Fast Metabolic Imaging of Systems With Sparse Spectra:Application for Hyperpolarized 13C Imaging

Dirk Mayer,1* Yakir S. Levin,1 Ralph E. Hurd,2 Gary H. Glover,1 andDaniel M. Spielman1

A fast spiral chemical shift imaging (spCSI) sequence was de-veloped for application to hyperpolarized 13C imaging. The se-quence exploits sparse spectra, which can occur in such appli-cations, and prior knowledge of resonance frequencies to re-duce the measurement time by undersampling the data in thespectral domain. As a consequence, multiple reconstructionsof a given data set have to be computed in which only compo-nents with frequencies within a certain bandwidth are recon-structed “in focus” while others are severely blurred (“spectraltomosynthesis”). The sequence was tested at 3 T on a phantomcontaining approximately 1.5-M solutions of alanine (Ala), lac-tate (Lac), and pyruvate-pyruvate hydrate C1-C2 ester (with tworesonances, PPE1 and PPE2) at thermal equilibrium polariza-tion, all enriched to 99% 13C in the C1 carbonyl positions.Results from spCSI with a single spatial interleaf (single-shotspCSI) and three interleaves (three-shot spCSI) were comparedwith those obtained by phase-encoded free induction decayCSI (FIDCSI). The metabolic maps of all four resonances forthree-shot spCSI, and of PPE1 and PPE2 for single-shot spCSIdemonstrate resolution and localization properties similar tothose of the FIDCSI images. The metabolic maps of Ala and Lacfor single-shot spCSI contain minor artifacts due to signal over-lap of aliased resonances. Magn Reson Med 56:932–937, 2006.© 2006 Wiley-Liss, Inc.

Key words: 13C; spiral CSI; spectral undersampling; pyruvate;lactate

The development of hyperpolarized MRI agents presentsboth unprecedented opportunities and new technical chal-lenges. In particular, with signal-to-noise ratio (SNR) en-hancements on the order of the 10000-fold, dynamic nu-clear polarization (1) of metabolically active substrates(e.g., 13C-labeled pyruvate or acetate) theoretically permitsin vivo imaging of not only the injected agent, but alsodownstream metabolic products. This feature of hyperpo-larized MR spectroscopy (MRS) provides investigators aunique opportunity to noninvasively monitor critical dy-namic metabolic processes in vivo under both normal andpathologic conditions. Important applications include tu-mor diagnosis and treatment monitoring, as well as assess-ment of cardiac function. In studies using hyperpolarizedsamples, the magnetization decays toward its thermal

equilibrium value and is not recoverable. Therefore, fastacquisition schemes are important. Furthermore, becauseof the very low natural abundance of 13C and its lowdegree of polarization at thermal equilibrium, virtually nobackground signal is present. Depending on the substrate,this can produce relatively sparse spectra, as is the case fora bolus injection of hyperpolarized [1-113C]pyruvate,where the metabolic products detectable by 13C-MRS con-sist of lactate, alanine, and bicarbonate (2). While a num-ber of fast chemical shift imaging (CSI) methods have beenproposed for more general in vivo MRS applications (3–5),the need for speed and a limited spectral content makespiral CSI (spCSI) (6) an ideal candidate for this applica-tion. Since gradients are applied in two directions duringdata acquisition, both spectral and spatial data are simul-taneously encoded, and speed is traded off for spectralwidth (SW). For a given field of view (FOV) and resolution,the SW is limited by the maximum slew rate and strengthof the gradient system, which is a significant constraint forfast CSI of 13C due to its low magnetic moment. The SWcan be increased with the use of interleaved acquisitionschemes in either spectral or spatial dimensions, but thisalso increases the minimum total measurement time. Onecan exploit the sparse spectral information and priorknowledge of the resonance frequencies and linewidthsdetectable in the sample by undersampling the data in thespectral domain while avoiding signal overlap.

