Spatial Encoding Using Multiple rf Coils: SMASH … · Spatial Encoding Using Multiple rf Coils: SMASH Imaging and Parallel MRI Daniel K. Sodickson Beth Israel Deaconess Medical Center

Spatial Encoding UsingMultiple rf Coils: SMASHImaging and Parallel MRI

Daniel K. Sodickson

Beth Israel Deaconess Medical Center and Harvard Medical School,Boston, MA, USA

1 INTRODUCTION

The speed of MR image acquisition has increased dramati-cally since the 1980s through a combination of technologicaland methodological advances. Nevertheless, many clinical ap-plications of MRI continue to require motion compensation insome form. In body regions containing moving structures suchas the heart or diaphragm, serious artifacts can arise if scantimes exceed the characteristic time scales of physiologicmotion. Accurate tracking of dynamic processes, such as car-diac contraction or the arrival and uptake of intravenouscontrast agents, may require high temporal resolutions withoutundue sacri®ces in spatial resolution. Meanwhile, the fastestimaging sequences and the most state-of-the-art scanners areapproaching certain basic limits of imaging speed. These limits,which have both a technological and a physiological com-ponent, are related to the maximum switching rates ofmagnetic ®eld gradients and rf pulses. Most of the fast imagingsequences now in use ± echo planar imaging (EPI), fast lowangle shot (FLASH), turbo spin echo (TSE), spiral, or BURST,for example ± achieve their high speeds by optimizing thestrengths, the switching rates, and the patterns of applied gradi-ents and pulses. Beyond a certain threshold, however, rapidlyswitched ®eld gradients are known to produce neuromuscularstimulation, while excessively dense rf pulse trains can lead tounacceptable levels of rf energy deposition and heating of tis-sue. One common feature of fast imaging sequences is thatthey all acquire data in a sequential fashion. Regardless of theparticular sequence the acquisition follows, the MR signal isalways acquired one point and one line at a time, with eachseparate line of data requiring a separate application of ®eldgradients and/or rf pulses. Therefore, imaging speed is gener-ally limited by the maximum switching rates compatible withscanner technology and patient safety.

Recently, a new paradigm of parallel MRI has been used toincrease imaging speeds beyond the basic limits just described.The term `parallel MRI' may be used to describe any MRIstrategy in which multiple MR signal data points are acquiredsimultaneously, rather than one after the other. Parallel imagingstrategies in general require the use of multiple distinct detec-tors, with each detector providing some component of distinctspatial information to the image. (A many-detector CCD cam-era is a familiar optical example of a parallel imaging devicewhile a FAX machine is an example of a sequential line-scan-ning device.) For MRI in particular, some of the burden ofspatial encoding traditionally accomplished by ®eld gradients

may be shifted instead to arrays of rf coils. Recent work hasshown that coil arrays may be used, in combination withappropriate image reconstruction strategies, to encode anddetect multiple MR signal or image components simultaneouslyand thereby to multiply the speed of existing imagingsequences without increasing gradient switching rate or rfpower deposition.

2 THE HISTORY OF PARALLEL MRI

Radiofrequency coil arrays were ®rst developed for use inMRI in the late 1980s. Prior to that time, single volume or sur-face coils were typically used for signal detection, or else pairsof coils were arranged in quadrature to increase signal-to-noiseratio (SNR). Work by Roemer and co-workers demonstratedthat arrays of suitably decoupled surface coils could be used toachieve further substantial SNR increases1,2 (see Whole BodyMachines: NMR Phased Array Coil Systems). When used incombination with traditional gradient-encoding sequences, coilarrays increased the achievable SNR for any given ®eld ofview (FOV) in any given imaging time, but ultimate imagingspeed was still governed by the imaging sequence and the gra-dient hardware.

The fact that spatial information from coil arrays might alsobe used directly for the encoding and decoding of images wasrealized in principle relatively early in the development of MR-compatible arrays. The simplest manifestation of the parallelimaging principle was the use of spatially separated coils toimage distant and nonoverlapping body regions simultaneously.More challenging was the prospect of imaging a continuousFOV rapidly using detectors overlapping in space and/or sensi-tivity. An early theoretical proposal by Carlson suggested thatthe Fourier coef®cients of signal voltages in multiple coils dis-posed around a cylinder could be used to calculate multiple k-space lines for magnetization within that cylinder.3 Hutchinsonand Raff suggested in 1988 that a large array of narrow loopssurrounding an object could, in principle, be used to acquire animage without the use of any phase-encoding gradients at all.4

Other proposals followed, and these proposals fall into twogeneral categories: massively parallel and partially parallelstrategies.

