In Vivo Method for Correcting Transmit/ReceiveNonuniformities with Phased Array Coils

Jinghua Wang,1* Maolin Qiu,1 and R. Todd Constable1,2,3

Phased array coils are finding widespread applications in boththe research and the clinical setting. However, intensity non-uniformities with such coils can reduce the potential benefits ofthese coils, particularly for applications such as tissue segmen-tation. In this work, a method is described for correcting thenonuniform signal response based on in vivo measures of boththe transmission field of body coil and the reception sensitivityof phased array coils, separately. For a uniform phantom, thereception sensitivity can be calculated using both Bloch equa-tions and transmission field maps. For a heterogeneous objectsuch as a brain, a minimal contrast acquisition must be ob-tained to map the receiver nonuniformities. This transmit field/receiver sensitivity (TFRS) approach is compared with the stan-dard methods of using the body coil to obtain a reference scanand low-pass filtering. The quantitative comparison resultsshows that the TFRS approach provides superior results incorrecting intensity nonuniformities for a uniform phantom.This approach reduces the ratio between signal intensity SD ofan image and its mean intensity from approximately 21% beforecorrection to 13% after correction. Results are also showndemonstrating the utility of this approach in vivo with humanbrain images. The method is general and can be applied withmost pulse sequences, any coil combination for transmissionand reception, and in any anatomic region. Magn Reson Med53:666–674, 2005. © 2005 Wiley-Liss, Inc.

Key words: RF inhomogeneity; phased array coils; high fieldMRI; quantitative MRI; sensitivity

Phased array coils are becoming widely available in anumber of applications not only because they can increasethe signal-to-noise (SNR), but also because parallel acqui-sition techniques based on the phased array coils canimprove the spatial and temporal resolution of magneticresonance imaging (MRI) or reduce the susceptibility-in-duced artifacts in echo planar imaging (EPI) (1–7). A po-tential drawback to using such coils, however, is thegreater intensity nonuniformity, relative to a volume coil.Images acquired using phased array coils include inhomo-geneous signal intensities (SI) resulting from the intrinsicconfiguration of the coils (2,8,9). Additionally, with theincreasing field strength, other sources of intensity varia-tions become bigger, including gradient-driven eddy cur-

rents, wave behavior, radio-frequency (RF) penetration ef-fects, and the interaction of the RF with the electromag-netic properties of the loaded tissues. These sources do notcome from the imperfect hardware configuration, but fromthe intrinsic electromagnetic properties of the object im-aged. The intensity nonuniformities that result can beparticularly troublesome for applications involving imagesegmentation or other quantitative analyses, such as flowquantification, and statistical clustering tasks (10). Thecorrection of these signal intensity nonuniformities there-fore is important in order to fully realize the benefits ofphased array coils.

A number of approaches have been developed to correctthe spatial nonuniformity of a coil’s response includingpostprocessing methods (11–17) and RF field mappingapproaches (18–21). The sensitivity profile of a phasedarray coil generally can be removed through filtering,based on the assumption that the spatial nonuniformitiesvary smoothly. Such low-pass filtering approaches are at-tractive because they do not require any information oncoil geometry or tissue content. For this same reason,however, they only provide a rough correction of the in-tensity nonuniformity. These methods can incorporateprior knowledge of the anatomy and/or the coil configura-tion in order to determine the characteristics of the filter,and with such information performance can be improved.In general, however, low-pass filtering methods lead toartifacts near the air–tissue interfaces or interfaces be-tween different tissues, which can be problematic if theapplication involves tissue segmentation.

Phased array coils are typically receive-only coils andthe body coil, which is usually a birdcage coil, is used forRF transmission. In order to correct signal intensity vari-ations caused by the phased array coils, a reference imageis obtained using the body coil for both transmission andreception. The intensity correction matrix can then beobtained by taking the ratio of the body coil/body coilacquisition and the body coil/phased array coil acquisi-tions. This correction matrix is then applied to subsequentacquisitions obtained with the phased array coils. Thisapproach is based on the assumption that the sensitivityprofile of the body coil is uniform. In practice, the sensi-tivity profile of the body coil is inhomogeneous for objectswith high dielectric constants (such as human tissues) atstatic field strengths of above 1.5 T. A number of experi-ments have indicated over 30% signal variations withbirdcage coils caused by both an inhomogeneous transmis-sion field and an inhomogeneous receiver sensitivity pro-file at field strength of more than 3.0 T (22–25). The result-ing intensity nonuniformities increase with increasingstatic field strength.

