auto-smash: a self-calibrating technique for smash imaging

Magnetic Resonance Materials in Physics, Biology and Medicine 7 (1998) 42–54

AUTO-SMASH: A self-calibrating technique for SMASH imaging

Peter M. Jakob a,*, Mark A. Griswold a, Robert R. Edelman a, Daniel K. Sodickson b

a Department of Radiology, Beth Israel Deaconess Medical Center, Har6ard Medical School, 330 Brookline A6e, Boston, MA 02215, USAb Department of Medicine, Cardio6ascular Di6ision, Beth Israel Deaconess Medical Center, Har6ard Medical School, Boston, USA

Received 19 December 1997; received in revised form 17 March 1998; accepted 18 May 1998

Abstract

Recently a new fast magnetic resonance imaging strategy, SMASH, has been described, which is based on partially parallelimaging with radiofrequency coil arrays. In this paper, an internal sensitivity calibration technique for the SMASH imagingmethod using self-calibration signals is described. Coil sensitivity information required for SMASH imaging is obtained during theactual scan using correlations between undersampled SMASH signal data and additionally sampled calibration signals withappropriate offsets in k-space. The advantages of this sensitivity reference method are that no extra coil array sensitivity mapshave to be acquired and that it provides coil sensitivity information in areas of highly non-uniform spin-density. Thisauto-calibrating approach can be easily implemented with only a small sacrifice of the overall time savings afforded by SMASHimaging. The results obtained from phantom imaging experiments and from cardiac studies in nine volunteers indicate that theself-calibrating approach is an effective method to increase the potential and the flexibility of rapid imaging with SMASH. © 1998Elsevier Science B.V. All rights reserved.

Keywords: SMASH; Simultaneous acquisition; RF coil array; MR image reconstruction

1. Introduction

One common feature of all standard fast imagingtechniques is that they all acquire data in a sequentialfashion. Only one portion of k-space is acquired at atime, which sets a methodological upper limit to theachievable scan time. Only a few proposals for parallelor partially parallel acquisitions (PPA) in MRI havebeen described in the past [1–6]. These techniques forMR scan time reduction are based on spatial encodingwith multiple spatially distinct receiver coils, whereeach array coil is characterized by a unique spatialresponse, so that each receiver adds spatial informationto the localization process. This information is used toreduce the number of phase encoding gradient steps.For their successful operation, all of the PPA tech-niques rely upon accurate knowledge or estimation of

the relative RF-sensitivities of the component coils inthe array used for imaging.

The SMASH technique [6], which stands for SiMul-taneous Acquisition of Spatial Harmonics, is a PPAtechnique which extracts additional spatial informationthrough the generation of sinusoidal spatial variationsin coil sensitivity. These spatial variations, or ‘spatialharmonics’, take the place of spatial modulations nor-mally produced by magnetic field gradients in conven-tional MR imaging which allows the simultaneousacquisition of multiple lines of MR data. It has beensuccessfully demonstrated that SMASH can be inte-grated with many of the fastest existing imaging se-quences, yielding multiplicative improvements inimaging speed [6]. A factor of two to three time savingshas been demonstrated in vivo using SMASH withcommercially available coil arrays and up to 8-foldimprovements have been achieved in phantoms usingspecialized RF hardware [7]. In principle, there is nolimit to the number of k-space lines that may be

* Corresponding author. Tel.: +1 617 6672047; fax: +1 6176677917; e-mail: [email protected]

1352-8661/98/$ - see front matter © 1998 Elsevier Science B.V. All rights reserved.PII S1352-8661(98)00015-5

P.M. Jakob et al. / Magnetic Resonance Materials in Physics, Biology and Medicine 7 (1998) 42–54 43

scanned simultaneously, assuming that coil arrays withsufficient numbers of independent component coils withappropriate sensitivities are available for a given field-of-view (FOV).

Although coil array based PPA imaging techniquescan provide a considerable improvement in imagingspeed, the greatest constraints of the PPA imagingtechniques are their dependence on the accurate mea-surement of component coil sensitivities, since PPAreconstructions rely upon an accurate estimate of theindividual coil sensitivity functions in the underlyingcoil array. Several strategies for coil sensitivity calibra-tion have been proposed [5,6,8,9].

First, the coil sensitivity profiles can be calculatedfrom the Biot–Savart law using knowledge of the coil’ssize, shape and position relative to the slice-of-interest(SOI). However, this approach is impractical in vivo,since the theoretical field map may correlate poorlywith the actual sensitivity profiles because of unpre-dictable coil loading effects and inaccurate coil posi-tioning.

Second, the sensitivity information can be obtainedfrom images of a uniform phantom taken at the sameposition as the in vivo images [6,8]. This approach of anin vitro reference can be problematic in many cases,since coil loading and/or coil position may changesignificantly from subject to subject, thereby changingthe effective coil sensitivities. In addition, acquiring andusing these reference data to correct subsequent in vivoimages can be impractical with flexible phased arrays,since the exact locations of the individual coils may beaffected by the subject anatomy.

