Mesh resolution impacts the accuracy of inverse and forward ECG problems

Electrocardiographic imaging (ECGI) has become an important medical diagnosis tool that assists scientists to noninvasively investigate cardiac electric activity. Many previous works have studied the inverse and forward ECG problems to understand how to reconstruct the cardiac electric activity from the body potential distribution. However, the inverse ECG problem is highly ill-conditioned and very sensitive to errors and noises. Thus, there is a need to study the sensitivity of inverse and forward ECG problems. In this paper, we investigated effects of mesh resolution on the accuracy of inverse and forward ECG problems. First, we employed the boundary element method to calculate the relationship between potential distributions on the body and heart surfaces and developed an algorithm to solve inverse and forward ECG problems. Second, we implemented the algorithm to solve the ECG problems in both a concentric spherical geometry and a realistic torso-heart geometry. Third, we evaluated the relative error between our solution and the analytical solution under the condition of different mesh resolutions. Experimental results explicitly show that the relative error in the inverse solution decreased from 30% to 17% when the mesh elements triangulating the two spheres increased from 24 to 400 in the concentric spherical geometry, and that decreased from 26% to 16% when the mesh elements triangulating the heart surface increased from 136 to 546 in the realistic torso-heart geometry.