This work demonstrates a simple method for separatelycorrecting the signal intensity variations arising from the

1Department of Diagnostic Radiology, Yale University School Medical Center,The Anlyan Center, New Haven, Connecticut.2Department of Biomedical Engineering, Yale University; New Haven, Con-necticut.3Department of Neurosurgery, Yale University School of Medicine, New Ha-ven, Connecticut.Grant sponsor: NIH; Grant numbers: NS40497, NS38467, EB00473.*Correspondence to: Jinghua Wang; Department of Diagnostic Radiology,Yale University, 300 Cedar Street, CAB-MRRC, New Haven, CT 06510.E-mail: Jinghua.wang@yale.eduReceived 13 April 2004; revised 1 September 2004; accepted 5 October2004.DOI 10.1002/mrm.20377Published online in Wiley InterScience (www.interscience.wiley.com).

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© 2005 Wiley-Liss, Inc. 666

transmission profile of the body coil and the receptionsensitivity profile of the phased array coil in MR experi-ments in vivo. The transmission field mapping for thebody coil and the reception sensitivity mapping of aneight-element phased array coil is performed using a spinecho segmented-EPI sequence. A homogeneous phantomis used to compare this new approach with the body coilreference image, as well as low-pass filtering approaches.Results are shown indicating that this technique for mea-suring the transmitted field and reception sensitivity mapsin vivo can allow for the correction of a number of pulsesequences with different flip angles and variable acquisi-tion parameters.

PRINCIPLES AND METHODS

Transmission Field

For a spin echo (SE) sequence with excitation flip angle�(x) and refocusing flip angle �(x), the signal intensity fornoninteracting spins without transverse coherence, andassuming that the repetition time TR �� longitudinal re-laxation time T1, can be written as follows (27,28),

SI�x� � C�x� � T�x� � S�x� � C�x� � sin ��x� � sin2��x�

2� S�x�,

[1]

where T(x) and S(x) are the transmission profile of thebody coil and the sensitivity profiles of body coil orphased array coils at the position x, respectively. Theparameter C(x) does not rely on the RF excitation field andreceiver sensitivity profile, but depends on the propertiesof tissue (proton density PD, longitudinal relaxation timeT1, and transverse relaxation time T2) and measurementparameters (echo time TE, flip angle, and TR).

If �(x) � 2�(x) for conventional SE, the signal intensitycan be written as

SI�x� � C�x� � S�x� � sin3 ��x�. [2]

To measure the transmission field and the reception fielddistribution, two SE images are acquired with differentexcitation flip angles such that �2(x) � 2�1(x) while main-taining the other imaging parameters identical. The ratio ofthe two images is given by

� �SI2�x�

SI1�x��

sin3 �2�x�

sin3 �1�x�. [3]

The transmitted field is then calculated by (18)

B1� �

1

� arccos��/8�1/3. [4]

where is the magnetogyric ratio, � is the ratio of signalintensities of two spin echo images with identical imageparameters (TE, TR), is the duration of the RF pulse, andB1

� is a positive circularly polarized component of the RFfield B1, which rotates in the same direction as nuclearspins precess.

