术中磁共振射频线圈设计
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摘要
磁共振成像是一种非常重要的医学成像技术,现已广泛应用于临床。在磁共振领域,多名科学家曾经先后五次分别获得诺贝尔奖,由此可见磁共振技术的科学价值和影响力。磁共振医学成像的突出优点是具有良好的软组织分辨能力,能够对器官组织功能成像以及对患者无电离辐射危害等,这些优点是其它医学成像手段,如X-射线成像、超声成像等都无法比拟的。磁共振成像在医学中的应用处于发展的初始阶段,仍有着巨大的潜力。
磁共振系统问世时间虽短,但已经得到飞速发展,从最早期的永磁体(低场)磁共振系统,发展到今天的超高场超导磁体系统(主磁场超过10T)。低场系统整体成本低,具有开放式结构,对电源要求不高,适合中小医院和偏远地区使用。高场磁共振系统,主要是1.5T和3.0T为代表的超导磁共振系统,是大型医院的主流设备,这类超导系统能够提供丰富的医学成像信息,临床价值有目共睹。不同系统能够发挥各自优势,形成了共存的局面,这是一种非常有趣的现象。
磁共振系统的主要组成部分包括主磁体、梯度线圈、射频线圈、谱仪系统、电源系统和辅助设备等。其中射频线圈既起到激发磁共振射频信号的作用,又起到接收磁共振信号的作用,是磁共振系统核心部件之一,对磁共振成像质量起到至关重要的作用,是磁共振系统重要研究课题,相关研究非常活跃,国外从事射频研究的学者和机构非常多,国内只有少数几所大学具有相关的科研条件和研究能力。根据射频线圈在系统中所起的作用不同,又分为发射线圈和接收线圈两类。起发射射频信号作用的称为发射线圈,起接收射频信号作用的称为接收线圈。射频线圈一般都是作用在射频频率范围内(几十兆赫兹到几百兆赫兹),因此射频线圈的研发遵循射频电磁场的普遍规律,同时又有着自身的特殊性。
对于不同频率范围的射频线圈,其研究方法也不相同。一般而言,对于低场射频线圈,可以采用准静态电磁分析方法,或者叫做等效电路方法。等效电路方法相对而言比较简单,这种方法能够比较准确地计算出射频线圈的共振频率和射频线圈不同单元之间的耦合、匹配等。但是随着共振频率的提高,这种方法的误差将增大。特别是当射频线圈或者人体器官的尺寸接近射频波长后,就不再适用了。对于高场射频线圈,需要采用全波电磁场分析方法,全波分析方法可以不受射频频率的限制,能够比较全面地反映射频线圈的性能,但是相对而言比较复杂。各种电磁场数值分析方法如时域有限差分法(FDTD)、矩量法(MoM)、有限元法(FEM)等都属于全波分析方法之一,它们各有优缺点,并且在射频线圈的设计中都有广泛的应用。FDTD方法的优点是适合计算具有不均匀电磁介质的电磁场,缺点是计算量比较大。MoM方法的优点是适合计算复杂形状的射频线圈的电流密度分布,缺点是不适合计算有不均匀电磁介质存在的电磁场分布。FEM方法一般是在频域求解电磁场问题,其网格划分的方法对电磁计算精度影响较大。最新的射频线圈的设计方法中还包含了各种不同的混合电磁计算数值方法,如混合FDTD/MoM方法,混合FEM/MoM方法等,这些混合方法能够结合不同数值方法的优势,同时避免其各自的劣势,有很好的发展前景。本论文作者对常用的电磁场数值分析方法和混合方法进行了相关的研究工作,并有部分研究成果发表。
根据不同的成像需求,射频线圈具有不同的几何形状。主要有螺线管形射频线圈,鞍形射频线圈,鸟笼型射频线圈,正交型线圈,表面线圈,阵列线圈,植入体内的微型线圈等多种形式。根据临床应用部位不同,又可以分为头线圈,颈线圈,头颈联合线圈,体线圈,肢体线圈,浅表组织线圈,腔内线圈等不同类别。可见,射频线圈具有复杂的几何形态,具有多种多样的临床用途。射频线圈总是基于一定的磁共振系统,因此射频线圈的研究和发展与磁共振系统的研究和发展是息息相关的。
对于磁共振系统而言,不断满足临床提出的新需求是其永恒的发展主题。近年来,术中应用是磁共振崭新的发展方向,实现术中磁共振测温引导的热消融肿瘤治疗技术宛若一颗冉冉升起的新星,备受业内人士关注。热消融是临床治疗肿瘤的重要手段,它通过一定的加热方法,使肿瘤组织的温度升高到一定程度从而使肿瘤组织坏死,达到治疗的目的。在热消融手术过程中,需要对加热部位的组织温度进行准确监测,以便正确控制热消融手术的温度和作用时间,恰当评估热消融手术效果。目前测温的方法分为有创和无创两种。有创测温是在术中利用温度探头,直接测量温度,虽然准确但是对病人有损伤,临床应用范围受到限制,无创测温是更佳的选择。在无创测温的各种方法中,最具有吸引力的就是磁共振术中测温。磁共振成像中,质子共振频率、弛豫时间等多种参数都是温度敏感的,能够反映人体组织温度变化情况,因此通过测量磁共振成像的相关参数可以准确测得目标器官的温度,目前高场下的测温精度已经可以达到±1℃。发展至今,磁共振测温已经成功应用于临床,成为最受欢迎、最有发展前景的一种体外无创测温技术。将热消融治疗装置和磁共振设备二者整合,实现磁共振影像引导下术中测温热消融治疗,一直是国内外生物医学工程领域的研究热点,特别是磁共振测温引导下的聚焦超声消融手术(MRgFUS),在无创治疗子宫肌瘤、乳腺癌、前列腺癌、肝癌、脑恶性胶质瘤等多个器官肿瘤疾病方面都具有巨大应用价值,被称为“颠覆性的技术革新”。
射频线圈作为磁共振系统的核心部件之一,自然也是术中磁共振系统的重点研究内容之一。与常规磁共振成像检查不同,术中磁共振系统对射频线圈提出了新的要求,主要包括：(1)术中射频线圈需要兼容采用的术中治疗手段,比如术中射频线圈需要为聚焦超声波提供物理通道等；(2)术中射频线圈的成像目标器官非常明确,是为治疗目的服务的,而常规射频线圈是为诊断目的服务的。当然,均匀的发射射频场,高的射频接收信噪比等是对术中线圈和常规线圈共同的要求。目前,常规的射频线圈只能部分满足术中磁共振的需求,还没有专门的术中测温磁共振系统射频线圈。针对术中磁共振系统对射频线圈的特殊要求,在导师陈武凡教授的指导下,依国家科技部973项目内容要求,本论文提出了面向器官的术中射频线圈设计理论模型,主要包括：逆方法设计面向器官的术中射频线圈理论方法和混合MoM/FDTD电磁计算数值方法工程优化术中射频线圈理论方法。并制作相应的原型实验线圈,验证理论模型的正确性。
