Highly Accelerated Contrast-Enhanced MR Angiography:Improved Reconstruction Accuracy and Reduced NoiseAmplification With Complex Subtraction

Ioannis Koktzoglou,1* John J. Sheehan,1 Eugene E. Dunkle,1 Felix A. Breuer,2

and Robert R. Edelman1

Contrast-enhanced magnetic resonance angiography is rou-

tinely performed using parallel imaging to best capture the

first pass of contrast material through the target vasculature,

followed by digital subtraction to suppress the appearance of

unwanted signal from background tissue. Both processes,

however, amplify noise and can produce uninterpretable

images when large acceleration factors are used. Using a

phantom study of contrast-enhanced magnetic resonance an-

giography, we show that complex subtraction processing

prior to partially parallel reconstruction improves reconstruc-

tion accuracy relative to magnitude subtraction processing

for reduction factors as large as 12. Time-resolved contrast-

enhanced magnetic resonance angiographic data obtained-

with complex subtraction in volunteers supported the results

of the phantom study and when compared with magnitude

subtraction processing demonstrated reduced geometry fac-

tors as well as improved image quality at large reduction

factors. Magn Reson Med 64:1843–1848, 2010. VC 2010 Wiley-

Liss, Inc.

Key words: angiography; contrast enhanced; parallel imaging;complex subtraction

The reference standard method for diagnosis of vascular

disease is X-ray digital subtraction angiography.

Although it provides excellent spatial resolution, draw-

backs of the method include invasiveness, injection of

potentially nephrotoxic contrast agent, and exposure of

the patient to ionizing radiation.

As an alternative to X-ray digital subtraction angiogra-

phy that does not involve ionizing radiation, contrast-

enhanced magnetic resonance angiography (CE-MRA)

can detect the presence and severity of vascular disease

with excellent sensitivity and specificity in several vas-

cular beds (1–6). The method entails infusing paramag-

netic contrast material into the blood stream and rapidly

imaging the first pass of the contrast material using an

undersampled as well as parallel imaging-accelerated

spoiled gradient-echo acquisition. Subtraction of a

‘‘mask’’ image set acquired before contrast is injected is

performed to suppress unwanted background tissue,

improve vascular-to-background contrast-to-noise ratio,

and aid image interpretation (7,8).

Signal-to-noise ratio during parallel accelerated CE-

MRA is decreased by the square root of the undersam-

pling factor as well as by an additional noise amplifica-

tion factor associated with the parallel imaging recon-

struction process. The former and the latter, governed

by the Fourier averaging principle (9) and by the geome-

try factor (i.e., g-factor) of the receiver coil array (10)

respectively, decrease signal-to-noise ratio in a multipli-

cative manner and can substantially degrade image

quality. Being that signal-to-noise ratio loss associated

with undersampling cannot be avoided without

decreasing either the spatial or temporal resolution of

the acquisition, reduction of g-factor-dependent noise

amplification may be sought as a means to improve

image quality.

A characteristic property of CE-MRA is the spatial

sparsity of blood vessels residing in an image of low sig-

nal intensity and reduced spatial support. Substantial

improvement in parallel imaging reconstruction quality

has been reported in images exhibiting reduced spatial

support (11). The purpose of this study was to examine

the influence of signal subtraction schemes on noise

amplification during parallel-accelerated CE-MRA. Spe-

cifically, this work sought to identify the performance

differences, if any, between complex subtraction and

magnitude subtraction in the setting of highly acceler-

ated CE-MRA.

MATERIALS AND METHODS

All experiments were performed on a 3.0-T MR system

(Verio, Siemens Healthcare, Erlangen, Germany) support-

ing up to 76 coil elements and 32 receiver channels and

capable of gradient amplitudes and slew rates of up to

45 mT/m and 200 T/(m s). The body coil of the MR sys-

tem was used to transmit the radiofrequency field.

