Adaptively Refined Gridsvs.Transmembrane Potentials
Transmembrane Potentialsvs.Extracellular Potentials
Transmembrane Potentialsvs.Extracellular Potentials
Adaptively Refined Gridsvs.Transmembrane Potentials |
Transmembrane Potentialsvs.Extracellular Potentials |
Transmembrane Potentialsvs.Extracellular Potentials |
| Remark:The bidomain model arises from modeling electrical wave propagation in the heart. It consists of a singularly perturbed reaction-diffusion system and a set of nonlinear stiff ordinary differential equations. The bidomain equations can be derived by a hogomenization process for the periodic microstructures of the cardiac tissue. Bidomain means that both intracellular and extracellular spaces co-exist in the heart. The electrical conductivity in the intracellular space is different from that in the extracellular space. Typically, the conductivities align with the fibers of the cardiac tissue. The conductivities in the longitudinal direction are much higher than those across the fibers. This is the so-called strong anisotropy of electrical conductivity. Since the fibers rotate from bottom to top in the heart, the anisotropy is thus usually called as rotational anisotropy. Rotational anisotropy of the electrical conductitives not only triggers complex patterns of electrical wave propagation in the heart, but also presents difficulties for efficient numerical simulations. In oder to resolve the fine details of electrical waves, high resolution grids and very small time steps must be used in the simulation. This results in a large-scale scientific computing problem. The adaptive mesh refinement (AMR) is suitable for solving the bidomain problems. It focuses the computational resources only on the regions where they are necessary. The sizes of time steps and grids are adaptively chosen in different part of the domain and different phase of the same area. For the cardiac problems, the AMR can gain tens of times speedup and tens of times memory savings on average, as reported recently by Cherry, Greenside and Henriquez for monodomain problems, which are the simplifed ones of the bidomain models. In the simulation presented above, the computational domain is the unit square [0, 1] X [0, 1]. The intracellular conductivity has an anisotropy ratio 10; and the extracellular conductivity has an anisotropy ratio 2. For the membrane dynamics, the Schaeffer's two-variable model is employed. The bidomain simulation with AMR in three dimensions (3D) has also been realized. The results will be presented soon once the 3D visualization problem is solved. |
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