MATERIALS AND METHODS

In the implemented 13C spCSI sequence, the data acquisi-tion is carried out while a series of oscillating gradientwaveforms are applied in both the x- and y-directions,sampling the data simultaneously in three k-space dimen-sions (kx, ky, kf). Each spiral gradient waveform, designedwith the use of an analytic algorithm (7), is followed by arewinding gradient lobe to return the k-space trajectory tothe (kx, ky)-origin. While the data are sampled equidis-tantly in kf, a gridding algorithm (8) is applied to interpo-late the data onto a Cartesian grid in (kx, ky). As thechemical shift (CS) evolves during the readout while thedata are sampled in (kx, ky), spectral and spatial informa-tion becomes mixed, which leads to spatial blurring foroff-resonance components (CS artifact) if it is not correctedfor in the reconstruction algorithm. The blurring artifactincreases with the degree of off-resonance. This is illus-trated in Fig. 1a–c by the profile along the y-direction ofthe spatial point-spread function (PSF) for the single-shotspCSI experiment, which was calculated for a spectralcomponent on-resonance and with frequency offsets oftwo and five times the SW, respectively. The correspond-ing reconstructed images of a simulated circular object

1Richard M. Lucas Center for Magnetic Resonance Spectroscopy and Imag-ing, Department of Radiology, Stanford University, Stanford, California, USA.2GE Healthcare ASL-West, Menlo Park, California, USA.Grant sponsor: Lucas Foundation; Grant sponsor: NIH; Grant numbers:RR09784; CA48269; AA12388.*Correspondence to: Dirk Mayer, Lucas MRS Imaging Center, Department ofRadiology, Stanford University, 1201 Welch Road, Stanford, CA 94305-5488.E-mail: dirk.mayer@stanford.eduReceived 2 November 2005; revised 5 June 2006; accepted 24 June 2006.DOI 10.1002/mrm.21025Published online 29 August 2006 in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 56:932–937 (2006)

© 2006 Wiley-Liss, Inc. 932

(10 mm in diameter) centered in the FOV are shown in Fig.1d–f. One can easily remove this artifact simultaneouslyfor spectral components with –SW/2 � f � SW/2 by ap-plying a frequency-dependent linear phase correctionalong the readout. In order to properly reconstruct spectralcomponents that have been aliased nal times, a frequencyoffset of nal*SW has to be added to the frequency-depen-dent linear phase correction. This can be interpreted aseffectively changing the center frequency in the recon-struction. Since the blurring of aliased frequency compo-nents is similar to the blurring of out-of-plane features inclassic tomosynthesis, this feature of spCSI with spectralundersampling can be viewed as “spectral tomosynthe-sis.”

Experimental

All measurements were performed on a 3 T Signa MRscanner (GE Healthcare Waukesha, WI) with software ver-sion E2M3 equipped with self-shielded gradients (40mT/m, 150 mT/m/ms). A doubly tuned (1H/13C) birdcagecoil (35-mm diameter) was used for both radiofrequency(RF) excitation and signal reception. Because no polarizerwas available, the sequence was tested with a phantomconsisting of three 2-ml vials (10-mm inner diameter) con-taining approximately 1.5-M solutions of alanine (Ala,tube 1), lactate (Lac, tube 2), and pyruvate-pyruvate hy-drate C1-C2 ester (PPE, tube 3) at thermal equilibriumpolarization, all enriched to 99% 13C in the C1 carbonylpositions. Pyruvate ester was used in place of pyruvate inan attempt to improve phantom stability. The ester has tworesonances with frequency offsets relative to Lac of ap-proximately –243 Hz (PPE1) and –592 Hz (PPE2), respec-tively. The small vials were placed in a 50-ml Falcon tubethat was filled with water to reduce susceptibility artifacts.A gradient recalled echo (GRE) proton imaging sequence(echo time (TE)/pulse repetition time (TR) � 7/300 ms, flipangle � 20°, FOV � 80 � 80 mm2, matrix � 256 � 128)was used to position the phantom.

Three 13C CSI experiments were performed: two spCSIacquisitions with different numbers of spatial interleaves,and a conventional excitation-acquire phase-encoded free

induction decay CSI (FIDCSI) experiment for comparison.The FOV was 80 � 80 mm2 with a nominal 5 � 5-mm2

in-plane resolution. A 1.8-ms minimum phase RF pulse(2289-Hz bandwidth) was used to excite a 5.4-mm slicealong the z-direction.