Third, an estimate of the coil sensitivity functions canbe obtained by acquiring the required coil references invivo in the desired image plane, an approach which wasused for the first in vivo implementations of SMASH[6]. However, this approach requires that a referenceimage set be acquired using an appropriate imagingtechnique, which we term ‘coil sensitivity weighted’,before the post-processing of the SMASH images ispossible. This procedure can be imperfect, since it re-quires a region of uniform spin density for a perfectcalibration. In vivo this requirement is often impossibleto fulfil especially in regions of highly varying spindensity such as in the chest, which has very low signal-to-noise in the area of the lungs. In addition, B0 and B1

magnetic field inhomogeneities may distort the true coilsensitivity profiles depending on the imaging techniqueused. Furthermore this procedure can also be timeconsuming, since it has to be performed for each SOI.

Fourth, to overcome the problems mentioned abovean estimate of the sensitivity profiles can be derivedfrom a combination of body coil and array coil imagesof the subject [9]. In this approach, the surface coilimage is divided by the body coil image to derive thearray coil sensitivity profile. This approach accurately

estimates the coil sensitivity functions in areas wheresufficient signal-to-noise ratio is available, which maynot be possible in areas such as the lungs. This methodalso increases scan time significantly, even when lowresolution pairs of body/array coil images are acquired.In addition, this approach is difficult in moving tissuestructures, since the body coil and phased array coilimage have to be obtained ideally in exactly the sameposition. Therefore, the accuracy of this coil sensitivitycalibration can be impaired in the situation of involun-tary subject motion, breathing and cardiac motion. Raand Rim [5] describe a similar method using a referencearray image set without the body coil image, but other-wise suffers from the same difficulties.

In summary, PPA techniques, including SMASH,rely upon accurate estimation of the sensitivity func-tions of individual coils in a coil array. This can be acumbersome, inaccurate and time-consuming procedurewhich in the worst case can eliminate the time advan-tage of PPA techniques and therefore limits potentialapplications of faster imaging with PPA.

In order to address these limitations, we have devel-oped a new internal calibration technique for SMASHimaging, called AUTO-SMASH, in which coil sensitiv-ity information can be detected during the actual scanby an auto-calibration mechanism. Details of both ac-quisition and reconstruction strategies in this newAUTO-SMASH approach are provided below, alongwith illustrative results from phantom imaging experi-ments. The benefits of faster imaging with SMASHmay be applied to many areas of MR imaging, but thetechnique holds particular promise for cardiac MRI.Since the thorax has a highly inhomogeneous spindensity, which renders standard sensitivity referenceestimation techniques difficult, cardiac experiments areparticularly well suited for the AUTO-SMASH ap-proach. Therefore, in order to validate the proposedauto-calibration scheme and to demonstrate thebenefits of imaging with AUTO-SMASH, a number ofcardiac imaging experiments were performed.

2. Theory

2.1. Brief re6iew of the SMASH technique

In order to highlight the key features of the AUTO-SMASH approach, we first summarize the basicSMASH technique by reviewing some results fromSodickson and Manning [6].

The SMASH procedure operates by using linearcombinations of simultaneously acquired signals frommultiple surface coils with different spatial sensitivities.These combinations are used to reconstruct missingsignals in a data set with reduced phase encoding. Inother words, the linear combination of component coil

P.M. Jakob et al. / Magnetic Resonance Materials in Physics, Biology and Medicine 7 (1998) 42–5444

signals substitutes for spatial modulations normallyproduced by phase encoding gradients.

In a coil array with L components, each coil l has adistinct sensitivity function Cl (x, y). For a standardimaging situation, the component coil signals are com-bined so as to produce a composite sensitivity C0

comp

which extends across the region of interest:

C0comp(x, y)= %

L

l=1

nl(0)Cl(x, y) (1)

The coil weights nl(0) may be chosen, for example, to

produce uniform image intensity. For such combina-tions, the composite MR signal for a plane with spindensity r(x, y) takes the form,

S comp(kx, ky)= %L

l=1

nl(0)Sl(kx, ky)

=&&

dx dy %L

l=1

nl(0)Cl(x, y)r(x, y)

exp{− ikxx− ikyy}

=&&

dx dy C0comp(x, y)r(x, y)

exp{− ikxx− ikyy} (2)

where kx gGxtx and ky gGyty as usual, with Gx andGy the magnitude of the x and y gradients, and tx andty the times spent in the x and y gradients respectively.Inverse Fourier-transformation of Eq. (2) with respectto kx and ky reconstructs the usual spin density functionr(x, y) multiplied by the composite sensitivity profileC0

comp.In the SMASH approach, signals from the various

array components are combined with different linearweights, nl

(m), to produce sinusoidal spatial sensitivityprofiles (spatial harmonics of order m) on top of theoriginal profile C0

comp:

Cmcomp(x, y)= %

L

l=1

nl(m)Cl(x, y)

=C0comp{cos(mDkyy)+ i sin(mDkyy)}

=C0comp exp(imDkyy) (3)

Here m is an integer, and Dky=2p/FOV, the mini-mum k-space interval corresponding to the desiredFOV. The composite MR signal then becomes:

Smcomp(kx, ky)=

&&dx dy Cm

compr(x, y)

×exp{− ikxx− ikyy}

−&&

dx dy C0compr(x, y)

×exp{− ikxx− i(ky−mDky)y} (4)

Therefore this new combination can be used to shiftthe measured k-space data by an amount (−mDky).

