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

Brocklehurst P, Adeniran I, Yang D, Sheng Y, Zhang H, Ye J - Biomed Res Int (2015)

Bottom Line: 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.The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

View Article: PubMed Central - PubMed

Affiliation: Engineering Department, Lancaster University, Lancaster LA1 4YR, UK.

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 Ca(2+) 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.

No MeSH data available.


Related in: MedlinePlus

Geometry of one clump/cell in the DEM model. Here, p1,…pn are the n particles, r is their radius, d is the distance between particle centres, L is the total length of the clump, and S is the area of the overlap region between particles.
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fig2: Geometry of one clump/cell in the DEM model. Here, p1,…pn are the n particles, r is their radius, d is the distance between particle centres, L is the total length of the clump, and S is the area of the overlap region between particles.

Mentions: Atrial cells have a roughly cylindrical shape, and our two-dimensional representation of a cell is a rectangle with initial length 100 μm and width 16 μm as used in the model of Courtemanche et al. [9]. The density of each particle is chosen as ρ = 1.053 g/mL, taken from values calculated in [35] for rat myocardial tissue regional densities. In our DEM model, n particles are arranged end to end as shown in Figure 2, using a radius of r = 8 μm. The number and amount of overlapping of the particles are chosen such that the length of the clump L = 100 μm. The amount of overlap is the same for each particle; hence, the equation for the length of the clump is(21)L=n−1d+2r,where d is the distance from the centre of one particle to the next. In this case we use n = 9, giving d = 10.5 μm when the cell is at rest. Using simple geometry, the total area A of the clump is given by(22)A=nπr2−n−1S,where the area S is(23)S=2r2arccosd2r−d24r2−d2.At every time step, the single-cell model of Section 2.1 outputs a sarcomere length for each cell. Since each cell consists of sarcomeres arranged end to end, we assume the total cell length is equal to a linear scaling of the sarcomere length. The area A is always held constant to satisfy the incompressibility condition of atrial tissue. Solving (21) and (22) simultaneously gives the two unknowns r and d, and the clump particle radii and positions are then modified to satisfy these new values. In this manner, the cell/clump may contract/expand in length while conserving 2D area.


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

Brocklehurst P, Adeniran I, Yang D, Sheng Y, Zhang H, Ye J - Biomed Res Int (2015)

Geometry of one clump/cell in the DEM model. Here, p1,…pn are the n particles, r is their radius, d is the distance between particle centres, L is the total length of the clump, and S is the area of the overlap region between particles.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4637066&req=5

fig2: Geometry of one clump/cell in the DEM model. Here, p1,…pn are the n particles, r is their radius, d is the distance between particle centres, L is the total length of the clump, and S is the area of the overlap region between particles.
Mentions: Atrial cells have a roughly cylindrical shape, and our two-dimensional representation of a cell is a rectangle with initial length 100 μm and width 16 μm as used in the model of Courtemanche et al. [9]. The density of each particle is chosen as ρ = 1.053 g/mL, taken from values calculated in [35] for rat myocardial tissue regional densities. In our DEM model, n particles are arranged end to end as shown in Figure 2, using a radius of r = 8 μm. The number and amount of overlapping of the particles are chosen such that the length of the clump L = 100 μm. The amount of overlap is the same for each particle; hence, the equation for the length of the clump is(21)L=n−1d+2r,where d is the distance from the centre of one particle to the next. In this case we use n = 9, giving d = 10.5 μm when the cell is at rest. Using simple geometry, the total area A of the clump is given by(22)A=nπr2−n−1S,where the area S is(23)S=2r2arccosd2r−d24r2−d2.At every time step, the single-cell model of Section 2.1 outputs a sarcomere length for each cell. Since each cell consists of sarcomeres arranged end to end, we assume the total cell length is equal to a linear scaling of the sarcomere length. The area A is always held constant to satisfy the incompressibility condition of atrial tissue. Solving (21) and (22) simultaneously gives the two unknowns r and d, and the clump particle radii and positions are then modified to satisfy these new values. In this manner, the cell/clump may contract/expand in length while conserving 2D area.

Bottom Line: 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.The developed DEM model is numerically stable and provides a powerful method for studying the electromechanical coupling problem in the heart.

View Article: PubMed Central - PubMed

Affiliation: Engineering Department, Lancaster University, Lancaster LA1 4YR, UK.

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 Ca(2+) 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.

No MeSH data available.


Related in: MedlinePlus