On the Application of Chemical Shift-Based MultipointWater-Fat Separation Methods in Balanced SSFP Imaging

Hyeonjin Kim,1* Alexander B. Pinus,1 Jinghua Wang,1 Philip S. Murphy,4 andR. Todd Constable1–3

Chemical shift-based multipoint water-fat separation meth-ods have been applied in balanced steady-state free preces-sion (bSSFP) sequences because of the high signal-to-noise-ratio (SNR) attainable. In this approach the echo formation isapproximated to occur concurrently for both water and fat atan echo time (TE) equal to half the repetition time (TR/2approximation). However, the degree to which the imagingconditions underlying the TR/2 approximation are satisfiedcan significantly vary in vivo depending upon the imagingregion of interest (ROI) and the pixels across a field of view(FOV). The consequence of the TR/2 approximation on chem-ical shift-based multipoint water-fat separation was investi-gated. The influence of a mismatch between the pass-bandprofiles of water and fat (pass-band mismatch) on fat quan-tification was also examined. Theoretical and experimentalresults demonstrate that the TR/2 approximation can resultin spatially dependent noise performance of multipoint wa-ter-fat separation methods, and the pass-band mismatch canrender the precision of fat quantification spatially dependent.Given that local tissue characteristics in affected liver can besubstantially variable, this study is of particular importance inliver imaging. Magn Reson Med 58:413– 418, 2007. © 2007Wiley-Liss, Inc.

Key words: MRI; fat quantification; multipoint water-fat sepa-ration; balanced SSFP; liver

The chemical shift-based water-fat separation methodoriginally reported by Dixon (1) has been applied in bal-anced steady-state free precession (bSSFP) sequences be-cause they provide superior signal-to-noise-ratio (SNR)compared to non-bSSFP sequences (2) with single- (3,4) ormultipoint data acquisition (multipoint water-fat separa-tion) (2,5–8).

It is well known that the higher SNR of bSSFP resultsfrom the spin-echo (SE)-like signal behavior of spins(9,10), which is similar to and yet distinguished from thatin conventional SE or fast SE (FSE) sequences. That is, thephase evolution of individual spin isochromats and thusthe formation of the echo in bSSFP strongly depend on

imaging parameters such as repetition time (TR), trans-verse relaxation time (T2), and frequency offset (f) (9–12).To simplify such subtle phase evolution, small f and T2 ��TR are implicitly assumed in multipoint water-fat separa-tion in bSSFP, and based on these assumptions the forma-tion of the echo is approximated to occur concurrently forboth water and fat at t � TR/2, and the refocused magne-tization vectors of the two spin species have either per-fectly parallel or antiparallel configurations depending onthe choice of TR (hereafter referred to as TR/2 approxima-tion). However, in vivo the degree to which the assump-tions underlying the TR/2 approximation are satisfied candiffer in different imaging regions of interests (ROIs), frompixel to pixel across the field of view (FOV), and at differ-ent main field strengths. Thus, the validity of the TR/2approximation can also be subject to variability.

Another factor that can influence the fat-to-water-ratio(FWR) estimation in bSSFP imaging is the unequal pass-band profiles of water and fat (hereafter referred to as thepass-band mismatch). Differences in the ratio of T2 to thelongitudinal relaxation time (T1) between water and fat invivo limit the optimization of the flip angle (�) when oneattempts to maintain the relative amplitude of the pass-bands of the two spin species across a given range of f.

In this report we investigate the consequence of the TR/2approximation and the pass-band mismatch on multipointwater-fat separation in bSSFP imaging under circum-stances where the assumptions underlying the approxima-tion are not strictly satisfied. Theoretical consideration isgiven from the perspective of signal modeling, vector con-figuration, and image reconstruction algorithms. For ex-perimental verification, the iterative decomposition of wa-ter and fat with echo asymmetry and least-squares estima-tion algorithm (IDEAL) (6,13) is used with three-point dataacquisition.

There are growing demands for precise quantification ofhepatic fat content in association with many clinical con-ditions (e.g., obesity, alcoholic/non-alcoholic fatty liver,and insulin resistance) that often accompany iron overload(14). Therefore, given that local f, T1 and T2 in the affectedliver can substantially vary (15), this study is of particularimportance in liver imaging.

