the resting phases. We demonstrate that solving an entire cardiac cycle for a real patient-specific geometry characterized through a transmembrane potential, four ion concentrations, thirteen gating variables, and fifteen ionic currents requires computation times of less than ten minutes on a standard desktop computer.

Subject Keywords

Nonlinear reaction-diffusion systems, Finite element method, Adaptive time stepping, Electrophysiology, Electrochemistry, Computational biophysics

URI

https://hdl.handle.net/11511/48457

Journal

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

DOI

https://doi.org/10.1016/j.cma.2011.07.003

Collections

Department of Civil Engineering, Article

Suggestions

OpenMETU
Core

Computational modeling of electrocardiograms: A finite element approach toward cardiac excitation Kotikanyadanam, Mohan; Göktepe, Serdar; Kuhl, Ellen (Wiley, 2010-05-01) The objective of this work is the computational simulation of a patient-specific electrocardiogram (EKG) using a novel, robust, efficient, and modular finite element-based simulation tool for cardiac electrophysiology. We apply a two-variable approach in terms of a fast action potential and a slow recovery variable, whereby the latter phenomenologically summarizes the concentration of ionic currents. The underlying algorithm is based on a staggered solution scheme in which the action potential is introduced...
Computational modeling of growth: systemic and pulmonary hypertension in the heart Rausch, M. K.; Dam, A.; Göktepe, Serdar; Abilez, O. J.; Kuhl, E. (2011-12-01) We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. ...
Computational Modeling of the Effects of Viscous Dissipation on Polymer Melt Flow Behavior During Injection Molding Process in Plane Channels Tutar, M.; Karakuş, Ali (2013-02-01) The present finite volume method based fluid flow solutions investigate the boundary-layer flow and heat transfer characteristics of polymer melt flow in a rectangular plane channel in the presence of the effect of viscous dissipation and heat transfer by considering the viscosity and density variations in the flow. For different inflow velocity boundary conditions and the injection polymer melt temperatures, the viscous dissipation effects on the velocity and temperature distributions are studied extensive...
Computational modeling of passive myocardium Göktepe, Serdar; Wong, Jonathan; Kuhl, Ellen (Wiley, 2011-01-01) This work deals with the computational modeling of passive myocardial tissue within the framework ofmixed, non-linear finite element methods. We consider a recently proposed, convex, anisotropic hyperelastic model that accounts for the locally orthotropic micro-structure of cardiac muscle. A coordinate-free representation of anisotropy is incorporated through physically relevant invariants of the Cauchy-Green deformation tensors and structural tensors of the corresponding material symmetry group. This model...
Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach Wong, J.; Göktepe, Serdar; Kuhl, E. (Wiley, 2013-10-01) Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemic...

Citation Formats

J. Wong, S. Göktepe, and E. Kuhl, “Computational modeling of electrochemical coupling: A novel finite element approach towards ionic models for cardiac electrophysiology,” COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, pp. 3139–3158, 2011, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/48457.