生物浅表组织电特性三维重建及其应用研究
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摘要
生物医学工程是目前发展最快的技术领域之一，已经取得了令人震惊的成就，并仍旧具有更广阔的发展前景。在生物医学工程众多的研究领域中，生物医学成像是一个重要分支，在病情诊断及身体检查中发挥着重要的作用。研究表明，高含水正常组织与低含水正常组织的介电常数和电导率差异很大，而病变组织与正常组织的介电常数和电导率差异也非常大，这为利用电磁技术探测不同的组织、以及检测病变组织的存在，尤其是癌症的早期发现提供了有利的依据。癌症的早期发现对提高治愈率有着至关重要的作用。
电磁成像技术中微波成像和低频电阻抗成像技术复杂、系统庞大，对浅表组织中的皮肤等薄层结构分辨率不足，只能提供该区域内多种组织的等效复介电常数，而利用各种探头直接测量生物组织介电特性时，只能测量均匀组织或不均匀组织总体等效复介电常数。针对这些缺点，本文提出了基于分层均匀生物组织模型，利用体表测量信息对浅表生物组织的电特性进行三维重建的方法。本文完成的主要工作有：提出了从体表电磁测量结果重建浅表生物组织三维电特性的方法；优化设计了适用于分层均匀生物组织的测量探头；研究了遗传算法在本文逆问题求解中的应用；分析了生物组织中的血管及血液流动对探头测量结果的影响；利用本文设计的测量探头与重建方法实现了人体背部浅表三层组织电特性与厚度的重建。
本文针对浅层皮下生物组织电特性的重建提出了基于分层均匀组织结构，从体表测量信息获得浅表生物组织三维电特性的方法。首先把复杂的生物浅表组织简化为由皮肤、脂肪、肌肉等组成的分层均匀组织，既考虑了生物体包含
中文摘要
皮肤这种薄层结构的实际，又在一定程度上进行了简化，这为本文问题的求解
带来了极大的方便。然后利用测量探头与皮肤接触时测得的反射系数，重建皮
肤、脂肪等薄层组织的电导率和介电常数。通过对一个区域的扫描测量，可以
获得该区域生物浅表组织电特性的三维分布。使用分层均匀组织模型的重要前
提是进行局部区域测量，所以测量探头具有辐射近场可以透入生物组织内部、
分布集中，反射系数对较深层组织的电特性变化敏感的特点。针对以往同轴探
头的不足，本文提出了同轴激励的微带贴片天线探头。
生物组织电特性的三维重建包括正问题求解和逆问题求解两部分。为了获
得宽频带测量探头的反射系数，正问题采用时域有限差分法(FDTD)求解生
物组织内电磁场分布并获得探头的反射系数。逆问题为非线性的病态问题，在
FDTD求解正问题的基础上，采用基于遗传算法(GA)的优化方法重建分层生物
组织的三维电特性。
通过利用FDTD与小种群遗传算法(MGA)相结合对同轴激励贴片探头的
尺寸进行了优化。优化后的探头具有轴对称结构，可以大幅度缩短正问题计算
时间。在ZGHo7GHz的频带范围内，该探头在分层生物组织中的近场透入深，
反射系数的频率响应特性好，而且反射系数对组织结构及电特性的变化敏感。
实验数据表明数值计算模拟结果与实验测量结果相吻合。
在传统遗传算法(CGA)的基础上设计了适用于本文逆问题求解的遗传算
子，即改进的GA，并且采用MGA(Miero一GA)对分层生物组织电特性的重建
进行了尝试。研究结果表明:无论是采用改进后的遗传算法还是MGA都可以
重建出分层生物组织的电特性与结构，对分层生物组织的厚度的重建非常精确，
对分层生物组织的电特性重建存在一定误差。
对改进遗传算法参数的分析研究中发现，对于类似逆问题的求解，种群规
模控制为100左右比较合适。采用均匀交叉算子、复制与联赛相结合的选择算
子，以及基于共享机制的小生境技术可以大大提高遗传算法的性能，加快算法
向最优结果的收敛。
测量信息对重建结果影响的研究表明:如果测量误差低于10%时，可以重
建分层组织的电特性及结构。测量结果并非越多越好，如果测量值个数过多，
则相邻频点的反射系数差别不大，再加上一定的测量误差，使能同时满足条件
的解不存在，搜索结果反而偏离真实解。但测量个数过少，不能提供足够的信
Il
四川大学博士学位论文
息，病态问题存在非唯一解，搜索出的结果不一定是真实解。分析结果表明，
对本文的重建问题，测量数据的个数应在20与50之间比较合适。实验表明，
采用该方法可以实现分层介质电特性的重建。
考虑到实际生物组织中分布有血管，有些情况下血管并非毛细血管，如挠
静脉、颈动脉等，其存在不能忽略。本文建立了有血管存在的生物分层组织模
型，在此基础上首次分析了血液的存在及流动对测量探头反射系数的影响。模
拟结果表明:1)如果有血管存在，在建模时考虑血管与否对测量探头反射系数
的模拟计算会产生很大的影响，而且随频率变化呈现较大的波动。如果在生物
组织的建模中不考虑血管的存在，反射系数的这种变化必将影响到分层生物组
织电特性的重建。2)血管管径的变化及血管位置在一定范围内的改变对测量探
头反射系数模拟计算的影响不大。3)血液流动速度低产生的感应电流非常小，
因此血液的流动对测量探头反射系数几乎没有影响。
One of the fastest growing fields of technology-a field of astounding recent achievements and even more ambitious hopes-is biomedical engineering. Medical imaging, one of the research branches in biomedical engineering, plays an important role in improving medical diagnosis and treatment.
Measurements indicate that the relative dielectric constant and conductivity of high-water-content tissues are about an order of magnitude greater than those of low-water-content tissues. Moreover, the dielectric constant and conductivity of tumors are quite different from those of normal tissues, which makes the tumor detection possible by using electromagnetic means.