In massively parallel strategies, the number of detectorsapproaches the number of data points or lines. These tech-niques aim to replace gradient encoding entirely, with resultingdramatic improvements in imaging speed. The original mas-sively parallel proposal of Hutchinson and Raff was intendedto show theoretical feasibility, and no direct practical im-plementation was suggested.4 A subsequent proposal formassively parallel imaging was made by Kwiat, Einav, andNavon in 1991.5 Their study included a more detailed investi-gation of practical issues, though no images were presented. Apreliminary array design based on the general principles of thisproposal was presented in 1995.6

In partially parallel imaging strategies, the number of detec-tors is signi®cantly smaller than the number of data points.Spatial encoding using multiple rf coils is used to supplementthe spatial encoding normally accomplished using magnetic®eld gradients. Kelton, Magin, and Wright,7 and later Ra andRim8,9 described a `subencoding'9 approach by which aliased

SPATIAL ENCODING USING MULTIPLE RF COILS: SMASH IMAGING AND PARALLEL MRI 1

For References see p. 11

component coil images acquired rapidly with reduced phaseencoding may be ùnaliased' using information about com-ponent coil sensitivities. Carlson and Minemura proposed usingnested volume coils with differing sensitivity patterns to ap-proximate multiple k-space lines from a series expansion.10 In1997, SiMultaneous Acquisition of Spatial Harmonics(SMASH)11 was introduced, and the ®rst accelerated in vivoMR images using a parallel imaging strategy were obtained.The SMASH technique uses linear combinations of componentcoil signals from a surface coil array to replace time-consuminggradient steps directly. Following the introduction of SMASH,the subencoding principle was revisited and re®ned in theSENSitivity Encoding technique (SENSE) of PruÈssmann, Wei-ger, and co-workers,12 which has also been used recently toobtain accelerated in vivo images. At the present time, variousother research groups both in academia and in industry havealso begun to investigate parallel imaging strategies.

Table 1 lists the various proposed parallel MRI techniques,further categorized by coil sensitivity calibration and imagereconstruction method. The principal message of this table isthat there are numerous ways to extract spatial informationfrom an array of rf detectors. We will now discuss some ofthese methods in greater detail, emphasizing approaches forwhich in vivo results have already been published, and whichare likely to be well suited for clinical MRI. We will beginwith the SMASH technique,11 for which the broadest range ofin vivo results have been achieved to date. We will then dis-cuss the image-domain subencoding reconstruction techniques.

3 SMASH IMAGING

3.1 Theory

The SMASH technique exploits sensitivity variations in asurface coil array to substitute for spatial modulations normallyproduced by phase-encoding gradients.11 This use of coilencoding in place of gradient encoding allows the whole of k-space to be traversed using a reduced number of phase-encoding gradient steps, thereby reducing image acquisitiontimes.

The function of phase-encoding gradients is to impose sinu-soidal modulations of magnetization across the image plane.The MR signal integrated against these sinusoids then corre-sponds to spatial Fourier components of the image, or thefamiliar k-space lines. Figure 1 illustrates schematically thiswell-known effect. In the ®gure, sinusoidal modulations ofvarying spatial frequency, resulting from spin evolution inphase-encoding gradients of varying strength, are shownnext to their associated k-space lines. In the SMASHtechnique, some of these sinusoidal modulations, or `spatialharmonics', are generated by manipulations of component coilsensitivities, rather than by gradient-induced modulations ofmagnetization.

An array of rf coils contains spatial information in the formof its component coil sensitivities (Figure 2). In a linear surfacecoil array with adjacent components, each coil j has a distinctbut overlapping sensitivity Cj(x, y). By forming appropriate lin-ear combinations of component coil signals (Figure 3), we maygenerate composite sensitivity pro®les Ctot which oscillate in

Figure 1 A k-space schematic, indicating the spatial modulationsresulting from phase-encoding gradients. Gradient steps on either sideof the central k = 0 line correspond to various harmonics of spinmodulation across the image plane

Table 1 Parallel MRI techniques

Technique Sensitivity calibration Image reconstruction

Partially parallelk-space techniques

Carlson and Minemura (1993)10 Known volume coil sensitivities k-space series expansionSMASHa (1996)11 Surface coil sensitivity reference

(phantom, in vivo, AUTO-SMASH)k-space linear combination (spatial harmonics)

Image domain techniquesKelton, Magin, and Wright (1989)7 Pixel-by-pixel sensitivity reference Pixel-by-pixel matrix inversion (subencoding)Ra and Rim (1991, 1993)8,9 Pixel-by-pixel image reference Pixel-by-pixel matrix inversion (subencoding)SENSEa (1997)12 Pixel-by-pixel sensitivity extraction from

full reference imagesPixel-by-pixel matrix inversion (subencoding)

Massively parallelHutchinson and Raff (1988)4 Not discussed Inverse sourceKwiat, Einav, and Navon (1991)5 Point source references Inverse source

SMASH, simultaneous acquisition of spatial harmonics; SENSE, sensitivity encoding technique.aIn vivo results have been published for this technique.

