Original Research

Computational and Experimental Optimization of aDouble-Tuned 1H/31P Four-Ring Birdcage Head Coilfor MRS at 3T

Yunsuo Duan, PhD,1,3 Bradley S. Peterson, MD,1,3 Feng Liu, PhD,1,3

Truman R. Brown, PhD,2 Tamer S. Ibrahim, PhD,4,5 and Alayar Kangarlu, PhD1,3*

Purpose: To optimize the homogeneity and efficiency of theB1 magnetic field of a four-ring birdcage head coil that isdouble-tuned at the Larmor frequencies of both 31P and 1Hand optimized to acquire magnetic resonance spectroscopy(MRS) data at 3T for the study of infants.

Materials and Methods: We developed a finite differencetime domain (FDTD) tool in-house to iteratively computeand seek the range of geometric and electromagnetic pa-rameters of a dual-tuned, four-ring birdcage coil that wouldproduce the desired resonance patterns, optimize homoge-neity of the B1-field, and maximize efficiency of the coil. Todemonstrate the validity of our computational results, weconstructed three RF coils: one dual-tuned coil that wasbased on the calculated optimized parameters and two sin-gle-tuned coils that had dimensions similar to those of thedual-tuned coil, but tuned at the Larmor frequencies ofboth 31P and 1H, respectively. We then tested and com-pared the performances of the dual-tuned coil and single-tuned coils at both of these frequencies.

Results: We found that a dual-tuned, four-ring birdcagecoil with a diameter of 180 mm, an inner birdcage length of100–300 mm, and an outer birdcage length of 25–100 mmproduces the desired resonance patterns. For the use ofthis coil with human infants, optimization of the homoge-neity of the B1 field, combined with improved coil efficiency,yielded a dual-tuned birdcage coil with diameter of 180mm,an inner birdcage length of 150 mm, an outer birdcagelength of 25 mm, and corresponding inner and outer ca-pacitances of 17.2 pF and 7.6 pF, respectively. The exper-imental results from a constructed coil having the samepa-rameters with the modeled coil agreed well with the

computational results from the modeled coil. This opti-mized design overcame the deficiencies of existing dual-tuned, four-ring birdcage coils.

Conclusion: The homogeneity and efficiency of the B1 fieldfor 31P/1H dual-tuned, four-ring birdcage coils can be op-timized well using our FDTD tool, especially at high staticmagnetic fields (B0).

Key Words: double-tuned RF coils; optimization; FDTD;numerical modeling; MRI; MRSJ. Magn. Reson. Imaging 2009;29:13–22.© 2008 Wiley-Liss, Inc.

MAGNETIC RESONANCE SPECTROSCOPY (MRS) is aninvaluable tool for the in vivo, noninvasive detectionand quantification of various metabolites in the humanbrain that provides the ability to investigate the biolog-ical functions of those metabolites within the brain inhealth and illness (1–5). To optimize the application ofMRS to biologically significant nonhydrogen nuclei,however, two major issues must be addressed first inthe design and construction of radiofrequency (RF)head coils (6,7). First, nonhydrogen MRS requires theuse of a dual-tuned coil that will provide homogenousB1 fields at the resonance frequencies of both hydrogen(1H) and nonhydrogen nuclei, and preferably doing sosimultaneously, for the most accurate localization ofregions of interest and measurement of metabolite con-centrations. Second, the low concentration and gyro-magnetic ratios of nonhydrogen nuclei require the useof a highly efficient coil in a high static magnetic field(B0) in order to maximize the signal-to-noise ratio (SNR).These stringent specifications greatly complicate thedesign and construction of maximally effective coils.Satisfying all of these criteria entails the optimization ofa coil’s geometric features.