If a total of M spatial harmonics can be generated byM different linear combinations of component coilsignals (including the original homogeneous combina-tion), then M lines of k-space may be reconstructed foreach application of a phase encoding gradient. Gradi-ent based spatial phase encoding can therefore be par-tially replaced by an analogous spatial encodingprocedure tied to the RF coil array, since the linearcombination of component coil signals produces spatialmodulations of precisely the same sinusoidal form asthe modulations normally produced by gradients. Sig-nal data sets may be acquired with a reduced number ofphase encoding gradient steps, and the sub-encodeddata from the various component coils may be com-bined with appropriate linear combinations to fill in theremainder of k-space required for an image with givenspatial resolution and FOV. Since phase encoding gra-dient steps constitute the temporal bottleneck in mosttraditional MR imaging, the omission of all but l/Mgradient steps corresponds to an M-fold increase inimaging speed.

The basic procedure for SMASH reconstruction maybe summarized as follows (Fig. 1(a, b)): Using knowl-edge of the position-dependent sensitivities of the indi-vidual coils in the RF coil array, weightedcombinations of signals from each of the coils areformed to approximate the required sinusoidal modula-tions in sensitivity across the FOV. The appropriatecomposite shifted k-space signals are then formed, andthe shifted data sets are interleaved, to yield the fullk-space matrix. The reconstructed SMASH image isthen obtained by Fourier-transformation of this matrix.

SMASH reconstructions rely upon the accurateknowledge of the RF coil sensitivity of each surface coilin the array in order to determine the optimal complexweights, nl

(m). In the original SMASH implementations[6], this determination was made by fitting of measuredcoil sensitivity data to the target spatial harmonic sensi-tivity profiles, using additional coil sensitivity weightedreference data sets.

2.2. AUTO-SMASH: principles

In what follows, it is shown that the set of optimalcomplex weights, nl

(m), necessary for SMASH postpro-cessing can also be determined using a small number ofadditionally recorded auto-calibration signals (ACS),which serve as a form of navigator measurement. TheACS represent lines at intermediate positions in k-space, which are phase encoded in a conventional man-ner using the phase encoding gradient and compared tothe signals from the

SMASH acquisition. When information from theseextra signals is incorporated into the reconstruction, the


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set of linear weights, nl(m), may be extracted automati-

cally for each acquisition without the intermediate stepof coil sensitivity measurements. This auto-calibratingapproach can be easily implemented with only a smallsacrifice of the overall time savings afforded bySMASH imaging.

In SMASH, linear combinations of component coilsignals are used to generate composite signals shifted byan amount (−mDky) in k-space. In AUTO-SMASH afew extra navigator ACS-lines are acquired during theactual scan which are exactly shifted by the sameamount(−mDky). Relations between the SMASH dataset and these extra ACS-data may then be used toextract the desired optimal complex weights, nl

(m), asfollows.

First consider the composite signal generated by uni-form combination of component coil signalsSl

ACS(kx, ky−mDky) at position (ky−mDky) in k-space:

S comp(kx, ky−mDky)= %L

l=1

nl(0)Sl

ACS(kx, ky−mDky)

=&&

dx dy %L

l=1

nl(0)Cl(x, y)r(x, y)

exp{− ikxx− i(ky−mDky)y}(5)

Alternatively, as outlined in the previous section, thesame composite signal may be formed by appropriatecombinations of signals Sl(kx, ky) at position ky ink-space, through generation of a spatial harmonic oforder m which has already been shown to produce ak-space shift of −mDky.

S comp(kx, ky−mDky)= %L

l=1

nl(m)Sl(kx, ky)

=&&

dx dy %L

l=1

nl(m)Cl(x, y)r(x, y)

exp− ikxx− ikyy} (6)

A simple comparison of Eq. (5) with Eq. (6) yields

%L

l=1

nl(m)Sl(kx, ky)= %

L

l=1

nl(m)Sl

ACS(kx, ky−mDky) (7)

Therefore, if extra k-space lines SlACS(kx, ky −mDky)

are acquired as auto-calibration signals during aSMASH acquisition, a composite reference lineS comp(kx, ky−mDky) may be formed from these signals.The SMASH lines Sl(kx, ky) may then be fitted directlyto the reference line S comp(kx, ky−mDky) without re-quiring the intermediate of spatial harmonic generation.The effect is the same as if coil sensitivities had beenfitted to spatial harmonic target profiles. Similarweights nl

(m) are produced, since the relation betweendifferent lines of k-space remains a relation of spatial

harmonics. After fitting, these same weights nl(m) may be

used to form the required signal combinations in aSMASH reconstruction. Fig. 1(c) is a pictorial sum-mary of stages in a practical AUTO-SMASH imagingprocedure, shown for comparison next to the corre-ponding procedure in the original SMASH technique.

