Mathematical modeling of detailed cardiac function has become possible in recent years. Computer simulations have been conducted to reproduce electrical phenomena of the heart. However, substantial effort and computational cost are required to construct an electrocardiogram (ECG) generation model based on multiple parameters of cardiac tissue. In addition, most previous studies simplified the anatomy and the region of the body considered. Such modeling may not be applicable for the system design of wearable sensing in ECG. In this study, we propose a computational model of ECG generation with multiple electric dipoles to reduce the complexity and computational cost of ECG modeling. In this study, first, the electrical potential distribution on the surface of an anatomically detailed model was computed with volume conductor (electrical) analysis. We subsequently simulated the propagation of the electrical excitation of the heart by sequentially placing electric dipoles according to conduction velocity. Our computational results demonstrate the effectiveness of the ECG model using electric dipoles in comparison with measurement and the necessity to discuss the ground in a 12-lead ECG for the whole-body model. The required computational time was less than 30 min even in a workstation (2 CPUs, 28 cores, and 2.20 GHz), i.e., significantly less than those of previous studies.INDEX TERMS Electrocardiography, electromagnetic modeling, finite difference methods.
The 12-lead electrocardiogram was invented more than 100 years ago and is still used as an essential tool in the early detection of heart disease. By estimating the time-varying source of the electrical activity from the potential changes, several types of heart disease can be noninvasively identified. However, most previous studies are based on signal processing, and thus an approach that includes physics modeling would be helpful for source localization problems. This study proposes a localization method for cardiac sources by combining an electrical analysis with a volume conductor model of the human body as a forward problem and a sparse reconstruction method as an inverse problem. Our formulation estimates not only the current source location but also the current direction. For a 12-lead electrocardiogram system, a sensitivity analysis of the localization to cardiac volume, tilted angle, and model inhomogeneity was evaluated. Finally, the estimated source location is corrected by Kalman filter, considering the estimated electrocardiogram source as time-sequence data. For a high signal-to-noise ratio (greater than 20 dB), the dominant error sources were the model inhomogeneity, which is mainly attributable to the high conductivity of the blood in the heart. The average localization error of the electric dipole sources in the heart was 12.6 mm, which is comparable to that in previous studies, where a less detailed anatomical structure was considered. A time-series source localization with Kalman filtering indicated that source mislocalization could be compensated, suggesting the effectiveness of the source estimation using the current direction and location simultaneously. For the electrocardiogram R-wave, the mean distance error was reduced to less than 7.3 mm using the proposed method. Considering the physical properties of the human body with Kalman filtering enables highly accurate estimation of the cardiac electric signal source location and direction. This proposal is also applicable to electrode configuration, such as ECG sensing systems.
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