Journal of Magnetic Resonance 223 (2012) 90–97

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Journal of Magnetic Resonance

journal homepage: www.elsevier .com/locate / jmr

Enhancement of spectral editing efficacy of multiple quantum filtersin in vivo proton magnetic resonance spectroscopy

Hyeonjin Kim a,b,c,⇑, Richard B. Thompson d, Peter S. Allen d

a Department of Radiology, Seoul National University Hospital, Seoul, Republic of Koreab Department of Medical Sciences, Seoul National University, Seoul, Republic of Koreac Department of Biomedical Sciences, Seoul National University, Seoul, Republic of Koread Department of Biomedical Engineering, University of Alberta, Edmonton, AB, Canada

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 June 2012Revised 12 July 2012Available online 02 August 2012

Keywords:Multiple quantum filterSpectral editingStrong couplingProton spectra

1090-7807/$ - see front matter � 2012 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.jmr.2012.07.017

⇑ Corresponding author at: Department of RadioloHospital, 101 Daehangno, Jongnogu, Seoul 110-744, R743 6385.

E-mail address: hyeonjinkim@snu.ac.kr (H. Kim).

The performance of multiple quantum filters (MQFs) can be disappointing when the background signalalso arises from coupled spins. Moreover, at 3.0 T and even higher fields the majority of the spin systemsof key brain metabolites fall into the strong-coupling regime. In this manuscript we address comprehen-sively, the importance of the phase of the multiple quantum coherence-generating pulse (MQ-pulse) inthe design of MQFs, using both product operator and numerical analysis, in both zero and double quan-tum filter designs. The theoretical analyses were experimentally validated with the examples of myo-ino-sitol editing and the separation of glutamate from glutamine. The results demonstrate that the phase ofthe MQ-pulse per se provides an additional spectral discrimination mechanism based on the degree ofcoupling beyond the conventional level-of-coherence approach of MQFs. To obtain the best spectral dis-crimination of strongly-coupled spin systems, therefore, the phase of the MQ-pulse must be includedin the portfolio of the sequence parameters to be optimized.

� 2012 Elsevier Inc. All rights reserved.

1. Introduction

Multiple quantum filters (MQFs) have been used in in vivo pro-ton magnetic resonance spectroscopy (1H MRS) for the detection ofmetabolites with coupled spins with effective background sup-pression [1–16]. Starting from the incorporation of the spatiallocalization technique into the filter design [2,3,17,18], many tech-nical advances have been made to improve the performance ofMQFs in vivo. For example, the first and the second echo times(TE1 and TE2, respectively; Fig. 1) must be optimized for the max-imum production of anti-phase coherences (APCs), because theycan significantly deviate from the conventional 1/2J approximation[5,19,20]. The mixing time (TM) should also be optimized for theeffective mixing of coherence [7,21]. The flip-angle (hread), duration(Lread), bandwidth (BWread) and offset frequency (fread) of the readpulse that converts multiple quantum coherences (MQCs) backinto APCs (the third 90� read-pulse in Fig. 1) should all be fine-tuned for maximum coherence transfer into the target peak[7,22]. Moreover, the directional adjustment of filter gradient(s)needs to be considered for additional water suppression [7,23,24].

ll rights reserved.

gy, Seoul National Universityepublic of Korea. Fax: +82 2

In addition to these MQF sequence parameters to be optimized,the potential role of the irradiation phase, u, of the MQC-generat-ing pulse (MQ-pulse; the second 90� pulse in Fig. 1) in the design ofa zero quantum filter (ZQF) was reported previously [13]. It wascommonly assumed that u needs to be tuned either in-phase foreven-order MQFs, or 90� out-of-phase for odd-order MQFs, relativeto that of the first 90� excitation pulse with appropriate gradientfiltering scheme [25], regardless of the degrees of coupling of spinsystems. As previously demonstrated [13], however, by tuning uorthogonal to that of the excitation pulse, the conventional ZQFcan be designed to filter out those coherences that arise duringTE1 solely from strong-coupling interactions. That is, the optimiza-tion of u not only allows for differentiating between coupled spinsand uncoupled spins, but also for discriminating strongly-coupledspins from weakly-coupled spins [13], an objective that was ad-dressed previously through the optimization of sequence timings.This is a significant point, given first that the performance of gen-eric MQFs can often be disappointing, particularly when the back-ground signal also arises from coupled spins; and secondly, that at3.0 T and even higher fields, the majority of the spin systems of keybrain metabolites fall into the strong-coupling regime [26–28].

In the present report we first analyze theoretically the behaviorof coupled spins as a function of u, including intermediate phaseangles and by extending its concept to double quantum filters(DQFs) as well. Both product operator analysis [29] and numericalmethods of solving the equation of motion of the density operator

Fig. 1. A simplified diagram of a generic multiple quantum filter sequence. Theduration of the filter gradient G2 is either 0 for a ZQF or 2 � G1 for a DQF.