In general for AUTO-SMASH, the pulse sequenceand gradient phase encoding tables have to bemodified, so that for every desired spatial harmonicfunction m, an additional signal Sl

ACS(kx, ky−mDky) isacquired along the ky−mDky line in k-space during theactual scan. Thus, for every spatial harmonic, an auto-calibration line of data is acquired, which adds only(M−1)T to the SMASH scan time, where T representsthe repetition time or inter-echo spacing of the appliedimaging technique.

In summary, the AUTO-SMASH self calibrationprocedure replaces an experimentally cumbersome andpotentially inaccurate coil sensitivity measurement witha targeted acquisition of a few extra lines of MR signaldata. The underlying spatial harmonic modulationsproduced by phase encoding gradients in these extradata lines are used to ‘train’ the linear combinationsrequired for SMASH reconstruction. Since it is therelations between MR signals rather than the absolutecoil sensitivities which are used for determination ofoptimal signal weightings, the effects of spin densityvariations are largely eliminated and AUTO-SMASHmay be used even in regions of markedly inhomoge-neous spin density. A flowchart of the AUTO-SMASHprocedure is shown in Fig. 2.

Fig. 2. A flow chart summarizing the major steps in the AUTO-SMASH procedure.


3. Methods

All raw data were generated on a Siemens Vision 1.5T whole body clinical MR scanner (Siemens, Erlangen,Germany). The system has a resonant EPI capabilitywith minimum gradient rise time of 300 ms or non-reso-nant rise time of 600 ms to a peak gradient amplitude of25 mT m−1 along all three axes. A prototype cardiaccoil array with four overlapped component coils, with atotal spatial extent of 260 mm in the phase encodingdirection and 230 mm in the read direction, was usedfor all cardiac scans. The array extends in the head-footdirection and was used in a receive only mode with thebody coil providing homogeneous excitation. Duringtransmit, the array was actively decoupled from thebody coil. The individual coil data were exported to aHewlett–Packard 735 UNIX workstation for postpro-cessing. Fitting of the coil weighting functions andimage reconstruction were performed in the Matlabprogramming environment (The Mathworks, Natick,MA).

3.1. Phantom images

In order to assess the performance of the AUTO-SMASH approach in a well-controlled experiment, aresolution phantom was imaged using the 4-elementarray. Images were acquired in an 8 mm thick coronalslice parallel to and approximately 60 mm above theplane of the array. A FLASH imaging sequence wasused, with TE=6 ms, TR=12 ms, and flip angle=15°. Phase encoding was performed in the direction ofthe array. FOV was 320×320 mm and matrix size was128×128 for the full-time reference images. Reduced-time data sets with two or three times the phase encodestep and hence one-half or one-third the FOV andmatrix size in the phase encode direction were used forSMASH and AUTO-SMASH reconstructions. Refer-ence component coil images were combined using aconventional sum of squares algorithm. SMASH recon-structions used coil sensitivity information taken fromintensity profiles across the center of the full FOVcomponent coil reference images to fit two or threespatial harmonics, as described above and in Sodicksonand Manning [6]. AUTO-SMASH reconstructions usedadditionally acquired auto-calibration signals with ap-propriate offsets corresponding to the first and secondspatial harmonics to determine component coil weightfactors. In order to test the robustness of the AUTO-SMASH fitting procedure, either high signal-to-noiseratio (SNR) echoes in the center of k-space or low SNRechoes from the edge of k-space were used in alterna-tive AUTO-SMASH reconstructions. It should benoted that the choice of reference weights nl

(0) forSMASH or AUTO-SMASH reconstructions is arbi-trary, however that choice will be reflected in the over-

all intensity profile of the reconstructed image. For thephantom images presented here, reference weightsyielding the most homogeneous intensity profile possi-ble (i.e. approximately a flat zeroth spatial harmonic)were used.

3.2. Cardiac images

Since SMASH effectively allows multiple acquisitionsto proceed simultaneously, it may be used to gatherhigh resolution information in a given acquisition time,or else to acquire images of a given spatial resolution ina shorter acquisition time. Thus, the SMASH tech-nique, when supplemented with AUTO-SMASH cali-bration, offers a possible remedy for the competingconstraints of spatial versus temporal resolution incardiac MRI. In this study two different acquisitionstrategies were implemented in order to demonstratethe benefits of AUTO-SMASH for cardiac imaging:I. Since a reduction in breath-hold times is particularly

important for patients with cardiac disease forwhom current long breath-hold times are impracti-cal, the AUTO-SMASH strategy was used to reducebreath-hold durations by a factor of 2 to 3 whilemaintaining constant spatial resolution.