Standard manufacturer-provided phased-array surface

coils were used to receive the MR signal.Complex raw data were exported from the MR scanner

and reconstructed offline using commercially availablesoftware (MATLAB, version 7.7.0; The Mathworks Inc.,Natick, MA). Undersampled data were reconstructed inthe k-space domain using the generalized autocalibratingpartially parallel acquisition (GRAPPA) methodology(12). The GRAPPA method constructs unacquired lines

1Department of Radiology, NorthShore University HealthSystem, Evanston,Illinois, USA.2Research Center Magnetic Resonance Bavaria, Wurzburg, Germany.

Grant sponsors: Auxiliary of NorthShore University HealthSystem, TheGrainger Foundation.

*Correspondence to: Ioannis Koktzoglou, PhD, Department of Radiology,NorthShore University HealthSystem, Walgreen Jr. Building, G507, 2650Ridge Ave., Evanston, Illinois 60201, USA.E-mail: ikoktzoglou@northshore.org

Received 4 October 2009; revised 8 June 2010; accepted 15 June 2010.

DOI 10.1002/mrm.22567Published online 21 September 2010 in Wiley Online Library (wileyonlinrlibrary.com).

Magnetic Resonance in Medicine 64:1843–1848 (2010)

VC 2010 Wiley-Liss, Inc. 1843

from nearby acquired lines using complex weights com-puted from autocalibration lines located in a fullysampled region of the k-space matrix. In this report, 24autocalibration lines were used in all GRAPPA recon-structions, and the size of the GRAPPA reconstructionkernel was 4 � 5 (phase-encoded � readout points) forreduction factors (R) � 7 and 2 � 5 for R � 8. Acquiredautocalibration lines of k-space were not used in thefinal reconstructions.

Phantom MR Imaging

A vascular phantom was imaged to examine the effectsof complex and magnitude data subtraction on parallelimaging reconstruction quality over a wide range ofacceleration factors (AF). The vascular phantom con-sisted of plastic intravenous extension tubing (inner di-ameter ¼ 2.5 mm; catalog #4429–48, Hospira Inc., LakeForest, IL) containing 0.125 mM gadopentetate dimeglu-mine (Gd-DTPA; MagnevistV

R

, Bayer Healthcare, Berlin)of T1 � 1400 msec, which was submerged in 0.5 mMGd-DTPA of T1 � 500 msec (13). The phantom wasimaged using a 3D fast low-angle shot acquisition withthe following parameters: pulse repetition time/echotime/flip ¼ 3.23 msec/1.3 msec/25�; field of view ¼ 320mm � 320 mm; matrix ¼ 320 � 320; slices ¼ 32; slicethickness ¼ 1.0 mm; and receiver bandwidth ¼ 710 Hz/pixel. Two 3D fast low-angle shot measurements, sepa-rated by 40 sec of quiescent time, were acquired. Duringthe 40-sec delay period, 31.25 mM Gd-DTPA (T1 < 50msec) solution was manually injected into the intrave-nous extension tubing. Thus, the first and second 3D fastlow-angle shot measurements simulated the precontrastand postcontrast environments during CE-MRA. Datafrom 18 receiver elements were collected; 12 and 6 ele-ments (element size � 14 cm � 14 cm) were located pos-terior and anterior to the phantom in 4 � 3 and 2 � 3grid patterns with three distinct element positions span-ning the phase-encoding axis.

Image Analysis for Phantom MR Imaging

Complex raw data were reconstructed to generate a fullysampled reference image set and decimated to simulateGRAPPA reconstruction data sets created using reduc-tion factors (R) ranging from 2 to 12, where R indicatesthe degree of undersampling outside of the autocalibra-tion region of k-space. Accounting for the time needed toacquire the autocalibration lines, reduction factors of 2and 12 provided net AF of 1.86 and 6.53 relative to afully sampled matrix. Two image reconstruction schemeswere investigated: (1) complex subtraction of the precon-trast and postcontrast complex data prior to GRAPPAreconstruction; and (2) magnitude subtraction of the pre-contrast and postcontrast magnitude images after theGRAPPA reconstruction. The sum of squares methodwas used to combine individual coils (14). Differencesbetween the reference and parallel-accelerated recon-structed images containing the enhanced intravenoustubing were quantified by computing the relative rootmean square error (RRMSE) (15), which is defined as

follows:

RRMSE ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPM

i¼1 I iA � I iR�� ��2

PMi I iR�� ��2

vuut ; ½1�

where M is the number of pixels in the image and IA andIR are the signal intensities of the accelerated and refer-ence images, respectively.