Reception Sensitivity

For a homogeneous phantom, the reception sensitivity canbe directly expressed as

Sphased�x� � SIphased�x�/�C�x� � Tphased�x��, [5]

where Tphased(x) is the transmission function that is cal-culated by Bloch equation with transmission field B1

� andthe duration time when the minimal contrast images at theflip angle of 90o are acquired with a body coil for transmitand phased array coils for receive. SIphased(x) is the signalintensity of the image obtained using the body coil fortransmission and the phased array coil for reception. Be-cause most of objects are heterogeneous, this equationcannot be used directly to determine the reception sensi-tivity. Signal intensity differences between tissues includenot only the contribution of RF inhomogeneities from thetransmit RF coil and receive RF coil, but also the contri-bution of tissue characteristics (T1, T2, and PD). In order tocorrect the intensity nonuniformities arising from RF non-uniformities, the contributions from the coils and the tis-sues must be separated. With the appropriate choice of TEand TR, it is possible to collect an image with minimaltissue contrast (for up to three tissues), thereby allowingthe reception sensitivity of the coils to be estimated usingEq. [5].

For conventional SE and GE sequences with the flipangle of 90o, the signal intensity of tissue i can be derivedby

SIi � �i�1 � exp � �TR/Tli�� � exp � �TE/T2i�, [6]

where T1i and T2i are T1 and T2 of tissue i, respectively,and SIi is the signal intensity of tissue i. Further, thecontrast Cij between tissues i and j can be given by

Cij � ��i � �1 � exp � �TR/T1i�� � exp � �TE/T2i�

� �j � �1 � exp � �TR/T1j�� � exp � �TE/T2j��, [7]

where the parameters T1, T2, and PD of tissue j are T1j, T2j,and �j, respectively, and the parameter �i is PD of tissue i.If the ROI includes three tissues, the optimized TE and TRcan be derived for the condition of zero contrast amongthese tissues because the number of the unknown param-eters (TE, TR) is equal to the number of the unrelatedequations. For three tissue types, Eq. [7] includes threeterms. If there are more than three tissues, TE and TR canbe chosen to minimize the contrast among all tissues usingthe Levenberg–Marquardt method (29). In the brain, thecontrast between the primary tissues of interest (gray mat-ter (GM), white matter (WM) and cerebrospinal fluid(CSF)) can be minimized by the careful selection of TE andTR, based on the T1, T2, and relative proton density of GM,WM, and CSF at the nominal flip angle of 90o.

Correction Matrix

Three methods are now briefly described for determiningthe correction matrix and these include the new approachproposed in this work referred to as the transmit field/

Nonuniformity Correction with Phased Array Coils 667

receive sensitivity (TFRS) method, to be compared withthe body coil method, and the low-pass filtering method.

TFRS Method

The TFRS method is based on the transmission field andreception sensitivity maps from Eqs. [4] and [5]. The cor-rection of its signal intensity is given by

SIcorrected�x� � SIphased�x�/�Sphased�x� � Tmeasured�x��, [8]

where Tmeasured(x) is a transmission function which iscalculated by Bloch equation with transmission field B1

�.Then the corrected images can be determined using Eq [8](30).

Body Coil Method

The transmitted field and reception sensitivity maps of thebody coil are assumed to be uniform and signal variationsdue to the body coil are ignored. The reception sensitivityof phased array coils is given by

SIcorrected�x� � SIphased�x�/Sphased�x�, [9]

where Sphased( x) � SIphased( x)/SIbody( x), SIbody(x) is thesignal intensity of the image obtained using the body coilfor both transmission and reception. The two images areacquired using identical imaging parameters and se-quences. This approach relies on the assumption that thesignal intensity nonuniformities of the images to be cor-rected are only dependent upon the reception sensitivity.

Low-Pass Filter Method

Based on the assumption that the intensity nonuniformityis slowly varying spatially, the low-frequency componentscan be filtered and the corrected image is given by

SIcorrected�x� � SIphased�x�/SIsmooth�x�, [10]

where SIsmooth( x)�SIphased( x) V G( x). G(x) is a three-di-mensional low-pass filter. V is a convolution operator.This approach is highly efficient and can correct for allslowly varying signal changes independent of the sourceof the changes.

