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Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements.

Cuccuru G, Fotia G, Maggio F, Southern J - Biomed Res Int (2015)

Bottom Line: High order approximation of spectral elements provides greater flexibility in resolving multiple length scales.We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases.We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

View Article: PubMed Central - PubMed

Affiliation: CRS4, Loc. Pixina Manna, Edificio 1, 09010 Pula, Italy.

ABSTRACT
We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

No MeSH data available.


Full scale complete human heart mesh derived from CT images. Panels (a) and (b) show two enlarged views of the high-resolution unstructured all-hexahedral mesh used to solve the monodomain equations.
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fig12: Full scale complete human heart mesh derived from CT images. Panels (a) and (b) show two enlarged views of the high-resolution unstructured all-hexahedral mesh used to solve the monodomain equations.

Mentions: Using the pipeline outlined above we are currently able to generate whole human heart meshes with very fine average edge length equal to 0.018 cm (35,021,521 nodes and 34,269,632 elements). Due to hardware constraints the version of the mesh used in the simulation study presented below has an average edge length of 0.036 cm and consists of 4,471,781 nodes and 4,283,704 elements. Figure 12 shows some detailed views of the all-hexahedral mesh we used in our simulations. In the present benchmark the cellular membrane dynamics were defined by the phase-I Luo-Rudy cell model [24], although any other ionic model could have been used. Spatial variation in fibre direction is not accounted for and homogenous membrane properties are assumed throughout all volume. The isotropic baseline conductivities were σi = diag(0.175,0.175,0.175) S/m and σe = diag(0.7,0.7,0.7) S/m, where diag(x, y, z) is a 3 × 3 diagonal matrix with values x, y, z along the diagonal. Other parameters were χ = 1400 cm−1 and C = 1.0 μF/cm2. A stimulus of magnitude 4.0 × 103 μA/cm2 and duration of 2.0 ms was applied to surface nodes within the apical region of the mesh (z < 5.0 cm) which elicited the propagation of a quasi-planar wavefront in approximately an apicobasal direction.


Simulating Cardiac Electrophysiology Using Unstructured All-Hexahedra Spectral Elements.

Cuccuru G, Fotia G, Maggio F, Southern J - Biomed Res Int (2015)

Full scale complete human heart mesh derived from CT images. Panels (a) and (b) show two enlarged views of the high-resolution unstructured all-hexahedral mesh used to solve the monodomain equations.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4637157&req=5

fig12: Full scale complete human heart mesh derived from CT images. Panels (a) and (b) show two enlarged views of the high-resolution unstructured all-hexahedral mesh used to solve the monodomain equations.
Mentions: Using the pipeline outlined above we are currently able to generate whole human heart meshes with very fine average edge length equal to 0.018 cm (35,021,521 nodes and 34,269,632 elements). Due to hardware constraints the version of the mesh used in the simulation study presented below has an average edge length of 0.036 cm and consists of 4,471,781 nodes and 4,283,704 elements. Figure 12 shows some detailed views of the all-hexahedral mesh we used in our simulations. In the present benchmark the cellular membrane dynamics were defined by the phase-I Luo-Rudy cell model [24], although any other ionic model could have been used. Spatial variation in fibre direction is not accounted for and homogenous membrane properties are assumed throughout all volume. The isotropic baseline conductivities were σi = diag(0.175,0.175,0.175) S/m and σe = diag(0.7,0.7,0.7) S/m, where diag(x, y, z) is a 3 × 3 diagonal matrix with values x, y, z along the diagonal. Other parameters were χ = 1400 cm−1 and C = 1.0 μF/cm2. A stimulus of magnitude 4.0 × 103 μA/cm2 and duration of 2.0 ms was applied to surface nodes within the apical region of the mesh (z < 5.0 cm) which elicited the propagation of a quasi-planar wavefront in approximately an apicobasal direction.

Bottom Line: High order approximation of spectral elements provides greater flexibility in resolving multiple length scales.We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases.We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

View Article: PubMed Central - PubMed

Affiliation: CRS4, Loc. Pixina Manna, Edificio 1, 09010 Pula, Italy.

ABSTRACT
We discuss the application of the spectral element method to the monodomain and bidomain equations describing propagation of cardiac action potential. Models of cardiac electrophysiology consist of a system of partial differential equations coupled with a system of ordinary differential equations representing cell membrane dynamics. The solution of these equations requires solving multiple length scales due to the ratio of advection to diffusion that varies among the different equations. High order approximation of spectral elements provides greater flexibility in resolving multiple length scales. Furthermore, spectral elements are extremely efficient to model propagation phenomena on complex shapes using fewer degrees of freedom than its finite element equivalent (for the same level of accuracy). We illustrate a fully unstructured all-hexahedra approach implementation of the method and we apply it to the solution of full 3D monodomain and bidomain test cases. We discuss some key elements of the proposed approach on some selected benchmarks and on an anatomically based whole heart human computational model.

No MeSH data available.