Reciprocity and gyrotropism in magnetic resonance transduction
Reciprocity and gyrotropism in magnetic resonance transduction
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DOI：
10.1103/physreva.74.062103
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发表时间：
2006-12-01
影响因子：
2.9
通讯作者：
Tropp, James
中科院分区：
文献类型：
--
作者：
Tropp, James
我们给出了磁共振中转导的公式，即。基于修正洛伦兹互易原理的自旋拉莫尔进动引起的电动势的出现（也称为“非互易”）介质，即磁化率张量通过对外部静场的反转而转置[参见，r.f. Harrington和a.t. Villeneuve IRE Trans。微波理论与技术[j].微波学报，2008,38（1958）。先前的互易性在磁共振中的应用，尽管取得了很大的成功，但忽略了由于核和/或不成对的电子自旋而必然产生的回旋性。对于以拉莫尔频率振荡的线极化场的检测，电动势用包含两个因素积的体积积分来表示，我们将这两个因素定义为天线方向图，即（H-1x +/- iH(1y)），其中，例如，对于单个收发器天线，H只是空间相关的振荡磁场强度，根据天线终端上的一些参考电流的应用，负号为传输。正极表示接收。类似的表达式也适用于分离的发射和接收天线；给出了场的圆偏振的表达式。然后，我们展示了用于质子磁共振成像的两个元素的仅接收阵列天线，由于元素的杂散反应耦合引起的强度伪影，尽管其本身具有双边对称性，但仍产生含有盐水水溶液的对称圆柱形幽灵的不对称质子核磁共振图像[J]。特罗普和T. Schirmer， J. Magn。《理性》，151,146（2001）。修改这个双端口天线，使其在发射-接收模式下工作，使我们能够展示高度非互反的行为：也就是说，当两个天线端口交换传输和接收的角色时，记录图像（含有盐水溶液的圆柱形测试幽灵）的外观发生了巨大变化，其中一个实例的信号强度模式的形式类似于伞（即，具有中等强度的中心柱，上面有一个明亮的顶篷），而另一个实例的信号强度模式是一个扭曲的椭圆形，在其水平极端处有轻微的凹陷。它的轮廓像猫眼。如果将静态偏振场反转，则图像模式与驱动方案之间的关系可以反转。电磁和电路计算，加上修正的互易原理，使我们能够在数值模拟中再现这些模式变化，密切而令人信服。虽然成像实验是在3.0 T的静态场下进行的，因此拉莫尔频率为128 MHz，但非互反效应与水介质中波长的长短无关，但在基于准静态或全电磁体制的模拟中都同样出现。最后，我们表明，尽管发射和接收的天线方向图随着极化场的反转而交换，这意味着接收方向图等于磁场反转的发射方向图，但这并不会使磁共振中熟悉的自旋动力学的旋转波模型失效。
We give formulas for transduction in magnetic resonance-i.e., the appearance of an emf due to Larmor precession of spins-based upon the modified Lorentz reciprocity principle for gyrotropic (also called "nonreciprocal") media, i.e., in which a susceptibility tensor is carried to its transpose by reversal of an external static field [cf., R. F. Harrington and A. T. Villeneuve IRE Trans. Microwave Theory and Technique MTT6, 308 (1958)]. Prior applications of reciprocity to magnetic resonance, despite much success, have ignored the gyrotropism which necessarily arises due to nuclear and/or unpaired electronic spins. For detection with linearly polarized fields, oscillating at the Larmor frequency, the emf is written in terms of a volume integral containing a product of two factors which we define as the antenna patterns, i.e., (H-1x +/- iH(1y)), where, e.g., for a single transceive antenna, the H's are just the spatially dependent oscillatory magnetic field strengths, per the application of some reference current at the antenna terminals, with the negative sign obtaining for transmission, and the positive for reception. Similar expressions hold for separate transmit and receive antennas; expressions are also given for circular polarization of the fields. We then exhibit a receive-only array antenna of two elements for magnetic resonance imaging of protons, which, due an intensity artifact arising from stray reactive coupling of the elements, produces, despite its own bilateral symmetry, asymmetric proton NMR images of a symmetric cylindrical phantom containing aqueous saline solution [J. Tropp and T. Schirmer, J. Magn. Reson. 151, 146 (2001)]. Modification of this two-port antenna, to function in transmit-receive mode, allows us to demonstrate highly nonreciprocal behavior: that is, to record images (of cylindrical test phantoms containing aqueous saline solution) whose appearance dramatically changes, when the roles of transmission and reception are swapped between the two antenna ports-giving in one instance a signal intensity pattern whose form resembles an umbrella (i.e., with a central column of moderate intensity surmounted by a bright canopy), and in the other, a distorted oval with slight concavities at its horizontal extremes, whose outline suggests that of a cat's eye. The relation between image patterns and drive scheme can be shown to reverse if the static polarizing field is reversed. Electromagnetic and circuit calculations, together with the modified reciprocity principle, allow us to reproduce these pattern changes in numerical simulations, closely and convincingly. Although the imaging experiments are performed at a static field of 3.0 T, and consequently a Larmor frequency of 128 MHz, the nonreciprocal effects are not related to the shortness of the wavelength in aqueous medium, but appear equally in simulations based in either the quasistatic or full electromagnetic regimes. Finally, we show that although antenna patterns for transmission and reception are swapped with reversal of the polarizing field, meaning that the receive pattern equals the transmit pattern with the field reversed, this in no way invalidates the familiar rotating wave model of spin dynamics in magnetic resonance.