Human MR Imaging

This portion of the study was approved by our institu-tional review board, and written informed consent wasobtained from all volunteer participants. CE-MRA wasperformed in seven healthy volunteers (six males; meanage, 34 years; range, 20–66 years) to verify the relevanceof the results from the phantom study. Manufacturer-pro-vided 16-channel peripheral vascular coils (3.0 T) and24-channel spine coils (3.0 T) were used for signal recep-tion. Data were received using 28 receiver elements (ele-ment size � 14 cm � 14 cm); 12 and 16 elements werelocated posterior and anterior to the volunteer in 4 � 3and 4 � 4 grid patterns with three and four distinct ele-ment positions spanning the phase-encoding axis.

Human imaging consisted of two time-resolved imag-ing with stochastic trajectories (TWIST) CE-MRA acquisi-tions (16) of the calf separated by 31.0 6 0.9 min. Tospan the range of AF simulated in the phantom study,the first acquisition was acquired using a relatively largeone-dimensional reduction factor of 8 (AF ¼ 4.33 exclud-ing and 5.00 including the use of partial Fourier in thephase-encoding direction), whereas the second acquisi-tion was performed using a modest reduction factor of 2(AF ¼ 1.77 excluding and 2.27 including the use ofphase partial Fourier). During each acquisition, 10 cm3

of 0.5 M Gd-DTPA was injected into an antecubital veinat a rate of 3 cm3/sec using a computer-controlled dis-pensing system (Spectris Solaris EP, Medrad Inc., War-rendale, PA) and followed by 15 cm3 of saline at 3 cm3/sec. Imaging parameters for the TWIST acquisitions wereas follows: pulse repetition time/echo time/flip ¼ 2.72msec/1.3 msec/25�; field of view ¼ 400 mm � 337 mm;matrix ¼ 384 � 195; slices ¼ 60; slice thickness ¼ 1.3mm; area of central k-space ¼ 25%; peripheral k-spacesampling density ¼ 25%; receiver bandwidth ¼ 720 Hz/pixel; slice partial Fourier ¼ 6/8th; phase partial Fourier¼ 6/8th; and acquisition time ¼ 90 sec. TWIST scansacquired with undersampling factors of 8 and 2 providedtemporal resolutions of 1.47 sec and 3.22 sec. Undersam-pling and GRAPPA reconstruction was performed alongthe phase-encoding axis, which was oriented left toright.

Image Analysis for Human MR Imaging

Magnitude subtracted reconstructions were obtained byreconstructing magnitude images for the data acquiredbefore and after contrast arrival followed by subtractionin the image domain. Complex subtracted images weregenerated by subtracting complex data acquired beforeand after the arrival of contrast material on a coil-by-coil

1844 Koktzoglou et al.

basis prior to transferring the result to the GRAPPAreconstruction algorithm.

Geometry factor maps were computed at the phase ofpeak arterial enhancement directly from the GRAPPAcoil weights using the methodology of Breuer et al. (17).These maps were used to quantify noise amplificationduring the reconstruction process. Geometry factors

maps for the magnitude subtracted images (Gm) werecomputed by the following relation:

Gm ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiG2

pre þ G2post;

q½2�

where Gpre and Gpost are the geometry factor mapsderived from the GRAPPA coil weights for the precon-trast and postcontrast reconstructions.

Voxels containing low-signal intensity and not resid-ing in the contrast-enhanced vessels, defined as havingless than 10% of the maximum signal intensity in the 3Dvolume, were ignored in our quantitative analysis. Themedian and mean geometry factors of the remaining vox-els located within the contrast-enhanced arterialbranches were computed. Values obtained with complexand magnitude subtraction were compared using pairedt-tests. Statistical tests were performed using commercialsoftware (SPSS, version 17.0; SPSS Inc., Chicago, IL),and a P value of less than 0.05 was considered to indi-cate the presence of a statistically significant difference.

