RF Engineering: Live Construction of A Coil Let s build an RF human coil. Hiroyuki Fujita, Ph.D. 1,2,3,4,5 with Tsinghua Zheng, MSEE 1,2

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1 RF Engineering: Live Construction of A Coil Let s build an RF human coil. Hiroyuki Fujita, Ph.D. 1,2,3,4,5 with Tsinghua Zheng, MSEE 1,2 1 Quality Electrodynamics (QED), LLC 2 eqed, LLC 700 Beta Drive, Suite 100, Mayfield Village, Ohio Department of Physics, Case Western Reserve University 4 Department of Radiology, University Hospitals of Cleveland Euclid Avenue, Cleveland, Ohio , USA 5 School of Information Technology and Electrical Engineering, The University of Queensland, Brisbane Qld 4072, Australia Introduction Last year, we gave our live demonstration entitled Live construction of coils in 60 minutes: an 8-channel cardiac array coil [1]. This is a continued program in which we will be constructing another RF human coil. Recent advances of MR scanner design involve an ever-increasing number of receiver channels (32-128) for faster scans. While 1.5T and 3T fast MRI clinical applications are now realized and accepted as everyday routine clinical practices, 7T MRI is also emerging because of its capability to study neurodegenerative diseases, e.g., Alzheimer, and biochemical functional imaging to analyze physico-chemical parameters used for examining tissue morphology, blood flow, metabolism and chemistry in vivo. Regardless of the field strengths, the key requirements are maximum achievable signal-to-noise ratio and multi-detector array coil optimization within the framework of the parallel imaging scheme to enable more advanced and faster clinical MR scans. lifiers are also one of the key components in the detector array coils. In this talk, while appreciating the RF coil theory, we will construct an RF human coil. To prepare ourselves for the demonstration, the important and fundamental principles of MRI RF array coils are reviewed. The reader is also encouraged to review our last year s presentation which is available online.

2 Background The subject on modern RF array coil designs is indeed quite deep and requires a broad-range knowledge of MR physics and electronics. It is informative for the reader to know that the number of components/parts used in today s typical detector array coils, from, say, an 8-channel head coil to a 32-channel head coil, ranges from 400 to If one component is broken or damaged, the coil no longer functions in its optimized way. This should indicate how complex/delicate today s array coils are. In order for the RF coil to function properly, every component of the RF coil must be integrated, assembled (soldered) and manufactured right. Provided below is the table listing what we typically need to build an RF coil. Some commercially available sources are given. Equipment, Parts Manufacturer Website & Materials Network Analyzer Agilent Technology DC Power Supply MASTECH Solder Station Hakko Solder Kester Digital Multi-meter Fluke Capacitor ATC, Voltronics Inductor CoilCraft Pin Diode MaCom Signal Diode Microsemi Resistor (Surface BREL Mount) Connectors (RF, ODU, Hypertronics

3 DC) Trimmer Capacitor Johanson Coaxial Cable Coast Wire RF Coil Theory Review Hoult provides a detailed overview and discussion on the NMR receiver in his historic paper [2]. Most of today s RF receive coil designs are based upon the phased array coil technology proposed by Roemer et al. in 1990 [3], and its application to volume imaging was discussed by Hayes et al. in 1991 [4]. The reader is also encouraged to read a detailed review of array coil theory and application by Wright and Wald [5]. It is well known that a small surface coil yields higher SNR at the distances closer to the surfaces of the coil when compared with that of a volume coil such as the birdcage coil [6]. On the other hand, a small surface coil B 1 -sensitive region is much smaller than that of a volume coil. What is remarkable in the phased array coil approach is that the high SNR associated with a small surface coil can be achieved and maintained over an extended FOV, by using a set of RF coils, which may be comparable to that of a volume coil. This is enabled by the development of various array coil designs for imaging applications of interest and the techniques to decouple the mutual inductances and thus the cross talk among the array coil elements. Adjacent coil elements are often partially overlapped to cancel the mutual inductance between the elements. Next nearest and other coil elements can be mutually decoupled by the use of a low input impedance (typically less than 5 Ohms) preamplifier decoupling circuit. Other decoupling techniques and methods are described briefly later in this paper. For detailed discussions of low noise amplifiers, the reader may refer to [7]. What the low input impedance preamplifier effectively does in conjunction with a coil matching/decoupling circuit is to eliminate the current flow in the coil element loop, thereby eliminating the magnetic fields induced in the neighboring coil elements, as shown later in this syllabus contribution. In designing array coils, baluns and considerations pertaining to cable routing are also important design factors to consider. Shown in Figure 1 is the illustration of how the cables couple with the patient and why baluns need to be implemented. The details are discussed elsewhere [8].