In the FIDCSI experiment, the data acquisition started2.9 ms after the end of the excitation pulse. A total of 2048complex data points were acquired at an SW of 2000 Hz foreach of the 16 � 16 phase-encoding steps. Because of thelong longitudinal relaxation constants of the solutions(�10 s), a flip angle of 23° was used for excitation. With aTR of 2 s and eight excitations performed without dataacquisition to establish a steady state, the total experimenttime was 8 min 48 s. All data processing was done withsoftware written in-house using Matlab (MathWorks Inc.,Natick, MA, USA). The data were apodized in the spectraldimension with a 5-Hz Gaussian line-broadening. Apo-dization in both spatial frequency dimensions consisted ofmultiplication with a generalized Hamming window(�apo � 0.66) and zero-padding up to 32 � 32 pixels. Wereconstructed the data by performing a 3D fast Fouriertransform (FFT), and calculated the metabolic maps forAla, Lac, PPE1, and PPE2 by integrating the signal withina 28-Hz interval around each peak in absorption mode andnormalizing it to the maximum intensity in the PPE2 map.For the peak integration, we phase-corrected each reso-nance separately by multiplying the spectrum with a con-stant phase so that the main peak would appear in absorp-tion mode. The baseline was estimated by means of astraight line through the spectral points at the beginningand end of the integration interval.

The first spCSI experiment used a single spatial inter-leaf, which allowed an SW of 109.7 Hz. In this study 60accumulations were carried out to increase the SNR; how-ever, one excitation is sufficient to collect all necessaryk-space data. The expectation is that in studies using hy-perpolarized samples, the SNR will be sufficiently high toobviate the need for signal averaging. In the following, thisexperiment is therefore referred to as “single-shot spCSI.”The excitation flip angle, number of excitations withoutdata acquisition, and TR were the same as in the FIDCSI

FIG. 1. Spatial PSF of the single-shot spCSIexperiment (SW � 109.7 Hz) along the y-direction calculated for a spectral compo-nent on-resonance (a) and a resonance witha frequency offset of 2*SW (b) and 5*SW (c).d–f: Corresponding reconstructed imagesof a simulated circular object (10-mm diam-eter) centered in the FOV.

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experiment. Data acquisition started 6.1 ms after the end ofthe excitation pulse. Hardware restrictions limit the num-ber of data points that can be sampled continuously at areadout bandwidth of 250 kHz to 16384. This correspondsto a maximum readout length of only 66 ms. To allow forlonger total readouts, data acquisition was restricted to thespiral lobes and no data were acquired over the duration ofthe rewinding gradient lobes. Trapezoidal crusher gradientlobes applied after data acquisition dephased any remain-ing transverse magnetization. Thirty-two spiral gradientlobes were played out after each excitation, and the totalexperiment time was 2 min 16 s. For the calculation ofspectra and metabolic images presented in the Resultssection, only the data acquired during the first 21 spirallobes were used. This corresponds to a minimum totaltime for excitation and readout of just less than 200 ms,which is desirable for any application requiring high tem-poral resolution. The data were apodized in the spectraldimension with a 5-Hz Gaussian line-broadening and zero-padded up to 128 points. After we performed an FFT alongkf, we applied a frequency-dependent linear phase correc-tion along the readout to remove the CS artifact. This wascarried out with three different frequency offsets (0 Hz,2*SW, and 5*SW) to account for aliased frequency com-ponents, resulting in three reconstructed data sets for theexperiment. After the data were interpolated onto a Carte-sian grid in (kx, ky), they were apodized in the same spatialfrequency dimensions used for the FIDCSI data, and a 2DFFT was performed. Metabolic maps were calculated inthe same manner as for the FIDCSI data.

The second spCSI experiment was carried out with threespatial interleaves (three-shot spCSI) at an SW of 276.2 Hzand with 20 accumulations. Sixty-four spiral gradientlobes were played out after each excitation, but only thedata acquired during the first 52 lobes, corresponding to aminimum TR of 200 ms, were used in postprocessing. Thefrequency offsets used to remove the CS artifact were 0 Hz,1*SW, and 2*SW. Other acquisition and postprocessingparameters were the same as for single-shot spCSI.