RESULTS

Phantom MR Imaging

Figure 1 shows images of the vascular phantom obtainedwith magnitude and complex subtraction processing forundersampling factors (R) ranging from 1 to 12 (AFrange: 1.86–6.53). Reconstructed images from acquisi-tions with R � 4 (AF � 3.26) demonstrated minimal arti-fact and approached the reconstruction quality of the ref-erence image. Artifacts were observed with bothmethods at large reduction factors (R � 8; AF � 5.25);however, these artifacts were substantially more appa-rent in images obtained using magnitude subtraction.

Figure 2 summarizes the RRSME data between the ref-erence and accelerated scans. RRMSE increased withincreasing AF. For AF less than or equal to the numberof unique receiver coil positions along the phase-encod-ing direction (AF � 3), RRMSE values were small andnearly equivalent for magnitude and complex subtractionschemes. Substantial increase in RRMSE was observedwith both subtraction schemes at AF > 3; however, therate of increase in RRMSE with magnitude subtraction

FIG. 1. Maximum intensity projection images obtained in thephantom study using magnitude subtraction and complex sub-

traction. At small R, magnitude and complex subtraction providesimilar image quality. At large R, artifacts are more pronouncedwith magnitude subtraction. Images are adjusted to the same win-

dow and level settings. R, reduction factor; AF, net accelerationfactor.

FIG. 2. Plots summarizing the relative root mean square error (RRMSE) data for magnitude and complex subtracted images obtained in

the vascular phantom study. a: Plot displaying the RRMSE relative to the reference acquisition for a range of simulated acceleration fac-tors. b: Plot showing the ratio of RRSME for magnitude subtraction versus that for complex subtraction.

Highly Accelerated CE-MRA Using Complex Subtraction 1845

was more than twice that measured with complexsubtraction.

Human MR Imaging

Figure 3 shows time-resolved CE-MRA images of the calfobtained with a modest reduction factor of 2 (AF ¼ 1.77;3.22 seconds per frame; temporal footprint ¼ 12.88 sec).Similar image quality and depiction of arteries wasobtained with magnitude and complex subtractionschemes at this low AF, in agreement with the findingsof the phantom study. Despite the similar appearance ofthe angiograms, geometry factors were larger with magni-tude subtraction.

Figure 4 shows magnitude and complex subtractedimages obtained at the larger reduction factor of 8 (AF ¼4.33; 1.47 seconds per frame; temporal footprint ¼ 5.88sec). Substantially better image quality was obtained

with complex subtraction processing, mainly in the formof reduced background noise and improved vessel con-spicuity. Consistent with the results in Fig. 3, geometryfactor maps were markedly larger with magnitude sub-traction processing than with complex subtractionprocessing.

Figure 5 summarizes the geometry factor data obtainedwith magnitude and complex subtraction at reductionfactors of 2 and 8. Significantly smaller geometry factorswere obtained with complex subtraction at both reduc-tion factors (P < 0.05).

DISCUSSION

CE-MRA performed with large AF can be limited by arti-facts relating to noise amplification during the parallelimaging reconstruction process. The use of large AF,however, may be desirable to improve temporal or

FIG. 3. Time-resolved CE-MRA of the calf in a volunteer obtained using R ¼ 2. Maximum intensity projection (MIP) images obtainedwith (a) magnitude and (b) complex subtraction appear similar and provide excellent depiction of the popliteal, anterior tibial, peroneal,and posterior tibial arteries. Geometry factor images obtained with (c) magnitude and (d) complex subtraction for voxels incorporated

into the MIP images in (a) and (b), respectively. Despite the similar appearance of the MIP images, substantially larger geometry factorsare obtained with magnitude subtraction.

FIG. 4. Time-resolved CE-MRA of the calf in a volunteer obtained using R ¼ 8. Maximum intensity projection (MIP) images obtainedwith (a) magnitude subtraction are severely degraded by noise amplification relating to the use of a large reduction factor. MIP imagesof the (b) complex-subtracted data demonstrate substantially better image quality. Geometry factor images obtained with (c) magnitude

and (d) complex subtraction corresponding to the MIP images in (a) and (b), respectively. Significantly smaller geometry factors areobtained with complex subtraction.

