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- W28346241 abstract "Computer simulation is an important tool for investigating the propagation behaviour of electrical excitation in cardiac tissue. When ionic models of cell membrane excitation are combined with the bidomain model of macroscopic tissue properties, numerical solution of the resulting partial differential equations requires a substantial amount of computation. Thus more efficient numerical methods are needed.One aspect of the computational complexity of this problem is the need for detailed spatial and temporal resolution while the depolarizing front of excitation propagates through the domain. During the subsequent, and more protracted, repolarization phase, the solution changes more slowly and a much coarser discretization would be adequate. Previous approaches have incorporated explicit integration methods whose stability limitations have prevented exploitation of this change in time scales.This study applies a stable implicit integration method which allows the time-step to be controlled, without concern for stability, to obtain a solution of desired accuracy. Using an approximate Newton method to solve the resulting nonlinear algebraic equations, the computational problem is reduced to one of solving a sequence of nonsymmetric linear systems. In a central result, each nonsymmetric matrix is reduced in linear time to a smaller, symmetric positive-definite matrix by a block-LU factorization. The resulting linear systems are solved by preconditioned conjugate gradient-type methods. This approach also applies to equations arising from the simpler monodomain model of cardiac tissue.Performance comparisons with other methods indicate that this method is competitive for simulations of depolarization, while in simulations of repolarization it can significantly reduce the computational cost. To demonstrate the utility of this approach, some example problems of electrophysiological relevance are addressed.In other studies, the bidomain equations have been manipulated in various ways before discretization for numerical solution. This study also presents a class of linear algebraic transformations that unifies these approaches and allows some comparative analysis. The transformational framework gives insight into the implications of various manipulations on the numerical methods subsequently used to solve the equations." @default.
- W28346241 created "2016-06-24" @default.
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- W28346241 date "1992-01-01" @default.
- W28346241 modified "2023-09-24" @default.
- W28346241 title "Efficient simulation of action potential propagation in a bidomain" @default.
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