H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97 91

[7,21,30] were employed. Experimental results are subsequentlypresented from phantoms to validate the theory. The phantomdata illustrate examples of editing of myo-inositol (mI) and theseparation of glutamate from glutamine (Glu and Gln, respectively,and collectively referred to as Glx). Finally, we propose that to ob-tain the best discrimination of strongly-coupled spins from theirbackground, u needs to be included in the portfolio of the se-quence parameters of MQFs that must be optimized.

2. Materials and methods

The chemical structures of the metabolites considered hereinare provided in Appendix A.

2.1. Theory

In order to examine the physical meaning of the phase, u, of theMQ-pulse in the design of MQFs, density operators, q(t)’s, of astrongly-coupled AB spin system of citrate (Cit) in response to aZQF and a DQF were calculated with u as a variable. All analyticalcalculations were based on the transformation equations of theCartesian product operators that were derived from the sphericalbasis set [31,32]. The numerical methods were also used as previ-ously described [7,21,30].

Upon the use of the full J-coupling Hamiltonian, HJ (= 2pJAB{Ax-

Bx + AyBy + AzBz}), the density operator just after TE1 (just beforethe MQ-pulse) becomes,

qðTE�1 Þ ¼ Ax � S1 þ Ay �Wþ2 þ 2AxBz �Wþ

1 þ 2AyBz � S2 � Bx � S1

þ By �Wþ2 þ 2BxAz �Wþ

1 � 2ByAz � S2; ð1aÞ

where

W�1 ¼ � sinðpJ � tÞfcos2ðK � t=2Þ þ ½ðdx=KÞ2 � ðpJ=KÞ2�

� sin2ðK � t=2Þg � ðpJ=KÞ sinðK � tÞ cosðpJ � tÞ; ð1bÞ

W�2 ¼ cosðpJ � tÞfcos2ðK � t=2Þ þ ½ðdx=KÞ2 � ðpJ=KÞ2� sin2ðK� t=2Þg � ðpJ=KÞ sinðK � tÞ sinðpJ � tÞ; ð1cÞ

S1 ¼ �2ðdx=KÞðpJ=KÞ sin2ðK � t=2Þ sinðpJ � tÞ; ð1dÞ

S2 ¼ 2ðdx=KÞðpJ=KÞ sin2ðK � t=2Þ cosðpJ � tÞ; ð1eÞ

and where

K ¼ ½ðdxÞ2 þ ðpJÞ2�1=2; dx ¼ ðxA �xBÞ=2; and t ¼ TE1: ð1fÞ

Alternatively, adopting a weak-coupling approximation ðHweakJ ¼

2pJABfAzBzgÞ, the coefficients in Eqs. (1b)–(1e) simplify to W�1 �

� sinðpJ � TE1Þ and W�2 � cosðpJ � TE1Þ, while S1, S2 � 0. Eq. (1a) then

becomes

qðTE�1 Þweak ¼ Ay �Wþ

2 þ 2AxBz �Wþ1 þ By �Wþ

2 þ 2BxAz �Wþ1

¼ Ay � cosðpJ � TE1Þ � 2AxBz � sinðpJ � TE1Þ þ By

� cosðpJ � TE1Þ � 2BxAz � sinðpJ � TE1Þ: ð2Þ

A comparison between Eqs. (1a) and (2) clearly shows that thecoherence terms in Eq. (1a), which are coupled to either S1 or S2

(Ax, 2AyBz, Bx and 2ByAz), are produced solely from strong-couplinginteractions during TE1 [13,33], whereas Ay, 2AxBz, By and 2BxAz

are produced from both weak- and strong-coupling interactions.In other words, the second terms in W�

1 and W�2 originate from

the strong-coupling interactions through coherence transfer. Inthe following calculations, those strong-coupling-specific coherenceterms can be identified by tracing the coefficients S1 and S2.

2.1.1. ZQFJust after the MQ-pulse with a variable phase of u with respect

to that of the excitation pulse, the density operator for a ZQFbecomes

qðTEþ1 ÞZQF � Az½S1 � sinðuÞ �Wþ2 � cosðuÞ� � Bz½S1 � sinðuÞ

þWþ2 � cosðuÞ� þ 2ðAxBy � AyBxÞ½S2 � sinðuÞ�; ð3aÞ

¼ cosðuÞ½�ðAz þ BzÞWþ2 � þ sinðuÞ½ðAz � BzÞS1 þ 2ðAxBy � AyBxÞS2�;

