Study of the Numerical Computational Methods in Biomedical Electromagnetic Forward and Inverse Problems
|Keywords||Forward Problem Inverse problem ECG MRI coil design MIT BEM h-aBEM Edge FEM Regularization method TLS TV method|
The electromagnetic calculation problem in the field of biomedical engineering, there are many, mathematically speaking, they have some common characteristics. Ask the source of the problem, the field relationships, The electromagnetic calculation problem can be divided into the calculation of the positive and inverse problems. Positive problem is the corresponding field distribution calculated by the source distribution, by due and fruit, it is often posed problems, namely the existence of solutions, uniqueness and continuous dependence conditions are met; inverse problem reconstruction of the corresponding source distribution based on the field distribution, from fruit and because of that it often is ill-posed problems, that solutions meet all three conditions. Meanwhile, n is the basis of the inverse problem, it is generally to provide the source for the latter, a field between the numerical calculation relationship; while the latter is the purpose of the former. Different numerical methods for the inverse problem of different characteristics: positive problem often using the conventional finite element, boundary element or finite difference method for the calculation generally relatively simple; inverse problem will have to combine specific prior information , and some appropriate regularization method of treatment in order to get a stable solution, it is often more complicated, it takes a lot of effort to find the appropriate solution. This study is focused in biomedical electromagnetic numerical calculation of the positive and negative issues, major research in the field of biomedical electromagnetic three questions: electrocardiogram (ECG), MRI coil design and magnetic induction tomography (MIT). ECG problem, the source is the heart, and the field is the surface potential distribution, and the corresponding ECG positive problem is starting from heart source simulation body surface potential distribution, and the ECG inverse problem is based on the distribution of body surface potential inversion cardiac source information . If you do not include the virtual heart, ECG pros and cons of the problem consists mainly of cardiac equivalent source volume conductor modeling, calculate the inverse problem of the forward problem computing research. In this paper, the use of the BEM method to calculate the ECG forward problem, where the volume conductor model using the virtual laboratory early development of the heart and torso model; ECG inverse problem regularization method to deal with the major reconstruction of the epicardial potential. MRI coil design problem through the current wire coil creates a magnetic field in a certain target area, the optimal location of these wire coil design is MRI coil design problem, which also includes a source, field relations: a wire coil through current source is The field is a magnetic field generated. The high-performance MRI gradient and RF coil design has been a hot research topics MRI academia and industry, has a large number of coil design method proposed, which are related to certain numerical calculation. MRI coil design method in this paper. MIT Research and ECG Research, as its purpose is to develop a novel imaging device, however, it is the imaging object is an electrolyte physical properties (conductivity). Based on the principle of electromagnetic induction, MIT provides a non-invasive and non-contact imaging technology, it has many potential applications in biomedical and industrial fields. This article focuses on the the MIT application in the biomedical field: cerebral hemorrhage detection and monitoring, mainly concentrated in the MIT system simulation and numerical methods. Three has its own characteristics, but on the angle of the electromagnetic field calculation they have many common characteristics, such as are based on the approximation of Maxwell's equations in the quasi-static conditions, its positive and inverse problems solution can be used in the same numerical methods. The main research work completed by the papers include: a systematic analysis of ECG forward problem and discussed the main content of the ECG forward problem and numerical methods. On the basis of analysis of the ECG is commonly used numerical method for the the ECG problem in grid complexity and importance of the proposed adaptive boundary element method (aBEM) calculated ECG forward problem. Selected the h-aBEM method, it is an iterative optimization grid process, add by BEM calculations based new node to establish the optimization of the boundary element mesh. Using the h-aBEM method, calculated ECG is the inverse problem the application of the h-aBEM method not only improve the accuracy of the solution of the positive and negative issues, and guidance on the optimal choice of the surface electrodes can be obtained through the simulation results. In order to save the overhead of the h-aBEM method of calculation, the paper further uses a hierarchical h-aBEM. H the layered-shaped function based on linear triangular elements are derived for the first time in the process of implementation of the hierarchical the h-aBEM method. And laboratory-based virtual heart model of in-depth study of two different aBEM method and grid optimization. The two ECG inverse problem regularization method research and analysis to discuss the the regularization method commonly used in the ECG inverse problem, and a comparative study of several different regularization parameter selection method. Actual ECG inverse problem: the impact of the volume conductor modeling and factors such as heart beat, discrete linear system on both sides there are varying degrees of error, this paper, based on total least squares (TLS) principle of regularization methods: truncated total least squares method (TTLS) and regularized total least squares (RTLS), calculate the ECG inverse problem. TTLS method proposed to solve the ECG inverse problem areas plagued 30 years can not handle the measurement noise and geometric noise problem. Analysis FTLS and RTLS method based on the basic principles and algorithms through simulation experiments show that the new proposed regularization method has better results in dealing with actual ECG inverse problem, and can be applied to clinical ECG functional imaging. , MRI coil design study based on the analysis and discussion of MRI coil design method proposed in this paper using BEM and regularization techniques combined designed MRI coil. By the stream function expression after the introduction of the current density of the source, source field region BEM method discrete calculation using Tikhonov regularization method in the calculation of the inverse problem of the coil design processing. Using the proposed method, designed dual-plane transverse gradient coil open MRI system and applied Parallel imaging RF phased array coil. The design results show that, the design method proposed in this paper is simple and practical, and can design based on an arbitrary two-dimensional or three-dimensional geometry of the coil. , MIT simulation study in this article the MIT study, the first edge FEM calculated eddy current electromagnetic problems and MIT image reconstruction Jacobian matrix, and then using the regularization method for the reconstruction of the conductivity information. Philips 16-channel MIT system, in the optimal design of the MIT system: including coil optimization and system size optimization, the electromagnetic safety assessment, the dog's head bleeding experimental feasibility assessment has done a lot of research work. Meanwhile, based on the characteristics of MIT image reconstruction to study fully variational (TV) method in MIT problem, simulation and experimental results show that the TV method to remove artifacts, maintaining border aspects the conventional l 2 Fan constraint method advantage.