Among the variety of coils that have been designedover the past 20 years, the birdcage coil is one of thebest suited for this type of optimization because itsstructure is circularly symmetric and it can be driven inquadrature. These characteristics, in turn, allow thebirdcage coil to achieve excellent B1 homogeneity andhigh efficiency at low specific absorption rates (SARs)

1Department of Psychiatry, Columbia University, New York, New York.2Department of Radiology, Columbia University, New York, New York.3New York State Psychiatric Institute, New York, New York.4Department of Radiology, University of Pittsburgh, Pittsburgh, Penn-sylvania.5Department of Bioengineering, University of Pittsburgh, Pittsburgh,Pennsylvania.Address reprint requests to: A.K., Columbia University and New YorkState Psychiatric Institute, 1051 Riverside Dr. 74, New York, NY 10032.E-mail: ak2334@columbia.edu Cc: kangarla@childpsych.columbia.eduReceived April 17, 2008; Accepted June 11, 2008.DOI 10.1002/jmri.21509Published online in Wiley InterScience (www.interscience.wiley.com).

JOURNAL OF MAGNETIC RESONANCE IMAGING 29:13–22 (2009)

© 2008 Wiley-Liss, Inc. 13

(8). The dual-tuned birdcage coil itself comes in a vari-ety of designs, including tank circuits on rings or legs(9), bandstop and bandpass filters (10), four-ring bird-cages (11), concentric birdcages (12), filters on half oflegs (13), and more recent coaxial spiral birdcage de-signs (14). Each of these designs has its own limitationseither in B1 field homogeneity or coil efficiency (13). Thepublished designs of four-ring birdcage coils tend todegrade the homogeneity of the B1 field at the 31P fre-quency, and the outer structure of the coil prevents thehead from being positioned in the center of the coil,where the magnetic field is relatively homogenous. Webelieve that optimizing the geometric structure of thefour-ring birdcage coil may improve the simultaneousoptimization of the coil at two of its resonance frequen-cies.

Optimization of the homogeneity and efficiency of adual-tuned coil requires computation not only of itsresonance pattern, but also of the B1 field of the coil,which in turn requires an algorithm for numerical elec-tromagnetic field computation. Furthermore, the cou-pling of a four-ring coil is much stronger than that of asingle-tuned coil, because the distance between therings of the four-ring coil is much less than that of thesingle-tuned coil, and thus the computation must ac-count for the geometry of the coil, especially at a high B0

field. We therefore selected a full-wave computationalmethod for optimization of the coil, finite difference timedomain (FDTD) (15). Although FDTD has been used forthe computational analysis of RF coils (16–19), it hasnever been used to optimize the homogeneity and effi-ciency of a dual-tuned birdcage coil.

We present a computational method that appliesFDTD to the optimization of a 31P/1H dual-tuned, four-ring birdcage head coil at 3T.

MATERIALS AND METHODS

Validation of FDTD

We first verified the validity of our FDTD tool beforeusing it to optimize coil performance. We validated ourFDTD tool by comparing the calculated resonance pat-tern and magnetic field of a circular LC loop coil with its

well-known analytical resonance pattern and magneticfield.

Structure of the Dual-Tuned Coil

A 31P/1H dual-tuned, four-ring birdcage coil consists ofthree connected, low-pass birdcages with N legs (11)(Fig. 1). The outer birdcages, the structures at each endof the coil, are tuned at 127.72 MHz, which is theLarmor frequency of 1H at 3T. The inner birdcage istuned at 51.70 MHz, the Larmor frequency of 31P at 3T.We constructed a dual-tuned four-ring birdcage coilhaving 16 legs (N � 16) using Plexiglas formers andadhesive-back copper strips with a thickness of 30 �mand a width of eight mm (w � 8 mm). Our coil wasconstructed for infants, who have head sizes that are�100 mm in diameter. We therefore selected a field ofview (FOV) of 120 � 120 � 120 mm3, which allows for�10 mm from the surface of the head to the edge of theFOV. In addition, to ensure that the entire FOV fallswithin the homogeneous portion of the B1 field, we setthe diameter of the coil, d, to 180 mm. The remainingparameters were determined via optimization, which wewill describe next. The coil was shielded with copperfoils placed 30 mm away from the surface of the coil.