ð3bÞ

which reduces upon the weak-coupling approximation to

qðTEþ1 ÞweakZQF � �ðAz þ BzÞ � cosðpJ � TE1Þ � cosðuÞ: ð4Þ

Since z-magnetizations also contribute to the final signal of aZQF, they are also included in Eqs. (3a), (3b), (4). In Eqs. (3a) and(3b), the changes in the level of coherence brought about by theMQ-pulse is reflected in the argument of the trigonometric func-tions. For instance, the cos(u) in Eq. (3a) can be rewritten as½[cos(u) + cos(�u)], and the 1�u and �1�u terms describe thechanges in the level of coherence from �1 ? 0 and from +1 ? 0,respectively [34]. Eqs. (3a) and (4) show that for a conventionalZQF with u = 0� (x), the ZQ-filtered signal of a two-spin system(either AX or AB) originates from z-magnetizations only (nonefrom ZQCs). However, as u is tuned to between 0� (x) and 90�(y), ZQCs that originate exclusively from the strong-coupling inter-actions during TE1 also contribute to the signal of the AB spin sys-tem [13].

Assuming TE1 = TE2 for simplicity, the signal, SAy, of the A-spin(2.54 ppm) of the AB spin system of Cit in real-mode is calculated(by taking the coefficient of Ay at the onset of acquisition) to be

SAy � cosðuÞ � ðWþ2 Þ

2 þ sinðuÞ � fS1ða �W�1 þ b �W�

2 Þþ S2ðb0 �W�

1 � a �W�2 Þg; ð5Þ

where a = (pJ/K)�sin(2K�TM), b = (dx/K)2 + (pJ/K)2�cos(2K�TM),and b0 = cos(2K�TM). Several important physical meanings of Eqs.(3a), (3b), and (5) should be noted.

(1) At certain phase angles of, for instance, 0�, 45� and 90�, Eqs.(3a) and (3b) are written as qZQF(u = 0�) = qZQF(Wþ

2 ),qZQF(u = 45�) = qZQF(Wþ

2 , S1, S2), and qZQF(u = 90�) = qZQF

(S1, S2). Therefore, the consequence of rotating u is to controlthe relative contribution to the final signal of the twodistinct groups of coherence terms with different origins.

(2) As shown in Eq. (5), those z-magnetizations and ZQCs in Eq.(3b) will continuously evolve during TM and TE2. For illus-trative simplicity, if the influence on the final filter yield ofthe characteristics of the third 90� read-pulse, namely, hread,Lread, BWread and fread is neglected, a general expression forthe u-dependent final signal for coupled spins, Scoupled, inresponse to a ZQF may be written in the form of

92 H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97

Scoupled � cosðuÞ � f ðTE1; TM; TE2Þ þ sinðuÞ � gðTE1; TM; TE2Þ: ð6Þ

In Eq. (6), f and g are the sums of coefficients of observable, in-phasesingle quantum coherences (SQCs; Ay and By in this Cartesian prod-uct operator analysis for an AB spin system), which are functions ofsequence timings. In other words, the u-dependent final filter yieldfor coupled spins can be characterized by a linear combination ofcosine and sine functions whose weighting factors are functionsof sequence timings. Thus, depending on the choice of sequencetimings, the u-dependence of the final filter yield for coupled spinscan exhibit various patterns, which would therefore provide addi-tional spectral contrast. For example, if either f or g is dominant overthe other for a given set of sequence timings, a monotonic signal de-cay or enhancement will occur, respectively, as a function of u. Ifthese two weighting factors are comparable to each other, a signalmaximum can occur even at an intermediate phase angle.

According to Eqs. (3a), (3b), (4), the u-dependence of the finalfilter yield for weakly-coupled spins can be simply characterizedas a monotonic decay obeying cos(u). For example, the densityoperator for the X3 doublet (�1.3 ppm) of lactate (Lac; a weakly-coupled AX3 spin system at 3.0 T) just after the MQ-pulse in aZQF is calculated to be

qðTEþ1 ÞZQF � fðXzÞ � cosðpJ � TE1Þ � ðAxXy � AyXxÞ � sin3ðpJ

� TE1Þg � cosðuÞ; ð7Þ

where Xl = X1l + X2l + X3l and l = x, y, or z. Therefore, the u-depen-dent response of the X3 doublet of Lac just after the MQ-pulse isidentical to that of AX spin system as in Eq. (4), which is a simpledecay as a function of cos(u), regardless of the choice of TE1. Like-wise, just after the MQ-pulse, the density operator for an uncoupledspin, I, is simply

qðTEþ1 ÞZQF � Iz � cosðuÞ; ð8Þ

which shows that the ZQF signal of an uncoupled spins such as cre-atine (Cr) and glycine (Gly) will also decay as a function of cos(u)irrespective of the choice of sequence timings.