RESULTS

Absorption-mode spectra acquired with FIDCSI from vox-els located in each of the three respective tubes are shownin Fig. 2a. The different linewidths of the peaks are duemainly to long-range scalar 13C-1H-coupling. While Lacand Ala split into quintets, the two ester resonances arequartets. The coupling constants were measured in theFIDCSI data set apodized with a 1-Hz line-broadening andwere approximately 4 Hz for Lac and Ala, 3 Hz for PPE1,and only 1.5 Hz for PPE2. The metabolic images, overlaidwith the contour of the phantom as calculated from thehigh-resolution proton localizer image, are shown in Fig.2b–e. Only the 40 � 40 mm2 part of the full FOV centeredon the phantom is displayed.

Spectra acquired with single-shot spCSI from the samethree voxels as in Fig. 2a are shown in Fig. 3a–c. For eachvoxel, the three spectra corresponding to the three differ-ent frequency offsets applied while the CS artifact wasremoved are plotted. With an SW of 109.7 Hz and theresonance frequency set to Lac, the signals from Ala andPPE1 were aliased twice, and hence were detected at 8 Hzand –23 Hz, respectively. The PPE2 resonance was aliasedfive times and detected at –43 Hz. The frequencies areindicated by the vertical lines in the spectra. While bothester resonances are well resolved, the Ala signal severelyoverlaps with Lac. However, since Ala is aliased twice, itsPSF is blurred when the appropriate linear phase correc-tion is applied for the reconstruction of Lac (solid linespectra), and vice versa (dashed line spectra). Therefore,most of the signal in the metabolic maps of these twometabolites (Fig. 4a and b) falls within the respective tube,but on top of a broad, low-intensity background signal.The metabolic images of PPE1 (Fig. 4c) and PPE2 (Fig. 4d)are similar to those acquired with FIDCSI.

The spectra acquired with three-shot spCSI from thesame three voxels as the FIDSCI spectra are shown in Fig.3d–f. With an SW of 276.2 Hz, the resonances of Ala, PPE1,and PPE2 alias to frequencies 64 Hz, –33 Hz, and –40 Hz,

FIG. 2. a: Absorption-mode spectra acquired with FIDCSI from voxels in tubes 1 (solid), 2 (dotted), and 3 (dashed). Metabolic maps of Ala(b), Lac (c), PPE1 (d), and PPE2 (e) reconstructed from the FIDCSI data set. The four maps have the same intensity scale. Only a 40 �40 mm2 part of the full FOV is displayed, and the contours of the phantom derived from the high-resolution proton image are outlined.

934 Mayer et al.

respectively, relative to Lac. Therefore, all four resonancesare well resolved. One example of the distorted PSF of analiased frequency component is the negative PPE2 signaldetected in the Lac tube (Fig. 3e, solid line spectrum).When the correct center frequency for this resonance isused during reconstruction (dotted line spectrum), noPPE2 is detected in that tube. The metabolic maps for allfour resonances (Fig. 4e–h) demonstrate resolution and

localization properties similar to those of the FIDCSI im-ages.

For a quantitative comparison of both spCSI acquisitionschemes with FIDCSI, the mean image intensity from aregion of interest (ROI) consisting of four voxels withineach of the three tubes was calculated for each of the fourresonances (Table 1). The ROIs are indicated in Fig. 2b–e.The data in columns printed in bold are the relative am-

FIG. 4. Metabolic maps of Ala (a), Lac (b), PPE1 (c), and PPE2 (d) reconstructed from the single-shot spCSI data set. The four maps havethe same intensity scale. Only a 40 � 40 mm2 part of the full FOV is displayed, and the contours of the phantom derived from thehigh-resolution proton image are outlined. e–g: The same as a–d, but for the three-shot spCSI data set.

FIG. 3. Spectra acquired with single-shot spCSI (SW � 109.7 Hz) from voxels in tubes 1 (a), 2 (b), and 3 (c). For each voxel the data werereconstructed using a frequency offset of 0 Hz (solid), 2*SW (dashed), and 5*SW (dotted). The vertical dotted lines mark the resonancefrequencies, taking into account the aliasing of signal components outside the SW. d–f: The same as a–c, but for three-shot spCSI (SW �276.2 Hz).