II. Alternatively, the breath-hold time was held con-stant, and AUTO-SMASH was used to double thespatial resolution in the phase encoding direction (incombination with a doubled resolution in the read-out direction). This strategy results in an increasedspatial resolution for a given breath-hold time.

Nine healthy volunteers (two females, seven males;age range 21–64 years) were examined according to theguidelines of the internal review board of the BethIsrael Deaconess Medical Center. Informed consentwas obtained before each study. For all the studiespresented here, cardiac AUTO-SMASH images withtwo and three harmonics (M=2 and 3) were acquiredusing a segmented turbo FLASH sequence. The seg-mented turbo FLASH sequence was used for all ourcardiac SMASH studies, since it is a widely used clini-cal technique for cardiac imaging and is easy to com-bine with the SMASH approach.

The following imaging protocols for strategy I and IIwere used:

For strategy I sequences with nine or five k-spacelines per segment were used:� Segmented turbo FLASH with 9 lines per segment:

flow compensation in slice and read direction, incre-mented flip angle series (18, 20, 22, 25, 31, 33, 38,48, and 90°). A TR of 14.4 ms and a TE of 7.3 msresulted in an effective temporal resolution of 131ms. The image matrix was 144×256 (reference) or72×256 (AUTO-SMASH, reconstructed to 144×256).


� Segmented turbo FLASH with five lines per seg-ment: flow compensation in slice and read direction,constant flip angles between 30 and 40°. A TR of11.8 ms and TE of 6.1 ms resulted in an effectivetemporal resolution of 59 ms. Image matrix was240×256 (reference) or 80×256 (AUTO-SMASH,reconstructed to 240×256).

For strategy II segmented turbo FLASH sequenceswith 9 lines per segment and an image matrix of144×256 (reference) or 144×512 (AUTO-SMASH,reconstructed to 288×512) were used.

For coronary imaging a chemical shift selective fat-saturation pulse was applied before each segment tonull the signal from epicardial fat and thus enhance thecontrast of coronary blood flow. The data were ac-quired in 5–9 mm thick slices, either in a coronalorientation or in an oblique plane extending from thecoronal to the sagittal direction. Prospective ECG-gat-ing was used to place the acquisition of each segment inmid diastole. All images were obtained during a singleend-expiratory breathhold with the subjects in a proneposition above the coil array.

As in the phantom experiment, reference images werecombined using a sum of squares algorithm. Since invivo sensitivity references were not readily available dueto the marked variation in spin density across thethorax, AUTO-SMASH was used to obtain componentcoil weighting factors. In all cases, a reduced data setplus one or two extra ACS lines with appropriateoffsets corresponding to the first and the second spatialharmonics were acquired.

For the in vivo implementation, only high SNRechoes in the center of k-space were used as ACS. Forconvenience, uniform reference weights nl

(0)=1 wereused for the in vivo images, which still corresponded toroughly homogeneous overall intensity profiles.

4. Results

As a verification of the basic relation expressed inEq. (7), Fig. 3 shows a comparison of composite signalsformed from the ACS data with composite SMASHsignals after the fitting procedure depicted in Fig. 1(c).Fig. 3(a) shows the composite signal S comp(kx, ky−mDky)formed by uniform combination of the ACSsignals of the four coils in the array (left before andright after Fourier-transformation). This compositeACS was used as a target for spatial harmonic fitting ofthe signals Sl(kx, ky). The results of the fit are shown inFig. 3(b) (left before and right after Fourier-transfor-mation) and demonstrate a good correlation with thetarget function.

Fig. 4 shows results obtained from the phantomexperiment, using two (left hand column) and three

Fig. 3. Comparison of composite signals formed from the ACS datawith composite SMASH signals in an actual AUTO-SMASH imple-mentation. (a) Composite signal Scomp(kx, ky−mDky) formed byuniform combination of the ACS signals of the four coils in the array(left before and right after Fourier-transformation). This compositeACS-signal was used as a target for spatial harmonic fitting of thesignals Sl(kx, ky). (b) Composite SMASH signals after fitting (leftbefore and right after Fourier-transformation).