In Fig. 2a, the analytically derived u-dependence of the repre-sentative coherence terms in Eqs. (3a) and (3b) are compared withthat calculated by using numerical methods. None of these termsshow a monotonic decay in response to varying u. For instance,Az has its maximum amplitude at u � 50� and the minimumamplitude of Bz appears at u � 40�, while the amplitude of theZQC term, 2(AxBy � AyBx), increases as a function of sin(u). To illus-trate the u-dependence of ZQCs for more complicated spin sys-tems, mI was chosen, which has a strongly-coupled 6-spin

Fig. 2. The u-dependence of the representative coherence terms of Cit and mI just afterand Bz; ‘4’), ZQC (2(AxBy � AyBx); ‘s’), and DQC (2(AxBy + AyBx); ‘d’) of Cit are comparednumerically calculated u-dependence of the two representative ZQCs of mI, 2(M1xN2y �M(dotted lines). (c) The numerically calculated u-dependence of the two representative DQ80 ms (dotted lines). Unlike for Cit shown in (a), the DQCs of mI have non-zero values atsolutions. Each curve was normalized to its own maximum amplitude.

system (AM2N2P at 3.0 T [26–28]). Fig. 2b illustrates the numeri-cally calculated u-dependence of representative ZQCs of mI,2(M1xN2y �M1yN2x) and 2(N1xPy � N1yPx), at 3.0 T for a TE1 of30 ms (solid lines) and 60 ms (dotted lines). Both MN- and NP-pairsare strongly-coupled. The u-dependence of 2(M1xN2y �M1yN2x) ofmI for TE1 = 30 ms and 60 ms is similar (with the opposite sign)to that of Az and Bz of Cit (Fig. 2a), respectively. The u-dependenceof 2(N1xPy � N1yPx) can be approximated as �cos(u) for TE1 = 30 msand �sin(u) for TE1 = 60 ms just as the 2(AxBy � AyBx) of Cit inFig. 2a. Although these MQC terms cannot directly be related tothe final filtered signal due to complicated spin evolution duringTM and TE2 [7,13,21,30,35], the u-dependence of 2(N1xPy � N1yPx)for these two different TE1’s clearly demonstrates that the analyticalform of these u-dependence can be described as a linear combina-tion of cos(u) and sin(u) whose weighting factors are sequencetiming-dependent, which is in line with Eq. (6). It is also clear inFig. 2 that for a given TE1 rotating u gives rise to changes not onlyin filter yield but in overall lineshape as well.

2.1.2. DQFThe changes in the level of coherence brought about by the MQ-

pulse for double quantum coherences (DQCs) differ from those forZQCs. Consequently, the u-dependence of the density operators forDQF differ from those for ZQF. That is, just after the MQ-pulse, thedensity operator for the AB spin system of Cit in response to a DQFbecomes,

qðTEþ1 ÞDQF � �2ðAxBy þ AyBxÞð1=2ÞfWþ1 � ½cosðuÞ þ cosð3uÞ�g: ð9Þ

The arguments of the cosine functions in Eq. (9), i.e., u and 3u,originate from the changes in the level of coherence from +1 ? +2,and from �1 ? +2, respectively [34]. The analytically derived u-dependence of 2(AxBy + AyBx) in Eq. (9) is illustrated in Fig. 2a, alongwith that from the numerical calculation. The minimum amplitudeof the DQC term occurs at u = 45� and 90�. Note that those strong-coupling-specific coefficients, S1 and S2, are not involved in Eq. (9).This means that for an AB spin system no DQC is produced fromstrong-coupling-specific APCs (e.g., 2AyBz and 2ByAz in Eq. (1a))irrespective of the choice of u. However, for more complicatedstrongly-coupled spin systems such as mI, DQC terms have anon-zero amplitude at u = 90� as for ZQCs. Using numerical meth-ods, this is illustrated in Fig. 2c. Since it is certain that for weakly-coupled spins no even-order MQC can be produced by the y-phased(u = 90�) MQ-pulse from APCs available at the end of the TE1 per-iod (such as 2AxXz, 4AyMzXz, and 8AxMzQzXz), the existence of DQCswith non-zero amplitude at u = 90�, such as 2(M1xN2y + M1yN2x)

the MQ-pulse. (a) The analytically calculated u-dependence of z-magnetizations (Az

with those numerically calculated (solid lines) after a TE1 period of 30 ms. (b) The1yN2x) and 2(N1xPy � N1yPx), are illustrated for a TE1 of 30 ms (solid lines) and 60 msCs of mI, 2(M1xN2y + M1yN2x) and 2(N1xPy + N1yPx), for a TE1 of 50 ms (solid lines) andu = 90�. A step size of 2� was used for the numerical calculations and 9� for analytic

H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97 93

and 2(N1xPy + N1yPx) of mI, must result exclusively from strong-coupling interactions during TE1. As indicated in Fig. 2c, the u-dependent final signal for coupled spins, Scoupled, in response to aDQF can also be characterized in the form of Eq. (6) except thatthe basis set constituting the linear combination for a DQF shouldalso include cos(3u) and sin(3u) in addition to cos(u) and sin(u)in order to account for the changes in the level of coherence from�1 to 2 brought about by the MQ-pulse.