Computational Modeling of the Dual-Tuned CoilUsing FDTD

Coil Modeling

The goal of optimization is 1) to maximize the homoge-neity of the B1 field within the FOV at the Larmor fre-quencies of both 1H and 31P simultaneously, and then2) to maximize the efficiency of the coil. The first step ofoptimization is to find the range of parameters of thecoil that meet the requirements of homogeneity. Thesecond step is to adjust those parameters within theidentified range in order to maximize the efficiency ofthe coil. Computational modeling with FDTD was usedto determine and optimize these parameters. Becausethe maximization of both the homogeneity of the B1 fieldand the efficiency of the coil can occur only at thedominant resonance frequency of the coil, however, we

Figure 1. Structure of the four-ring dual-tuned birdcage coil. a: Schematic view. d: diameter of the coil; li: length of the innerbirdcage; lo: length of the outer birdcage; Ci: capacitors on the inner birdcage; Co: capacitors on the outer birdcage; w: width ofthe copper strips; and N: number of legs. b: Longitudinal plane view. Point A: feeding and sampling point for the outer birdcage;Point B: feeding and sampling point for the inner birdcage; Point O: sampling point in the center of the coil.

14 Duan et al.

must first determine the range of coil parameters thatwould produce the desired dominant resonance fre-quency.

FDTD is derived directly from Maxwell’s equations bydiscretizing those equations over a finite space andestimating the derivatives with centered difference ap-proximations (15). The use of FDTD has been shown tobe efficient for the computation of coil resonance pat-terns and the homogeneity of the B1 field (16–19). Weused FDTD to construct a computational model for cal-culating the performance of our coil on phantoms. TheFDTD model had a grid of 2 mm in the x-, y-, andz-directions. The model deviated from the actual coil’sstructure in certain instances because the dimensionsof various components of the actual coil were smallerthan the resolution of the FDTD model. For example,the thickness of the copper strips was represented inthe computational model by a voxel 2 mm in size ratherthan by their actual thickness of 30 �m. Capacitorswere also represented in the model by a single voxel.The computational domain was set to at least 40 cellslarger than the coil dimensions in order to provideenough separation between the coil structure and theabsorbing boundary. For the absorbing boundary con-ditions we used the method of perfectly matched layers(PML) (20,21) assuming 20 cells for the thickness ofeach side. Thus, given the coil’s dimensions of 180 mmdiameter and 200 mm length, the grids were set to210 � 210 � 220 Yee cells, including the absorbingboundary. The capacitors were modeled according to amodified lumped element FDTD algorithm (22). We de-veloped the FDTD software in-house rather than usingcommercial software to achieve sufficient flexibility inaccurately representing the coil’s complex structuralelements.

Source Signal

For the computation of the B1 field at a given frequency,f0, we used a sine wave at the Larmor frequency as theexciting source of signal and applied it to the selectedfeed points on the surface of the coil (Fig. 1b). We chosetwo inner capacitors for 31P and two outer capacitorsfor 1H as the feed points for quadrature excitation. Theexcited capacitors in each pair were placed respectivelyon two coil legs that were 90° apart azimuthally. Nextwe applied each of the following source signals to one ofthe capacitors in each pair:

s1�t� � �1 � e��2�f0t/5�2�sin�2�f0t� [1]

s2�t� � �1 � e��2�f0t/5�2�sin�2�f0t � �/2� [2]

The use of the coefficient (1 � e���0t/5�2) acceleratesstabilization of the computation (16).

We obtained the resonance pattern via recording ofthe calculated B1 field at selected sampling points ineach time step and use of FFT to compute the frequencyspectra of the recoded B1 field. Thus, the excitingsource signal for computation of the resonance patternmust have a wide bandwidth in order to contain a suf-ficient number of frequencies. Usually, the resonancefrequency of the highest mode of the birdcage coil for 1H

at 3T is below 500 MHz. We therefore selected as thesource signal a Gaussian function whose frequency at�3 dB was not less than 500 MHz, ie:

S�t� � e�� t2T0

�3� 2

[3]

Where T0 � 1/�3dB � 1/�5 � 108 � 2��.