THEORY

In bSSFP off-resonant spins possess an initial phase, �o,immediately after radiofrequency (RF) pulses (10,12). It isa time-independent function of TR, T2, and f that can bewritten (11,12) for water (�o

W) as

�oW � tan�1� � E2

Wsin�2��TR

1 � E2Wcos�2��TR� [1a]

1Department of Diagnostic Radiology, Yale University School of Medicine,New Haven, Connecticut, USA.2Department of Biomedical Engineering, Yale University School of Medicine,New Haven, Connecticut, USA.3Department of Neurosurgery, Yale University School of Medicine, New Ha-ven, Connecticut, USA.4Clinical R&D, Pfizer, Sandwich, UK.Grant sponsor: Pfizer, Inc.*Correspondence to: Hyeonjin Kim, Ph.D., Anlyan Center, MRRC, N125, YaleUniversity School of Medicine, 300 Cedar Street, P.O. Box 208043, NewHaven, CT 06520-8043. E-mail: hyeonjin.kim@yale.eduReceived 19 September 2006; revised 11 March 2007; accepted 18 April2007.DOI 10.1002/mrm.21303Published online in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 58:413–418 (2007)

© 2007 Wiley-Liss, Inc. 413

and for fat (�oF) as

�oF � tan�1� � E2

Fsin�2��� � fTR

1 � E2Fcos�2��� � fTR�, [1b]

where � is the field inhomogeneity, f is the chemical-shiftdifference between the two spin species, E2

W � exp(–TR/T2

W), E2F � exp(–TR/T2

F), and T2W and T2

F are T2 of water andfat, respectively. It is this initial phase that is responsiblefor the periodic and discontinuous phase profile of spinsin bSSFP (3,10,12). Following RF excitation the phaseevolution of spins is simply described as 2�f as in non-bSSFP sequences such as spoiled gradient echo (SPGR).Thus, the role of the initial phase may be considered aspreparing individual spin isochromats such that they forman echo approximately at t � TR/2 by compensating for theinterpulse phase evolution. Then, the total phase evolu-tion in bSSFP can be described as � � �o � 2�ft � �sys,where �sys denotes the spatially varying but time-indepen-dent phase of spins resulting from a non-ideal system, andis typically assumed to be identical for both water and fatresiding in the same voxel (3,4). Defining the difference ininitial phase between water and fat as �o (� �o

F � �oW), and

� W� and � F� as the magnitude of water and fat spin density,respectively, a signal model for a pixel containing waterand fat at t � tn can be written without approximation as

Sn�tn � � w�ei��oW�2��tn��sys � � F�ei��o

F�2����ftn��sys [2a]

� � W � Fei�2�ftn��oei�2��tn��oW [2b]

� � �W � �Fei2�ftnei2��tn [2c]

where W � � w �ei�sys, F � � F �ei�sys, �W � wei�oW

� � w �ei��oW��sys and �F � Fei�o

F

� � F �ei��oF��sys. That is,

the complex spin densities W and F in Eq. [2b] contain�sys, whereas �W and �F in Eq. [2c] contain all time-inde-pendent phase terms as defined in the original IDEALalgorithm (6). Note that at t � TR/2 the inner and outerphase terms in Eq. [2b] become 2�f(TR/2) � �o and2��(TR/2) � �o

W, respectively. Writing TR in the form ofTR � (–m/f) � TR where m is an integer closest to –TR �f, the inner phase term at t � TR/2 further reduces to–m� � 2�f(TR/2) � �o. It will be made clear later inthis section that TR is a measure of the extent of thepass-band mismatch. Now, define �refoc and �asym as theamount of residual dephasing of spins and additionalphase offset between W and F at t � TR/2, respectively.That is,

�refoc � 2���TR2 � � �o

W [3a]

�asym � 2�f�TR2 � � �o. [3b]

Then, it is clear that the perfect rephasing and parallel/antiparallel alignment of W and F at t � TR/2 under theTR/2 approximation are achieved when both �asym and�refoc approach to zero. This occurs if T2

W, T2F �� TR and ���

��1/2�TR. For instance, under these conditions �oW in Eq.