Microwave imaging (MI) and electrical impedance tomography (BIT) have been developed for many years. However, their resolutions are limited and not suitable to determine the electric properties of thin tissues, such as skin. Moreover, the techniques of MI and BIT are much complicated, and the equipments are either complex or expensive.
A 3-dimensional (3D) reconstruction method of electric properties of superficial tissues by noninvasive measurement of human body is presented in this paper. By this reconstruction method, the dielectric constant and conductivity of each tissue in multi-layered superficial structure, especially of very thin tissues, such as skin, can be obtained.
In the reconstruction based on a stratified uniform tissues model, a patch-antenna probe excited by coaxial line is designed and optimized by MGA (Micro Genetic Algorithm) combined with FDTD (Finite Difference Time Domain). Near fields established by the optimized probe are concentrated in a small region and able to penetrate into deeper layers of the tissues. Thus, the complex superficial tissues can be described by a multi-layered-uniform tissues model.
The reconstruction of dielectric constant and conductivity of tissues at each layer is a nonlinear and ill-posed problem. Both GA and MGA methods are used to solve the inverse problem. Simulation results indicate that not only the dielectric constant and conductivity of each tissue can be reconstructed, but also the thickness of first two layers can be achieved.
The appropriate population size of GA is about 100 for this problem. Some techniques, such as niching technology based on sharing scheme, tournament selection with elitism, and uniform crossover, are used to improve the performance of GA and MGA.
The influences of measurement data on reconstruction results are investigated in this paper. The reconstruction results are no longer reliable when the measurement error is larger than 10%. The appropriate number of measurement data should be between 20 and 50 when the number of unknown parameters is 14 in this problem. Simulated results are also in agreements with experimental results, which shows the validity of this reconstruction method.
There always exist some blood vessels in superficial tissues. Sometimes these blood vessels are large and cannot be ignored in modeling. Therefore, the impacts of blood vessels and flowing blood on the reflection coefficient are studied. Simulation results show that: a) The blood vessels in layered tissues may have a great influence on the reflection coefficient. The influence on reflection coefficient depends much on frequency, which will also definitely affect the reconstruction of the electric properties of tissues, b) The change of reflection coefficient resulted from the variation of diameter and position of blood vessel is not dramatic, c) The change of reflection resulted from the flowing blood can hardly be noticed.