METHODS

When conventional imaging techniques are used to obtainthe transmission field and reception sensitivity maps forcorrecting the intensity nonuniformity, the extended scantime of the method makes it impractical for routine use.Thus, fast acquisition methods are needed for such mea-surements. Fast acquisition sequences, such as EPI andturbo SE sequences, can be employed to reduce scannertimes, although the latter approach can be constrained byspecific absorption rate (SAR) issues, particularly withhigh-field multislice acquisitions. In this work, a seg-mented SE-EPI sequence is used to acquire these maps. Asegmented sequence is used because it reduces the imagedistortion artifacts that are such a problem in single-shot

EPI acquisitions. It should be noted that only low-resolu-tion maps of the transmission field and reception sensitiv-ity need to be obtained and these can then be interpolatedto correct high-resolution images, since the intensity var-ies slowly and smoothly in MR images.

All images were obtained on a Siemens 3.0-T Trio sys-tem with a body coil and an eight-channel phased arrayreceive coil. A Siemens phantom, with a cylinder (15 cmdiameter, 36 cm length) filled with distilled water and1.24 g/liter of NiSO4 and 2.62 g/liter of NaCl, was em-ployed to evaluate the methods for correcting signal non-uniformities. The axial images of the phantom with bodycoil transmission and reception were obtained using twosegmented SE-EPI sequences with excitation flip angles of60 and120o and refocusing flip angles of 120 and 240o, atTR/TE � 4000/15 ms, FOV 200 200 mm2, matrix 128 128, slice thickness of 5 mm, bandwidth 752 Hz/pixel, and7 shots. The transmission field map of the body coil iscalculated using these two images according to Eqs. [3]and [4]. A third image is acquired using the body coil fortransmission and the phased array coils for reception withan excitation flip angle of 90o and refocusing flip angle of180o, and the remaining parameters were identical to thosein transmission field map acquisition. The total time foreach image is about 1.24 min. The reception sensitivitymap of the phased array coil is calculated using the trans-mission field map and the third image using Eq. [5].

A range of axial phantom images were obtained usingdifferent flip angles and conventional sequences (SE andGE sequences) at TR/TE � 6000/15 ms, FOV 200 200 mm2, matrix 256 256, slice thickness of 5 mm,bandwidth 130 Hz/pixel, in order to evaluate the correc-tion method across a variety of imaging parameters. Fourimages were acquired using a conventional GE sequencewith flip angles of 10, 30, 60, and 90o, and another fourimages were acquired using a conventional SE sequencewith excitation flip angles of 50, 80, 90, and 110o and withrefocusing flip angles double the excitation flip angles ineach case. Long TR was used to assure that saturationeffects did not influence the signal intensity, while shortTE was used to provide high SNR.

Three multislice brain images were acquired with thefollowing imaging parameters: FOV 240 180 mm2; ma-trix 128 96; slice thickness of 4 mm; distance betweenslices 2 mm; number of slices 18; bandwidth 752 Hz/pixel;with 7 shots; excitation flip angle 60, 90, and 120o andrefocusing flip angle120, 180, and 240o, respectively. TR/TEs are 2500/16 for the excitation field map and 2000/16 ms for the minimal contrast image (where contrast wasminimized among CSF, GM, and WM). Total acquisitiontime for the transmission field mapping of the body coiland the reception sensitivity mapping of the phased arraycoil was 102 s. To test the correction schemes, in vivoimages to be corrected were obtained using a multisliceinversion recovery turbo spin echo sequence: FOV 240 180 mm2; matrix 256 256; slice thickness 2 mm; dis-tance between slices 2 mm; number of slices 36; band-width 130 Hz/pixel; turbo factor 7; TI 1380 ms; TR7750 ms; TE 12 ms; exciting flip angle 90o, and refocusingflip angle 150o. Total acquisition time for these multisliceimages was 7 min and 23 s.

668 Wang et al.

RESULTS

The transmission field map of the body coil and the recep-tion sensitivity map of phased array coil for a homoge-neous phantom were calculated using the three imagesacquired by segmented spin echo sequences, and these areshown in Fig. 1a and b. Equation [2] shows that the sin3�flip angle dependence of signal intensity for �(x) � 2�(x)makes the B1

� mapping very sensitive to small changes inthe B1 field for spin echoes. The curve of sin3� indicatesthat a maximum slope is obtained at 60 and 120o, therebyensuring that the B1

� map is sensitive to small changes inthe B1 field. Therefore, using two spin echo sequences,with excitation and refocusing flip angles of 60/120o and120/240o, respectively, the B1

