Solvers for the Cardiac Bidomain Equations
By Edward J. Vigmond, R. D. Santos, Anton J. Prassl, Makarand Deo, Gernot Plank. Progress in Biophysics and Molecular Biology, 2007
355 citations recorded by the source corpus.
The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue. They are especially important for accurately modelling extracellular stimulation, as evidenced by their prediction of virtual electrode polarization before experimental verification. However, solution of the equations is computationally expensive due to the fine spatial and temporal discretization needed. This limits the size and duration of the problem which can be modeled. Regardless of the specific form into which they are cast, the computational bottleneck becomes the repeated solution of a large, linear system. The purpose of this review is to give an overview of the equations, and the methods by which they have been solved. Of particular note are recent developments in multigrid methods, which have proven to be the most efficient.
Subfields: Cardiology and Cardiovascular Medicine, Radiology, Nuclear Medicine and Imaging
View Paper: https://www.semanticscholar.org/paper/641a87b725237d77a823d9d0cf67594299152f80
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Citations in the corpus
- Evaluation of a Rapid Anisotropic Model for ECG Simulation (2017, methodology): “The current state of the art in forward simulation of the electrocardiogram (ECG) is to use a bidomain reaction-diffusion model to simulate propagating electrical activation and repolarization as well as the potential field in the torso (Vigmond et al., 2007).”
- Models of cardiac tissue electrophysiology: progress, challenges and open questions. (2011, methodology): “In parallel implementations the optimal number of levels of the multigrid approach depends on the number of processors and on the available memory (Vigmond et al., 2008).”
- Arrhythmia risk stratification of patients after myocardial infarction using personalized heart models (2016, methodology): “The software utilizes sophisticated solver techniques that have been optimized to ensure the high levels of accuracy, stability and efficiency in obtaining solutions on the large computational meshes necessary to model electrical behaviour in human hearts 46,47 .”