A three field bi domain based approach to the strongly coupled electromechanics of the heart

Date

2011-04-21

Author

Dal, Hüsnü
Göktepe, Serdar

Metadata

Show full item record

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

Item Usage Stats

105
views

0
downloads

We propose a novel, unconditionally stable and fully coupled finite element method for the bidomain based approach to cardiac electromechanics. To this end, the transmembrane potential, the extracellular potential, and the displacement field are treated as independent variables such that the already coupled electrophysiology problem in the bidomain setting is further extended to the electromechanical coupling. In this multifield problem, the intrinsic coupling arises from both excitation‐induced contraction of cardiac cells and the deformation‐induced generation of intra‐cellular currents. The respective bidomain reaction‐diffusion and the momentum balance equations are recast into the corresponding weak forms through a conventional isoparametric Galerkin approach. The resultant set of non‐linear residual equations is consistently linearized. The monolithic scheme is employed to avoid stability issues that may arise due to the strong coupling between excitation and deformation. The performance of the put forward framework is further assessed through three‐dimensional representative electromechanical initial‐boundary value problems.

URI

https://hdl.handle.net/11511/41325

DOI

https://doi.org/10.1002/pamm.201110442

Collections

Department of Mechanical Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

A fully implicit finite element method for bidomain models of cardiac electromechanics Dal, Hüsnü; Göktepe, Serdar (Elsevier BV, 2013-01-01) We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced gen...
A fully implicit finite element method for bidomain models of cardiac electrophysiology Dal, Hüsnü; Göktepe, Serdar (Informa UK Limited, 2012-01-01) This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential phi(i) - phi(e) and the extracellular potential phi(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method result...
An Efficient Formula Synthesis Method with Past Signal Temporal Logic Ergurtuna, Mert; Aydın Göl, Ebru (2019-01-01) In this work, we propose a novel method to find temporal properties that lead to the unexpected behaviors from labeled dataset. We express these properties in past time Signal Temporal Logic (ptSTL). First, we present a novel approach for finding parameters of a template ptSTL formula, which extends the results on monotonicity based parameter synthesis. The proposed method optimizes a given monotone criteria while bounding an error. Then, we employ the parameter synthesis method in an iterative unguided for...
A DRBEM Approach for the STOKES Eigenvalue Problem Tezer, Münevver; Türk, Önder (2016-07-04) In this study, we propose a novel approach based on the dual reciprocity boundary element method (DRBEM) to approximate the solutions of various Steklov eigenvalue problems. The method consists in weighting the governing differential equation with the fundamental solutions of the Laplace equation where the definition of interior nodes is not necessary for the solution on the boundary. DRBEM constitutes a promising tool to characterize such problems due to the fact that the boundary conditions on part or all...
A projection based variational multiscale method for a fluid–fluid interaction problem Ağgül, Mustafa ; Eroğlu, Fatma Güler ; Kaya Merdan, Songül; Labovsky, Alexer E. (Elsevier BV, 2020-06-15) The proposed method aims to approximate a solution of a fluid–fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the atmosphere–ocean coupling. Thus, the proposed method should be viewed as potentially applicable to air–sea coupled flows in turbulent regime. The method consists of two key ingredients. The geometric averaging approach is used for efficient and stable decoupling of the pr...

Citation Formats

H. Dal and S. Göktepe, “A three field bi domain based approach to the strongly coupled electromechanics of the heart,” 2011, vol. 11, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/41325.