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plitudes of the four resonances as measured with the threeCSI sequences. Nonzero values in the other two columnsfor each resonance indicate noise and/or artifacts. Therelative difference in amplitude ratios as measured withsingle-shot spCSI compared to FIDCSI are 12% for Ala/PPE2, 6% for Lac/PPE2, and 9% for PPE1/PPE2. The re-spective values for three-shot spCSI are 11% for Ala/PPE2,14% for Lac/PPE2, and 8% for PPE1/PPE2. For compari-son, the SNR of the PPE2 resonance in the voxel at thecenter of the PPE tube was 72.5 for single-shot CSI and74.3 for three-shot CSI. The noise level was calculatedfrom voxels outside the phantom within a spectral regioncontaining no resonances. The overlap of the Ala and Lacresonances in the single-shot variant of spCSI combinedwith the distorted PSF for aliased frequency componentsleads to some artifacts for these two metabolites outsidetheir respective tubes. Because of better spectral separa-tion in the three-shot acquisition scheme, the signal con-tamination outside the tube containing the respective me-tabolite is comparable to the FIDCSI data. The differencesin amplitude ratios are due mainly to dispersion-modesignal contributions from aliased spectral components.

DISCUSSION AND CONCLUSIONS

A fast spCSI technique was developed for the special con-ditions present in hyperpolarized 13C metabolic imaging.The method takes advantage of the sparse spectral contentby undersampling the data in the spectral domain in orderto reduce the minimum measurement time. It is necessaryto have prior knowledge of the detectable resonance fre-quencies and the linewidths in the sample (as determinedby J-coupling, transverse relaxation, and B0 inhomogene-ities) in order to choose the SW to avoid signal overlap dueto aliased peaks. Note that only the frequency differencesbetween the spectral components determine the aliasingpattern. Hence, the method is not affected by frequencyshifts between voxels due to B0 inhomogeneities, sincethese offsets are the same for all resonances within a spe-cific voxel. The CS artifact, which results in a blurred PSFin spCSI, cannot be removed simultaneously for spectralcomponents that have been aliased a different number oftimes. Therefore, separate reconstructions for aliased fre-quency components have to be carried out. This leads tomultiple reconstructed data sets in which only compo-nents with resonance frequencies within a certain band-width are reconstructed “in focus” while components out-side of that band are severely blurred (“spectral tomosyn-thesis”). Consequently, these blurred componentscontribute signal beyond their true distribution, as shown

in the results for the three-shot spCSI data. While all fourresonances were resolved (the minimum frequency differ-ence was 31 Hz with a maximum full width at half maxi-mum (FWHM) of the peaks of 13 Hz), dispersion-modesignal contributions of aliased peaks from different voxelsaffect the calculation of peak intensities. At the same time,the blurred PSF makes it possible to distinguish the spatialdistributions of otherwise severely overlapping reso-nances, as demonstrated by the data acquired with a singlespatial interleaf. While the current reconstruction perfor-mance is limited for quantitative mapping of metabolitedistributions, it may be sufficient for applications that aimto localize “hot spots” of metabolites. In certain applica-tions, such as the bolus injection of hyperpolarized pyru-vate, where the initial concentration of the substrate can bemuch larger than the concentrations of the metabolic prod-ucts, signal contributions due to the distorted PSF canseverely hamper the quantitation. Furthermore, blurringand lower SNR could potentially make phasing more dif-ficult in vivo. It may be possible to reduce artifacts due tothe distorted PSF by using the prior knowledge of reso-nance frequencies, scalar coupling constants, and trans-verse relaxation times, and estimating the relative ampli-tudes with a minimum least-squares solution.

In the case of imaging hyperpolarized samples, the ini-tial longitudinal magnetization is not recoverable; rather,it decays toward the undetectable thermal equilibriumlevel. Hence, lower flip angles have to be used in multishotexperiments, and there is no penalty in SNR for single-shottechniques (9). While a 90° pulse can be applied in asingle-shot acquisition when imaging at a single timepoint, i.e., when all of the magnetization should be usedduring the acquisition, the excitation flip angles in ann-interleaf spCSI experiment have to be adjusted to yieldthe same amount of transverse magnetization for eachinterleaf. Neglecting relaxation and metabolic turnover,the flip angle for the ith excitation pulse is then given by�i � atan�1/�n � i� (9). If permitted by the SNR, lower flipangles (5–10°) (10) should be applied for imaging in adynamic time series in order to preserve the magnetiza-tion.