1846 Koktzoglou et al.

spatial resolution during time-resolved or multistationCE-MRA examinations. We showed that CE-MRA per-formed using complex subtraction prior to the parallelimaging reconstruction process, in comparison with mag-nitude subtraction, reduced geometry factors andimproved image quality when large reductions factors(�4) were used.

To our knowledge, this is the first report examiningthe use of complex subtraction processing in relation tomagnitude subtraction processing for improving thequality of highly accelerated CE-MRA. Prior to the rou-tine use of parallel imaging during CE-MRA examina-tions, Huang et al. (18) presented a detailed analysis ofsubtraction schemes during nonaccelerated CE-MRA. Onthe basis of the lower background signal intensity levelsand improved depiction of low contrast vessels providedby magnitude subtraction, they concluded that magni-tude subtraction processing was preferred to complexsubtraction for high-resolution 3D CE-MRA acquisitions.Consistent with the findings of a prior report (19), theauthors also concluded that complex subtraction proc-essing was preferred to magnitude subtraction for reduc-ing partial volume averaging effects during lower resolu-tion of 3D- or 2D-projective CE-MRA.

The improved reconstruction quality provided by com-plex difference processing in combination with GRAPPAreconstruction likely relates to the reduced signal inten-sity as well as the spatial sparsity of undersampled data.Huang et al. (11) reported that GRAPPA reconstructionquality of nonvascular images can be substantiallyimproved by reducing the support of the image, wheresupport corresponds to the proportion of pixels bearingsignal above that found in background air. In that work,background signals defined by low-spatial frequencieswere suppressed by high-pass filtering of k-space priorto the GRAPPA reconstruction process, with low-spatialfrequencies later incorporated into k-space to obtain the

final reconstructed image. Although different, subtrac-tion of complex CE-MRA data can similarly be regardedas a form of high-pass filtering where low-spatial fre-quencies describing static background signal are sup-pressed and high frequencies describing the contrast-enhanced vasculature are retained.

In this work, a large 1D undersampling factor of 8combined with complex subtraction processing was usedto improve the temporal resolution during time-resolvedMRA. Rather than improving temporal resolution, a largeundersampling factor could instead be used to improvespatial resolution, which could be preferred in otherapplications, such as in the detection of microvessels orsmall enhancing tumors. Assuming that the receiver coildesign is sufficient, the use of larger 1D undersamplingfactors or parallel imaging in the slice-encoding directioncoupled with complex subtraction may provide for addi-tional levels of acceleration over and above the resultsshown here. Although the difference between the per-formance of complex and magnitude subtraction was notevaluated, Haider et al. (20) reported on the feasibility of2D parallel imaging during CE-MRA with an undersam-pling factor of 8 (4 phase encoding � 2 slice encoding)using specialized surface coils. Such highly acceleratedCE-MRA may provide the additional benefit of amplify-ing vascular signal due to the sampling of a larger pro-portion of k-space when the concentration of contrastmaterial within the blood pool is maximal (21).

With complex subtraction CE-MRA, there is no loss ofinformation because one can always generate the imagesets associated with conventional CE-MRA. Even thoughCE-MRA performed with complex subtraction appears tobe highly advantageous only when large parallel imagingAF are used, the method can also be used with smallerAF (<4) simply to reduce the computational burden ofthe image reconstruction process. Complex subtractionprocessing entails only one calculation of the GRAPPAcoil weights for every reconstructed slice, whereas mag-nitude subtraction requires two calculations. Of note,subtraction of complex coil-by-coil data after theGRAPPA reconstruction provided substantially worseimage quality than complex subtraction prior to theGRAPPA reconstruction (data not shown). This observa-tion results from the subtraction of k-space data con-structed from two different sets of coil weights, whichamplifies artifact in the final reconstructed images.