4 Sample Figure 1 A side (sagittal) view of MRI scanner showing the electromagnetic coupling due to the stray capacitances present. Baluns are added to block the common mode current and allow the differential mode current to flow. Signal-to-Noise Ratio SNR is one of the most important parameters to be optimized in MRI applications, and its detailed discussion is given in [9]. (It is, however, noted that SNR is destined to be degraded or lowered from the starting point, i.e., the signal source, to the end point of the receive chain. Thus, the question is how to minimize the loss of SNR in that process.) Here, it is essential to understand how SNR relates to the coil-related parameters. The signal is written as 3 γ B 2 S ( r) Eq. (1) 0 B xy 1 where γ is the nuclear gyromagnetic ratio, B 0 the static magnetic field, and B xy 1 (r) the RF magnetic field produced by a coil with a unit current 1A. Thus, in designing a coil, B xy 1 (r) must be optimized. What this means is that the coil size over a target FOV and the distance from the FOV both need to be appropriately chosen to maximize B xy 1 (r). The size to be chosen also depends upon the number of available receiver channels, in general. On the other hand, NMR/MRI noise is thermal noise, and the noise generated from the coil is given by N = 4 ktδfr Eq. (2) where k is the Boltzmann constant, T the temperature in K, Δf the bandwidth,

5 and R=R C +R S. It is noted that R C is the coil resistance and R S the sample energy loss (i.e. the equivalent series resistance due to the induced eddy current losses in the conductive sample). Combining Eqs. (1) and (2), SNR can be expressed by using the coil-related parameters as S N B R xy ( r) 1 Eq. (3) + C R S To optimize SNR, B xy 1 (r) can be maximized by having the coil closer to the sample, and R S can be minimized by choosing the coil size to match the target FOV. In fact, Wright and Wald compare an N-element array to a single coil with respect to the resultant SNR while their overall coil dimension remains unchanged [5]. For example, they showed that the SNR improvement disappears at the depth equal to the diameter of the array, when comparing a single coil with an 8x8 array, a 4x4 array and a 2x2 array. However, for the distances in-between, the SNR curves vary depending upon the number of receiver channels. If each coil is made too small, then the coil resistance loss dominates the sample noise. This implies that an optimization is required for a given specific application (e.g., target depth and available number of receiver channels). R C is minimized by making the unloaded coil Q high. It is well known that at low-b 0 field systems ( 0.3T) the coil resistance is dominant or at least comparable to the sample noise, but at 1.5T and above, the sample noise dominates (i.e. R S >> R C ). Furthermore, it is useful to be aware that if two coils yield the same relative sensitivity in free space and if they are each sample noise dominated, the two coils have the same absolute sensitivity [10]. This reference discusses the coil unloaded Q, loaded Q, and the sensitivity in detail, which should be useful to the coil engineer. Low Noise lifier As mentioned earlier, a preamplifier is one of the key hardware elements in an RF coil from a standpoint of SNR performance. Furthermore a preamplifier plays a critical role in designing a detector array coil. It is noted that the characteristic parameters of preamplifiers, such as the noise figure, certainly affect SNR. Below is a brief summary of the function of a preamplifier. The electromotive force or induced voltage (i.e., signal) in a coil is very small and typically on the order of a few μv. This small signal is amplified to a few mv by a preamplifier whose gain is, say, 30dB (i.e., 1000 times greater).