逆方法根据预先设定的目标电磁场分布来倒推出射频线圈表面电流密度分布,由线圈表面电流密度分布再倒推出射频线圈表面导线排布,最终完成射频线圈设计。国际上,逆方法研究的最新进展包括Li,Y等提出的乳房线圈设计和Muftuler, L. T等提出的并行成像阵列线圈设计。Li,Y等运用逆方法,依据乳房器官特殊的几何形状,设计了一种倒三角锥形状的射频线圈,并成功实现磁共振扫描成像。Muftuler, L. T等设计的并行成像阵列线圈是为了提高磁共振成像速度而设计的,也是采用逆方法原理倒推出设计方案。目前,还未见将逆方法应用于设计磁共振术中测温系统专用射频线圈的相关报道。关于术中适用磁共振射频线圈设计的理论研究少见报道的原因,大致有以下几个方面：(1)磁共振术中测温应用是近几年兴起的临床应用新技术,许多相关的技术和理论都还有待深入研究；(2)对传统的磁共振射频线圈做相应改进后,可以部分满足MRgFUS系统等的需求；(3)术中磁共振射频线圈设计,形状复杂,比较困难。术中射频线圈在排布导线的时候,要求能够同时结合术中应用的需求,比如留置术中通道等,这些都将使设计和工程实现的难度大幅增加。针对磁共振术中测温系统对射频线圈的特殊需求,在现有国内外射频线圈设计理论研究成果的基础上,本论文借鉴Li,Y等人乳房射频线圈的研究成果,结合磁共振术中测温专门针对某个器官的特点,提出了面向器官的逆方法设计思路,即设计的目标是使器官所在部位的射频场(B1场)分布尽量均匀一致。同时,由于术中通道的存在,在逆方法设计时,需要结合术中通道的位置建立相关模型。逆方法在设计过程中,需要对射频线圈表面电流密度积分方程组进行求解来得到射频线圈表面电流密度分布图。一般情况下,该积分方程组是病态的,需要正则化后求解。因此,求得的解是近似解。由近似解进一步抽象出来的射频线圈设计方案,与设计目标相比本身就具有一定的误差,需要进一步优化。Li,Y等采用的优化方法是在线圈表面设定数个控制点,调整控制点的位置,通过准静态场(quasi-static)近似计算方法来计算B,场的分布。这种优化方法有两个缺点,一是控制点的选取有随意性,二是B1场的计算仅仅依靠比奥-萨伐尔定律(Biot-Savart law),方法过于简单,没有考虑工程中必然遇到的B1场与人体组织之间复杂的电磁作用效应,仅适用于低场,高场下误差比较大。
为了解决优化问题,作者借鉴MoM/FDTD混合方法最新研究成果,提出了计算电磁混合MoM/FDTD工程优化方法。MoM/FDTD混合方法的最新进展是Feng Liu等人提出的基于惠更斯等效面原理的MoM方法和FDTD混合方法。本文在此基础上,提出了建立目标器官的电磁模型,作为负载代入FDTD域,在该混合方法中考虑了工程中必然遇到的B,场与人体组织之间复杂的电磁作用效,使优化设计结果更符合工程实际。作者运用MoM电磁场算法计算结构复杂的术中射频线圈的电流密度分布。在用MoM法计算电流密度分布图时,考虑了工程实际需要,设置合适的电路参数,使线圈在设定的频率上共振,同时选择合适的去耦电路和去谐电路进行仿真。所选用的去耦电路呈容性特性,选用的去谐电路起保护电路的作用,对共振电流没有影响。接下来,依据惠更斯等效原理,设置惠更斯等效面,作为MoM方法和FDTD方法结合的纽带,将用MoM法计算得到的电流密度分布图等效映射到惠更斯等效面上。选用的惠更斯等效面围蔽的空间就是FDTD作用域,该域包含了设定的目标器官。目标器官建立电磁模型,将电磁模型作为负载代入FDTD域求解。FDTD方法的优势是能够方便求解包含复杂介质的电磁场,作者在本研究中利用FDTD方法的这个优势,将目标器官作为线圈负载,选取合适时间步长,空间步长,以及设定合适的完全吸收边界条件(PML),考虑实验室计算机硬件条件和解的精度需要等情况,通过实验最终确定FDTD解。FDTD域内的解代表形成稳定的共振后FDTD区域边界,即惠更斯等效面上的新的电流密度分布图。根据耦合原理,用新得到的电流密度分布图来修正待优化的射频线圈表面的电流密度分布,也就是修正射频线圈表面上的导线排布位置。然后,对修正后的射频线圈再一次重复上述的优化过程。当惠更斯等效面的电流密度分布最终达到稳定时,优化循环结束,得到最终射频线圈优化设计方案。混合MoM/FDTD工程优化方法研究部分成果被业界普遍认可的2011年IEEE ISBI会议收录。
作者最后制作了相应的原型实验射频线圈,对上述的理论设计模型进行了验证,证明该理论方法可行,能够满足磁共振系统术中测温的需求。相关研究的部分成果发表在" Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering"杂志上(SCI收录)。
Magnetic resonance imaging (MRI) is an important medical imaging technology, and now it is applied at clinic widely. MRI and related technology have great influence and scientific values because the scientists get the Nobel prizes five times totally in this field. The prominent advantages of MRI are the wonderful solution for soft issues and no risk of radioactivity. From these points of view, MRI is much better than other medical imaging technology such as X-ray CT, ultrasound etc. It is still at the beginning for the development of medical MRI technology and there should be great achievement for its application at clinic in prospect.
