Solving the Magnetocardiography Forward Problem in a Realistic Three-Dimensional Heart-Torso Model

The forward problem in magnetocardiography (MCG) is important for understanding the relationship between the electric activity of the heart and the body surface magnetic field (BSM), and providing insight into the clinical application of MCG. In this paper, we proposed a computational framework based on the finite element method (FEM) to solve the MCG forward problem. For the subject-specific heart-torso geometry established from the medical image, the modified FitzHugh-Nagumo (FHN) equation was used to describe the volumetric myocardial dynamic transmembrane potential (TMP), then the quasi-static Maxwell equations was applied to simulate the propagation of cardiac magnetic field produced by TMP. The two parts were validated on the simplified one-dimensional FHN equation and the source model of the straight wire respectively, in which the analytical solutions exist. Further, under a realistic geometry heart-torso model, the distribution of the body surface magnetic vector field was presented, the component in the direction perpendicular to the body surface ( $B_{y}$ ) of which was in very good agreement with the actual observations from the same subject on a pulse-pumped Rb atomic magnetometer.