[3a] reduces to –2�� � (TR/2) and therefore �refoc 3 0.However, if these conditions are not strictly satisfied, non-negligible �refoc and �asym can exist at t � TR/2. Theexistence of �refoc was briefly discussed previously (10).In particular, in order to achieve perfect parallel/antipar-allel alignment of W and F at t � TR/2 when the condi-tions of T2

W, T2F �� TR, and ��� ��1/2�TR are not strictly

satisfied, additional conditions of T2W � T2

F and TR � 0are required. Then, due to the periodicity of the trigono-metric functions in Eqs. [1a] and [1b], �o

W � �oF and thus

�asym 3 0. However, in vivo the extent to which theseconditions are satisfied can significantly vary, and typi-cally TR � 0 due to the demand of a large samplinginterval and sampling asymmetry that strongly influencesthe noise performance of multipoint water-fat separationmethods (6,13,16–18). For instance, in the liver, T2

W isshort (46 ms at 1.5T (19)) and � can range beyond �50 Hzacross the FOV even at 1.5T. Moreover, T2

F is not clearlyknown in general due to the variable degree of J-(de)cou-pling of fat spins depending on the measurement protocol(20).

Influence of �refoc and �asym on FWR Estimation

Both �refoc and �asym are spatially dependent but time-independent. Therefore, in the original IDEAL algorithm,where water and fat spin densities are defined as complex(6), these terms are taken into consideration equivalentlyas �sys (Eq. [2c]) without influencing the estimates of �, � W�,� F� and thus FWR (4,21). However, for other multipointmethods, �asym as well as �refoc may need to be includedin the signal model for more robust water-fat separation inbSSFP imaging.

Influence of �asym on the Noise Performance

According to Eq. [2b], for a symmetric three-point datasampling with m � 1 and sampling interval t (i.e., TEn �TR/2 � t, TR/2 and TR/2 � t), the �F’s with respect to �W’s form an angular configuration of {�asym � 2�f � t,�asym, �asym � 2�f � t}. Thus, if �asym is not negligible,the desired symmetric vector configuration (Fig. 1a) isshifted by �asym (Fig. 1b). As the sampling interval isunchanged, this can be considered as if asymmetric sam-pling were prescribed on purpose, as in IDEAL (13). Notethat due to the dependence of �o on T2 and �, �asym isalso a function of these variables. Therefore, the degree ofvariability in the vector configuration will be spatiallydependent (Fig. 1c). If the original IDEAL is used, such anunwanted asymmetric sampling phenomenon does notcreate a bias in the estimation of FWR. However, it mayperturb the asymmetric phase angle, �asym, that was ini-tially chosen to minimize the FWR-dependent noise per-formance of multipoint water-fat separation methods(13,16,22), which is typically evaluated in terms of thenumber of signal averages (NSA) (6,13,16–18). The highsensitivity of the NSA to �asym in bSSFP has been demon-strated by Pineda et al. (16).

A similar analysis can be carried out starting with theIDEAL asymmetric sampling instead of the symmetricsampling assumed herein.

414 Kim et al.

Influence of Pass-Band Mismatch on FWR Estimation

In bSSFP the signal amplitude profile of spins is a functionof not only TR, T2, and f, but also of T1 and � (9,11,12).Figure 2 illustrates the signal amplitude profiles of water(on resonance) and fat as well as FWR calculated at TR �4.5 ms (TR � 0 ms; Fig. 2a) and 5.5 ms (TR � 1.0 ms;Fig. 2b). The relaxation times used were for water in theliver and for subcutaneous fat (19). As shown in Fig. 2a,even for TR � 0 ms where the pass-bands for both spinspecies are centered, the field dependence of FWR may benegligible only in the range of ��� � 1/2�TR. This is exac-

erbated in Fig. 2b due to nonzero TR, where the transi-tion region of the fat band lies in the pass-band of water.For TR � 0 ms, which is typically encountered in mul-tipoint water-fat separation in vivo, the FWR in pixelswith � � 0 Hz will be subject to underestimation and viceversa. Due to this pass-band mismatch, banding artifactswill also not be observed as clearly.

MATERIALS AND METHODS

All experiments were conducted on a 1.5T Siemens Sonatascanner with a volume coil (USA Instruments, Inc., Au-rora, OH, USA). All data were collected using trueFISP(Siemens Medical Solution, Erlangen, Germany). Imageswere reconstructed from raw data according to the originalIDEAL algorithm (6) written in MATLAB™ (MathWorksInc., Natick, MA, USA). In image reconstruction, the fieldmaps were smoothed by using a 3 � 3 boxcar filter (6).

