Study Of Regularization Methods And Dynamic Electrocardiography Inverse Problem Solutions

The inverse problem of electrocardiography (ECG) aims to quantify the cardiac electrical activity from noninvasive body surface potential maps (BSPMs) by mathematic physics method, together with the knowledge of the geometric and electromagnetic property of the intervening volume conductor. The main difficulty of the ECG inverse problem lies in its non-uniqueness and ill-posedness. The ECG inverse problem based on the epicardial potential maps is to deduce the epicardial potential (EPS) from the BSPMs, which overcomes the non-uniqueness of the ECG inverse problem. This means that there exist unique and definite epicardial potentials for the given BSPMs. Another difficulty of the ECG inverse problem is its ill-posedness, and in this respect the regularization methods may be adopted to seek the approximate inverse solutions. Regularization methods and its parameters selections play an important role in solving the ECG inverse problem. Study of the regularization methods in ECG inverse problem is a main job of this thesis.The cardiac systole and diastole have not been considered in previous ECG inverse problem studies, and the cardiac displacement during the cardiac motion has also not been taken into account. The ECG inverse problem under the static heart assumption is called the static ECG inverse problem. Since the heart motion displacements have been neglected in the static ECG inverse problem, something like the geometry system errors is introduced, and thus affect the performances of inverse solutions unavoidably. It is the first time that the cardiac motion is considered in the ECG inverse problem research, and such ECG inverse problem is called the dynamic ECG inverse problem. Obviously, the dynamic ECG inverse-problem can reconstruct more accurate epicardial potentials and get more cardiac electrical information than that of the static ECG inverse problem. The dynamic ECG inverse problem study is another main job of this thesis.The author has done the following main research work: 1. Study of regularization methods in the ECG inverse problemTwo common regularization methods and their parameter selections in the ECG inverse problem have been analysized and discussed, including the direct regularization method (Tikhonov, TSVD) and iterative regularization method (LSQR, CGLS). Then, two new hybrid regularization frameworks, LSQR-Tik and Tik-LSQR, which integrate the properties of the direct regularization method and iterative regularization method (LSQR), have been proposed and investigated for solving ECG inverse problems. The results show that the computation cost of the LSQR-Tik method is much less than that of Tikhonov method, while the Tik-LSQR scheme can reconstruct the epcicardial potential distribution more accurately. This investigation suggests that hybrid regularization methods may be more effective than separate regularization approach for ECG inverse problems.2. Combination of regularization method and genetic algorithm for solving the ECG inverse problemIf the genetic algorithm (GA) alone is used to slove the ECG inverse problem, it is found that the solutions are not the global optimum of the fitness function but a local optimum one. Combined with other regularization method, however, the GA method can overcome the local optimum and improve its performance a lot. Therefore, we propose a new approach which combines regularization method with genetic algorithm to solve the ECG inverse problem. Results show that, by using the solutions of regularization methods as the initial population of GA, the ECG inverse solutions can be improved a lot. This investigation suggests that the combination of regularization methods with GA may be a good scheme for solving the ECG inverse problem.3. Study of the dynamic ECG inverse problemThe concept of dynamic ECG inverse problem is introduced for the first time. The dynamic ECG inverse problem is solved based on the beating heart model, from which the cardiac motion can be simulated. In the forward computation, the heart surface source model method is employed to calculate the epicardial potentials, and then the simulated epicardial potentials are used to calculate body surfaces potentials. In the epicardial potential-based inverse studies, the Tikhonov regularization method is used to handle ill-posedness of the ECG inverse problem. The simulation results demonstrate that the solutions obtained from both the static and the dynamic ECG inverse problem approaches are approximately the same during QRS complex period, due to the minimal deformation of the heart in this period. However, for the most obvious deformation occurring during the ST-T segment, the static assumption of heart always generates something akin to geometry noise in the ECG inverse problem, and thus causes the inverse solutions with large errors. The dynamic ECG inverse problem, however, can obtain more accurate and acceptable inverse solutions.4. Reseach work on ECG forward problem and Vheart software developmentECG forward problem is the basic for ECG inverse problem. The cardiac boundary nodes are picked based on the LFX heart model, and then auto-segmentation method is used to segment the cardiac surface and form the triangular meshes. Consequently the heart-torso volume conductor has been built. The boundary element method (BEM) is adopted to seek the transfer matrix between the EPs and BSPMs. Then the dipole sources method and heart surface source method are employed to simulate the EPs and BSPMs for the purpose of solving the ECG forward problem.The developed Vheart software is highly interactive and manipulable software. It reflects the relationship between ECG forward problem and ECG inverse problem, as well as the ECG and the body surface potential. Moreover, it provides a good platform for the research of the ECG inverse problem.