2 SPATIAL ENCODING USING MULTIPLE RF COILS: SMASH IMAGING AND PARALLEL MRI

For list of General Abbreviations see end-papers

much the same way as the gradient-induced modulations of

Figure 1:

Ctot�x; y� �Xj

njCj�x; y� � exp�im�kyy� �1�

where nj are complex weight factors, m is an integer, and

ky = 2�/FOV is the minimum k-space interval corresponding to

the desired FOV.If a composite sensitivity pro®le generated in this way

forms an accurate spatial harmonic pattern, the same k-space

step is produced as would have resulted from a traditional gra-

dient step.11 In other words, each combined signal Stot,

generated from linear combinations of component coil signals

Sj using the weights nj from Equation (1), is shifted in k-space

by an amount (ÿm�ky):

Sj�kx; ky� ��

d x d yCj�x; y��x; y�expfÿikxxÿ ikyyg

Stot�kx; ky� �Xj

njSj�kx; ky�

��

d x d yXj

njCj�x; y��x; y�expfÿikxxÿ ikyyg

��

d x d yCtot�x; y��x; y�expfÿikxxÿ ikyyg

��

dx d y��x; y�expfÿikxxÿ i�ky ÿm�ky�yg

� ~��kx; ky ÿm�ky� �2�

where �(x, y) represents the spatial distribution of spin densityin the image plane and ~� is its spatial Fourier transform. Thisk-space shift is precisely the same shift as would be producedby evolution of spins with gyromagnetic ratio for time ty in ay gradient of magnitude Gy, with Gyty =ÿm�ky.

Such a coil-encoded k-space step combines naturally withany gradient-encoded k-space steps. When a coil array withmultiple elements is used, multiple harmonics may be gener-ated from a single data set (Figure 3). The result is that areduced number of phase-encoded lines (thick lines in Figure4) may be acquired in a reduced acquisition time, and theremaining lines of k-space (thin lines in Figure 4) may bereconstructed using linear combinations of component coil sig-nals. If a total of M spatial harmonics are generated, then Mlines of k-space may be reconstructed for each application of aphase-encoding gradient. The full signal matrix may, therefore,be generated in a fraction 1/M of the usual acquisition time.

3.2 Implementation

An important ®rst step in a practical SMASH implemen-tation is to measure the rf sensitivities of the various arrayelements. These sensitivities may be extracted in a straightfor-ward manner from images of homogeneous phantoms, sinceany intensity variations in such images may be traced to vari-ations in coil sensitivity. Typically, intensity pro®les across animage plane of interest are extracted from a stored phantomdata set and are used as sensitivity references. (Often, intensitypro®les along a single central line of the image plane suf®cefor calibration.) For cases in which phantom sensitivity refer-ence measurements are cumbersome or inaccurate (for examplewhen ¯exible coil arrays are used, the particular conformationsof which for any given patient are not known a priori), sensi-tivity pro®les may also be obtained in vivo by examiningcomponent coil images in regions of comparatively uniformspin density such as the spine. Alternative in vivo sensitivitycalibration procedures, such as the self-calibrating approach

Figure 2 The rf sensitivities of a linear coil array. Each of the threeoverlapping sensitivity distributions corresponds to one of the threecomponent coils in the array pictured at the top. (The conductor pathsof adjacent component coils are also typically overlapped, as shown inthis example, to minimize inductive coupling between coils.) Onlysensitivity magnitudes are shown here. In practice, coil sensitivitiesmay also have spatially varying phase distributions

Figure 3 Multiple spatial harmonic pro®les derived by linearcombination of component coil sensitivities in an eight-element array



called AUTO-SMASH,13 may be used for imaging in regionsof heterogeneous spin density such as the thorax, where largedifferences in signal between the heart and lungs precludestraightforward estimation of rf sensitivity. In AUTO-SMASH,a small number of reference k-space lines are added to the ac-quisition, and the relation between these reference lines and theusual MR signal data lines are used to `train' SMASH recon-structions directly in k-space.

Following sensitivity calibration, the sensitivity pro®les are®tted to the desired spatial harmonic functions, using a numeri-cal optimization algorithm with the complex weight factors nj

as ®tting parameters. For favorable array geometries, the result-ing ®ts can, in practice, be quite as good as the schematic ®tsshown in Figure 3.