6 One of the parameters to measure the performance of the preamplifier is the noise figure (NF) discussed in detail elsewhere [2, 11]. Depicted in Figure 2 is a simple model for preamplifier noise. V Ns r Np Figure 2 Depiction of a preamplifier noise model. V, N S, r and N P denote the signal, the noise generated by the resistance r of the input signal source and the noise generated inside the preamplifier, respectively. In Figure 2, V, N S, r and N P denote the signal, the noise generated by the resistance r of the input signal source and the noise generated inside the preamplifier, respectively. Using these quantities, NF is defined as 2 + P S NF = 10 ( ) where = 4 ktδfr Eq. (4) 2 log 10 2 N N N S N S The industry standard preamplifier NF is currently less than 0.5 db. It is also well-known that the first NF and gain have the most significant impact in the entire electronics circuit, which is often cascaded, as shown in low noise amplifier design textbooks such as [7, 11]. Noise is generated in any passive elements, including cables, in any electronics that dissipates power. This is the reason that most detector array coils have preamplifier integrated design, which is to minimize undesirable noise contributions. As seen later in this paper, the multi-detector array is the key hardware component needed for today s advanced MRI applications. These array coils are constructed of many (32-128) detectors. As emphasized again, a key feature of these detectors is the preamplifier. These preamplifiers serve many functions beyond the simple amplification of the signal. One additional critical function, as shown later, is to aid in the decoupling of the individual detectors from the others, which is critical for the optimal performance of parallel imaging. An additional feature of modern preamplifiers is that they must be very small, so that as many detectors as possible can be tightly packed together to form an optimized array.

7 A Single Coil Model A Building Block To understand how the detector array coil works, we start with a schematic representation of a single coil, a building block, including a simplified preamplifier decoupling circuit shown in Figure 3. This coil circuit is a building block of an array coil. L 1 and R 1 represent the coil inductance and resistance (typically around 0.5 Ohms in air and approximately 5 Ohms when placed on a phantom), respectively. C 1 and C 2 are tuning and matching capacitances, respectively. L 2 is a matching inductor that plays an extremely important role as we will discuss later; that is, a part of L 2 functions to match the coil impedance to 50 Ohms together with C 2 when looked at from the side of the preamplifier. At the same time, L 2 achieves a parallel resonant circuit formed with C 2, in particular, when the input impedance of the preamplifier, r preamp, becomes small (say, 0 to 2 Ohms). What this means is that when looked at from the side of the coil, the impedance is infinity, thereby, a high-impedance or open circuit. What is extremely important to note here is that the current cannot then flow in an open coil, which eliminates the possibility of producing any induced magnetic field through non-zero mutual inductances present among all the neighboring coil elements. This is the underlying principle that explains why the cross talk among all coil elements can be eliminated. This decoupling mechanism is explained in more detail later in this paper. Note also that the Q of the coil (characterized by C 1, L 1 and R 1 ), when the decoupling circuit is in effect, remains unchanged. It is worth mentioning here that the original signal source is changed from the current source (without preamplifier decoupling) to the voltage source (with preamplifier decoupling) that contains all the necessary information without losing the integrity of the original signal information. Figure 3 A single coil model with a low-input impedance preamplifier.

8 lifier Decoupling While other decoupling techniques are available, in this contribution, we mainly focus on a system of two coupled coils and see how the decoupling between the two coils is enabled by preamplifier. Shown in Figure 4 is a schematic representation depicting two coils, Coil 1 and Coil 2, which are coupled through the mutual inductance, M 12. Coil 1(2) is represented by its self-inductance, L 1(2), resistance, R 1(2), and capacitance C 1(2). The signal induced in Coil 1 is given by V signal, and the output voltage is V out. When the AC current, I 1, flows in Coil 1, the induced AC current, I 2, will flow in Coil 2 through the non-zero mutual coupling between the two coils. Figure 4 A system of two coils coupled through the non-zero mutual inductance. Thus, the output voltage is expressed, assuming the harmonic time dependence (i.e., e -iωt ), as V out 1 = Vsignal + R1 i ω L + 1 I1 + iωm 12I 2 ωc Eq. (5) 1 This equation is essential to understand why the coil needs to be resonated at the target Larmor frequency and how the preamplifier decoupling works. First, the second term in the right hand side in Eq. (5) associated with I 1 may be realized as the noise related to Coil 1, and the third term associated with I 2 is recognized as the noise due to the coupling between Coil 1 and Coil 2. The noise related to Coil 1 can be minimized by tuning and matching Coil 1 for its resonance, i.e., the imaginary part of the term associated with I 1 vanishes, and