Since the MRI system was developed several decades ago, it has been developed very rapidly. The strength of the main magnetic field covers from 0.2 Tesla to more than 10Tesla. The low field system is open, costs less money, has no restrict demand for the power supply. It is a good choice for small hospitals in rural areas. The high field system, such as the 1.5 Tesla system or the 3.0 Tesla system, is the first choice for big hospitals. The high field system could provide highly qualified medical imaging for doctors. It is very interesting that the different systems are present at the same time and shared by different hospitals due to their distinctive advantages.
The MRI system is composed of main magnetic, gradient coil, radiofrequency (RF) coil, spectrometer system, power supply system and other affiliated parts. The RF coil is in charge of the emission and receive of the RF signals. It is one of the core parts in MRI system. Research of RF coil is very active and important in MRI field. There are many scholars who do great deal of research abroad. However the domestic research groups are much less, only several groups could do some research work in this field. RF coil could be divided into two kinds as the emission RF coil and the receive RF coil according to the different functions in the MRI system. The signals of RF coil are from tens of mega hertz to hundreds of mega hertz. The research of RF coil follows the ordinary laws in the electromagnetic field and also its own specialties.
The research method is different for RF coil working in different frequency. Generally speaking, quasi-static method, also named equivalent circuit method, is used to analyze the RF coil at low field. This method is simple and could provide accurate results of resonance frequency, decoupling, matching in RF coil. With the increase of the resonance frequency, the errors will increase obviously. While the sized of RF coil or human body are similar with the wave length, this method is not adaptive any more. For high field RF coil, full wave analysis method is developed to analyze the RF coil. The full wave method, including the time domain finite difference method (FDTD), the method of moment (MoM), the finite element method (FEM), could provide complete analysis of RF coil at high field without the restriction of the frequency. The FDTD, MoM and FEM are all taken as tools for the analysis of high field RF coil. The advantage of FDTD is that it is convenient to analyze the inhomogeneous media in the electromagnetic field. The disadvantage of FDTD is that the need of calculation resources is much. The advantage of MoM is that it is a good choice to get the current density distribution of RF coil with complex structures. The disadvantage of MoM is that it is not appropriate for the analysis of inhomogeneous media. The FEM method is usually used to solve problems in frequency field. The grid method of FEM has much relation to the accuracy. The latest development includes the hybrid method, such as the hybrid MoM/FDTD or the hybrid FEM/MoM. The hybrid method could provide both the advantages of the two methods and has promising application in RF coil field. The author has done some research work using the above methods and published some papers.
For the different demands of medical imaging, the geometrical shapes of RF coils are very different. There are solenoidal coil, saddle coil, birdcage coil, orthogonal coil, surface coil, array coils, implanted coil, etc. According to the different imaging parts of human body, the coils are divided as head coil, neck coil, head-neck coil, body coil, extremity coil, small organ coil, intra-cavity coil, etc. So the complicated structures of different RF coils have versatile medical applications. Because the RF coil is based on MRI system always, the development of RF coil is also related to the development of MRI system closely.
For the development of MRI system, it is always the theme trying to reach the new clinical demand. Recently it is a new development of MRI system for intra-operative application, especial for the MRI guided focused ultrasound surgery, which is developing very rapidly and becoming very attractive in this field. The thermal surgery of tumors is a main method to kill tumors. During the process of surgery, it is necessary to monitor the temperature of the targeted organ to control and evaluate the surgery. There are two ways to monitor the temperature, one is the invasive method and the other is the non-invasive method. Obviously the non-invasive method is better than the invasive one. The MR thermometry is a wonderful non-invasive method. Many parameters in MRI, including the proton resonance frequency, relaxation time, are temperature sensitive. The accuracy of MR thermometry is very encouraging and it is within±1℃at high field. The research to combine the MRI system and the focused ultrasound devices is the hot topic recently. There are great potential values of MRgFUS system in the surgery of fibroid, breast cancer, prostate cancer, liver cancer, brain cancer, etc. MRgFUS technology is even called "disruptive technology innovation"
RF coil is one of the core parts of MRI system, the research of RF coil in MRgFUS system is certainly an important topic. Comparing to the ordinary RF coil, the demand of intra-operative MRI system is different. It includes:(1) the physical path should be left for the pass of ultrasound beam, or for the intra-operative purposes; (2) the targeted organ is decided at first. At the same time, the general demands for RF coil, such as the homogeneous magnetic field for emission coil and high signal to noise ratio for receive coil, are still there. There is no specialized RF coil for intra-operative MRI system. Under the guidance of the supervisor professor Chen Wufan, with the aid of the 973 programs, a theoretical model, which is organ-oriented and specialized for intra-operative MRI, is proposed. The theoretical model includes the inverse method for the design of the organ-oriented RF coil, and the hybrid MoM/FDTD method for the optimization of RF coil. The prototype coils are built to verify the theoretical model.