The remaining steps in the SMASH reconstructionprocedure are summarized in Figure 5. The left-hand sideof Figure 5 shows a k-space schematic, and the right-handside shows image data from a water phantom at each ofthe corresponding stages of reconstruction. With thenecessary weights in hand, MR signal data are acquiredsimultaneously in the coils of the array. A fraction 1/M of theusual number of phase-encoding steps are applied, with Mtimes the usual spacing in k-space (Figure 5A, left). The com-ponent coil signals acquired in this way correspond to imageswith a fraction 1/M of the desired FOV (Figure 5A, right).With 1/M times fewer phase-encoding steps, only a fraction 1/M of the time usually required for this FOV is spent on datacollection.

Next, the appropriate M linear combinations of the com-ponent coil signals are formed to produce M shifted compositesignal data sets (Figure 5B). The composite signals are theninterleaved to yield the full k-space matrix (Figure 5C, left),which is Fourier transformed to give the reconstructed image(Figure 5C, right).

The schematic summary in Figure 5 shows a SMASHreconstruction with acceleration factor M = 2 using a 3-elementrf coil array. Substantially larger factors are possible, however,when coil arrays with larger numbers of elements are used. Infact, for favorable image plane and coil array geometries, themaximum achievable SMASH acceleration factor M is equal tothe number of independent component coils in the array, sincea maximum of M distinct harmonics may be generated using atotal of M independent coils. Since generation of spatial harmo-nics does not depend upon how the gradient-encoded k-spacelines were generated, the SMASH reconstruction is to a largeextent sequence independent. Nearly all existing rapid imagingsequences may be accelerated in this manner, and, to date,SMASH has been successfully tested with a wide range ofsequence types. Both two-dimensional and three-dimensionalacquisitions are amenable to acceleration using SMASH, pro-vided distinct coil sensitivity information is available along oneor more phase-encoding directions.

3.3 In Vivo Results

The improvements in imaging ef®ciency afforded by a par-allel imaging strategy may be put to use in a number of ways.The following examples demonstrate some of the applicationsfor which SMASH imaging has been used to increase imagingspeed and improve image quality.

Reductions in breath-hold duration for scans requiringbreath-holding can be achieved, which increases patient com-fort and compliance and allows scans free of respiratorymotion artifact in patients incapable of prolonged breath-holds.Figure 6 demonstrates a twofold reduction in breath-hold dur-ation for abdominal MR imaging.

Improvements in spatial resolution can be achieved in anygiven imaging time: images of increased spatial resolution may

Figure 4 Schematic k-space trajectory for a partially parallel acquisition using ®ve spatial harmonics. Thick lines represent k-space linescorresponding to applied phase-encoding gradient steps, while thin lines represent additional k-space lines reconstructed using the linearcombinations shown in Figure 3. The additional reconstructed lines substitute for omitted phase-encoding gradient steps



be generated in a given acquisition time by carrying the fasterSMASH acquisition farther out in k-space. Figure 7 shows theuse of SMASH for spatial resolution enhancement in a cardiacscan. Additional resolution bene®ts can result from the use ofSMASH or other partially parallel techniques in single-shotimaging sequences such as HASTE (half-Fourier single-shotturbo spin echo), EPI, or BURST.14 Indeed, single-shot imageswith both reduced acquisition time and increased spatial resol-ution compared with the corresponding reference images havebeen obtained. This is possible because a reduced aquisitiontime also entails reduced relaxation, and hence reduced attenu-ation of high spatial frequencies in single-shot sequences.14

Improvements in temporal resolution (i.e., reductions inimage-acquisition interval for gated or ungated scans) minimizeundesired effects of physiologic motion while allowing accu-rate tracking of time-dependent phenomena. Figure 8 illustratesa twofold and a fourfold reduction in acquisition window at®xed spatial resolution in cardiac MR images. These progress-ive increases in temporal resolution result in progressivelyreduced motional blurring of the right coronary artery and othercardiac structures in the SMASH images. SMASH has alsobeen used to increase true frame rate in real-time cardiac MRscans up to and beyond current two-dimensional echocardio-graphic frame rates.

Reductions in the overall duration of long MR scansincrease patient comfort and compliance and also increase thethroughput of clinical MR scanners and the cost-effectivenessof MR diagnosis. Noncontrast MR coronary angiogramsobtained using SMASH are shown in Figure 9. Reduction inoverall acquisition time in these navigator-gated scans has thefurther advantage of reducing long-term diaphragmatic driftover the course of the scans.

4 IMAGE-DOMAIN SUBENCODING TECHNIQUES

4.1 Theory

A subencoding image reconstruction begins at the samestarting point as a SMASH reconstruction ± namely, with a setof component coil signals acquired using a reduced number ofphase-encoding gradient steps. Fourier transformation of thesesignal sets results in aliased component coil images like thoseshown in Figure 5A. From that point on, the subencodingreconstruction operates entirely in the image domain.