Optimization of the Dual-Tuned Coil

We optimized the coil in the following steps: 1) We iden-tified the available range of coil parameters that couldproduce the desired resonance patterns. We set a smallinitial value for the lengths of both the inner and outerbirdcages and we computed the resonance pattern ofthe coil. We adjusted the values for both inner andouter capacitors until we either obtained the desiredresonance pattern or we demonstrated that the coilcould not produce the desired resonance pattern. Wethen increased the length of the inner or outer birdcageby 5 mm and recomputed the resonance pattern untilidentifying the available range of coil parameters. 2) Wethen computed the B1 field of the coil at the Larmorfrequencies of both 31P and 1H at 3T for every combi-nation of parameters in the range identified in Step 1. 3)We measured the homogeneity and intensity of the cal-culated B1 field for each combination of parameters anddetermined the parameters that met the homogeneityrequirements while also having the highest intensity ofB1 field within the FOV. 4) We then constructed a realcoil using the optimized parameters, measured its res-onance pattern, and acquired 1H images and 31P CSIs(chemical shift images) of a phantom within that coil. 5)We compared the calculated and experimental resultsto assess the validity of the optimization procedure.

Resonance Pattern

Determining the dominant frequency of a dual-tuned,four-ring birdcage coil is a more complex task than it isfor a single-tuned, two-ring empty birdcage coil. In asingle-tuned, two-ring empty birdcage coil having Nlegs and N1 resonance modes, Mode 1 (the dominantmode) occurs only at a single frequency and thereforecan be discriminated easily. With a dual-tuned, four-ring birdcage coil, however, each mode splits into twofrequencies on the surface of the coil (eg, point A or B inFig. 1) because of the coupling between outer birdcages,and only the higher frequency of Mode 1 can serve asthe dominant resonance frequency (11). Furthermore,Mode 1 may overlap with the higher modes of the innerbirdcage, making difficult the discrimination of thedominant resonance frequency. Thus, we added a sam-pling point O at the center of the coil (Fig. 1b) to simplifythe discrimination of the dominant resonance fre-quency, because the B1 field at the center of the coil isrelatively strong only at this frequency.

Considering the realistic dimensions of the coilneeded to accommodate an infant’s head, we selectedthe range of lengths of the inner and outer birdcage tobe 50–300 mm and 10–100 mm, respectively, in orderto reduce the enormous time required for the iterativecomputation. We also used the lumped parameter

Analysis of Dual-Tuned RF Coils 15

model of the coil to select initial values for the capaci-tors that were as close as possible to the correct values.The inner birdcage operates like a single-tuned bird-cage coil because the capacitance of Co is much lowerthan that of Ci, and there Co creates much greaterimpedance at the Larmor frequency of 31P. Thus, theinitial value for Ci of the inner birdcage can be obtainedby the following formula used to calculate the single-tuned, low-pass birdcage coil (23):

Ci �1

ki2

4sin2��k/N�

Lri � 4Lmisin2��k/N�[4]

where Lri and Lmi are the equivalent inductances of theinner rings and inner legs, respectively.

With the outer birdcage, because of mode splitting,the resonance patterns must be calculated by:

ok

2 �1Co� 1

Lo � Lc� [5]

Where Lo �Lro � 4Lmosin2��k/N�

4sin2��k/N�and Lc is the coupling

inductance between outer birdcages.Although precise calculation of Lc is difficult, in our

experience we can estimate Lc as Lo/10.

B1 Field Homogeneity and Efficiency

We deem the B1 field homogenous if the amount of itsrelative distortion is not more than 10% of its averagestrength within the FOV. Thus, we define the homoge-neity criterion of B1 field as:

��B1 � B� 1��FOV

B� 1� 10% [6]

where B� 1 is the mean B1 field within the FOV.We assess the efficiency of the coil by measuring the

intensity of the B1 field within the FOV when it is excitedby a unit source (1 Volt). The optimization thereforeshould minimize ��B1 � B� 1��FOV and maximize the inten-sity of the B1 field as a function of li, lo, Ci, and Co at theLarmor frequencies of both 1H and 31P within the FOV.In practice, we evaluated the homogeneity and intensityof the B1 field only in three orthogonal planes (axial,coronal, and sagittal), rather than in the whole volume.