In the inverse method, the current density distribution of the surface of RF coil is calculated from the magnetic field distribution of targeted organ. The coil design is deduced from the current density distribution. The latest development of inverse method includes the inverse design of breast coil proposed by Li,Y and the inverse design of phased array coils proposed by Muftuler, L.T. Li, Y designed a cone-shape breast coil and made MRI scan with the designed coil. Muftuler, L.T designed the phased array coils to shorten the time spent in MRI. By now, there are no reports of the application of inverse method in the design of the intra-operative RF coil. The reasons maybe are:(1) the technologies in the intra-operative MRI field are not well researched because of the youth of these technologies; (2) the need of intra-operative RF coil could be satisfied partially by the modification of traditional RF coil; (3) it is difficult to design the specialized intra-operative RF coil because of the complex structures. The physical path in the RF coil will make the design and manufacture more difficult. In order to solve the problems mentioned above, the author gives a new method to design the intra-operative RF coil, it is the organ-oriented inverse method. The new method is based on the current research, especial the research by Li,Y. The object of the new method is to improve the homogeneity of the B1 field. Because of the physical aperture in the designed RF coil, the mathematical model should be specialized. It is necessary to solve the integration equations to get the current density distribution on the surface of the RF coil. Usually the integration equations are ill-conditioned, they should be regularized to get the solutions. The final design of the inverse method is contoured from the solutions of the current density. So there must be errors between the final design and the original targeted distribution of magnetic field. The final design of the inverse method should be optimized further. Li,Y etc set several control nodes, and adjusted the positions of the different nodes according to the calculation results by quasi-static method. It is simple but there are two disadvantages. One is the causal setting of the control nodes and the other is that the quasi-static method could not meet the demand at high field.
In order to optimize the design result by the inverse method, the author proposed the hybrid MoM/FDTD method combining the human-body tissue model as load. The new hybrid MoM/FDTD method is based on the proposals of Huygens equivalent surfaces from Feng,Liu. Furthermore the complex coil-tissue interactions are considered in the new method. The current density distribution of the intra-operative RF coil is calculated by MoM method. It is necessary to set appropriate parameters of resonance capacitors, decoupling capacitors, detuning circuits and matching circuits. Then the Huygens equivalent surfaces are set according to the Huygens equivalence law. The Huygens equivalent surfaces are the interconnections between MoM and FDTD. The current density distribution of the Huygens equivalent surfaces is decided through mapping from the MoM results. The inner space surrounding by the Huygens equivalent surfaces is the FDTD domain, where the targeted organ is located. The electromagnetic model of the targeted organ is established and taken as load in FDTD domain. The author takes the advantage of FDTD to calculate the electromagnetic field with the inhomogeneous targeted organ model. The appropriate time and space steps are set in the FDTD solver. The perfect matched layers are set also. The accuracy of the solution is related to the resources of the computer also. After the steady solution is achieved in the FDTD domain, the current density distribution on the Huygens equivalent surfaces is changed accordingly. Then the new current density distribution is mapped back to change the current density distribution on the surfaces of the RF coil. After that a new round of optimization would restart again till the current density distribution on the Huygens equivalent surfaces reach the final stabilization and would not change any more. Thus the optimization is finished and the final design of the RF coil is decided. Some research work using the hybrid MoM/FDTD is accepted for publication in the IEEE ISBI meeting in 2011.