(right hand column) spatial harmonics. The top rowshows the full time reference images. The second rowshows the reconstructed half/third time SMASH im-ages. The SMASH images were reconstructed using coilsensitivity information obtained from a vertical inten-sity profile across the component coil reference imagesof the phantom. The third row shows the correspond-ing half/third time images after AUTO-SMASH recon-struction using high SNR echoes in the center ofk-space as ACS. The fourth row shows the half/thirdtime images after AUTO-SMASH reconstruction usinglow SNR k-space echoes from the edge of k-space asACS. Finally, the bottom row shows AUTO-SMASHimages which were reconstructed using deliberately mis-tuned coil-weighting factors (the weighting factors forsecond and third spatial harmonics were arbitrarilychosen to be replicas of the zeroth harmonic referenceweights). These inappropriate weights were used inorder to demonstrate the nature of image artifactswhich arise when no effort is made to obtain correctcoil weighting information from the ACS. Table 1contains the fitted coil weighting factors obtained in thecase of two spatial harmonics for each of the SMASHor AUTO-SMASH reconstruction strategies shown inFig. 4.

The images in Figs. 5–7 demonstrate in vivo resultsobtained with the AUTO-SMASH technique with twoto three spatial harmonics and a nearly twofold orthreefold increase in acquisition speed.

The images in Fig. 5 are results obtained from acoronary imaging study with strategy I and II usingtwo spatial harmonics. This data set was acquired in an8 mm thick coronal slice parallel to and approximately


Fig. 4. Imaging results from a phantom study using various SMASH and AUTO-SMASH reconstructions. Left hand column: acceleration factorM=2, right hand colum: acceleration factor M=3. Top row: Full time reference images. Second row: Reconstructed half/third time SMASHimages. Third row: Corresponding half/third time images after AUTO-SMASH reconstruction using high SNR echoes in the center of k-space asACS. Fourth row: Half/third time images after AUTO-SMASH reconstruction using low SNR echoes from the edge of k-space as ACS. Bottomrow: Images reconstructed using inappropriate coil-weighting factors (second and third harmonic weights chosen to be simple replicas of thezeroth harmonic weights).

50 mm above the plane of the cardiac array. Fig. 5(a)shows as a reference the full time (16 cardiac cycles)image with a 144×256 matrix size. Fig. 5(b) showsthe corresponding half time (eight cardiac cycles) im-

age obtained with strategy I with a 144×256 matrixsize after AUTO-SMASH reconstruction. The imagequality is preserved in the accelerated AUTO-SMASHimage. Fig. 5(c) shows the corresponding double


Table 1Coil weighting factors used for SMASH/AUTO-SMASH reconstructions with two spatial harmonics displayed in Fig. 4, left column

coil 2 Coil 3 Coil 4Coil 1

−0.036−1.765i −0.256+0.408iSMASH −0.256+1.400i0.270−1.198i−0.513+0.451i −0.227+1.221i−0.060−1.317i0.124−1.330iAUTO-SMASH (center of k-space)

−0.471−0.771i 1.292+0.326i 1.221−0.079i 0.154+0.940iAUTO-SMASH (edge of k-space)0.489+0.048i −0.573−1.328iInappropiate weights −0.129−1.472i0.328−0.776i

resolution image obtained with strategy II in the sametotal acquisition time as the reference image. Matrixsize in this image was 288×512 after AUTO-SMASHreconstruction. Details from Fig. 5(a and c) are shownin Fig. 5(d and e), respectively. A long segment of theright coronary artery may be seen running verticallynear the mid-line in both these images (black arrows),but is significantly sharper in the high-resolutionAUTO-SMASH image. Branches of the left coronarysystem (thick white arrow) may also be discerned in theAUTO-SMASH image, whereas they are not seen inthe reference image. Finally, internal mammary arter-ies, invisible in the reference image, may be discernedrunning down the center of the AUTO-SMASH image(thin white arrow). The visibility of the internal mam-mary arteries along with the anterior heart surface inthis slice results from the 8 mm slice thickness, theprone positioning of the subject (which brings the heartforward), and the anterior position of the coronal slice.

Fig. 6 presents two additional cardiac data sets. Theoblique slices extending from the coronal to the sagittaldirection were obtained in a healthy subject with strat-egy I and II using two spatial harmonics. Fig. 6(a andd) show as a reference the full time (16 cardiac cycles)images (144×256 matrix size). Fig. 6(b and e) show thecorresponding half time (eight cardiac cycles) strategy IAUTO-SMASH images (144×256 matrix size). Againthe image quality is preserved in the acceleratedAUTO-SMASH images. Fig. 6(c and f) show the corre-sponding double resolution strategy II AUTO-SMASHimages (288×512 matrix size) obtained in the sametime as the reference images. In the oblique imagesshown in Fig. 6(d–f), the left main coronary artery maybe seen near its origin. This image data set demon-strates that the AUTO-SMASH reconstruction is ro-bust enough to accommodate a certain degree of imageplane angulation. Note that the AUTO-SMASH recon-structions are almost entirely free of foldover artifacts.These cardiac examples confirm that AUTO-SMASHallows for an accurate calibration in regions of highlynon-uniform spin density, where no reliable in vivosensitivity reference map could be obtained.