Experimental Measurement

We determined the resonance pattern of the real dual-tuned coil by measuring its S-parameters using an Agi-lent (Palo Alto, CA) 4395A network analyzer. We used a90° hybrid coupler to connect the analyzer to the trans-mitting and receiving ports of the coils for quadratureexcitation. The matching and tuning circuits were thesame as that used in prior studies (11). We acquired 1Himages of a phantom using the dual-tuned coil and aGE 3T Signa scanner (Milwaukee, WI) operating inquadrature mode. These 1H images were acquired us-ing a gradient echo pulse sequence with a 90° flip angle,500 msec repetition time, and 10 msec time to echo. We

also acquired 31P spectra of the phantom in which vox-els were localized by the 1H images.

The phantom used to acquire both MRI images of 1Hand CSI images of 31P had the following ingredients: 50mm potassium phosphate monobasic, 12.5 mmN-acetyl-l-aspartic acid (NAA), 10 mm creatine hydrate,3 mm choline chloride, and 12.5 mm L-glutamic acid.

RESULTS

Validation of FDTD

Our circular LC coil had a diameter of 100 mm. It wascomposed of a capacitor of 6.2 pF and a copper wirewith a diameter of 4 mm. Its theoretical inductance was0.25 uH. Thus, the theoretical resonance frequency ofthe loop coil was 127.72 MHz (given by f � /�2��� 1/�2��LC�). The calculated resonance frequency us-ing FDFD was 128 MHz. This calculated resonancefrequency agreed well with its theoretical value, andwas within the resolution of the calculated resonance(0.5 MHz). We also found that the calculated magneticfield that was distributed along the center line perpen-dicular to the coil loop (in the z-direction) agreed withthe theoretical distribution of that field (Fig. 2), demon-strating that our FDTD tool accurately calculated themagnetic field of this coil.

Resonance Pattern of the Dual-Tuned Coil

Our calculations using FDTD showed that, althoughthe distance between different modes would vary withthe lengths of the inner and outer legs, a four-ring coilhaving an inner leg length, li, between 50 and 300 mmand an outer leg length, lo, between 25 and 100 mmwould produce acceptable resonance patterns, ie, pat-terns in which the dominant mode (Mode 1) resonatedat the desired frequency and yet was clearly distin-guishable from other modes within the resonance pat-tern (Fig. 3).

Figure 2. The calculated and analytical results of normalizedmagnetic field of a loop coil along the center line perpendicularto the loop. There is no distinct difference between the tworesults.

16 Duan et al.

Calculated Homogeneity and Intensity of theDual-Tuned Coil

From the calculated homogeneity and intensity of theB1 field of a coil with an inner leg length between 50 mmand 300 mm and an outer leg length of 25 mm (Fig. 4),the length of the cylindrical region of the calculatedhomogenous B1 field in the center of the coil was ap-proximately proportional to the length of the inner leg.The intensity of B1 field decreased, however, with anincreasing length of the inner leg. Also, a coil with aninner leg length between 150 and 200 mm could pro-duce the desired length (�120 mm) of the cylindricalregion of homogeneity of the B1 field while having anacceptable field intensity (�90% of maximum) for theLarmor frequencies of both 31P and 1H. We therefore

deemed a coil with an inner leg length of 150 mm andan outer leg length of 25 mm would produce optimalhomogeneity and intensity of the B1 field. The corre-sponding calculated values of the inner and outercapacitors for this coil were 17.2 pF and 7.6 pF, respec-tively. Thus, together with its predetermined parame-ters, the parameters of the optimized coil were d � 180mm, li � 150 mm, lo � 25 mm, l � li 2lo � 200 mm, Ci

� 17.2 pF, Co � 7.6pF, w � 8 mm, and N � 16.