Finally the prototype RF coil is built to verify the theoretical model. It is proved that the proposed theoretical model is practical and could meet demand of the MR thermometry. The related research results were published in "Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering" which is SCI indexed.
磁共振系统问世时间虽短,但已经得到飞速发展,从最早期的永磁体(低场)磁共振系统,发展到今天的超高场超导磁体系统(主磁场超过10T)。低场系统整体成本低,具有开放式结构,对电源要求不高,适合中小医院和偏远地区使用。高场磁共振系统,主要是1.5T和3.0T为代表的超导磁共振系统,是大型医院的主流设备,这类超导系统能够提供丰富的医学成像信息,临床价值有目共睹。不同系统能够发挥各自优势,形成了共存的局面,这是一种非常有趣的现象。
磁共振系统的主要组成部分包括主磁体、梯度线圈、射频线圈、谱仪系统、电源系统和辅助设备等。其中射频线圈既起到激发磁共振射频信号的作用,又起到接收磁共振信号的作用,是磁共振系统核心部件之一,对磁共振成像质量起到至关重要的作用,是磁共振系统重要研究课题,相关研究非常活跃,国外从事射频研究的学者和机构非常多,国内只有少数几所大学具有相关的科研条件和研究能力。根据射频线圈在系统中所起的作用不同,又分为发射线圈和接收线圈两类。起发射射频信号作用的称为发射线圈,起接收射频信号作用的称为接收线圈。射频线圈一般都是作用在射频频率范围内(几十兆赫兹到几百兆赫兹),因此射频线圈的研发遵循射频电磁场的普遍规律,同时又有着自身的特殊性。
对于不同频率范围的射频线圈,其研究方法也不相同。一般而言,对于低场射频线圈,可以采用准静态电磁分析方法,或者叫做等效电路方法。等效电路方法相对而言比较简单,这种方法能够比较准确地计算出射频线圈的共振频率和射频线圈不同单元之间的耦合、匹配等。但是随着共振频率的提高,这种方法的误差将增大。特别是当射频线圈或者人体器官的尺寸接近射频波长后,就不再适用了。对于高场射频线圈,需要采用全波电磁场分析方法,全波分析方法可以不受射频频率的限制,能够比较全面地反映射频线圈的性能,但是相对而言比较复杂。各种电磁场数值分析方法如时域有限差分法(FDTD)、矩量法(MoM)、有限元法(FEM)等都属于全波分析方法之一,它们各有优缺点,并且在射频线圈的设计中都有广泛的应用。FDTD方法的优点是适合计算具有不均匀电磁介质的电磁场,缺点是计算量比较大。MoM方法的优点是适合计算复杂形状的射频线圈的电流密度分布,缺点是不适合计算有不均匀电磁介质存在的电磁场分布。FEM方法一般是在频域求解电磁场问题,其网格划分的方法对电磁计算精度影响较大。最新的射频线圈的设计方法中还包含了各种不同的混合电磁计算数值方法,如混合FDTD/MoM方法,混合FEM/MoM方法等,这些混合方法能够结合不同数值方法的优势,同时避免其各自的劣势,有很好的发展前景。本论文作者对常用的电磁场数值分析方法和混合方法进行了相关的研究工作,并有部分研究成果发表。
根据不同的成像需求,射频线圈具有不同的几何形状。主要有螺线管形射频线圈,鞍形射频线圈,鸟笼型射频线圈,正交型线圈,表面线圈,阵列线圈,植入体内的微型线圈等多种形式。根据临床应用部位不同,又可以分为头线圈,颈线圈,头颈联合线圈,体线圈,肢体线圈,浅表组织线圈,腔内线圈等不同类别。可见,射频线圈具有复杂的几何形态,具有多种多样的临床用途。射频线圈总是基于一定的磁共振系统,因此射频线圈的研究和发展与磁共振系统的研究和发展是息息相关的。
对于磁共振系统而言,不断满足临床提出的新需求是其永恒的发展主题。近年来,术中应用是磁共振崭新的发展方向,实现术中磁共振测温引导的热消融肿瘤治疗技术宛若一颗冉冉升起的新星,备受业内人士关注。热消融是临床治疗肿瘤的重要手段,它通过一定的加热方法,使肿瘤组织的温度升高到一定程度从而使肿瘤组织坏死,达到治疗的目的。在热消融手术过程中,需要对加热部位的组织温度进行准确监测,以便正确控制热消融手术的温度和作用时间,恰当评估热消融手术效果。目前测温的方法分为有创和无创两种。有创测温是在术中利用温度探头,直接测量温度,虽然准确但是对病人有损伤,临床应用范围受到限制,无创测温是更佳的选择。在无创测温的各种方法中,最具有吸引力的就是磁共振术中测温。磁共振成像中,质子共振频率、弛豫时间等多种参数都是温度敏感的,能够反映人体组织温度变化情况,因此通过测量磁共振成像的相关参数可以准确测得目标器官的温度,目前高场下的测温精度已经可以达到±1℃。发展至今,磁共振测温已经成功应用于临床,成为最受欢迎、最有发展前景的一种体外无创测温技术。将热消融治疗装置和磁共振设备二者整合,实现磁共振影像引导下术中测温热消融治疗,一直是国内外生物医学工程领域的研究热点,特别是磁共振测温引导下的聚焦超声消融手术(MRgFUS),在无创治疗子宫肌瘤、乳腺癌、前列腺癌、肝癌、脑恶性胶质瘤等多个器官肿瘤疾病方面都具有巨大应用价值,被称为“颠覆性的技术革新”。
射频线圈作为磁共振系统的核心部件之一,自然也是术中磁共振系统的重点研究内容之一。与常规磁共振成像检查不同,术中磁共振系统对射频线圈提出了新的要求,主要包括：(1)术中射频线圈需要兼容采用的术中治疗手段,比如术中射频线圈需要为聚焦超声波提供物理通道等；(2)术中射频线圈的成像目标器官非常明确,是为治疗目的服务的,而常规射频线圈是为诊断目的服务的。当然,均匀的发射射频场,高的射频接收信噪比等是对术中线圈和常规线圈共同的要求。目前,常规的射频线圈只能部分满足术中磁共振的需求,还没有专门的术中测温磁共振系统射频线圈。针对术中磁共振系统对射频线圈的特殊要求,在导师陈武凡教授的指导下,依国家科技部973项目内容要求,本论文提出了面向器官的术中射频线圈设计理论模型,主要包括：逆方法设计面向器官的术中射频线圈理论方法和混合MoM/FDTD电磁计算数值方法工程优化术中射频线圈理论方法。并制作相应的原型实验线圈,验证理论模型的正确性。
逆方法根据预先设定的目标电磁场分布来倒推出射频线圈表面电流密度分布,由线圈表面电流密度分布再倒推出射频线圈表面导线排布,最终完成射频线圈设计。国际上,逆方法研究的最新进展包括Li,Y等提出的乳房线圈设计和Muftuler, L. T等提出的并行成像阵列线圈设计。Li,Y等运用逆方法,依据乳房器官特殊的几何形状,设计了一种倒三角锥形状的射频线圈,并成功实现磁共振扫描成像。Muftuler, L. T等设计的并行成像阵列线圈是为了提高磁共振成像速度而设计的,也是采用逆方法原理倒推出设计方案。目前,还未见将逆方法应用于设计磁共振术中测温系统专用射频线圈的相关报道。关于术中适用磁共振射频线圈设计的理论研究少见报道的原因,大致有以下几个方面：(1)磁共振术中测温应用是近几年兴起的临床应用新技术,许多相关的技术和理论都还有待深入研究；(2)对传统的磁共振射频线圈做相应改进后,可以部分满足MRgFUS系统等的需求；(3)术中磁共振射频线圈设计,形状复杂,比较困难。术中射频线圈在排布导线的时候,要求能够同时结合术中应用的需求,比如留置术中通道等,这些都将使设计和工程实现的难度大幅增加。针对磁共振术中测温系统对射频线圈的特殊需求,在现有国内外射频线圈设计理论研究成果的基础上,本论文借鉴Li,Y等人乳房射频线圈的研究成果,结合磁共振术中测温专门针对某个器官的特点,提出了面向器官的逆方法设计思路,即设计的目标是使器官所在部位的射频场(B1场)分布尽量均匀一致。同时,由于术中通道的存在,在逆方法设计时,需要结合术中通道的位置建立相关模型。逆方法在设计过程中,需要对射频线圈表面电流密度积分方程组进行求解来得到射频线圈表面电流密度分布图。一般情况下,该积分方程组是病态的,需要正则化后求解。因此,求得的解是近似解。由近似解进一步抽象出来的射频线圈设计方案,与设计目标相比本身就具有一定的误差,需要进一步优化。Li,Y等采用的优化方法是在线圈表面设定数个控制点,调整控制点的位置,通过准静态场(quasi-static)近似计算方法来计算B,场的分布。这种优化方法有两个缺点,一是控制点的选取有随意性,二是B1场的计算仅仅依靠比奥-萨伐尔定律(Biot-Savart law),方法过于简单,没有考虑工程中必然遇到的B1场与人体组织之间复杂的电磁作用效应,仅适用于低场,高场下误差比较大。
为了解决优化问题,作者借鉴MoM/FDTD混合方法最新研究成果,提出了计算电磁混合MoM/FDTD工程优化方法。MoM/FDTD混合方法的最新进展是Feng Liu等人提出的基于惠更斯等效面原理的MoM方法和FDTD混合方法。本文在此基础上,提出了建立目标器官的电磁模型,作为负载代入FDTD域,在该混合方法中考虑了工程中必然遇到的B,场与人体组织之间复杂的电磁作用效,使优化设计结果更符合工程实际。作者运用MoM电磁场算法计算结构复杂的术中射频线圈的电流密度分布。在用MoM法计算电流密度分布图时,考虑了工程实际需要,设置合适的电路参数,使线圈在设定的频率上共振,同时选择合适的去耦电路和去谐电路进行仿真。所选用的去耦电路呈容性特性,选用的去谐电路起保护电路的作用,对共振电流没有影响。接下来,依据惠更斯等效原理,设置惠更斯等效面,作为MoM方法和FDTD方法结合的纽带,将用MoM法计算得到的电流密度分布图等效映射到惠更斯等效面上。选用的惠更斯等效面围蔽的空间就是FDTD作用域,该域包含了设定的目标器官。目标器官建立电磁模型,将电磁模型作为负载代入FDTD域求解。FDTD方法的优势是能够方便求解包含复杂介质的电磁场,作者在本研究中利用FDTD方法的这个优势,将目标器官作为线圈负载,选取合适时间步长,空间步长,以及设定合适的完全吸收边界条件(PML),考虑实验室计算机硬件条件和解的精度需要等情况,通过实验最终确定FDTD解。FDTD域内的解代表形成稳定的共振后FDTD区域边界,即惠更斯等效面上的新的电流密度分布图。根据耦合原理,用新得到的电流密度分布图来修正待优化的射频线圈表面的电流密度分布,也就是修正射频线圈表面上的导线排布位置。然后,对修正后的射频线圈再一次重复上述的优化过程。当惠更斯等效面的电流密度分布最终达到稳定时,优化循环结束,得到最终射频线圈优化设计方案。混合MoM/FDTD工程优化方法研究部分成果被业界普遍认可的2011年IEEE ISBI会议收录。