Two bottle phantoms (�400 ml in volume) were made(one consisting of a 0.9% saline solution, and one consist-ing of vegetable oil with the same proportion in volume).For both phantoms T 1

F/T 2F of oil was 220/132 ms. Water in

both phantoms was doped with CuSO4 � 5H2O such thatthe T 2

W in one phantom was adjusted to 162 ms (6 mM)similar to that of oil (phantom 1). In this range of T 2

W andT 2

F in phantom 1 (both over 100 ms) �asym resulting fromthe difference in T2 should be negligible particularly whenTR � 0 ms (see Fig. 3). On the other hand, in order toamplify the effect of unwanted asymmetric sampling inthe presence of a smaller (compared to in vivo) frequencyoffset in the phantom, the T 2

W in phantom 2 was adjustedto 15 ms (80 mM of CuSO4 � 5H2O). T 1

W was 195 ms and17 ms in phantom 1 and 2, respectively. For the T1 mea-surements an inversion-recovery gradient echo sequencewas used. For the T 2

W measurements a conventional SEwas used. To avoid a potential error due to J-(de)couplingeffect (20) the T 2

F of the oil was calculated using trueFISPfrom the relative signal intensity of oil with respect to thatof water with known T 1

W, T 1F, and T 2

W. The water-fat chem-ical shift difference, f, was obtained in both phantoms

FIG. 3. (a) Source, (b) water-only, and (c) fat-only images obtainedfrom phantom 1 at TR � 9.5 ms (TR � 0 ms) using IDEAL. d: �asym

map, which is homogeneous in most regions due to negligible andthus field-independent �asym.

FIG. 1. a: Configuration of fat vectors with respect to water vectorsunder the TR/2 approximation for a symmetric three-point datacollection. b: Configuration of the vectors for short T2, large f andlonger TR, which are shifted by �asym. The sampling interval (� �2�fTE) is maintained. c: Contour plot of the calculated �asym (°)as a function of T2 (vertical axis) and � (horizontal) at 1.5T whereT2

W � T2F, TR � 5.5 ms, and f � –220 Hz were assumed. For spins

with T2 � 45 ms, �asym ranges from a few degrees (� � 0) up to �20° (� � 0). The asymmetric distribution of �asym about � � 0 arisesfrom the phase profile of fat, the center of which is shifted towardthat of water due to nonzero, positive TR (� 1.0 ms). In terms ofsignal amplitude profile, this effect arises from the smoothing oftransition regions between the pass-bands and the stop-bands ofbSSFP sequences with short T2.

FIG. 2. Water and fat pass-band mismatch effect calculated at (a)TR � 4.5 ms (TR � 0 ms) and (b) 5.5 ms (TR � 1.0 ms), where � �45°, T1

W/T2W � 586/46 ms and T1

F/T2F � 343/58 ms were assumed. All

curves were normalized to the maximum amplitude of fat. In b, dueto nonzero TR the FWR changes by as much as �35% even in thesmall range of ��� � 30 Hz.

Multipoint Water-Fat Separation With bSSFP 415

using a single-voxel spectroscopy technique (stimulated-echo acquisition mode (STEAM); TR/TE � 2000/20 ms,2 � 1 � 3 mm3 voxel, 32 averages). It was estimated to be–211 and –234 Hz in phantoms 1 and 2, respectively. TheTRs for which TR � 0 ms are therefore 4.7 (m � 1) and9.5 ms (m � 2) for phantom 1, and 4.3 and 8.5 ms forphantom 2. To achieve a null TR with a large � and anonzero �asym simultaneously, TRs with m � 2 were cho-sen.