� distribution can be deter-mined (20). In order to quantify the homogeneity of animage, we introduce the parameter ��SD/mean 100,where the mean is the averaged signal intensity of image,and SD is a standard deviation of the averaged signalintensity. With complete intensity uniformity the SD andtherefore � would be the inverse of the image signal-to-noise ratio. In the case of the phantom, � of the transmittedfield map of the body coil is 14.7%, and � of the receptionsensitivity map for phased array coil is 15.7%. The SInonuniformities in the images obtained with this hard-ware then clearly result from not only the reception sen-sitivity profile of the phased array coil, but also the trans-mission profile of the body coil. Although the contributionof body coil transmission to signal nonuniformities issmaller than the contribution of phased array coils’ recep-tion at fields below 1.5 T, the former can be comparable to,or larger than, the latter at higher fields, such as 3.0 T.Thus, the contribution of the transmission profile cannotbe ignored. For this same reason, if the body coil is used as

a reference for correcting the signal nonuniformities withphased array data at high field, a significant error can arisesince such a calculation assumes a uniform transmissionprofile.

The signal intensity can be corrected using Eq. [8], basedon the calculated transmitted field and reception sensitiv-ity maps in Fig. 1. The original gradient echo image withthe flip angle of 60o, shown in Fig. 2a, and the imagescorrected using the body coil method, low-pass filtermethod, and field map method, are shown in Fig. 2b–d,respectively. Images obtained using the spin echo se-quence with excitation flip angle of 90o and refocusing flipangle of 180o are shown in Fig. 2e, and the images cor-rected by the various methods are shown in Fig. 2f–h,respectively. In the original images (Fig. 2a and e), signif-icant signal intensity nonuniformities are observed. Thebody coil method, Fig. 2b and f, is not very effective due tothe contribution of both the transmission field and thereception sensitivity errors. The low-pass filter correctsintensity nonuniformities very well in the center of phan-tom, but gives rise to the artifacts at the boundary of thephantom (Fig. 2c and g). In Fig. 2d and h, the field map-ping method corrects the intensity nonuniformitiesthroughout the image and does not lead to artifacts at theboundary of the phantom.

Quantitative comparisons of these methods are providedin the histograms shown in Fig. 3 and Table 1. Both thehistograms and � indicate that the uncorrected images aremore homogeneous than the images corrected using thebody coil reference method. The averaged � for the uncor-rected images increases from approximately 22 to 35%after correction using the body coil reference approach.While this technique has been shown to be effective at 1.5

FIG. 1. Calculated transmission field map for thebody coil (a) and the reception sensitivity map forthe phased array coil (b).

FIG. 2. Original phantom image acquiredusing a gradient echo sequence (a) with aflip angle of 60o and a spin echo sequence(e) with excitation flip angle of 90o. Cor-rected images using body coil method (b, f),low-pass filter method (c, g), and the fieldmap method (d, h), respectively.

Nonuniformity Correction with Phased Array Coils 669

T clearly it is not appropriate at higher field strengths. Thelow-pass filtering method improves the intensity unifor-mity tremendously for a uniform phantom such as thatused here. The averaged � for various images decreasesfrom around 21% in the uncorrected images to below 14%in the images corrected by this method, shown in Table 1.For the gradient echo acquisitions, GE-60 and GE-90, thelow-pass filter corrected images, display more nonunifor-mity than the original images. In all cases, the field mapmethod significantly improves the uniformity of signalintensity. The averaged � for various images is reduced

from around 20% before correction to about 10% in thecorrected images, as summarized in Table 1. In the phan-tom results, both the low-pass filter approach and theTRFS approach the residual value of �, primarily reflectingSNR and not transmit or receive inhomogeneity effects.The results shown in Fig. 3 and Table 1 also indicate thatthe TFRS approach is more effective for gradient echoimages obtained with small flip angles relative to thoseobtained with large flip angles. The reason for this is likelythat the difference between the nominal prescribed flipangle and true flip angle increases with increasing flip

FIG. 3. Histograms of the imagesacquired using both conventionalGE acquisitions with flip angles of10o (a), 30o (b), 60o (c), and 90o (d)and conventional SE acquisitionswith excitation flip angles of 50o

(e), 80o (f), 90o (g), and 110o (h).Each panel includes the histo-grams of the uncorrected andcorrected images after applica-tion of the body coil reference,low-pass filter, and transmit field/reception sensitivity mappingapproaches.