作者最后制作了相应的原型实验射频线圈,对上述的理论设计模型进行了验证,证明该理论方法可行,能够满足磁共振系统术中测温的需求。相关研究的部分成果发表在" Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering"杂志上(SCI收录)。
Magnetic resonance imaging (MRI) is an important medical imaging technology, and now it is applied at clinic widely. MRI and related technology have great influence and scientific values because the scientists get the Nobel prizes five times totally in this field. The prominent advantages of MRI are the wonderful solution for soft issues and no risk of radioactivity. From these points of view, MRI is much better than other medical imaging technology such as X-ray CT, ultrasound etc. It is still at the beginning for the development of medical MRI technology and there should be great achievement for its application at clinic in prospect.
Since the MRI system was developed several decades ago, it has been developed very rapidly. The strength of the main magnetic field covers from 0.2 Tesla to more than 10Tesla. The low field system is open, costs less money, has no restrict demand for the power supply. It is a good choice for small hospitals in rural areas. The high field system, such as the 1.5 Tesla system or the 3.0 Tesla system, is the first choice for big hospitals. The high field system could provide highly qualified medical imaging for doctors. It is very interesting that the different systems are present at the same time and shared by different hospitals due to their distinctive advantages.
The MRI system is composed of main magnetic, gradient coil, radiofrequency (RF) coil, spectrometer system, power supply system and other affiliated parts. The RF coil is in charge of the emission and receive of the RF signals. It is one of the core parts in MRI system. Research of RF coil is very active and important in MRI field. There are many scholars who do great deal of research abroad. However the domestic research groups are much less, only several groups could do some research work in this field. RF coil could be divided into two kinds as the emission RF coil and the receive RF coil according to the different functions in the MRI system. The signals of RF coil are from tens of mega hertz to hundreds of mega hertz. The research of RF coil follows the ordinary laws in the electromagnetic field and also its own specialties.
The research method is different for RF coil working in different frequency. Generally speaking, quasi-static method, also named equivalent circuit method, is used to analyze the RF coil at low field. This method is simple and could provide accurate results of resonance frequency, decoupling, matching in RF coil. With the increase of the resonance frequency, the errors will increase obviously. While the sized of RF coil or human body are similar with the wave length, this method is not adaptive any more. For high field RF coil, full wave analysis method is developed to analyze the RF coil. The full wave method, including the time domain finite difference method (FDTD), the method of moment (MoM), the finite element method (FEM), could provide complete analysis of RF coil at high field without the restriction of the frequency. The FDTD, MoM and FEM are all taken as tools for the analysis of high field RF coil. The advantage of FDTD is that it is convenient to analyze the inhomogeneous media in the electromagnetic field. The disadvantage of FDTD is that the need of calculation resources is much. The advantage of MoM is that it is a good choice to get the current density distribution of RF coil with complex structures. The disadvantage of MoM is that it is not appropriate for the analysis of inhomogeneous media. The FEM method is usually used to solve problems in frequency field. The grid method of FEM has much relation to the accuracy. The latest development includes the hybrid method, such as the hybrid MoM/FDTD or the hybrid FEM/MoM. The hybrid method could provide both the advantages of the two methods and has promising application in RF coil field. The author has done some research work using the above methods and published some papers.