The development of very rapid hyperpolarized 13C met-abolic imaging, as discussed in this report, can potentiallyopen up a range of new applications, including measurementof metabolic fluxes, bolus dynamics, and cardiac function.For example, for the latter application, it is highly desirableto restrict the acquisition time to less than 200 ms. Thiswould allow the data to be acquired during diastole, andhence would significantly reduce motion artifacts.

Table 1Mean Image Intensity in the Metabolic Maps From an ROI in Each of the Three Tubes for the Three Different CSI Acquisitions*

Ala Lac PPE1 PPE2

Tube 1 Tube 2 Tube 3 Tube 1 Tube 2 Tube 3 Tube 1 Tube 2 Tube 3 Tube 1 Tube 2 Tube 3

FIDCSI 0.83 0.06 0.01 0.06 1.24 0.04 0.02 0.05 0.89 0.02 0.01 0.91Single-shot spCSI 0.93 0.15 0.28 0.14 1.17 0.20 0.04 0.06 0.81 0.00 0.04 0.91Three-shot spCSI 0.74 0.01 0.04 0.07 1.07 0.01 0.05 0.02 0.82 0.07 0.02 0.91

*The columns bold font indicate the tubes that contain the respective metabolite: Ala in tube 1, Lac in tube 2, and pyruvate-pyruvate hydrateester in tube 3.

936 Mayer et al.

For metabolites with scalar coupling patterns similarto those used in our experiments, the lower spectralresolution associated with the short readout does notsignificantly reduce the method’s ability to separate theindividual resonances even in the case of long T2*’s,since the linewidth is dominated by the multiplet struc-ture. For applications in which the transverse relaxationtime is much larger than T2*, the presented pulse se-quence could be modified to refocus the transverse mag-netization. It could then be either resampled or con-verted to longitudinal magnetization and excited againat a later time point.

REFERENCES

1. Ardenkjaer-Larsen JH, Fridlund B, Gram A, Hansson G, Hansson L,Lerche MH, Servin R, Thaning M, Golman K. Increase in signal-to-noiseratio of 10,000 times in liquid-state NMR. Proc Natl Acad Sci USA2003;100:10158–10163.

2. in’t Zandt R, Lerche M, Thaning M, Gram A, Servin R, Fridlund B,Ellner F, Wolber J, Ardenkjaer-Larsen JH, Golman K. Hyperpolarized

probes for molecular imaging. In: Proceedings of the 13th AnnualMeeting of ISMRM, Miami Beach, FL, USA, 2005.

3. Mansfield P. Spatial mapping of the chemical shift in NMR. MagnReson Med 1984;1:370–386.

4. Norris DG, Dreher W. Fast proton spectroscopic imaging using thesliced k-space method. Magn Reson Med 1993;30:641–645.

5. Dreher W, Geppert C, Althaus M, Leibfritz D. Fast proton spectroscopicimaging using steady-state free precession methods. Magn Reson Med2003;50:453–460.

6. Adalsteinsson E, Irarrazabal P, Topp S, Meyer C, Macovski A, SpielmanDM. Volumetric spectroscopic imaging with spiral-based k-space tra-jectories. Magn Reson Med 1998;39:889–898.

7. Glover GH. Simple analytic spiral k-space algorithm. Magn Reson Med1999;42:412–415.

8. Jackson JI, Meyer CH, Nishimura DG, Macovski A. Selection of aconvolution function for Fourier inversion using gridding [comput-erised tomography application]. IEEE Trans Med Imaging 1991;10:473– 478.

9. Zhao L, Mulkern R, Tseng CH, Williamson D, Patz S, Kraft R,Walsworth RL, Jolesz FA, Albert MS. Gradient-echo imaging consider-ations for hyperpolarized 129Xe MR. J Magn Reson B 1996;113:179–183.

10. Moller HE, Chen XJ, Saam B, Hagspiel KD, Johnson GA, Altes TA, deLange EE, Kauczor HU. MRI of the lungs using hyperpolarized noblegases. Magn Reson Med 2002;47:1029–1051.

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