Electric and magnetic fields from two-dimensional anisotropic bisyncytia

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue

Numerical solution for optimal control of the reaction-diffusion equations in cardiac electrophysiology

Bidomain model, Reaction-diffusion equations, Ionic model, Optimal control with PDE constraints, Existence and uniqueness, FEM, Rosenbrock type methods, NCG method,