The theoretical analyses given here strongly suggest that thephase of the MQ-pulse in a MQF can provide additional spectralcontrast in the editing of strongly-coupled spins.

2.2. Experiments

Five spherical phantoms (6-cm in diameter) were produced,four with 50 mM concentrations of Glu, Gln, Lac and mI, respec-tively, and the fifth with a mixture of Cit and taurine (Tau;strongly-coupled 4-spin system (A2B2)) each in a concentration of50 mM. Moreover, to demonstrate the efficacy of u-optimizationin the mI-editing against its background metabolites, an additionalmixed phantom was made containing mI, Gly and Tau [13,35] inthe relative physiological concentrations of the normal humanbrain, namely,�1:0.2:0.5 (mI at 50 mM) [36–38]. For a similar pur-pose a mixed phantom of Glu and Gln (both AMNPQ spin system)was also made (�2:1 [36–38] (Glu at 50 mM)). For all phantoms,10 mM of Cr was also included as an uncoupled spin reference,and the pH was adjusted to 7.1 ± 0.1. All chemicals (purity P 98%)were purchased from Sigma Chemical Co. (St. Louis, USA) exceptfor Cr (ICN Biomedicals, Inc., Aurora, USA).

All experiments were carried out at 3.0 T in an 80-cm bore mag-net (Magnex Scientific PLC, Abingdon, UK) with a SMIS spectrome-ter console (Surrey Medical Imaging Systems PCL, Guilford, UK). Ahome-built quadrature birdcage coil (28-cm in diameter) was usedfor both RF transmission and signal reception. For the design of aMQF, the first 90� excitation pulse is an optimized sinc pulse of3 ms duration (L) and 4000 Hz bandwidth (BW) [39]. A rectangular,hard pulse was chosen for the second 90� MQ-pulse (L = 250 ls). Ifthe phase of this MQ-pulse, u, is tuned coherently with that of thefirst excitation pulse, the signal from uncoupled spins in responseto a ZQF is maximized [13]. Therefore, u was calibrated manuallyby resorting to the behavior of the Cr methyl singlet at �3.0 ppm.After optimizing u in this manner, both ZQF and DQF experimentswere carried out. The third 90� read pulse was a sinc-Gaussianpulse (L = 5 ms), which was tuned to excite 1.0–4.5 ppm range asan additional water suppression strategy. The two 180� refocusingpulses were numerically optimized sinc-like pulses (L = 3.5 ms,

Fig. 3. The response of the strongly-coupled AB spin system of Cit to a ZQF at {TE1 = 30, TMangle of 0� to 90�. (a) Signal in real mode. (b) Signal in magnitude mode. (c) The calcula

BW = 1200 Hz) [39]. In order to remove unwanted signals, each180� pulse was sandwiched by a pair of spoiler gradients(L = 2 ms) with an amplitude of 20 mT m�1. All RF pulses werephase-cycled in 16-steps to remove unwanted coherences whichcould potentially arise from outside the voxel [40]. The filter gradi-ents during TM (5 ms, 20 mT m�1) and TE2 (for a DQF only) wereapplied at the magic angle to facilitate the suppression of residualwater signal resulting from the demagnetizing dipole–dipole inter-actions between water molecules [7,23,24]. Since the purpose ofthe study was to demonstrate the effect of varying u on filteredsignal, spectra were acquired at several representative symmetricTEs ({TE1, TE2}) and all other sequence parameters were kept fixed(repetition time (TR) = 3 s and TM = 9 ms). For all experiments, avoxel size of 3 � 3 � 3 cm3 was used, and a total of 32 averageswere taken with a spectral bandwidth of 2500 Hz and 2048 datapoints for acquisition.

Because no reference singlet is available in DQ-filtered spectra,phase corrections in the post-data processing cannot be made con-sistently to the individual spectra being compared. As a conse-quence, the use of the areas, or maximum amplitudes, of spectrameasured in the real-mode, as filtered signal yields can be mislead-ing. This difficulty also arises for ZQ-filtered spectra acquired withu tuned around orthogonality to that of the excitation pulse,where all singlet signals are suppressed [13]. As a result, all spectrawere processed in magnitude-mode, and the peak areas thus mea-sured were used as filtered signal intensity.

3. Results

Fig. 3 shows the u-dependent spectra of the AB multiplet of Citin response to a ZQF at {TE1, TE2} = {30, 30} in ms. In Eq. (5), theweighting coefficients of cos(u) and sin(u) are calculated to be0.43 and 0.48, respectively. Since these weighting factors are com-parable in this case, the maximum signal of the A-spin occurs at anintermediate phase angle (54� in Fig. 3a). Note that the u-depen-dence of both A- and B-spins in Fig. 3a are consistent with thoseof Az and Bz in Fig. 2a, respectively. Thus, for this simple, 2-spinsystem only, the u-dependence of the final filter yield may bepredicted from the density operator immediately after the MQ-pulse. The influence of rotating u on the lineshape is also welldemonstrated in this example.