Coil Performance

To verify these computational results, we constructed areal coil having the optimized parameters that weredetermined using FDTD (Fig. 5). For the purposes of

Figure 3. Measured and calculated resonance patterns of a coil with parameters of li � 100 mm, Ci � 23.6 pf, lo � 50 mm, Co �5.7 pf, d � 180 mm, l � 200 mm, w � 8 mm, and N � 16. The dominant mode of the inner birdcage (31P) is marked P1; the twopeaks of the split dominant mode of the outer birdcage (1H) are marked H1 and H1�. The measured resonance patterns agree withthe resonance patterns calculated using FDTD. In addition, the dominant frequencies were best identified at the center of thecoil. a–c: Resonance pattern obtained when excited at the legs of the inner birdcage (31P): (a) self reflection (S11) measured in thereal coil; (b) FFT calculated at the feeding and sampling point of the inner birdcage (Point B in Fig. 1b); (c) FFT calculated at thesampling point in the center of the coil (Point O in Fig. 1b). d–f: Resonance pattern obtained when excited at the legs of the outerbirdcage (1H): (d) self reflection (S11) measured in the real coil; (e) FFT calculated at the feeding and sampling point on the outerbirdcage (Point A in Fig. 1b); (f) FFT calculated at the sampling point in the center of the coil (Point O in Fig. 1b).

Analysis of Dual-Tuned RF Coils 17

comparison, we also constructed two single-tuned, two-ring, low-pass birdcage coils having the same dimen-sions of the inner birdcage of the optimized four-ringcoil and tuned these two coils at the Larmor frequenciesof 31P and 1H, respectively.

We computed the homogeneities and efficiencies ofthese coils by modeling the coils individually andbench-testing their unloaded and loaded Q factors (Ta-ble 1). We found that all coils met the requirements ofhomogeneity (ie, the length of homogenous cylindricalregion in the center of each coil was greater than 120mm). The efficiencies of the four-ring coil were greaterthan 91% of the two-ring coils operating at each fre-quency separately. The loaded and unloaded Q factorsof the four-ring coil were also greater than 90% of thetwo-ring coils operating at each frequency separately.

We obtained the 1H MRI images and 31P CSI images ofa phantom using the optimized dual-tuned four-ringbirdcage coil (Fig. 6). These demonstrated that the realcoil provided the desired homogeneity of the B1 field.

DISCUSSION

Discrimination of the Dominant Mode

The discrimination of the dominant resonance fre-quency of the resonance pattern is of crucial impor-tance in the design of RF coils. We found that the res-onance pattern of the inner birdcage (31P) was similar tothat of the analogous single-tuned, two-ring, low-passbirdcage coils (Fig. 3). At the inner surface of the bird-cage, all modes could be distinguished clearly. Mode 1occurred at 51.7 MHz, the Larmor frequency of 31P at3T, and Mode 2 occurred at 79 MHz, a frequency at asufficient distance from Mode 1 to avoid overlap of thetwo modes. The other modes of the resonance patternfor the inner birdcage were at even higher frequenciesthan the frequency of Mode 2. Thus, Mode 1 could serveas the dominant and easily identified resonance fre-quency for 31P.

Identifying the dominant resonance frequency of theouter birdcage was not as easy as for the inner birdcage.

Figure 4. Calculated B1 field: homogeneity and intensity vs. Leg length (a) curvilinear relationship of the inner leg length, li, withthe length of the cylindrical region of B1 homogeneity in the center of the coil, lh; (b) Curvilinear relationship of the inner leglength, li, with the normalized field intensity, Ih. Solid line: lo � 25 mm, f � 127.72 MHz; dotted line: lo � 25 mm, f � 51.70 MHz;Solid stars: lo � 50 mm, f � 127.72 MHz; solid circles: lo � 50 mm, f � 51.70 MHz. Homogeneity and efficiency are optimal withan inner leg length between 150 and 200 mm.

Figure 5. The optimized coil after construction. a: Coil structure li � 150 mm, Ci � 17.2 pf, lo � 25 mm, Co � 7.6 pf, d � 180mm, l � 200 mm, w � 8 mm, N � 16. b: Outer shape of the coil.