The dielectric constants and conductivities of skin, fat and muscle, as well as thickness of the skin and fat on the back of a human body are reconstructed using the above method. The reconstructed thicknesses of skin and fat are in good agreements with the specimen, and the electric properties of tissues are in agreement with the literature results. Both experimental results and reconstructed results show that the distribution of electric properties o
电磁成像技术中微波成像和低频电阻抗成像技术复杂、系统庞大，对浅表组织中的皮肤等薄层结构分辨率不足，只能提供该区域内多种组织的等效复介电常数，而利用各种探头直接测量生物组织介电特性时，只能测量均匀组织或不均匀组织总体等效复介电常数。针对这些缺点，本文提出了基于分层均匀生物组织模型，利用体表测量信息对浅表生物组织的电特性进行三维重建的方法。本文完成的主要工作有：提出了从体表电磁测量结果重建浅表生物组织三维电特性的方法；优化设计了适用于分层均匀生物组织的测量探头；研究了遗传算法在本文逆问题求解中的应用；分析了生物组织中的血管及血液流动对探头测量结果的影响；利用本文设计的测量探头与重建方法实现了人体背部浅表三层组织电特性与厚度的重建。
本文针对浅层皮下生物组织电特性的重建提出了基于分层均匀组织结构，从体表测量信息获得浅表生物组织三维电特性的方法。首先把复杂的生物浅表组织简化为由皮肤、脂肪、肌肉等组成的分层均匀组织，既考虑了生物体包含
中文摘要
皮肤这种薄层结构的实际，又在一定程度上进行了简化，这为本文问题的求解
带来了极大的方便。然后利用测量探头与皮肤接触时测得的反射系数，重建皮
肤、脂肪等薄层组织的电导率和介电常数。通过对一个区域的扫描测量，可以
获得该区域生物浅表组织电特性的三维分布。使用分层均匀组织模型的重要前
提是进行局部区域测量，所以测量探头具有辐射近场可以透入生物组织内部、
分布集中，反射系数对较深层组织的电特性变化敏感的特点。针对以往同轴探
头的不足，本文提出了同轴激励的微带贴片天线探头。
生物组织电特性的三维重建包括正问题求解和逆问题求解两部分。为了获
得宽频带测量探头的反射系数，正问题采用时域有限差分法(FDTD)求解生
物组织内电磁场分布并获得探头的反射系数。逆问题为非线性的病态问题，在
FDTD求解正问题的基础上，采用基于遗传算法(GA)的优化方法重建分层生物
组织的三维电特性。
通过利用FDTD与小种群遗传算法(MGA)相结合对同轴激励贴片探头的
尺寸进行了优化。优化后的探头具有轴对称结构，可以大幅度缩短正问题计算
时间。在ZGHo7GHz的频带范围内，该探头在分层生物组织中的近场透入深，
反射系数的频率响应特性好，而且反射系数对组织结构及电特性的变化敏感。
实验数据表明数值计算模拟结果与实验测量结果相吻合。
在传统遗传算法(CGA)的基础上设计了适用于本文逆问题求解的遗传算
子，即改进的GA，并且采用MGA(Miero一GA)对分层生物组织电特性的重建
进行了尝试。研究结果表明:无论是采用改进后的遗传算法还是MGA都可以
重建出分层生物组织的电特性与结构，对分层生物组织的厚度的重建非常精确，
对分层生物组织的电特性重建存在一定误差。
对改进遗传算法参数的分析研究中发现，对于类似逆问题的求解，种群规
模控制为100左右比较合适。采用均匀交叉算子、复制与联赛相结合的选择算
子，以及基于共享机制的小生境技术可以大大提高遗传算法的性能，加快算法
向最优结果的收敛。
测量信息对重建结果影响的研究表明:如果测量误差低于10%时，可以重
建分层组织的电特性及结构。测量结果并非越多越好，如果测量值个数过多，
则相邻频点的反射系数差别不大，再加上一定的测量误差，使能同时满足条件
的解不存在，搜索结果反而偏离真实解。但测量个数过少，不能提供足够的信
Il
四川大学博士学位论文
息，病态问题存在非唯一解，搜索出的结果不一定是真实解。分析结果表明，
对本文的重建问题，测量数据的个数应在20与50之间比较合适。实验表明，
采用该方法可以实现分层介质电特性的重建。
考虑到实际生物组织中分布有血管，有些情况下血管并非毛细血管，如挠
静脉、颈动脉等，其存在不能忽略。本文建立了有血管存在的生物分层组织模
型，在此基础上首次分析了血液的存在及流动对测量探头反射系数的影响。模
拟结果表明:1)如果有血管存在，在建模时考虑血管与否对测量探头反射系数
的模拟计算会产生很大的影响，而且随频率变化呈现较大的波动。如果在生物
组织的建模中不考虑血管的存在，反射系数的这种变化必将影响到分层生物组
织电特性的重建。2)血管管径的变化及血管位置在一定范围内的改变对测量探
头反射系数模拟计算的影响不大。3)血液流动速度低产生的感应电流非常小，
因此血液的流动对测量探头反射系数几乎没有影响。
One of the fastest growing fields of technology-a field of astounding recent achievements and even more ambitious hopes-is biomedical engineering. Medical imaging, one of the research branches in biomedical engineering, plays an important role in improving medical diagnosis and treatment.
