三极同心电极表面Laplacian近似测量理论及其误差分析

Surface Laplacian Approximation Theory of the Triple Concentric Electrode and Its Error Analysis

基于表面Laplacian的九点差分数值近似方法提出了一种新的表面Laplacian传感电极——三极同心电极传感器,从理论上分析了该传感器测量体表势表面Laplacian的相对误差,并与双极同心电极做了比较．结果表明: 三极同心电极传感器的误差远小于双极同心电极的误差;当源深度与电极内环半径之比大于4时,三极同心电极传感器的误差小于2％,即其误差几乎不受电极与源之间距离的影响．理论计算与偶极子模拟实验结果的一致性表明该传感方法是可行的,为表面Laplacian心电的直接测量奠定了基础．

The surface Laplacian of the body surface potential is a new technique for detecting cardiac electrical activity. Based on a nine-point numerical approximation of the analytical Laplacian, a new Laplacian sensor——a tripolar concentric （TC） ring electrode sensor, is developed and its relative error （RE） of the Laplacian approximation is discussed theoretically. Comparing with the bipolar concentric （BC） ring electrode sensor, it shows that the RE of TC sensor is less than that of BC sensor, and the RE of TC sensor is less than 2% when the ratio of the source dipole depth to the radius of the inner ring of TC sensor is more than 4. It means that the distance between the sensor to source dipole has almost no influence on the RE of TC sensor. The consistency between the theoretical and the experimental results suggests the feasibility of measuring the surface Laplacian. This lays the foundation for measuring surface Laplacian directly.