18 Duan et al.

At the surface of outer birdcage, although all modeswere easily visible, each mode split into two peaks inboth the measured pattern of the real coil (Fig. 3d) andin the calculated pattern of the modeled coil (Fig. 3e), asexpected. The lower frequency of Mode 1 occurred at118 MHz, whereas the higher frequency of Mode 1 oc-curred at 128 MHz, the Larmor frequency of 1H. Thelower frequency of Mode 2 occurred at 218 MHz, adistance of 90 MHz from Mode 1. The highest modeoccurred at 432 MHz. At the center of the coil (Fig. 3f),however, only the higher frequency of Mode 1 could bedistinguished; the lower frequency of Mode 1, and thoseof the other modes, were degraded by a factor of 15(�23.5 dB), demonstrating that the coil could producethe desired B1 field only at the higher frequency of Mode1. Therefore, only this frequency can serve as the dom-inant resonance frequency for 1H.

During bench-testing, experimentally identifying thedominant frequency for 1H in a real four-ring birdcagecoil may be more difficult, because the dominant modemay split into even more than two peaks before the coilis well-tuned, and these split modes may overlap withthe higher modes of the inner birdcage (Fig. 7a). Thus,computation of the resonance pattern at the center ofthe coil becomes even more important, as it will greatlyaid and simplify tuning of the coil.

Limitation of Coil Length

Computational results showed that the length of theouter birdcage, lo, did not strongly influence the homo-geneity of the B1 field; increasing lo, however, didslightly reduce the efficiency of the coil. Therefore, loshould be sufficiently short to increase the efficiency ofthe coil and to allow the subject’s head to reach thehomogenous region within the coil. However, an lo thatis too short will split the dominant frequency. Compu-tation showed an lo shorter than 17 mm splits the res-onance pattern of the outer birdcage into more than twopeaks, because of the inductance of coupling. In thisinstance, four peaks are seen at Mode 1 at the surfaceof the coil (Fig. 7b) and two peaks close to high reso-nance frequency of Mode 1 are detected at the center ofthe coil (Fig. 7c). Thus, a four-ring coil having an lo thatis too short does not produce the desired resonancepattern. This is an important finding, given that short locoils are often viewed as the solution for the problem ofpositioning the subject’s head at the center of the coil.We finally selected an lo of 25 mm because it producedthe desired resonance pattern while allowing properpositioning of the subject’s head at the center of thecoil.

Other parameters were needed to be optimized toachieve B1 homogeneity as well. From Fig. 4 we learnthat we should increase the length of the inner bird-cage, li, to increase the size of the homogenous portionof the B1 field at the center of the coil. We shoulddecrease li, however, to improve the efficiency of thecoil. Finding the optimum value required simulation,which showed that the optimal length of the inner bird-cage is �1.3 times of the length of the FOV if we are toachieve the desired size of the homogeneous B1 fieldwithin the FOV while simultaneously maximizing theefficiency of the coil. Thus, in this case, for an infant’shead and an FOV of 120 � 120 � 120 mm3, the lengthof inner birdcage should be 150 mm.

Unequal Loading

When scanning a living infant, the head is positioned atthe center of the coil, the outer birdcage on the bodyside is loaded with the tissue of the infant’s neck, andthe outer birdcage is unloaded, producing the problemof unequal loading. To study the influence of this un-equal loading on coil performance we measured theperformance of the real coil using a cylindrical phantompositioned at the center of the inner birdcage and one ofthe outer birdcage, leaving the other birdcage un-loaded. We found that the resonance frequency at 31Pwas not affected by the unequal load, whereas the res-onance frequency at 1H shifted from 127.72 MHz to127.53 MHz. This shift could be compensated by pre-tuning the loaded birdcage to 127.94 MHz.

Assessment of Homogeneity and Efficiency

In addition to the resonance patterns, we validated thecalculated homogeneity and efficiency of the coil withexperimental measurements. We measured the homo-geneity of the coil by acquiring 1H MRI images and 31PCSI images with the coil using a homogeneous cylindri-cal phantom, as described above. The homogeneity ofintensity of the 31P CSI and 1H MRI images indexed thedegree of homogeneity of the B1 field at the frequenciesof 31P and 1H, respectively. At the 31P frequency (51.7MHz), the CSI images (Fig. 6d) revealed a homogenouscylindrical region 122 mm long in the center of the coil,satisfying our criterion for homogeneity (Eq. [6]). At the1H frequency (127.72 MHz), 1H MRI images (Fig. 6j) hada cylindrical homogenous region 131 mm long, againlarger than the minimum of 120 mm that was desired.Furthermore, our results showed that the size of themeasured homogeneous region agreed with the size ofthe calculated homogeneous region (Table 1).