670 Wang et al.

angle, because the deviation from a linear relationshipbetween flip angle and B1

� becomes larger with the increas-ing angles (18). This is also supported by the fact that thespin echo images do not exhibit this effect.

The field map method is easily applied for objects suchas a uniform phantom, but it is also important to be able tocorrect in vivo images. Since most objects imaged in vivoare nonuniform (having different tissues with differentsignal intensities), it is essential that data be obtained withcontrast minimized to obtain accurate reception sensitiv-ity maps. Based on the characteristic parameters of braintissues (such as averaged proton density, T1, and T2 ofbrain tissues) at 3.0 T, the contrast among CSF, GM, andWM can be minimized at TE and TR of 16 and 2000 ms,respectively. With a TE of 16 ms and TR of 2000 ms, theimages of a normal volunteer obtained with the body coilfor both transmission and reception were acquired using asegmented spin echo EPI sequence with the different flipangles and a matrix of 128 96, shown in Fig. 4a and b.The minimal contrast image in Fig. 4c was acquired withthe body coil transmission and phased array coil forreception, using the same acquisition parameters as theformer two images and with an excitation flip angle of90° at TR/TE � 2000/16 ms. The contrast among cerebraltissues (CSF, WM, and GM) is minimal through theskull, although residual fat signal does show some con-trast. From these three images the transmission field

map of the body coil and reception sensitivity map ofphased array coil can be calculated using Eqs. [4] and[5], respectively, and the results are shown in Fig. 4dand e. Because the transmission field map is calculatedby the ratio of the two images with identical acquisitionparameters, the measured homogeneity is not affectedby variations in tissue relaxation properties observed indifferent parts of the brain. But the reception sensitivitymap shown in Fig. 4e is calculated using both the trans-mit field map in Fig. 4d and the minimal contrast imagein Fig. 4c. The homogeneity of the reception sensitivitycan be influenced by residual tissue contrast. However,the contribution of residual tissue contrast to the recep-tion sensitivity is comparable with the SNR and can beneglected. Alternatively, applying the low-pass filter ap-proach to the reception sensitivity map prior to calcu-lation of the correction image can help to remove anyresidual tissue contrast.

Figure 5 shows in vivo results for images (a,e) acquiredwith conventional spin echo and gradient echo sequence,when corrected using the body coil method (b,f), the low-pass filter method (c,g), and the TFRS method (d,h), respec-tively. The original images display high signal intensity inthe posterior regions of the brain primarily reflecting coilsensitivity. The primary limitation of the body coil method ispoor SNR, due to the poor SNR in the reference imagesobtained while using the body coil for reception. The low-pass filter method does an excellent job of improving signaluniformity, as shown in Fig. 5c and g, but can lead to someedge enhancement at high contrast boundaries particularly atthe edge of the brain. The proposed TFRS method improvesthe signal uniformity without these edge effects, as shown inFig. 5d and h. The in vivo results demonstrate the power ofthe TFRS method for correcting transmit and receiver non-uniformities in vivo.

High-resolution multislice brain images acquired using aninversion recovery SE sequence are shown in Fig. 6a–f. Thecorresponding images shown in Fig. 6g–l were correctedusing the TFRS method. Because the minimal contrast imagedoes not minimize contrast of the residual signal in the skull,the skulls were stripped prior to correction in this example.The corrected images exhibit better contrast among CSF,WM, and GM and a more homogenous distribution of inten-sities within each tissue group, relative to the uncorrectedimages. This example demonstrates that high-resolution ac-quisitions, including 3D acquisitions, can be corrected usingthis fast TFRS approach.