For the different demands of medical imaging, the geometrical shapes of RF coils are very different. There are solenoidal coil, saddle coil, birdcage coil, orthogonal coil, surface coil, array coils, implanted coil, etc. According to the different imaging parts of human body, the coils are divided as head coil, neck coil, head-neck coil, body coil, extremity coil, small organ coil, intra-cavity coil, etc. So the complicated structures of different RF coils have versatile medical applications. Because the RF coil is based on MRI system always, the development of RF coil is also related to the development of MRI system closely.
For the development of MRI system, it is always the theme trying to reach the new clinical demand. Recently it is a new development of MRI system for intra-operative application, especial for the MRI guided focused ultrasound surgery, which is developing very rapidly and becoming very attractive in this field. The thermal surgery of tumors is a main method to kill tumors. During the process of surgery, it is necessary to monitor the temperature of the targeted organ to control and evaluate the surgery. There are two ways to monitor the temperature, one is the invasive method and the other is the non-invasive method. Obviously the non-invasive method is better than the invasive one. The MR thermometry is a wonderful non-invasive method. Many parameters in MRI, including the proton resonance frequency, relaxation time, are temperature sensitive. The accuracy of MR thermometry is very encouraging and it is within±1℃at high field. The research to combine the MRI system and the focused ultrasound devices is the hot topic recently. There are great potential values of MRgFUS system in the surgery of fibroid, breast cancer, prostate cancer, liver cancer, brain cancer, etc. MRgFUS technology is even called "disruptive technology innovation"
RF coil is one of the core parts of MRI system, the research of RF coil in MRgFUS system is certainly an important topic. Comparing to the ordinary RF coil, the demand of intra-operative MRI system is different. It includes:(1) the physical path should be left for the pass of ultrasound beam, or for the intra-operative purposes; (2) the targeted organ is decided at first. At the same time, the general demands for RF coil, such as the homogeneous magnetic field for emission coil and high signal to noise ratio for receive coil, are still there. There is no specialized RF coil for intra-operative MRI system. Under the guidance of the supervisor professor Chen Wufan, with the aid of the 973 programs, a theoretical model, which is organ-oriented and specialized for intra-operative MRI, is proposed. The theoretical model includes the inverse method for the design of the organ-oriented RF coil, and the hybrid MoM/FDTD method for the optimization of RF coil. The prototype coils are built to verify the theoretical model.
In the inverse method, the current density distribution of the surface of RF coil is calculated from the magnetic field distribution of targeted organ. The coil design is deduced from the current density distribution. The latest development of inverse method includes the inverse design of breast coil proposed by Li,Y and the inverse design of phased array coils proposed by Muftuler, L.T. Li, Y designed a cone-shape breast coil and made MRI scan with the designed coil. Muftuler, L.T designed the phased array coils to shorten the time spent in MRI. By now, there are no reports of the application of inverse method in the design of the intra-operative RF coil. The reasons maybe are:(1) the technologies in the intra-operative MRI field are not well researched because of the youth of these technologies; (2) the need of intra-operative RF coil could be satisfied partially by the modification of traditional RF coil; (3) it is difficult to design the specialized intra-operative RF coil because of the complex structures. The physical path in the RF coil will make the design and manufacture more difficult. In order to solve the problems mentioned above, the author gives a new method to design the intra-operative RF coil, it is the organ-oriented inverse method. The new method is based on the current research, especial the research by Li,Y. The object of the new method is to improve the homogeneity of the B1 field. Because of the physical aperture in the designed RF coil, the mathematical model should be specialized. It is necessary to solve the integration equations to get the current density distribution on the surface of the RF coil. Usually the integration equations are ill-conditioned, they should be regularized to get the solutions. The final design of the inverse method is contoured from the solutions of the current density. So there must be errors between the final design and the original targeted distribution of magnetic field. The final design of the inverse method should be optimized further. Li,Y etc set several control nodes, and adjusted the positions of the different nodes according to the calculation results by quasi-static method. It is simple but there are two disadvantages. One is the causal setting of the control nodes and the other is that the quasi-static method could not meet the demand at high field.
In order to optimize the design result by the inverse method, the author proposed the hybrid MoM/FDTD method combining the human-body tissue model as load. The new hybrid MoM/FDTD method is based on the proposals of Huygens equivalent surfaces from Feng,Liu. Furthermore the complex coil-tissue interactions are considered in the new method. The current density distribution of the intra-operative RF coil is calculated by MoM method. It is necessary to set appropriate parameters of resonance capacitors, decoupling capacitors, detuning circuits and matching circuits. Then the Huygens equivalent surfaces are set according to the Huygens equivalence law. The Huygens equivalent surfaces are the interconnections between MoM and FDTD. The current density distribution of the Huygens equivalent surfaces is decided through mapping from the MoM results. The inner space surrounding by the Huygens equivalent surfaces is the FDTD domain, where the targeted organ is located. The electromagnetic model of the targeted organ is established and taken as load in FDTD domain. The author takes the advantage of FDTD to calculate the electromagnetic field with the inhomogeneous targeted organ model. The appropriate time and space steps are set in the FDTD solver. The perfect matched layers are set also. The accuracy of the solution is related to the resources of the computer also. After the steady solution is achieved in the FDTD domain, the current density distribution on the Huygens equivalent surfaces is changed accordingly. Then the new current density distribution is mapped back to change the current density distribution on the surfaces of the RF coil. After that a new round of optimization would restart again till the current density distribution on the Huygens equivalent surfaces reach the final stabilization and would not change any more. Thus the optimization is finished and the final design of the RF coil is decided. Some research work using the hybrid MoM/FDTD is accepted for publication in the IEEE ISBI meeting in 2011.
Finally the prototype RF coil is built to verify the theoretical model. It is proved that the proposed theoretical model is practical and could meet demand of the MR thermometry. The related research results were published in "Concepts in Magnetic Resonance Part B-Magnetic Resonance Engineering" which is SCI indexed.