Finally, Fig. 7 shows results obtained from a cardiacstudy with strategy I, in this case using three spatialharmonics. Fig. 7(b) shows the third time aliased image(80×256 matrix size), which was formed by combining

the component coil images pixel-by-pixel as the squareroot of the sum of square magnitudes. Fig. 7(c) rightshows the corresponding third time image after AUTO-SMASH reconstruction (240×256 matrix size). Thiscorresponds to a threefold reduction in breathhold-time. For image comparison a reference image shown inFig. 7(a) was obtained in 48 cardiac cycles correspond-ing to a breath-hold time of 40 s. Even though there aresome residual foldover and ghosting artifacts visible inthe AUTO-SMASH reconstruction, the heart and theleft coronary artery are still well depicted in the acceler-ated AUTO-SMASH image.

5. Discussion

One notable constraint of the original SMASH imag-ing technique is its dependence on the measurement ofcomponent coil sensitivities for spatial harmonic gener-ation. AUTO-SMASH is a flexible tool for internalsensitivity reference estimation. It has the major advan-tage that optimal component coil weights can be deter-mined for each individual scan independently andwithout a significant increase in imaging time.

However, AUTO-SMASH, like SMASH, presumesthat the coil encoding procedure provided by the under-lying coil array matches the conditions of Fourier-en-coding or in other words that the necessary spatialharmonics may be faithfully represented by linear su-perpositions of component coil sensitivities. In cases forwhich the combined sensitivities deviate from idealspatial harmonics, reconstruction artifacts are visible inboth SMASH and AUTO-SMASH image reconstruc-tions. The phantom images of Fig. 4 illustrate theappearance of N/2 and N/3 ghosts for the M=2 and 3reconstructions with various degrees of imperfection inthe component coil weights. Similar artifacts may beseen in the in vivo M=3 AUTO-SMASH reconstruc-tion in Fig. 7, and these artifacts are responsible formuch of the apparent degradation in image quality.Thus, just as in the original SMASH procedure, anyerrors in spatial harmonic generation will lead to imageartifacts which cannot be removed by the AUTO-SMASH approach. In general, AUTO-SMASH sharesthe same operating limits as SMASH. The geometry ofthe underlying coil array will place certain limitations


Fig. 5. Coronary imaging with AUTO-SMASH (a) Reference image (144×256 matrix size) obtained in 16 cardiac cycles. (b) The correspondingimage obtained with strategy I in eight cardiac cycles with 144×256 matrix size after AUTOSMASH reconstruction. (c) Double resolution imageobtained with strategy II in 16 cardiac cycles with a 288×512 matrix size after AUTO-SMASH reconstruction. (d, e) Details from (a) and (b)and (c), respectively. A long segment of the right coronary artery may be seen running vertically near the mid-line in these images (black arrows).Branches of the left coronary system (thick white arrow) may also be discerned in the AUTO-SMASH image, whereas they are not seen in thereference image. Finally, internal mammary arteries, invisible in the reference image, may just be discerned running down the center of theAUTO-SMASH image (thin white arrow).

on the FOV, the position across the subject, and theangulation of planes suitable for the SMASH/AUTO-SMASH reconstruction. PPA techniques, includingSMASH and AUTO-SMASH, rely upon accuratematching of the sensitivity functions of individual coilsin a coil array with a given FOV. Therefore, future workmust involve the design of tailored RF coil arrays forAUTO-SMASH, which will allow accurate and flexiblespatial harmonic generation over appropriate fields-of-view.

As demonstrated in the phantom study, componentcoil weights produced by SMASH and AUTO-SMASHare similar but not exactly the same. Just as in thecoil-sensitivity fitting procedure used in SMASH, theaccuracy of the self-calibration approach is affected bynoise, which is demonstrated in Fig. 4, where the resultsof reconstructions using ACS from the center and theedge of k-space were compared. ACS from the edge ofk-space with higher noise levels produce significantlydifferent coil-weighting factors, though viable recon-structions with only a partial increase in aliasing artifactswere still produced (The quality of AUTO-SMASHreconstructions using these uniformly low SNR calibra-tion signals is also indicative of what may be expected

for situations in which one or more component coilshave comparatively low signal). By contrast, the deliber-ately mis-tuned weights produced markedly aliased im-ages in Fig. 4. These results give a sense of the degreeof robustness of the AUTO-SMASH fitting procedure.

In our current in vivo implementations, only highsignal-to-noise k-space lines were used as ACS. Ingeneral, it would also be possible to use several ACSlines for each harmonic in order to improve the determi-nation of the optimal coil weights and the accuracy ofthe image reconstruction. Alternatively, one extra ACScould be acquired after switching the read and the phaseencoding directions. The result of such an acquisitionwould be an ACS data line spanning many spatialharmonics. The relations between many different har-monics ky and ky−mDky could then be derived from thissingle ACS line. In general a variety of different acqui-sition strategies is possible. Future studies will addressthe optimum postprocessing procedure in the presence ofnoise.