This study had limitations. First, the study was lim-ited to normal volunteers. Further investigation wouldbe useful to determine whether our findings in normalvolunteers translate to patients with disease. Nonethe-less, given the consistent results of our study, we expectthe improved performance of complex subtraction proc-essing at large AF to hold true. Another limitation of ourstudy was that parallel imaging was limited to one direc-tion. With the growing use of 2D parallel imaging meth-ods that support larger AF with reduced artifact relativeto 1D parallel imaging, the relative benefit of complexversus magnitude subtraction in this setting is importantand should be investigated. Based on the concept ofimage support (11), one should expect the benefit ofcomplex subtraction would extend to the second dimen-sion of parallel acceleration.

FIG. 5. Plot summarizing the mean and median geometry factorsobtained in the volunteer studies with time-resolved CE-MRA

using reduction factors of 2 and 8. Significantly smaller geometryfactors were obtained with complex subtraction for all compari-sons (*P < 0.05; **P < 0.01).

Highly Accelerated CE-MRA Using Complex Subtraction 1847

Interestingly, the key findings of this study are notlimited to highly accelerated CE-MRA. Complex subtrac-tion processing should also serve to improved imagequality during highly accelerated dynamic CE-MRIexaminations, as long as the images exhibit reduced sup-port. Furthermore, our findings have important implica-tions for nonenhanced MR angiography techniques thatuse subtraction to completely suppress background sig-nal, such as arterial spin labeling (22) and fresh bloodimaging (23). In this setting, larger AF made possiblewith the use of complex subtraction could be used toshorten the echo train length and thereby reduce the sus-ceptibility of these techniques to artifacts such as blur-ring and signal loss.

In conclusion, CE-MRA using complex subtractionprocessing prior to GRAPPA reconstruction reduces ge-ometry factors and better supports the use of large AFthan CE-MRA based on magnitude subtraction. The ben-efits of CE-MRA with complex relative to magnitude sub-traction increase with larger parallel imaging AF. Futurework will seek to quantify the benefits of complex sub-traction in other applications such as highly accelerateddynamic CE-MRI and nonenhanced MRA.

REFERENCES

1. Prince MR, Narasimham DL, Stanley JC, Chenevert TL, Williams

DM, Marx MV, Cho KJ. Breath-hold gadolinium-enhanced MR angi-

ography of the abdominal aorta and its major branches. Radiology

1995;197:785–792.

2. Hany TF, Debatin JF, Leung DA, Pfammatter T. Evaluation of the aor-

toiliac and renal arteries: comparison of breath-hold, contrast-

enhanced, three-dimensional MR angiography with conventional

catheter angiography. Radiology 1997;204:357–362.

3. Neimatallah MA, Ho VB, Dong Q, Williams D, Patel S, Song JH,

Prince MR. Gadolinium-enhanced 3D magnetic resonance angiogra-

phy of the thoracic vessels. J Magn Reson Imaging 1999;10:758–770.

4. Fain SB, King BF, Breen JF, Kruger DG, Riederer SJ. High-spatial-re-

solution contrast-enhanced MR angiography of the renal arteries: a

prospective comparison with digital subtraction angiography. Radiol-

ogy 2001;218:481–490.

5. Oudkerk M, van Beek EJ, Wielopolski P, van Ooijen PM, Brouwers-

Kuyper EM, Bongaerts AH, Berghout A. Comparison of contrast-

enhanced magnetic resonance angiography and conventional pulmo-

nary angiography for the diagnosis of pulmonary embolism: a pro-

spective study. Lancet 2002;359:1643–1647.

6. Yamashita Y, Mitsuzaki K, Ogata I, Takahashi M, Hiai Y. Three-

dimensional high-resolution dynamic contrast-enhanced MR angiog-

raphy of the pelvis and lower extremities with use of a phased array

coil and subtraction: diagnostic accuracy. J Magn Reson Imaging

1998;8:1066–1072.

7. Adamis MK, Li W, Wielopolski PA, Kim D, Sax EJ, Kent KC, Edel-

man RR. Dynamic contrast-enhanced subtraction MR angiography of

the lower extremities: initial evaluation with a multisection two-

dimensional time-of-flight sequence. Radiology 1995;196:689–695.