The u-dependence of (a) the uncoupled Cr singlet and (b) theweakly-coupled X3 doublet of Lac in response to a ZQF at {30,30}, are illustrated in Fig. 4. As calculated in Eqs. (7) and (8), thesignals of Cr and Lac both decay monotonically as a function ofcos(u).

= 9, TE2 = 30 ms} with varying phase of the MQ-pulse from the conventional phaseted spectra in magnitude mode using numerical methods.

Fig. 4. The response of uncoupled Cr (methyl group) at �3.0 ppm and weakly-coupled Lac (methyl group) at �1.3 ppm to varying phase of the MQ-pulse for a ZQFat {TE1 = 30, TM = 9, TE2 = 30 ms}. As the phase of the pulse is tuned from theconventional x-phase towards y-phase, signal decays monotonously for bothmetabolites.

Fig. 5. The u-dependence of the strongly-coupled spin systems of Cit (a), Tau (b) and mtimings. For each individual responsive curves, the type of MQF and {TE1, TE2} in msdependence of strongly-coupled spin systems are diverse depending on the spin systemthe areas of the peaks were measured as signal intensity. The spectral ranges used for t3.5 ppm for the A2B2 multiplet of Tau, 3.45–3.75 ppm for the M2N2 multiplet of the AM2

Fig. 6. The optimization of the phase of the MQ-pulse for the discrimination of mI fromsignal of the M2N2 multiplet of mI at u = 0� is contaminated by interfering backgroundapproaches 90�, the mI signal is enhanced, while the Tau and Gly signal is effectively supphantom containing a mixture of mI + Tau + Gly converges to those from mI only (middleTM = 9, TE2 = 80 ms}. Similar to (a), the optimization of u results in both signal enhance

94 H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97

In contrast to the response of both uncoupled and weakly-cou-pled spins to a variation in u, the signal from strongly-coupledspins can be enhanced relative to that observed at u = 0�. This isdemonstrated experimentally in Fig. 5. For curve #1, which corre-sponds to the spectra shown in Fig. 3b, the filter yield is enhancedby �20% if u is tuned from x (0�) to y (90�) at the given sequencetimings. Such an enhancement is also observed in curves #2, #3,#9 and #11–13 in Fig. 5. Furthermore, Fig. 5 demonstrates thatthe choice of the {TE1, TE2} pair influences the amount of u-depen-dent signal enhancement or loss in a ZQF and/or a DQF, e.g., curves#1 vs. #2, #4 vs. #6, and #5 vs. #7 in Fig. 5. In particular, a compar-ison between curves #8 and #9, or between curves #10 and #13strikingly demonstrates the u-dependent sensitivity of the filteryield to the sequence times (a 50% increase or decrease). Moreover,the maximum or minimum signal can even occur at an intermedi-ate phase angle (curve #3, #11, #12). It should also be noted thatthe response of Cit, Tau and mI to a ZQF at, for instance, {30, 30}

I (c–d) in ZQF and DQF experiments at various representative symmetric sequenceare shown. Unlike those of uncoupled and weakly-coupled spin systems, the u-

s and the sequence timings. All spectra were obtained in magnitude mode and thenhe estimation of the peak areas were: 2.4–2.8 ppm for the AB multiplet of Cit, 3.2–N2P spin system of mI.

Tau and Gly. In a ZQF experiment at {TE1 = 60, TM = 9, TE2 = 60 ms} (a), the initialsignal from the A2B2 multiplet of Tau and uncoupled Gly (top row). However, as upressed. As a result, the lineshape and the signal amplitude of mI obtained from therow). Also shown in (b) are the experimental results with a DQF taken at {TE1 = 80,

ment for mI and suppression for the neighboring Tau signal.

Fig. 7. The optimization of the phase of the MQ-pulse for the discrimination of Glu from Gln. In response to both (a) ZQF at {TE1 = 40, TM = 9, TE2 = 40 ms} and (b) DQF{TE1 = 50, TM = 9, TE2 = 50 ms}, the MNPQ multiplet (�2.0–2.6 ppm) of Glu is severely contaminated by that of Gln at the initial phase angle of u = 0� (top row). However, bytaking advantage of the u-dependence of Glu (middle rows) that is different from that of Gln (bottom rows) at the specific sequence timings, the spectral integrity of Glu canmarkedly be improved in both ZQF and DQF experiments.

H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97 95

are different from each other as shown in curves #1 (Cit; �20% in-crease), #4 (Tau; �30% decrease) and #8 (mI; �50% decrease).