The basis of the technique lies in the fact that each pixel inan aliased image is in fact a superposition of multiple pixels

Figure 5 Schematic representation of the SMASH reconstruction procedure (left: k-space cartoon, right: corresponding phantom images). (A)Acquisition of data with reduced phase encoding. (B) Formation of shifted data sets using spatial harmonic combinations. (C) Interleaving of shifteddata sets to generate a full signal matrix, corresponding to an image with full FOV



from a corresponding full unaliased image (Figure 10). In otherwords, as a result of Nyquist aliasing, an M-times aliasedimage Ifold is related to the full image Ifull as follows:

I fold�x; y� � I full�x; y� � I full�x; y��y� � I full�x; y� 2�y�

� � � � �XMÿ1m�0

I full�x; y�m�y� �3�

When Ifold is acquired using a single coil, this superpositioncannot be ùnfolded' without a priori knowledge of the fullimage.

The situation changes when an array of coils is used. Thefull image I full

j in each coil j is actually made up of two pieces:the spin density �, and the coil sensitivity function Cj:

I fullj �x; y� � Cj�x; y��x; y� �4�

and in an array, each component coil j has a different sensi-tivity Cj. Therefore, we now have multiple `views' of thealiasing that can be used to deduce just how much of each

aliased pixel belongs at any position in the full image. Substi-tuting Equation (4) into Equation (3) gives

I foldj �x; y� �

XMÿ1m�0

I fullj �x; y�m�y�

�XMÿ1m�0

Cj�x; y�m�y��x; y�m�y� �5�

For any particular aliased pixel (x,y), this may be written asfollows:

I foldj �

XMÿ1m�0

I fulljm �

XMÿ1m�0

Cjm�m �6�

where I fulljm � I full

j (x,y + m�y), Cjm:Cj(x,y + m�y), and �m:�(x,y + m�y).

Let us study the particular example (illustrated in Figure 11)in which a four-coil array is used with a factor of three alias-ing. We may write

Figure 6 Turbo spin echo (TSE) images taken along the thoracic and lumbar spine of a healthy adult volunteer, demonstrating the use of SMASHimaging for reduction of breath-hold times in vivo (TR 700 ms, TE 32 ms, 9 echoes per excitation, in-plane spatial resolution 1.9 mm�1.0 mm).These images were obtained using four active elements of a six-element circularly polarized spine array on a 1.5 T Siemens Vision imaging system.The reference image was obtained in a breath-hold lasting 22 s and reconstructed using a standard sum of squares combination of component coilimages.1 The SMASH image with the same ®nal spatial resolution and FOV was obtained in only 11 s



I fold1 � C11�1 � C12�2 � C13�3

I fold2 � C21�1 � C22�2 � C23�3

I fold3 � C31�1 � C32�2 � C33�3

I fold4 � C41�1 � C42�2 � C43�3

�7�

This equation may be rewritten in matrix form as

I fold1I fold2I fold3I fold4

26643775 �

C11 C12 C13C21 C22 C23C31 C32 C33C41 C42 C43

26643775 � �1

�2�3

24 35 �8�

or, in other words,

Ifold � C� �9�

As long as the number of coils Nc is greater than or equal tothe aliasing factor M (as in our exemplary case for whichNc = 4, M = 3), Equation (9) may be inverted:

� � Cÿ1Ifold �10�

and the unaliased spin density over the full FOV may be deter-mined. This ùnaliasing' approach bears some kinship with theprinciple of computed tomography, in the sense that multipledifferent `views' or projections are used to extract full two-dimensional image information.

4.2 Implementation

Subencoding implementations differ from SMASH im-plementations primarily in their approaches to sensitivitycalibration and in the nature and numerical stability of theirimage reconstruction algorithms. Sensitivity estimates at eachpixel of the full FOV are generally required to perform thepixel-by-pixel subencoding matrix inversion of Equation (10).Ra and Rim describe the use of an in vivo sensitivity referencein the form of full-FOV component-coil images of the targetimage plane, manipulated in the reconstruction in such a waythat the spin density divides out.9 The SENSE technique incor-porates a different in vivo sensitivity calibration method inwhich full-FOV component coil images are divided by an ad-ditional full-FOV body coil image, and the quotient images arethen subjected to several stages of interpolation, ®ltering, andthresholding.12 Phantom sensitivity references can also, in prin-ciple, be used for subencoding reconstructions.