The timing of AUTO-SMASH acquisitions may alsovary. The extra ACS may be acquired before, during, orimmediately after the actual scan, or else in an indepen-dent scan.


Fig. 6. Cardiac imaging with AUTO-SMASH. Oblique slices obtained in a healthy volunteer with strategy I and II and two spatial harmonics.(a, d) Full time reference images obtained in 16 cardiac cycles with 144×256 matrix size. (b, e) The corresponding half time images obtained withstrategy I in eight cardiac cycles with 144×256 matrix size after AUTO-SMASH reconstruction. (c) The corresponding double resolution i;nagesobtained with strategy II in 16 cardiac cycles with 288×512 matrix size after AUTO-SMASH reconstruction

Although we have so far described AUTO-SMASHin terms of extracting necessary coil sensitivity informa-tion, it may also be viewed in another way. Rather thansimply producing ideal spatial harmonics, using combi-nations of component coil sensitivities, AUTO-SMASHreproduces as accurately as possible the actual effects ofthe experimentally applied phase encoding gradients.Each fit to an ACS target line constitutes an approxi-mation of the actual gradient profiles, including anynonlinearities or other imperfections which may bepresent in these profiles. Thus, each fit acts as aneffective gradient set similar in structure to the physi-cally applied gradients. Reconstruction artifacts, whenthey occur, will result from mismatch between theseeffective gradient sets.

In this study of healthy volunteers, diagnostic imagesof the heart and the coronary arteries were consistentlyproduced and clearly demonstrate the potential of theAUTO-SMASH technique for cardiac imaging andMR coronary angiography. As expected, the AUTO-SMASH images obtained with strategy II showed im-proved spatial resolution. For fine structurespredominantly oriented parallel to the phase encodingdirection, such as the right coronary artery in Fig. 5(e),some of the apparent improvement results from higherread-direction resolution. However, for structures such

as the left main coronary artery shown in Fig. 6(f)running almost parallel to the read-direction, improvedvisibility is predominantly a result of the increasedspatial resolution in the phase encode direction. Oneconsequence of the higher spatial resolution in strategyII is a reduced SNR, as may be appreciated in theimages of Figs. 5 and 6. In addition, factors involvingthe component coil weightings affect SNR in SMASHand AUTO-SMASH reconstructed images. Reconstruc-tion-related SNR considerations are the same inAUTO-SMASH as in SMASH, and these are treated indetail elsewhere [10,11].

Cardiac AUTO-SMASH, as evaluated in this study,has one important limitation: The need to acquireimages nearly parallel to the underlying linear phasedarray coil. Since multiple image plane orientations arecommonly used in cardiac imaging, careful engineeringof shaped coil arrays with an increased number of arrayelements and optimization of postprocessing algorithmsare called for in order to maintain full flexibility forroutine cardiac MR applications.

The results presented in this report show the poten-tial advantages of the AUTO-SMASH approach. It canprovide important information about coil sensitivitieseven in areas of inhomogeneous spin density, whichwould otherwise render in vivo coil sensitivity mapping


Fig. 7. Results obtained from a cardiac study with strategy I using three spatial harmonics. (a) Reference image (240×256 matrix size) obtainedin 48 cardiac cycles corresponding to a breath-hold time of 40 s. (b) Aliased image (80×256 matrix size) obtained in 16 cardiac cycles withreduced gradient phase encoding. This image was formed by combining the component coil reference images pixel-by-pixel as the square root ofthe sum of square magnitudes. (c) The corresponding full FOV image after AUTO-SMASH reconstruction (240×256 matrix size). Acquisitiontime of this image was 16 cardiac cycles or 1/3 of the reference acquisition time.

and therefore SMASH and other PPA image recon-structions difficult. AUTO-SMASH allows for moreflexible and more convenient acquisition and postpro-cessing procedures.

6. Conclusion

We have developed an internal sensitivity calibra-tion technique for the SMASH imaging method usingadditionally acquired self-calibration signals. This pro-cedure acquires the necessary coil sensitivity informa-tion in the course of the actual scan, rather than in aseparate calibration experiment. The advantage of thissensitivity reference method is that no extra coil arraysensitivity maps need to be acquired. In addition,AUTO-SMASH provides coil sensitivity informationin areas of non-uniform spin-density and movingtissue structures, where no reliable direct coil sensitiv-ity measurements are possible. Data post-processingis easy to implement and the underlying concept canbe combined easily with most conventional or fastimaging techniques. The results from the self-calibrat-ing SMASH approach in phantoms and human sub-jects indicate that this technique is an effectivemethod for internal calibration of SMASH images.Since parallel imaging techniques have the potential toplay an important role in the area of fast MR imag-ing, the need for a fast and accurate coil sensitivitycalibration will likely increase. Therefore the approachof using additionally sampled calibration signals, asdemonstrated with AUTO-SMASH, may play an im-

portant role for rapid parallel imaging techniques intimes to come.

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auto-smash: a self-calibrating technique for smash imaging

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