Potyagaylo Danila, Cortés Elisenda Gil, Schulze Walther H W, Dössel Olaf
Institute of Biomedical Engineering, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany,
Med Biol Eng Comput. 2014 Sep;52(9):717-28. doi: 10.1007/s11517-014-1176-4. Epub 2014 Jul 10.
The goal of ECG-imaging (ECGI) is to reconstruct heart electrical activity from body surface potential maps. The problem is ill-posed, which means that it is extremely sensitive to measurement and modeling errors. The most commonly used method to tackle this obstacle is Tikhonov regularization, which consists in converting the original problem into a well-posed one by adding a penalty term. The method, despite all its practical advantages, has however a serious drawback: The obtained solution is often over-smoothed, which can hinder precise clinical diagnosis and treatment planning. In this paper, we apply a binary optimization approach to the transmembrane voltage (TMV)-based problem. For this, we assume the TMV to take two possible values according to a heart abnormality under consideration. In this work, we investigate the localization of simulated ischemic areas and ectopic foci and one clinical infarction case. This affects only the choice of the binary values, while the core of the algorithms remains the same, making the approximation easily adjustable to the application needs. Two methods, a hybrid metaheuristic approach and the difference of convex functions (DC), algorithm were tested. For this purpose, we performed realistic heart simulations for a complex thorax model and applied the proposed techniques to the obtained ECG signals. Both methods enabled localization of the areas of interest, hence showing their potential for application in ECGI. For the metaheuristic algorithm, it was necessary to subdivide the heart into regions in order to obtain a stable solution unsusceptible to the errors, while the analytical DC scheme can be efficiently applied for higher dimensional problems. With the DC method, we also successfully reconstructed the activation pattern and origin of a simulated extrasystole. In addition, the DC algorithm enables iterative adjustment of binary values ensuring robust performance.
心电图成像（ECGI）的目标是从体表电位图重建心脏电活动。这个问题是不适定的，这意味着它对测量和建模误差极其敏感。解决这一障碍最常用的方法是蒂霍诺夫正则化，即通过添加一个惩罚项将原始问题转化为一个适定问题。尽管该方法具有诸多实际优势，但仍有一个严重缺点：所得到的解往往过度平滑，这可能会妨碍精确的临床诊断和治疗规划。在本文中，我们将一种二元优化方法应用于基于跨膜电压（TMV）的问题。为此，我们假设根据所考虑的心脏异常情况，跨膜电压取两个可能的值。在这项工作中，我们研究了模拟缺血区域和异位病灶的定位以及一个临床梗死病例。这仅影响二元值的选择，而算法的核心保持不变，使得该近似方法能够轻松根据应用需求进行调整。测试了两种方法，一种混合元启发式方法和凸函数差（DC）算法。为此，我们对一个复杂的胸部模型进行了逼真的心脏模拟，并将所提出的技术应用于获得的心电图信号。两种方法都能够定位感兴趣的区域，因此显示出它们在心电图成像中的应用潜力。对于元启发式算法，有必要将心脏划分为多个区域，以获得一个对误差不敏感的稳定解，而解析DC方案可以有效地应用于更高维的问题。使用DC方法，我们还成功重建了模拟期外收缩的激活模式和起源。此外，DC算法能够对二元值进行迭代调整，确保性能稳健。