Figure 7 Coronal cardiac images showing the use of SMASH for increased spatial resolution (2D segmented-k-space FLASH, 9 echoes persegment, TR 14.4 ms, TE 7.3 ms, custom-designed four-element array, Siemens Vision scanner). The reference image has a matrix size of 144�256,corresponding to an in-plane resolution of 2.2 mm�1.2 mm. The SMASH image has double the spatial resolution in both dimensions (288�512matrix size, in-plane resolution 1.1 mm�0.6 mm). Both images were obtained in a breath-hold lasting 16 cardiac cycles. A long segment of theright coronary artery (thick black arrows) may be seen in both images but is notably sharper in the higher-resolution SMASH image. Branches ofthe left coronary system (thick white arrow) may also be discerned in the SMASH image, whereas they are not seen in the reference image. Finally,internal mammary arteries (thin white arrow), invisible in the reference image, may just be discerned running down the center of the SMASH image



Whereas the quality of SMASH reconstructions is governedby the `goodness' of spatial harmonic ®ts, the principal algo-rithmic concern of subencoding reconstructions is thenumerical stability of the inverse Cÿ1. For Nc>M, the inversemay be implemented, for example, as a Moore±Penrosepseudoinverse, resulting in a least squares solution to the over-determined problem for each pixel. For Nc = M, a standardmatrix inverse may be used. The use of a pixel-by-pixel inver-sion affords the advantage of ®ne regional control over thereconstruction: it does not, for example, require a global spatialharmonic ®t. A disadvantage of the pixel-by-pixel approach,however, is that in regions of low actual or apparent coil sensi-tivity, the matrix C may be poorly conditioned, and errorpropagation through the inverse may amplify the effects bothof noise and of sensitivity miscalibrations.

4.3 In Vivo Results

Image-domain subencoding techniques can be used formany of the same applications as were demonstrated withSMASH in Section 3.3. The resulting images will resembleaccelerated SMASH images, with some particular differencesin image artifacts and noise distribution resulting from thedifferent approaches to sensitivity calibration and image recon-struction. In vivo SENSE images in the brain and the heartwith two- to threefold accelerations have been presented.12,15

An in vivo sensitivity calibration method similar to thatsuggested by Ra and Rim has also been used by the SMASHgroup to obtain accelerated subencoding images for direct com-

parison with SMASH reconstructions of the same data sets.Figures 12 and 13 compare reference, SMASH, and subencod-ing images from contrast-enhanced angiography and real-timecardiac MR imaging studies.

5 A RECIPE FOR PRACTICAL PARALLELIMAGING

The following is a list of essential elements needed foreffective implementations of partially parallel imaging strat-egies such as SMASH or subencoding.

1. rf coil array. Arrays should be designed with overalldimensions appropriate to the desired FOV for imaging appli-cations of interest. Inductive decoupling of array elements ishelpful for improved SNR and for increased spatial selectivityof the sensitivity pro®les, although some degree of couplingbetween array elements can generally be tolerated. The imagingsystem must be equipped with a suf®cient number of receiverchannels to allow simultaneous data acquisition in the variouscomponent coils of the array. Alternative data-receptionschemes such as time-domain multiplexing may also beused.16,17

2. Sensitivity calibration. Accurate coil sensitivity cali-bration is crucial for all parallel imaging techniques. A greatdeal of effort has been devoted over the years to the under-standing and calibration of gradient waveforms in MRscanners. Since parallel imaging strategies use rf coils in placeof gradients for spatial encoding, it is not surprising that some

Figure 8 Coronal cardiac images from a 3D data set demonstrating the use of SMASH to increase temporal resolution at ®xed spatial resolution(3D turbo ®eld echo, TR 8.8 ms, TE 2.4 ms, in-plane spatial resolution 1.5 mm�1.5 mm, with fat suppression, T2 preparation, electrocardiogramtriggering, and navigator gating/correction using a 6-element linear coil array on a 1.5 T Philips NT scanner). The reference image (sum of squaresreconstruction) has an acquisition window of 200 ms per cardiac cycle. The twofold- and fourfold-accelerated SMASH images show progressivelyreduced motional blurring and improved visualization of the right coronary artery running near the midline of the images



degree of analogous effort must go into the calibration of coilsensitivities.

3. Scan planning. After a target image plane and FOV havebeen selected, all that is required on most MR scanners to plana SMASH or subencoding scan is a simple FOV reduction inthe phase-encode direction. The need to perform spatial encod-ing with the rf coil array places some limitations on the choiceof image plane position and orientation. For example, phaseencoding must be performed along a direction in which thesensitivities of different array elements are suf®ciently distinct.Substantial angulations between the image plane and the coilarray are often possible (see, for example, the double-obliqueimages in Figures 9 and 13), though some penalty in SNR maybe incurred.

4. Image reconstruction. Signal and image processingrequirements are modest, but some capabilities for variablecomponent coil signal combinations are required, whether inthe MR scanner itself or in of¯ine processors with access to

the raw MR signal data. Details of software and/or hardwareimplementations will depend upon which parallel reconstruc-tion strategy is elected.