Practical examples of u-optimization are illustrated in Fig. 6 forthe discrimination of mI from strongly-coupled Tau and uncoupledGly [13,35]. For the conventional ZQF (u = 0�), Gly passes throughthe filter [13] and subsequently contaminates the target multipletof mI (Fig. 6a). Moreover, the significant amount of Tau signal atthis sequence timing exacerbates the contamination of mI. A con-ventional ZQF at {60, 60} is not, therefore, a good choice for mIdetection. However, as u is varied towards 90� (y), Gly is graduallyremoved, and at this specific sequence timing Tau is also substan-tially reduced (also shown in curve #6 in Fig. 5b). In contrast, themI target signal is enhanced by a factor of 2.5 (curve #9 inFig. 5c). Therefore, the ZQF contamination of the mI signal by amixture of Tau and Gly at u = 0� can be effectively edited by opti-mizing u at the same sequence timings. A similar advantage of u-optimization for mI editing is illustrated in a DQF experiment at{80, 80} as shown in Fig. 6b. Here, Gly singlet is removed regardlessof u [13], whereas �95% of Tau signal is suppressed as u ap-proaches 90� (curve #7 in Fig. 5b). Meanwhile, mI signal is en-hanced by 67% at u = 90� through its initial reduction by 30% atu = 18� (curve #12 in Fig. 5d).

Fig. 7 illustrates another example of u-optimization for editing,namely the MNPQ multiplet of Glu against that of Gln. In bothFig. 7a and b, the initial Glu spectra taken at u = 0� are severelycontaminated by Gln spectra. However, as u varies towards 90�,80% and 90% of Gln signal is suppressed, whereas 70% and 50% ofGlu signal is still retained, in Fig. 7a and b, respectively.

These examples altogether clearly demonstrate that the optimi-zation of u provides additional spectral contrast over and abovethe use of {TE1, TE2} in the design of a MQF not only for suppressingresonances from uncoupled and weakly-coupled spins but for evendifferentiating between strongly-coupled spins.

4. Discussion

For strongly-coupled spins, strong-coupling-specific in-phaseand anti-phase SQCs are created during inter-pulse delays, throughactive coherence transfer that is facilitated by the strong-couplingHamiltonian [13,33]. We have previously demonstrated that thesestrong-coupling-specific coherence terms can be exclusively fil-tered by tuning u orthogonal to that of the excitation RF pulse ina conventional ZQF [13]. The purpose of this study was to investi-

gate more comprehensively the u-dependent evolutions of cou-pled spins in response to a MQF by including intermediate phaseangles of u in the analysis and by extending its applications to aDQF. Several important physical insights into the role of u in aMQF were gained. First, the physical consequence of varying u isto control the relative contribution to the final signal of thestrong-coupling-specific coherences created during TE1. Secondly,the u-dependence of the final filter yield for coupled spins maybe described as a linear combination of cosine and sine functionswhose arguments are the product of u and the changes in the levelof coherence brought about by the MQ-pulse, and whoseweighting factors are functions of sequence timings. Thirdly, theu-dependence of the final filter yield for coupled spins exhibitsvarious patterns, depending on the choice of the sequence timings.Cumulatively, these findings clearly suggest that u provides anadditional spectral contrast in MQF experiments.

For the strongly-coupled AB spin system used in the productoperator analysis, no DQC is produced from strong-coupling-specific APCs, irrespective of u. In order to examine analyticallythe u-dependence of coupled spins in a MQF in general, therefore,a more complicated strongly-coupled spin model needs to be em-ployed such as an ABC spin system. However, it should be notedthat even for the AB spin system, the calculations of the evolutionsof the density operator are not trivial, particularly when u is in-cluded as another variable. By using numerical methods[7,21,30], the existence and u-dependence of strong-coupling-specific MQCs for more complicated strongly-coupled spins wereinvestigated with the representative MQC terms of Tau and mI.

The metabolite-discriminating efficacy of u per se was clearlydemonstrated in the experiments at several, representative sym-metric TEs. For the mI-editing, the uncoupled Gly and strongly-coupled Tau background signal were all effectively suppressedfor both a ZQF and a DQF by optimizing u at the TEs shown. Theseare TEs that would be otherwise useless in terms of the specificityto the target signal. Despite its better signal yield over a DQF, by afactor of two in principle, the conventional ZQF has not beenwidely used in vivo due to its inherent problem of being unableto suppress uncoupled spin resonances. Thus, the demonstrationpresented here encourages more vigorous applications of a ZQFfor the spectral filtering of strongly-coupled spins from any uncou-pled spins. The filtering efficacy of u in the design of a MQF wasfurther demonstrated for the separation of Glu from Gln. In thecoupling networks of the AMNPQ spin systems of Glx [27], theMN- and PQ-pairs are strongly-coupled. The degrees of coupling,

