Rodrigo Weber dos Santos

PubMed2005

Interpreting biomagnetic fields of planar wave fronts in cardiac muscle.

The recent results of Holzer and co-workers reveal the existence of net currents that flow along the front of a planar wave propagating through cardiac tissue. This is an important contribution toward the better understanding of the physics of biomagnetic fields. However, although the authors claim their results reveal particular bidomain properties, we show in this short letter that the results allow multiple interpretations. For instance, cardiac anisotropy by itself may also explain the existence of a net current along the wave front. Based on our calculations, we suggest additional experiments that would allow distinguishing between these two explanations and thus provide further evidence on the basic physics behind cardiac biomagnetism.

Animals↗

PubMed2004

Parallel multigrid preconditioner for the cardiac bidomain model.

The bidomain equations are widely used for the simulation of electrical activity in cardiac tissue but are computationally expensive, limiting the size of the problem which can be modeled. The purpose of this study is to determine more efficient ways to solve the elliptic portion of the bidomain equations, the most computationally expensive part of the computation. Specifically, we assessed the performance of a parallel multigrid (MG) preconditioner for a conjugate gradient solver. We employed an operator splitting technique, dividing the computation in a parabolic equation, an elliptical equation, and a nonlinear system of ordinary differential equations at each time step. The elliptic equation was solved by the preconditioned conjugate gradient method, and the traditional block incomplete LU parallel preconditioner (ILU) was compared to MG. Execution time was minimized for each preconditioner by adjusting the fill-in factor for ILU, and by choosing the optimal number of levels for MG. The parallel implementation was based on the PETSc library and we report results for up to 16 nodes on a distributed cluster, for two and three dimensional simulations. A direct solver was also available to compare results for single processor runs. MG was found to solve the system in one third of the time required by ILU but required about 40% more memory. Thus, MG offered an attractive tradeoff between memory usage and speed, since its performance lay between those of the classic iterative methods (slow and low memory consumption) and direct methods (fast and high memory consumption). Results suggest the MG preconditioner is well suited for quickly and accurately solving the bidomain equations.

Algorithms↗