Table 1Comparison of the Homogeneity and Efficiency of Single-Tuned, Two-Ring coils and the Dual-Tuned, Four-Ring Coil

Coil TypeOperatingfrequency

(MHz)

Length of homogenousregion (mm)

Relativeefficiency

(%)

Measured Q factor ( 5%)

Unloaded Loaded

2-ring 51.7 (31P) 126 100 332 1314-ring 51.7 (31P) 122 94.3 306 1172ring 127.72 (1H) 138 100 294 984-ring 127.72 (1H) 132 91.2 272 86

Analysis of Dual-Tuned RF Coils 19

Figure 6. Acquired images and calculated B1 fields of the optimized coil. The homogeneities of the measured and calculated B1

fields were similar, and both met our requirement for homogeneity at the Larmor frequencies of both 31P and 1H. a–f: Excitationat the inner legs at 51.70 MHz (31P). Axial plane (Z � 0): (a) 31P CSI; (b) calculated B1-map; (c) calculated B1-field along thetransverse center line (Y � 0,Z � 0); Coronal plane (Y � 0): (d) 31P CSI; (e) calculated B1-map; (f) calculated B1-map along thelongitudinal center line (X � 0, Y � 0; solid), the longitudinal lines located at 30 mm (X � 30 mm, Y � 0; dotted) or 60 mm (X �60 mm, Y � 0; dashed) from the longitudinal center. g–l: Excitation at the outer legs at 127.72 MHz (1H). Axial plane (Z � 0): (g)1H image; (h) calculated B1 map; (i) calculated B1 field along the transverse center line (Y � 0, Z � 0); Coronal plane (Y � 0): (j)1H image; (k) calculated B1 map; (l) calculated B1 field along the longitudinal center line (X � 0, Y � 0; solid), the lines locatedat 30 mm (X � 30 mm, Y � 0; dotted) or 60 mm (X � 60 mm, Y � 0; dashed) from the longitudinal center line.

20 Duan et al.

We evaluated the efficiency of the real coils by mea-suring and comparing the RF power required for thedual-tuned coil and single-tuned coils to flip the nucleiinside the phantom by 90° when using the same gradi-ent recalled echo (GRE) pulse sequence. The empiricalresults demonstrated that 253W of RF power wereneeded to flip the nuclei when using the optimized four-ring coil. This value is 8.6% higher than the powerneeded to flip the nuclei using the single-tuned, two-ring birdcage coil. This confirmed that the efficiency of

the optimized dual-tuned, four-ring coil is high, beingmore than 90% of that of the single-tuned, two-ring coil.

In conclusion, using an FDTD tool developed in-house we have designed a dual-tuned, four-ring bird-cage coil. We identified the range of the length of itsinner and outer legs needed to produce the desiredresonance pattern, and we calculated the limits of theparameters needed to construct the coil. We further-more successfully optimized the parameters of thecoil, which included 16 legs, 150 mm long inner legs,17.2 pF inner capacitors, 25 mm long outer legs, 7.6pF outer capacitors, a 180 mm diameter, and 8 mmwide copper strips. We then constructed a real coilusing these calculated optimal parameters and usedthe coil to acquire 1H MRI images and 31P CSI imagesfrom a phantom. The experimental performance ofthe real coil agreed with the calculated performanceof the modeled coil. Optimizing the design of the coilovercame several of the limitations and deficiencies ofthe performance characteristics of existing dual-tuned four-ring birdcage coils. This included design-ing the coil to provide a high efficiency and enlargingthe size of the homogeneous portion of the B1 field atboth the 31P and 1H frequencies simultaneously whileallowing positioning the head of the subject into thecenter of the coil.

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