Measurements indicate that the relative dielectric constant and conductivity of high-water-content tissues are about an order of magnitude greater than those of low-water-content tissues. Moreover, the dielectric constant and conductivity of tumors are quite different from those of normal tissues, which makes the tumor detection possible by using electromagnetic means.
Microwave imaging (MI) and electrical impedance tomography (BIT) have been developed for many years. However, their resolutions are limited and not suitable to determine the electric properties of thin tissues, such as skin. Moreover, the techniques of MI and BIT are much complicated, and the equipments are either complex or expensive.
A 3-dimensional (3D) reconstruction method of electric properties of superficial tissues by noninvasive measurement of human body is presented in this paper. By this reconstruction method, the dielectric constant and conductivity of each tissue in multi-layered superficial structure, especially of very thin tissues, such as skin, can be obtained.
In the reconstruction based on a stratified uniform tissues model, a patch-antenna probe excited by coaxial line is designed and optimized by MGA (Micro Genetic Algorithm) combined with FDTD (Finite Difference Time Domain). Near fields established by the optimized probe are concentrated in a small region and able to penetrate into deeper layers of the tissues. Thus, the complex superficial tissues can be described by a multi-layered-uniform tissues model.
The reconstruction of dielectric constant and conductivity of tissues at each layer is a nonlinear and ill-posed problem. Both GA and MGA methods are used to solve the inverse problem. Simulation results indicate that not only the dielectric constant and conductivity of each tissue can be reconstructed, but also the thickness of first two layers can be achieved.
The appropriate population size of GA is about 100 for this problem. Some techniques, such as niching technology based on sharing scheme, tournament selection with elitism, and uniform crossover, are used to improve the performance of GA and MGA.
The influences of measurement data on reconstruction results are investigated in this paper. The reconstruction results are no longer reliable when the measurement error is larger than 10%. The appropriate number of measurement data should be between 20 and 50 when the number of unknown parameters is 14 in this problem. Simulated results are also in agreements with experimental results, which shows the validity of this reconstruction method.
There always exist some blood vessels in superficial tissues. Sometimes these blood vessels are large and cannot be ignored in modeling. Therefore, the impacts of blood vessels and flowing blood on the reflection coefficient are studied. Simulation results show that: a) The blood vessels in layered tissues may have a great influence on the reflection coefficient. The influence on reflection coefficient depends much on frequency, which will also definitely affect the reconstruction of the electric properties of tissues, b) The change of reflection coefficient resulted from the variation of diameter and position of blood vessel is not dramatic, c) The change of reflection resulted from the flowing blood can hardly be noticed.
The dielectric constants and conductivities of skin, fat and muscle, as well as thickness of the skin and fat on the back of a human body are reconstructed using the above method. The reconstructed thicknesses of skin and fat are in good agreements with the specimen, and the electric properties of tissues are in agreement with the literature results. Both experimental results and reconstructed results show that the distribution of electric properties o
引文
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