The common sequence parameters used in the experi-ments were: slice thickness � 10 mm, one slice, FOV �270 � 170 mm2, matrix size � 144 � 256, and � � 75°. Forexperimental verification of �asym three-point data werecollected from phantom 1 at TR � 9.5 ms (TR � 0 ms)and phantom 2 at TR � 7.5 ms (TR � –1.0 ms). The slicewas defined horizontally with water: oil of �3:1 in vol-ume. Other sequence parameters were: four averages, sam-pling interval, � � 114° and IDEAL asymmetric phaseangle, �asym, of 23°. Due to the constraints on the selectionof TR (or TR) the optimal � and �asym of 120° and 90°,respectively (13,16), were not attainable. TE � 3.55/5.05/6.55 ms and 2.67/4.02/5.37 ms for phantoms 1 and 2,respectively. After water-fat separation the relative phasemaps of �F with respect to �W (�o maps) were obtained forboth phantoms, which were then added by 2�f(TR/2) toobtain �asym maps according to Eq. [3b]. The field depen-dence of �o and �asym was obtained both theoreticallyand experimentally for phantom 2.

To examine the effect of �asym on the noise performanceof multipoint water-fat separation, 50 sets of three-pointdata (one average) were collected from each of phantom 1at TR � 9.5 ms and phantom 2 at TR � 8.5 ms (TR � 0 msfor both phantoms). The slice was defined obliquely for acontinuum of FWR across the slice (13). To sensitize theeffect, the three-point data were symmetrically sampled(TEs � 3.5/4.75/6.00 ms and 3.12/4.25/5.38 ms for phan-

toms 1 and 2, respectively; � � 95° for both). Then theNSA of water was obtained as previously described (13),and the results were compared. The results were alsocompared to the theoretical NSA (22) calculated for phan-tom 1, which is identical to that for FSE in this TR range.

To demonstrate the variability in FWR estimation due tothe pass-band mismatch, data were acquired from phan-tom 2 at TRs of 7.5 (TR � –1.0 ms; TE � 2.67/4.02/5.37 ms) and 8.5 ms (TR � 0 ms; TE � 3.17/4.52/5.87 ms). The slice included water and oil horizontally(� 3:1 in volume). Other sequence parameters were: fouraverages, � � 114°, and �asym � 23°.

RESULTS

Figure 3 shows the results of the three-point IDEAL sepa-ration of (b) water and (c) oil from (a) the source imageacquired from phantom 1 at TR � 9.5 ms. The �asym mapis shown in Fig. 3d, which is equivalent to the �o map forthe null TR. As TR � 0 ms, and T 2

W and T 2F are over

100 ms and comparable to each other, �asym is relativelyfield-independent.

Figure 4 shows the results from phantom 2 at TR � 7.5(TR � –1.0 ms). The calculated fieldmap is shown in Fig.4a. In contrast to Fig. 3d from phantom 1, the field depen-dence of �asym is clearly demonstrated in Fig. 4b resultingfrom field-dependent �o. The experimentally obtained�o and �asym plotted against offset frequency in Fig. 4dare in good agreement with the theoretical results shownin Fig. 4c. In this example, the pixels with � � 0 have�asym � 0.

The NSAs of water as a function of log10(FWR) obtainedfrom phantom 1 at TR � 9.5 ms and phantom 2 at TR �8.5 ms (TR � 0 ms for both phantoms) are shown in Fig.5a and b, respectively. The theoretical curve is also shown(solid line). There is a trend that the overall NSA distribu-tion in Fig. 5b is much more dispersive towards higherNSA with respect to that in Fig. 5a, which results mostlikely from field-dependent �asym distribution in thephantom. On the other hand, the lower bound of the NSAdistribution across FWRs is relatively invariant. This is

FIG. 4. a: Field map from phantom 2 at TR � 7.5 ms (TR �–1.0 ms) using IDEAL. b: �asym map, where the field dependence isclearly shown. c: Theoretically calculated �o

W, �oF, �o, and �asym as

a function of �. d: Experimentally obtained �o and �asym from thepixels with � � 1/2�TR, which are in close agreement with thosein c.

FIG. 5. Experimentally obtained NSA of water as a function oflog10(FWR) from (a) phantom 1 at TR � 9.5 ms and (b) phantom 2 atTR � 8.5 ms. For both, data were symmetrically sampled (� � 95°)and the slice was positioned obliquely to obtain a continuum ofFWRs across the slice. The theoretical FWR-dependent NSA curve(solid line) is also shown. In comparison to a, the lower bound of theNSA distribution across FWRs in b is relatively invariant, whereasthe overall NSA distribution is much more dispersive toward higherNSA.