8. Ho KY, de Haan MW, Kessels AG, Kitslaar PJ, van Engelshoven JM.

Peripheral vascular tree stenoses: detection with subtracted and non-

subtracted MR angiography. Radiology 1998;206:673–681.

9. Cho ZH, Kim HS, Song HB, Cumming J. Fourier transform nuclear

magnetic resonance tomographic imaging. Proc IEEE 1982;70:

1152–1173.

10. Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P. SENSE: sen-

sitivity encoding for fast MRI. Magn Reson Med 1999;42:952–962.

11. Huang F, Li Y, Vijayakumar S, Hertel S, Duensing GR. High-pass

GRAPPA: an image support reduction technique for improved par-

tially parallel imaging. Magn Reson Med 2008;59:642–649.

12. Griswold MA, Jakob PM, Heidemann RM, Nittka M, Jellus V, Wang J,

Kiefer B, Haase A. Generalized autocalibrating partially parallel

acquisitions (GRAPPA). Magn Reson Med 2002;47:1202–1210.

13. Sasaki M, Shibata E, Kanbara Y, Ehara S. Enhancement effects and

relaxivities of gadolinium-DTPA at 1.5 versus 3 Tesla: a phantom

study. Magn Reson Med Sci 2005;4:145–149.

14. Roemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM. The

NMR phased array. Magn Reson Med 1990;16:192–225.

15. Wang Z, Fernandez-Seara MA. 2D partially parallel imaging with k-

space surrounding neighbors-based data reconstruction. Magn Reson

Med 2006;56:1389–1396.

16. Lim RP, Shapiro M, Wang EY, Law M, Babb JS, Rueff LE, Jacob JS,

Kim S, Carson RH, Mulholland TP, Laub G, Hecht EM. 3D time-

resolved MR angiography (MRA) of the carotid arteries with time-

resolved imaging with stochastic trajectories: comparison with 3D

contrast-enhanced Bolus-Chase MRA and 3D time-of-flight MRA.

AJNR Am J Neuroradiol 2008;29:1847–1854.

17. Breuer FA, Kannengiesser SA, Blaimer M, Seiberlich N, Jakob PM,

Griswold MA. General formulation for quantitative G-factor calcula-

tion in GRAPPA reconstructions. Magn Reson Med 2009;62:739–746.

18. Huang Y, Webster CA, Wright GA. Analysis of subtraction methods

in three-dimensional contrast-enhanced peripheral MR angiography.

J Magn Reson Imaging 2002;15:541–550.

19. Wang Y, Johnston DL, Breen JF, Huston J, III, Jack CR, Julsrud PR,

Kiely MJ, King BF, Riederer SL, Ehman RL. Dynamic MR digital sub-

traction angiography using contrast enhancement, fast data acquisi-

tion, and complex subtraction. Magn Reson Med 1996;36:551–556.

20. Haider CR, Glockner JF, Stanson AW, Riederer SJ. Peripheral vascu-

lature: high-temporal- and high-spatial-resolution three-dimensional

contrast-enhanced MR angiography. Radiology 2009;253:831–843.

21. Riederer SJ, Hu HH, Kruger DG, Haider CR, Campeau NG, Huston J,

III. Intrinsic signal amplification in the application of 2D SENSE par-

allel imaging to 3D contrast-enhanced elliptical centric MRA and

MRV. Magn Reson Med 2007;58:855–864.

22. Edelman RR, Siewert B, Adamis M, Gaa J, Laub G, Wielopolski P.

Signal targeting with alternating radiofrequency (STAR) sequences:

application to MR angiography. Magn Reson Med 1994;31:233–238.

23. Miyazaki M, Takai H, Sugiura S, Wada H, Kuwahara R, Urata J. Periph-

eral MR angiography: separation of arteries from veins with flow-spoiled

gradient pulses in electrocardiography-triggered three-dimensional half-

Fourier fast spin-echo imaging. Radiology 2003;227:890–896.

1848 Koktzoglou et al.