96 H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97

J/Dd (Dd: chemical-shift difference between coupled spins in Hz),for the MN-pairs are estimated to be 1.45 for Glu and 5.66 forGln at 3.0 T. For the PQ-pairs, they are 12.44 for Glu and 6.00 forGln. Thus, degree of coupling alone cannot be considered as anabsolute measure of the amount of signal at u = 90� from strong-coupling-specific interactions. For instance, for an AB spin system,the APC terms, 2AyBz and 2ByAz in Eq. (1a), are coupled to the coef-ficient S2 in Eq. (1e) whose oscillation amplitude is proportional tothe term, (dx/K)(pJ/K). This term can be rewritten in terms of J/Ddas (J/Dd)/[1 + (J/Dd)2]. The amplitude of this quantity is propor-tional to J/Dd only for J/Dd 6 1 and beyond that range it is inverselyproportional. Therefore, for an AB spin system whose J/Dd is largerthan unity, the degree of coupling by itself cannot be taken as ameasure of the amount of signal available from strong-coupling-specific interactions. The different u-dependence of MNPQ multi-plets of Glx demonstrated in both ZQF and DQF experiments hereinis most likely mainly due to active coherence transfer in the courseof the evolution of strongly-coupled spins during TM and TE2

[7,13,21,30,35]. For instance, the in-phase SQCs of M- and N-spinsof Glx at the onset of acquisition that contribute to the MN multi-plets of Glx (�2.0–2.2 ppm) can result from substantially differentcoherence pathways. For a ZQF, for instance, various ZQCs consist-ing of different spin species can evolve into the SQCs of M- and N-spins to be detected, such as ZQC(MN), ZQC(MP) and ZQC(NQ). Inaddition to these ZQC terms, even a ZQC term such as ZQC(PQ)can contribute to the MN multiplets via the form of ZQC(MP) orZQC(NQ) [21,35]. As a result, the TM-dependence of the SQCs ofM- and N-spins of Glu at the onset of acquisition period can be sig-nificantly different from that of Gln. Since coherence transfer is ac-tive during TE2 as well, the choice of TE2 also influences theamount of final filter output of Glx [30,35].

The phase of the MQ-pulse needs to be precisely tuned to obtaina desired outcome. A phase error can result in a significant loss ofsignal and an unexpected lineshape of a target peak. A mismatchbetween the phase of an RF pulse coded in an NMR pulse sequenceprogram and the actual phase of that pulse is mainly due to phaseaccumulation during the switching of the synthesizer frequency,which is necessary when slice-selective pulses are used withnon-zero offset frequencies [6,41–43]. The phase error of this kindmight be compensated for, for instance, by comparing the responseof the water resonance acquired with and without an additional180� pulse [42]. However, imperfect hardware performance suchas instability of the RF and/or gradient amplifiers can also poten-tially give rise to phase errors, which can be intractable. Such anadditional phase error can be identified by acquiring data from a

Fig. 8. The chemical structures of citrate, creatine, glutamate, glutamine,

voxel located at the isocenter. To cope with these potential phaseerrors as a whole in this study, u was calibrated manually byresorting to the behavior of the Cr singlet at �3.0 ppm in responseto a ZQF. This was based on the fact that when u is tuned coher-ently to that of the first excitation pulse, the amplitude of uncou-pled (and weakly-coupled) resonances is maximized. Afteroptimizing u in this manner, DQF experiments were also carriedout by turning on the second filtering gradient, which is the onlycomponent of a DQF that differs from a ZQF. Although additionalscan time is required, this method can be used in vivo as we dem-onstrated previously [13].

Finally, since the purpose of the study was to demonstrate themetabolite-discriminating efficacy of u per se, all spectra were ac-quired within the same family of representative symmetric TEs,thereby focusing on signal-to-background ratio. All other sequenceparameters were kept fixed. In practical MQF design, however, allof the sequence parameters must be optimized to maximize sig-nal-to-noise ratio as well. The u-dependent changes in lineshapeof the signal should also be considered in the optimizationprocedure.

In conclusion, this methodology will find applications wheneverthe target metabolite contains strongly-coupled spins. It providesanother means by which one can control the relative acquisitionperiod magnitudes of the coherences that originate from uncou-pled, weakly- and strongly-coupled spins at the end of the TE1 evo-lution period. In other words, the MQ-pulse itself possessesfiltering capability that works based on the degree of coupling inaddition to the filter gradients that perform filtering based on thelevel of coherence. Since the responses of various metabolites tothe u-variation are different, it also expands the toolbox for differ-entiating between metabolites with strongly-coupled spins.

Acknowledgments

This research was supported by grants from the Canadian Insti-tute for Health Research and by Basic Science Research Programthrough the National Research Foundation of Korea (NRF) fundedby the Ministry of Education, Science and Technology (2009-0077642 and 2010-0002896).

Appendix A

The chemical structures of the metabolites [13,27,44] consid-ered herein are shown in Fig. 8.

glycine, lactate, myo-inositol, and taurine (�: exchangeable proton).

H. Kim et al. / Journal of Magnetic Resonance 223 (2012) 90–97 97

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