416 Kim et al.

due to the fact that for a symmetric sampling both positiveand negative �asym (or �asym) increases the NSA (13,16).

The effect of a water-fat passband mismatch on the es-timation of FWR is demonstrated in Fig. 6. Even in thissmall range of ��� � 1/2�TR, the field-dependent variabil-ity of FWR is noticeable. When TR � 0 ms, the variationin FWR is symmetric about � � 0 Hz as shown in Fig. 6c.For TR � 0, FWR is underestimated for the pixels with� � 0 Hz.

DISCUSSION

In bSSFP transverse magnetization in the steady state iscoherently superposed with longitudinal magnetization(9,11,12). As a result, the recycled transverse magnetiza-tion possesses an initial phase at the beginning of each TRperiod that is imposed on the spins from the previous TRperiods (10,12). When T2 �� TR and ��� ��1/2�TR, both �o

W

and �oF are well-prepared such that both water and fat spins

are refocused concurrently at t � TR/2, and their magne-tization vectors form either perfectly parallel or antiparal-lel configurations depending on the choice of TR. Whensuch conditions are not fully satisfied, however, residualdephasing of spins (�refoc) and unwanted shifts in vectorconfiguration (�asym) occur. If the original IDEAL algo-rithm is used, in which water-and fat spin densities arecomplex (6), both �refoc and �asym are taken into consid-eration and therefore do not create a bias in FWR estima-tion (4,21). For other multipoint methods, these terms mayneed to be considered in signal modeling for more robustwater-fat separation in bSSFP imaging, which would re-quire a priori knowledge about T 2

W and T 2F for each pixel

in addition to �. Irrespectively of the image reconstructionalgorithm, however, the presence of �asym will introducespatially dependent, variable NSA in the calculated waterand fat images. In this context, if �asym is not negligible,

NSA can be a function of not only the sampling intervaland FWR, but also the T2, � and TR. Another source of thespatially dependent performance of multipoint water-fatseparation methods in bSSFP imaging arises from the pass-band mismatch between the two spin species. As it di-rectly influences the precision of FWR estimation withadditional dependence on T1 and �, the effect of the pass-band mismatch will be far greater than that of the TR/2approximation. Given that iron overload occurs in a vari-ety of chronic liver diseases, such as non-alcoholic steato-hepatitis (NASH) (23) and hepatitis C (24), the variabilityin �, T1, and T2 across the FOV in the liver can be sub-stantial. Therefore, the analysis given herein will be ofparticular relevance in liver imaging. For instance, in ratliver specimens at 2.35T, changes in iron concentrationfrom its baseline to 2.5 mg/gm-liver altered T1 and T2 from400 to 220 ms and from 40 to 9 ms, respectively (15).

To minimize the effect of both unwanted samplingasymmetry and pass-band mismatch in general, the TRshould be adjusted closer to a multiple of –1/f. However,reducing TR requires the use of a smaller t and �asym,thereby reducing the NSA and increasing sensitivity to theFWR dependence of NSA, respectively. Therefore, TR, tand �asym all need to be carefully considered when opti-mizing the sequence parameters. The use of partial Fourierfollowed by zero-filling (7) or homodyne reconstructionwith IDEAL (25) will be good alternatives.

For non-bSSFP sequences the optimum � and �asym canbe fully incorporated to achieve FWR-independent NSA.In this context, the advantage of higher SNR with bSSFPcan be compensated for by the spatially dependent perfor-mance of the sequence.

In summary, the SE-like signal behavior of bSSFP yieldsexcellent SNR and renders the sequence attractive as asequence of choice for multipoint water-fat separation,particularly when imaging time is highly limited. How-ever, the large frequency offset and the variable relaxationtimes of water and fat in vivo further complicate the spinevolution underlying the echo formation in bSSFP. Com-bined with the large TR typically required for multipointwater-fat separation, the complicated spin evolution canbe manifested in the magnitude and phase response of thespins as pass-band mismatches and unwanted samplingasymmetry, respectively. The former renders the precisionof FWR estimation spatially dependent. The latter givesrise to spatially dependent noise performance of multi-point water-fat separation methods in addition to its de-pendence on FWR in the pixels. To profit from the higherSNR of bSSFP, these sources of variability should be con-sidered in the sequence optimization procedures.

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