9 we are left with the intrinsic real resistance R 1. For decoupling, it is required that the third term, i.e., the noise through the mutual coupling, in the right hand side in Eq. (5), iωm 12 I 2, be zero. For this condition to be satisfied, we can arrive at two cases: either M 12 =0 or I 2 =0. M 12 =0 corresponds to the case where the two coils, Coil 1 and Coil 2, are overlapped to null the mutual inductance between the two coils. Capacitive decoupling may be employed here to cancel the mutual inductance [12]. The principle behind the capacitive decoupling is that the non-zero mutual impedance is modeled as an inductance and the inductance is canceled by the addition of capacitance (i.e., the two coils are connected by a capacitor). I 2 =0 corresponds to the case of so-called preamplifier decoupling. Figure 5 A system of two coils coupled through the non-zero mutual inductance. A low-input impedance preamplifier is added to Coil 2 for preamplifier decoupling. Now Coil 2 is integrated with a preamplifier decoupling and matching circuit as shown in Figure 5. Here, L 2 is a matching inductor, and the input impedance of the preamplifier is shown as r preamp. It is recognized that as r preamp becomes 0, the inductor L 2 and the capacitor C 2 can be chosen to form a parallel resonant circuit at the target MR frequency, which yields a high impedance (i.e., infinity, theoretically speaking). Coil 2 then becomes an open circuit, and there is no current flow, i.e., I 2 =0. At this stage, even if the mutual coupling between the two coils is not zero, Coil 1 and Coil 2 are decoupled via the use of a low-input impedance preamplifier. This is the art of preamplifier decoupling. Furthermore, it is emphasized that the matching inductor, L 2, now denoted as L 2A and L 2B in Figure 6, indeed plays several crucial functions, which may not be too obvious, as illustrated in Figure 6. First, L 2A functions to match the coil impedance to 50 Ohms together with C M when looked at from the side of the preamplifier (III II). At the same time, L 2A (and L 2B and C 2 which are adjusted to be short, i.e., the series resonance) achieves a parallel resonant circuit formed with C M, in

10 particular, when the input impedance of the preamplifier, r preamp (approximately R L2B +R C2 ), becomes small (say, 0 to 2 Ohms). What this means is that when looked at from the side of the coil (I II), the impedance is infinity, thereby, a high-impedance or open circuit. In other words, the decoupling circuit considered here and shown in Figure 6 (sandwiched by two dashed lines) is λ equivalently a mismatched (quarter wavelength cable) circuit; one end open 4 and the other end short. It is furthermore instructive and meaningful to view the circuit (regions denoted as II and III) that each region may be represented as a λ corresponding circuit with its characteristic impedance Z 0. For a 4 transmission line that is an odd multiple of quarter wavelengths long terminated in an impedance Z Load at the far end presents an input impedance Z in 2 Z 0 = where Z 0 = the characteristic impedance. This equation in turn reads Z Load Z 0 = Z in Z Load. In other words, a quarter-wave section can be used to match any two impedances by choosing the characteristic impedance of the matching section appropriately. This is what is happening in sections II and III of Figure 6. As each region has its associated and appropriate characteristic impedance, the impedance transformations from I to II to III and in the reverse directions are executed in a correct and consistent manner. With this quarter-wave matching section mechanism, we turn to the preamplifier side. A preamplifier is noise matched. What this means is that for a given field-effect transistor (FET) there exists a signal-source impedance that optimizes or minimizes the noise figure. Thus, the optimum noise figure can be achieved when the impedance of the receive coil matches the source impedance of the FET. The FET impedance is relatively high (>>50 Ohms), and thus there exists an impedance transformer consisting of L 2B and C 2 together forming a λ/4 circuit in section III of Figure 6 that transforms 50 Ohms to the high input impedance of the FET for the lowest noise figure. An optimal impedance for the lowest noise figure of typical FET is on the order of a few-hundred Ω. Thus, L 2B and C 2 transform the coil s 50 Ohms to the high impedance of FET for the lowest noise figure. As an additional note, the input impedance of the preamplifier in Figure 6