Table 1� of the Uncorrected and Corrected Phantom Images using theBody Coil (BC) Method, Low-Pass Filter Method, and theTransmit Field/Receive Sensitivity (TFRS) Mapping Method for theDifferent Flip Angles

�(original)

�(BC method)

�(low-pass)

�(our method)

SE-50 35.8 51.8 12.1 9.3SE-80 23.2 36.8 11.5 9.9SE-90 19.4 32.3 9.7 8.2SE-110 18.9 19.4 10.1 9.8GE-10 21.1 35.7 10.3 8.0GE-30 22.1 34.8 15.0 11.6GE-60 21.0 31.8 18.4 13.0GE-90 19.1 25.4 20.8 13.3

Note. GE-10, GE-30, GE-60, and GE-90 were acquired using agradient echo sequence with flip angles of 10, 30, 60, and 90°,respectively. SE-50, SE-80, SE-90, and SE-110 reflects similar no-menclature for spin echo acquisitions with the excitation flip angles50, 80, 90, and 110°, where the corresponding refocusing flip angleswere double the excitation flip angles.

FIG. 4. Spin echo images of a volunteer acquired with minimal contrast and excitation flip angles of 60o (a), 120o (b) using the body coilas a receiver, and with the same parameters, using the phased array coils (c) for reception. The window has been narrowed to emphasizethe residual contrast differences, which are actually quite small. Calculated transmission field (d) and reception sensitivity (e) maps.

Nonuniformity Correction with Phased Array Coils 671

DISCUSSION

Intensity nonuniformities arise from inhomogeneities inboth the transmission and the reception fields. Correctionmethods that rely on the acquisition of a body coil refer-ence image assume a homogeneous transmission profile,which holds for low field (1.5 T or less), but not high fieldimaging (31). The body coil reference image approach alsoassumes that interactions between the body coil or phasedarray coils and the object are the same. At low field thisassumption is valid and the wave behavior and interac-tions between the object and the coil are small, while athigh field strength they become strong. For example, thesize of the phantom used in these studies, 15 cm diameter,is comparable to the wavelength of the RF in this phantom,about 24 cm, at 3.0 T. As a result, the coherent addition ofelectromagnetic waves gives a maximal signal intensity atthe center of phantom when the body coil is used fortransmission as shown in Fig. 1b, and the intensity nonuniformity of the transmit field across the phantom is up to18%. As MR moves to imaging at higher field strengths itis important to develop methods to measure and correctfor both transmission field and reception sensitivity pro-files in vivo.

The low-pass filter method has the advantage of notrequiring any extra image acquisitions to correct intensity

variations. Since the correction with a low-pass filter doesnot need to take into account coil geometry and tissuecontent, this method is attractive for its simplicity, and itprovides excellent correction of intensity nonuniformitiesin most cases. However, the low-pass filter approach doesrisk losing information on true low spatial frequency sig-nal variations as it removes all such variations indepen-dent of their source. At small window sizes, the tissuecontrast characteristics can be lost which is undesirable.With larger window sizes, the correction is less effective(in the limit if the window equals the whole image, nocorrection at all would be performed). In most applicationsa window size of (20–40) voxels can be used (assuming at256 256 image matrix size), and this serves to removemost of the intensity variations without a significant effecton tissue contrast (32). For the phantom studies presented,the filter bandwidth used was that which has previouslybeen shown to be applicable to brain images (14), since theultimate goal was to correct signal nonuniformities invivo. It is very difficult to set a fixed filter bandwidth as theoptimal bandwidth changes with subject and the anatomyof interest. Thus, care must be exercised in application ofthe low-pass filter method as the assumption of clear sep-aration of wanted and unwanted spatial frequency inten-sity variations does not always hold (33).

FIG. 5. Comparison showing original spinecho (a) and gradient echo images (e) ofhuman brain corrected using the body coilmethod (b, f), the low-pass filter method (c,g), and the TFRS method (d, h), respec-tively.

FIG. 6. The uncorrected multislice brain images acquired using an inversion recovery turbo spin echo sequence (a–f) and theircorresponding corrected images (g–l) with the TFRS method.