引文
[1]王涛,谭小丹,李贞姬,陈炜晨,辛学刚,医用物理学,北京：北京邮电大学出版社,2009.
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[3]J.M. Jin, Electromagnetic analysis and design in magnetic resonance imaging, Boca Raton FL:CRC,1998.
[4]F.W. Grover, Inductance calculations:working formulas and tables:Dover Pubns, 1962.
[5]K. Yee, Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media, Ieee T Antenn Propag, vol.14, (no.3), pp.302-307,1966.
[6]T.L. Wang and A.C. Tripp, FDTD simulation of EM wave propagation in 3-D media, Geophysics, vol.61, (no.1), pp.110-120,1996.
[7]K.L. Shlager and J.B. Schneider, A selective survey of the finite-difference time-domain literature, Antennas and Propagation Magazine, IEEE, vol.37, (no. 4), pp.39-57,1995.
[8]Y. Han and S.M. Wright, Analysis of RF penetration effects in MRI using finite-difference time-domain method, in Book Analysis of RF penetration effects in MRI using finite-difference time-domain method, Series Analysis of RF penetration effects in MRI using finite-difference time-domain method,1993, pp.* 1327.
[9]H.C. Taylor, M. Burl and J.W. Hand, Experimental verification of numerically predicted electric field distributions produced by a radiofrequency coil, Phys Med Biol, vol.42, (no.7), pp.1395-1402,1997.
[10]C.M. Collins and M.B. Smith, Calculations of B(1) distribution, SNR, and SAR for a surface coil adjacent to an anatomically-accurate human body model., Magn Reson Med, vol.45, (no.4), pp.692-9,2001.
[11]J.H. Wang, Q.X. Yang, X.L. Zhang, C.M. Collins, M.B. Smith, X.H. Zhu, G. Adriany, K. Ugurbil, and W. Chen, Polarization of the RF field in a human head at high field:A study with a quadrature surface coil at 7.0 T, Magnet Reson Med, vol.48, (no.2), pp.362-369,2002.
[12]J.M. Jin, J. Chen, W.C. Chew, H. Gan, R.L. Magin, and P.J. Dimbylow, Computation of electromagnetic fields for high-frequency magnetic resonance imaging applications., Phys Med Biol, vol.41, (no.12), pp.2719-38,1996.
[13]J. Chen, Z.M. Feng and J.M. Jin, Numerical simulation of SAR and B-1-field inhomogeneity of shielded RF coils loaded with the human head, Ieee T Bio-Med Eng, vol.45, (no.5), pp.650-659,1998.
[14]A. Taflove and S.C. Hagness, Computational electrodynamics:the finite-difference time-domain method:Artech House Boston,1995.
[15]A. Taflove and M.E. Brodwin, Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations, Microwave Theory and Techniques, IEEE Transactions on, vol.23, (no.8), pp.623-630,1975.
[16]J.P. Berenger, A PERFECTLY MATCHED LAYER FOR THE ABSORPTION OF ELECTROMAGNETIC-WAVES, J Comput Phys, vol.114, (no.2), pp. 185-200,1994.
[17]F. Bloch, Nuclear induction, Physica, vol.17, (no.3-4), pp.272-281,1951.
[18]E.M. Purcell, H.C. Torrey and R.V. Pound, Resonance Absorption by Nuclear Magnetic Moments in a Solid, Physical Review, vol.69, (no.1-2), pp.37-38, 1946.
[19]B. Cook and I.J. Lowe, Large-inductance, high-frequency, high-Q, series-tuned coil for NMR., J. MAGNETIC RESON., vol.49, (no.2), pp.346-349,1982.
[20]J.J.H. Ackerman, T.H. Grove, G.G. Wong, D.G. Gadian, and G.K. Radda, Mapping of metabolites in whole animals by 31P NMR using surface coils, Nature, vol.283, (no.5743), pp.167-170,1980.
[21]D.M. Ginsberg and M.J. Melchner, Optimum geometry of saddle shaped coils for generating a uniform magnetic field, Rev Sci Instrum, vol.41, (no.1), pp. 122-123,1970.
[22]H.J. Schneider and P. Dullenkopf, Slotted tube resonator:a new NMR probe head at high observing frequencies, Rev Sci Instrum, vol.48, (no.1), pp.68-73, 1977.
[23]D.A.A.D. Grant, An Efficient Decoupler Coil Design which Reduces Heating in Conductive Samples in Superconducting Spectrometers, in Book An Efficient Decoupler Coil Design which Reduces Heating in Conductive Samples in Superconducting Spectrometers, vol.36, Series An Efficient Decoupler Coil Design which Reduces Heating in Conductive Samples in Superconducting Spectrometers,1979,pp.*447-451.
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[25]H. Barfuss, H. Fischer, D. Hentschel, R. Ladebeck, A. Oppelt, R. Wittig, W. Duerr, and R. Oppelt, In vivo magnetic resonance imaging and spectroscopy of humans with a 4t whole-body magnet, Nmr Biomed, vol.3, (no.1), pp.31-45, 1990.
[26]C.E. Hayes, W.A. Edelstein, J.F. Schenck, O.M. Mueller, and M. Eash, An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5 T, vol.63, (no.3), pp.622-628,1985.
[27]M.C. Leifer, Theory of the quadrature elliptic birdcage coil., Magn Reson Med, vol.38, (no.5), pp.726-32,1997.
[28]S. Bobroff and M.J. McCarthy, Variations on the slotted-tube resonator: Rectangular and elliptical coils, Magn Reson Imaging, vol.17, (no.5), pp. 783-789,1999.
[29]C.E. Hayes, An endcap birdcage resonator for quadrature head imaging, Magn. Reson. Med, vol.5, pp.39-40,1986.
[30]D. Ballon, M.C. Graham, S. Miodownik, and J.A. Koutcher, A 64 MHz half-birdcage resonator for clinical imaging, Journal of Magnetic Resonance (1969), vol.90, (no.1), pp.131-140,1990.
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