11 is approximated as the sum of resistances associated with L 2B and C 2. However, since the Q of the capacitor is typically much higher than that of the inductor, the input impedance is dominated by the contribution of the resistance associated with the inductor. λ 4 λ 4 Figure 6 The matching inductor L 2 (L 2A +L 2B ) plays several critical functions in preamplifier decoupling. Each quarter-λ circuit has its characteristic impedance for necessary impedance matching. With this preamplifier decoupling method in mind, it is straightforward to extend the array concept to 8-channel, 16-channel, and even larger numbers of channels. Figure 7 shows an 8-channel array coil to illustrate the concept. Each coil has its own B 1 sensitivity profile as shown in Figure 8. Because the coil is a surface coil, which yields a high SNR only over a small region, high SNR can be generated over a larger field of view or region of interest, i.e., FOV or ROI, if each channel SNR is combined by a sum-of-squares method [3], for example. This achieves an overall high SNR over the target FOV, illustrated in Figure 8. The number of the coil channels is determined by the number of available receiver channels and the target FOV or ROI while considering the appropriate size of each coil with SNR optimization in mind, as already discussed earlier.

12 There are many references that discuss different array coil designs and their principles for various imaging applications at different field strengths [13]. No matter what RF coil design we choose, we need to construct it correctly, and it is the topic of today s demonstration. Coil 1 Coil 2 Coil 3 Coil 4 Coil 5 Coil 6 Coil 7 Coil 8 Digital MUX Figure 7 Schematic representation of a detector array coil (8-channel). Figure 8 Depiction of B 1 sensitivity profile in an array coil.

13 References [1] Fujita H, Zheng T. Live construction of coils; let s build an RF human coil, In: ISMRM 19 th Scientific Meeting Weekend Syllabus [2] Hoult DI. The NMR receiver: a description and analysis of design. Progress in NMR spectroscopy 1978; 12: [3] Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The NMR phased array. Magn Reson in Med 1990; 16: [4] Hayes CE, Hattes N, Roemer PB. Volume imaging with MR phased arrays. Magn Reson in Med 1991; 18: [5] Wright SM and Wald LL. Theory and application of array coils in MR spectroscopy. NMR in Biomed 1997; 10:402. [6] Hayes CE, Edelstein WA, Schenck JF, Mueller OM, Eash M. An efficient, highly homogeneous radiofrequency coil for whole-body NMR imaging at 1.5T. Journ of Magn Reson 1985; 63: [7] Kucera J, Lott U. Low noise amplifier design, In: Golio M. The RF and microwave handbook. CRC Press, 2001; [8] Yang X, Zheng T, Fujita H. T/R switches, baluns, and detuning elements in MRI RF coils, In: ISMRM 14 th Scientific Meeting Weekend Syllabus [9] Hoult DI, Richards RE. The signal to noise ratio of the nuclear magnetic resonance. Journ of Magn Reson 1976; 24: [10] Froncisz W, Jesmanowicz, Kneeland JB, Hyde JS. Counter rotating current local coils for high-resolution magnetic resonance imaging. Magn Reson in Med 1986; 3: [11] Horowitz P, Hill W. In: Chapter 7 The art of electronics 2 nd edition. Cambridge University Press, 1989; [12] Li BK. The design and analysis of high frequency phased array coils for MRI. Ph.D. Thesis. The University of Queensland, 2006; [13] Fujita H. New Horizons in MR Technology: RF Coil Designs and Trends. Magnetic Resonance in Medical Sciences, Vol. 6, No. 1, 2007;