【作者】 田海燕；

【导师】 何为；

【作者基本信息】 重庆大学 ， 电气工程， 2002， 博士

【摘要】 电阻抗断层成像技术（Electrical Impedance Tomography，EIT）是一种新兴的计算机断层成像技术。它通过在目标物体四周安放电极阵列并注入交流电流，在产生电流场的同时，通过电极测量目标物体四周的电压，由注入的交流电流信号和测量的电压数据，以及一些附加信息，可以重构出目标物体横截面内（或空间）的电导率（或电阻率）分布，从而得到反映物体内部组织特性的电导率断层图像。EIT技术用于生物医学工程领域，其基本原理是通过配置于人体体表的电极阵，提取与人体生理、病理状态相关的组织或器官的电特性信息。生物组织的电导率含有大量的反映组织、器官的生理状态及功能的信息，EIT技术就是以低频电流流过人体组织时呈现出的这种电特性为依据，进行无创成像。EIT技术无创、廉价、便携、安全，能够反复成像，重复使用，可用于高危病房的床旁检测，脑血肿的动态检测，心脏,胃及肺功能的监测等，因而该技术在临床医学领域有潜在的应用价值。此外，EIT技术不仅能够反映目标物体的解剖学结构，更重要的是，它可以给出功能性图像结果，即在组织或器官结构性变化出现之前，及时检测和确认该组织与器官的功能性变化，这对于相关疾病的普查、预防与诊断治疗非常有利。EIT技术在理论上是一个电流场计算的逆问题，其核心是重建算法，但重建算法至今仍然没有得到很好的解决，这是因为完善它的理论基础非常困难。EIT技术的理论基础实质上是数学物理的反问题，如何求解EIT重建方程涉及到偏微分方程、有限元理论、数值计算、矩阵论、非线性方程组求解、病态问题、误差分析等领域。首先，本文全面、系统、综合地阐述了EIT技术涉及到的各种数学物理问题，并指出EIT在理论上的各种困难集中表现在问题的病态性。对此本文给出了基于有限元计算的反映EIT问题病态程度的定量数据，用以说明求解EIT重建方程的难度所在。其次，论文提出了四种新的用于EIT图像重建的算法。第一，提出拟牛顿法作为重建算法，该算法考虑了场域内所有参数对场域的作用，提高了边界电位对场域电导率的敏感程度。在得到很高的重建计算精度的同时，重建矩阵的病态程度也得到明显的改善。第二，将外推法在正向计算中的应用推广到重建计算中，极大地降低了计算规模，很好的解决了拟牛顿法的计算精度与计算规模不可兼得的矛盾。第三，用数值延拓法有效地扩大初始值的收敛区间。生物活体组织的生理参数因不同的人、器官、组织和病况，有很大的差异，因此在重建算法中<WP=5>放宽对计算参数初始值的要求对EIT技术走向临床应用有重要的意义。论文在正则化方法的基础上，利用数值延拓法有效地扩大初始值的收敛区间，改善了拟牛顿法对初始值的苛刻要求。第四，用局部加速收敛法提高计算精度和降低计算规模。局部加速收敛法是在重建计算的过程中加入目标区域的已知信息作为重建计算的判据，重点求解部分关注的信息。该方法降低了高精度成像时计算规模过大的问题，同时提高了计算精度。此外，将EIT技术用于脑血肿病例的动态实时监测的仿真研究。由于脑血肿病例的特殊性，其病情发展快、不易移动、需实时监测等需要，EIT技术在该领域有潜在的应用价值。论文将从临床诊断的角度出发，对脑血肿病例实时监测的全过程进行了仿真研究，得到的数据及图像表明，EIT重建算法及技术手段用于脑血肿病例的动态监测是成功的。最后，人体胸部实测数据的重建计算结果表明，重建图像能够分辨出心脏、左右肺及脊椎等器官，重建算法是有效的，具有一定的临床参考价值。综上所述，电阻抗断层成像技术是一种有前途的医学成像技术。对该技术更加深入地研究必将对医疗器械的发展产生深远的影响。更多还原

【Abstract】 Electrical Impedance Tomography (EIT) is a new type of medical imaging technique. In EIT an array of electrodes is attached around the object and small alternating currents are injected via these electrodes and resulting voltages are measured. Using different current injections and voltage measurements, an approximation for the spatial distribution of impedance (or conductivity) within the object can be reconstructed. The principal potential applications of EIT lie in biomedical imaging, whose biological basis is to acquire the information of physiology and pathology, via injecting electrical current on the periphery of cross section of a human body. The impedance of biological tissue represents some information from function or disease of organs. Depending on the electrical impedance property of tissue, EIT can provide a kind of non-invasive tomography.The advantages are that the technique is inexpensive, portable, and safe. It has the potential for widespread use in medicine for continuous monitoring at the bedside, in the intensive care unit, or in remote medical facilities. In medicine, its accuracy has been demonstrated in imaging lung, heart, stomach and brain hematoma. Moreover，the technique can be used not only in imaging anatomical structures , but also in imaging functional structures. This is most helpful for preventing and diagnosing disease, prior to disease happened. Theoretically EIT is an inverse problem of low frequency electric current field calculation, whose core is reconstruction algorithm. The reconstruction algorithm of EIT is not perfect so far, because it is very difficult in mathematics. As an Inverse Problem of Mathematical Physics, how to solve it involves Partial Differential Equations, Finite Element Method, Numerical Analysis, Matrix Theory, Nonlinear Equations, Error Analysis, Ill-posed Problem, etc.At first, this thesis expatiates on the inverse problem of mathematic physics in details, which is involved by EIT, and points out that, as a representation, all kinds of difficulties focus on ill-posed problem. Withal this thesis gives the quantitative data to measure the degree of ill-posed problem, which demonstrates the problem of<WP=7>EIT is ill posed badly.Secondly, in this thesis new approaches of EIT image reconstruction are proposed. Four novel methods are developed. The first one, Quasi-Newton method, considers the effect from all of parameters in the cross section of an object. Thus, the ill-posed nature and the precision of solution are all improved, due to the greater sensitivity between boundary potentials and interior conductivities. The second proposed method is extrapolation method, which makes it possible to improve the reconstruction computing velocity. Even though the Quasi-Newton method is a powerful method to solve nonlinear equations, it suffers from a high computational cost while employing fine mesh systems. Extrapolation method can reduce the computing load, besides improving calculating precision. The third method is Continuation method, which is proposed in Electrical Impedance Tomography. Since there is a great difference in physiological parameters between different objects, between varieties of ill cases, and different tissues, it is important to loosen the limits of initial values of reconstruction algorithm. Simulating calculation results are given to validate the approach. The last one is Local Area Accelerating Convergence (LAAC) method, which is based on prior known information of the conductivity distribution. LAAC dramatically reduces the accumulated calculation error into a small number, and also improves computation speed greatly.Thirdly, the technique is applied to real-time monitoring for brain hematoma. Due to the special demands for these cases, such as non-moving, fast variety of states of illness, etc, real-time monitoring is necessary. In this thesis simulation research describes the whole process of dynamic variety of brain hematoma case with EIT. A series of reconstruction images show that it is successful to apply EIT更多还原