Occurring as they do on either side of the Fourier transform,the k-space and the image-domain reconstructions bear a theor-etical kinship, but their practical speci®cations differ. Thechoice of reconstruction strategy may be in¯uenced by a num-ber of factors:

(a) Ease of implementation. SMASH uses a small numberof weight factors (a minimum of one per component coil perspatial harmonic), and operates in k-space prior to Fouriertransformation. Consequently, it is particularly amenable to in-line implementations in which the coil-encoded k-space dataare generated as soon as each gradient-encoded data point isread out. By contrast, the large numbers of weight factors insubencoding (one per component coil per image pixel) provide®ner pixel-by-pixel control at the expense of increased cali-bration and reconstruction time. In the future, compromisesbetween these two extremes may be anticipated, using variousextrapolation schemes.

(b) Image artifacts. In SMASH, residual aliasing artifactsresult from errors in sensitivity calibration or spatial harmonic®tting.11 In subencoding images, localized pixel-by-pixel arti-facts are more commonly seen as a result of pixel-by-pixelerrors in the coil sensitivity references. (These local artifactsmay be accompanied by global aliasing artifacts when there aresystematic errors in sensitivity calibration.) In some circum-stances, however, both techniques can actually lead to artifactreduction. Not only can accelerated acquisitions reduce motionartifacts, but they have also been shown to reduce geometricaldistortions in single-shot SMASH EPI images through reduced

Figure 9 Noncontrast MR coronary angiograms obtained in reducedtotal scan time using SMASH (same basic sequence, coil array, and MRscanner as in Figure 8, with an acquisition window of 70 ms and an in-plane resolution of 0.7 mm�1.0 mm). Double oblique image planeswere planned along the major axis of the right coronary artery (RCA).(A) A 7.5 cm length of the native RCA in a healthy adult volunteer isseen in this high-resolution image. The 3D data set from which thisimage was taken was obtained during free breathing in a total of 11 minusing a SMASH acceleration factor of two. (B) The RCA is interruptedby a region of signal dropout from a coronary stent in this localmaximum intensity projection of a twofold-accelerated 3D SMASHimage set (11 min free-breathing acquisition) in a patient with coronaryartery disease

Figure 10 Superposition of pixels (white squares) in an aliased image



accumulation of phase discrepancies in the shortened acqui-sition time.

(c) SNR. The SNR in a partially parallel image reconstruc-tion is a balance between coil-speci®c, reconstruction-speci®c,and sequence-speci®c effects. Theoretical and experimental stu-dies of SNR in SMASH imaging have been reported.18

Generally speaking, both SMASH and subencoding techniquesare bound by the well-known limit that SNR scales as thesquare root of the acquisition time for any given coil andsequence. With either class of technique, then, there is someexpected loss of SNR compared with optimal combinations1 oftraditionally acquired full data sets in the same array, thoughparallel acquisitions may still show improved SNR when com-pared with sequential acquisitions using single surface coilsspanning the same FOV. For certain imaging sequences,furthermore, some additional SNR beyond the square root limitmay be recovered through reduced relaxation in the shortenedacquisition times.

6 THE FUTURE OF PARALLEL MRI

Since the initial demonstration in 1997 of twofold-acceler-ated in vivo images using SMASH, new in vivo work has

shown up to fourfold increases in acquisition speed, and asmuch as eightfold improvements have been achieved in phan-toms using specialized rf hardware.17 What future progressmay be expected, and what are the key technical and methodo-logical hurdles to further development?

Coil array design and rf sensitivity calibration top the list ofdevelopments that will be crucial for future improvements inparallel imaging, since array geometry and sensitivity character-istics determine the degree of spatial encoding which may beaccomplished in any particular region of interest. The design oftailored arrays and the availability of increased numbers ofreceiver channels will greatly facilitate the optimization ofimage quality and SNR, and the maximization of achievableacceleration factors. In-line reconstruction hardware will be ofbene®t for real-time imaging applications. When the necessaryweight factors are known in advance, the use of onboard ana-log signal combiners prior to digitization may even allow large`smart' arrays to be interfaced to existing MR scanners withlimited numbers of receivers. Methodological advances furtherin the future may also allow a return to the principle of mas-sively parallel imaging. The potential gains of massivelyparallel imaging approaches are dramatic (they include thepossibility of acquiring an entire image in a single echo, forexample), but serious technological and theoretical hurdlesremain to be overcome in areas such as electric decoupling oflarge arrays, massively parallel data reception, and SNR.

Figure 11 Superposition of pixels (white squares) in an aliased or subencoded image set from an array, corresponding to Equation (7). Theinversion of this equation, and hence the unraveling of pixel-by-pixel superpositions, forms the basis of the image-domain subencoding techniques



In the meantime, clinical implementation of partially parallelimaging is possible now using existing arrays and receiver sys-tems. Indeed, clinical studies in selected patient populations arenow being initiated using parallel acquisition techniques. Par-ticularly for applications with stringent requirements onimaging speed, parallel imaging can be a useful tool to enhanceimage quality, to improve imaging ef®ciency, and, in general,to overcome the acquisition speed limit in magnetic resonanceimaging.

