Limits...
Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System.

Ying W, Henriquez CS - Biomed Res Int (2015)

Bottom Line: The equations governing the distribution of electric potential over the system are solved in time with the method of lines.At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones.The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Minhang, Shanghai 200240, China.

ABSTRACT
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

No MeSH data available.


Recursive advancing of three mesh refinement levels.
© Copyright Policy - open-access
Related In: Results  -  Collection


getmorefigures.php?uid=PMC4637156&req=5

fig3: Recursive advancing of three mesh refinement levels.

Mentions: Figure 3 illustrates the recursive advancing or integration of three different mesh refinement levels. Coarse levels are advanced/integrated before fine levels. Each level has its own timestep of different size: a coarser level has a larger timestep size and a finer level has a smaller timestep. The algorithm first advances level ℓ0 by Δt0 (indicated by “1”), next advances level ℓ1 by Δt1 = Δt0/2 (indicated by “2”), and then advances level ℓ2 by two steps with Δt2 = Δt1/2 (indicated by “3” and “4”). Upon the synchronization of levels ℓ1 and ℓ2, data on the fine level ℓ2 are upscaled to the coarser level ℓ1. The recursive integration continues with Steps “5,” “6,” “7,” and so forth.


Adaptive Mesh Refinement and Adaptive Time Integration for Electrical Wave Propagation on the Purkinje System.

Ying W, Henriquez CS - Biomed Res Int (2015)

Recursive advancing of three mesh refinement levels.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4637156&req=5

fig3: Recursive advancing of three mesh refinement levels.
Mentions: Figure 3 illustrates the recursive advancing or integration of three different mesh refinement levels. Coarse levels are advanced/integrated before fine levels. Each level has its own timestep of different size: a coarser level has a larger timestep size and a finer level has a smaller timestep. The algorithm first advances level ℓ0 by Δt0 (indicated by “1”), next advances level ℓ1 by Δt1 = Δt0/2 (indicated by “2”), and then advances level ℓ2 by two steps with Δt2 = Δt1/2 (indicated by “3” and “4”). Upon the synchronization of levels ℓ1 and ℓ2, data on the fine level ℓ2 are upscaled to the coarser level ℓ1. The recursive integration continues with Steps “5,” “6,” “7,” and so forth.

Bottom Line: The equations governing the distribution of electric potential over the system are solved in time with the method of lines.At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones.The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematics, MOE-LSC and Institute of Natural Sciences, Shanghai Jiao Tong University, Minhang, Shanghai 200240, China.

ABSTRACT
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.

No MeSH data available.