A 2D Electromechanical Model of Human Atrial Tissue Using the Discrete Element Method

Abstract

Cardiac tissue is a syncytium of coupled cells with pronounced intrinsic discrete nature. Previous models of cardiac electromechanics often ignore such discrete properties and treat cardiac tissue as a continuous medium, which has fundamental limitations. In the present study, we introduce a 2D electromechanical model for human atrial tissue based on the discrete element method (DEM). In the model, single-cell dynamics are governed by strongly coupling the electrophysiological model of Courtemanche et al. to the myofilament model of Rice et al. with two-way feedbacks. Each cell is treated as a viscoelastic body, which is physically represented by a clump of nine particles. Cell aggregations are arranged so that the anisotropic nature of cardiac tissue due to fibre orientations can be modelled. Each cell is electrically coupled to neighbouring cells, allowing excitation waves to propagate through the tissue. Cell-to-cell mechanical interactions are modelled using a linear contact bond model in DEM. By coupling cardiac electrophysiology with mechanics via the intracellular Ca2+ concentration, the DEM model successfully simulates the conduction of cardiac electrical waves and the tissue's corresponding mechanical contractions. The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

Structural modelling of the cardiovascular system

“…There are a few exceptions to the rule such as venous valves (Nasar 2016 ) and atrial tissue (Brocklehurst et al. 2015 ) where simple discrete models have been implemented. In addition, coarse-graining of DEM models has allowed a larger number of structures to be represented in a single simulation.…”

“…Simulation results were able to capture local effects caused by varying cell alignment within the tissue (Brocklehurst et al. 2015 ) …”

“…However, a recent study has modelled human atrial tissue using a discrete element model integrated into an electro-mechanical method citing the limitations of modelling the tissue as a continuous medium and therefore neglecting cell arrangement (Brocklehurst et al. 2015 ). By clumping particles together to represent a cell as shown in Fig.…”

Electro-mechanical dynamics of spiral waves in a discrete 2D model of human atrial tissue

“…(b) The contact plane between two particles, with a spring and dashpot in the normal and shear directions. k n and k s are the normal and shear spring stiffnesses, β n and β s are the dashpot normal and shear critical damping ratios, and T F and S F are the tensile and shear strengths of the contact under force [22]. (c) Demonstration of how clumps are bonded to their neighbours, creating a tight spatial distribution of particles representing atrial fiber tissue.…”

Depth Attenuation Degree Based Visualization for Cardiac Ischemic Electrophysiological Feature Exploration

“…Keller et al [6] established a heterogeneous electrophysiological and three-dimensional anatomical model of human atria to explore atrial functional mechanism. Brocklehurst et al [7] implied the discrete element method (DEM) to investigate the electromechanical mechanism for human atrial tissue. Then, mechanical contractions of cardiac tissues and their corresponding electrical waves' conduction were successfully simulated.…”