7 RELATED ARTICLES

Image Formation Methods; Radiofrequency Systems andCoils for MRI and MRS; Spin Warp Data Acquisition; Surfaceand Other Local Coils for In Vivo Studies; Whole Body Ma-chines: NMR Phased Array Coil Systems.

8 REFERENCES

1. P. B. Roemer, W. A. Edelstein, C. E. Hayes, S. P. Souza, and O.M. Mueller, Magn. Reson. Med., 1990, 16, 192.

2. C. E. Hayes and P. B. Roemer, Magn. Reson. Med., 1990, 16,181.

3. J. W. Carlson, J. Magn. Reson., 1987, 74, 376.4. M. Hutchinson and U. Raff, Magn. Reson. Med., 1988, 6, 87.5. D. Kwiat, S. Einav, and G. Navon, Med. Phys., 1991, 18, 251.6. D. Kwiat and S. Einav, Med. Eng. Phys., 1995, 17, 257.

7. J. R. Kelton, R. L. Magin, and S. M. Wright, Proc. VIIIth Annu.Mtg Soc. Magn. Reson. Med., Amsterdam, 1989, p. 1172.

8. J. B. Ra and C. Y. Rim, Proc. Xth Annu. Mtg Soc. Magn. Reson.Med., San Francisco, 1991, p. 1240.

9. J. B. Ra and C. Y. Rim. Magn. Reson. Med., 1993, 30, 142.10. J. W. Carlson and T. Minemura, Magn. Reson. Med., 1993, 29,

681.11. D. K. Sodickson and W. J. Manning, Magn. Reson. Med., 1997,

38, 591.12. K. P. Pruessmann, M. Weiger, M. B. Scheidegger, and P. Boesi-

ger, Proc. VIth Sci. Mtg (Int.) Soc. Magn. Reson. Med., Sydney,1998, p. 579.

13. P. M. Jakob, M. A. Griswold, R. R. Edelman, and D. K. Sodick-son, MAGMA, 1998, 7, 42.

14. M. A. Griswold, P. M. Jakob, Q. Chen, J. W. Goldfarb, W. J.Manning, R. R. Edelman, and D. K. Sodickson, Magn. Reson.Med., 1999, 41, 1236.

15. M. Weiger, K. P. Pruessmann, M. B. Scheidegger, and P. Boesi-ger, Proc. VIth Sci. Mtg (Int.) Soc. Magn. Reson. Med., Sydney,1998, p. 803.

16. J. R. Porter, S. M. Wright, and N. Famili, Magn. Reson. Med.,1994, 32, 499.

17. D. K. Sodickson, J. A. Bankson, M. A. Griswold, and S. M.Wright, Proc. VIth Sci. Mtg (Int.) Soc. Magn. Reson. Med., Syd-ney, 1998, p. 577.

18. D. K. Sodickson, M. A. Griswold, P. M. Jakob, R. R. Edelman,and W. J. Manning, Magn. Reson. Med., 1999, 41, 1009.

Biographical Sketch

Daniel K. Sodickson. b 1966. B.Sc. (Physics) and B.A. (Humanities),1988, Yale college, Ph.D., 1994, Massachusetts Institute of Technol-

Figure 12 Maximum intensity projections of contrast-enhanced 3D MR angiograms of the abdominal aorta and renal arteries in a healthy adultvolunteer (3D T1-weighted rf-spoiled gradient-echo imaging sequence, TE 1.5 ms, TR 7.0 ms, in-plane spatial resolution 2.7 mm�1.4 mm, 6-element array, Philips NT scanner). The reference image set was obtained in a 23 s breath-hold following gadolinium injection, whereas thetwofold accelerated data set used for SMASH and subencoding reconstruction was obtained in 11.5 s



ogy, M.D., 1996, Harvard Medical School. Graduate work in solid-state NMR involved methodological developments for molecular struc-ture determination and studies of the classical and quantum physicsunderlying spin diffusion in lattices. Appointed Research Associate,Beth Israel Deaconess Medical Center, Boston, MA, 1996. Appointed

Instructor in Medicine, Harvard Medical School, 1997. Developed theSMASH imaging technique at Beth Israel Deaconess Medical Centerin 1996. Approx. 10 papers and 1 patent in areas related to NMR. Pri-mary research interests: parallel acquisition strategies in MRI, rapidMRI, cardiovascular MRI.



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Spatial Encoding Using Multiple rf Coils: SMASH … · Spatial Encoding Using Multiple rf Coils: SMASH Imaging and Parallel MRI Daniel K. Sodickson Beth Israel Deaconess Medical Center