672 Wang et al.

The TFRS technique presented here, where the effect ofboth the transmission and the reception profiles are con-sidered, is robust, effective for all images, and not con-strained to particular levels of anatomic detail. The calcu-lated transmission field map of the body coil is indepen-dent of the tissue parameters such as relaxation time andproton density. The reception sensitivity map, on the otherhand, is calculated using a minimal contrast image at thegiven acquisition parameters and the field map. The con-trast among tissues cannot be eliminated completely be-cause even in the same tissue relaxation parameters varysomewhat, and the contrast is minimized only for theaveraged relaxation of the tissues of interest. In most cases,the contribution of the residual contrast on the receptionsensitivity can be ignored. However, if the residual con-trast is large, it can be reduced using low-pass filtering.Here the calculated transmitted field and reception sensi-tivity maps were filtered by a Gaussian low-pass filter withthe kernel of 10 10 mm2 and SD of 2 mm to reduce bothresidual contrast and noise. Although the transmissionand reception maps are filtered, the fine details of imageare not affected. This is an advantage of the field mapmethod over the low-pass filter method.

The TFRS method for correcting the intensity nonuni-formities depends on accurate and fast estimation of trans-mission and reception sensitivity maps. Transmissionfield maps of human brain and a phantom were measuredwith relatively short TR, TR/TE � 4000/15 ms, and withvery long TR, TR/TE � 9000/15 ms. Quantitative compar-ison of the two field maps revealed an error of less than 3%when reducing TR down to 4 s. With a 4-s TR such mapscan be acquired quickly in reasonable imaging times withfast imaging techniques.

Slice profile effects must also be taken into consider-ation when mapping the transmission field. For example,transmission field maps obtained with slice-selectivepulses may differ from those obtained with non-slice-selective pulses, and this will lead to errors in the correc-tion. We did not find a significant difference between 2Dand 3D correction, probably due to the excellent sliceprofiles with the acquisitions we used and the relativelythick slices chosen. However, with shorter RF pulses andthinner slices this could become an issue.

The field mapping method described here does have anumber of limitations. First, the method relies on knowl-edge of the nominal flip angle, where by nominal we meanthat entered at the console. In practice, the actual flip anglevaries across the sample (both in-plane and through-plane), and thus the definition of the nominal flip anglecan be problematic (34). Differences between the nominalflip angle and the true flip angle will produce an error inthe correction. Second, the issue of minimizing contrast inan image to calculate the reception sensitivity is anothersource of error. As discussed above, residual contrast be-tween tissues can lead to inaccuracies in the receptionsensitivity map, which then propagate into errors in theintensity correction. Third, the TR used to acquire thesegmented EPI images was less than 4–5 times the T1 ofthe tissues. With shorter TRs, saturation effects could leadto intensity variations reflecting T1 effects rather thantransmit/receive effects thereby negatively impacting thecorrection scheme. Fourth, if the subject moves between

the scan to acquire field map and the scan(s) to be cor-rected, errors will be introduced in the correction. It ispossible, however, to register all of the images prior tocorrection to minimize sensitivity to such motion (35). Theassumption of linearity between the flip angle and B1

�

may not be true for larger flip angles and deviations fromthis assumption will introduce errors in the determinationof the transmission profile. While it is important to under-stand the potential sources of error, in practice these errorsare small and the technique presented represents a pow-erful approach for correcting intensity nonuniformities,particularly at high field.

CONCLUSIONS

A rapid field mapping method is proposed to measure thepositive circularly polarized component of the RF trans-mission field when using a body coil and the receptionsensitivity for phased array coils. The phantom resultspresented illustrate that it is necessary to consider both thetransmission and the reception spatial sensitivity in de-signing a correction scheme. The field map approach isshown to be superior relative to a reference image ap-proach and the low-pass filter approach for correctingintensity nonuniformities that arise for a range of se-quences and flip angles. The application of the field mapmethod in vivo demonstrates a significant improvement intissue signal uniformity and therefore better contrast be-tween different tissues. The total additional acquisitiontime for multislice transmission field and reception sensi-tivity mapping is only 105 s, making this approach prac-tical for a wide range of applications.

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