Measurement and Correction of Transmitter and ReceiverInduced Nonuniformities In Vivo

Jinghua Wang,1* Maolin Qiu,1 Qing X. Yang,2 Michael B. Smith,2 andR. Todd Constable1,3,4

Signal intensity nonuniformities in high field MR imaging limitthe ability of MRI to provide quantitative information and cannegatively impact diagnostic scan quality. In this paper, a sim-ple method is described for correcting these effects based on invivo measurement of the transmission field B1

� and receptionsensitivity maps. These maps can be obtained in vivo with eithergradient echo (GE) or spin echo (SE) imaging sequences, butthe SE approach exhibits an advantage over the GE approachfor correcting images over a range of flip angles. In a uniformphantom, this approach reduced the ratio of the signal SD to itsmean from around 30% before correction to approximately 6%for the SE approach and 9% for the GE approach after correc-tion. The application of the SE approach for correcting intensitynonuniformities is demonstrated in vivo with human brain im-ages obtained using a conventional spin echo sequence at 3.0T. Furthermore, it is also shown that this in vivo B1

� and recep-tion sensitivity mapping can be performed using segmentedecho planar imaging sequences providing acquisition times ofless than 2 min. Although the correction presented here isdemonstrated with a simultaneous transmit and receive volumecoil, it can be extended to the case of separate transmissionand reception coils, including surface and phase arraycoils. Magn Reson Med 53:408–417, 2005. © 2005 Wiley-Liss,Inc.

Key words: RF inhomogeneity; high field MRI; MRI; in vivo,sensitivity

Signal intensity (SI) nonuniformities in magnetic reso-nance (MR) imaging can arise from a wide variety of fac-tors. These include such factors as imperfections in theradiofrequency (RF) pulse profile; nonuniform flip anglescaused by an inhomogeneous transmit field; nonuniformreception sensitivity; RF penetration effects dependentupon the electromagnetic parameters of the object (1);wave behavior when the object size is equal to or morethan one-half the wavelength of electromagnetic radiation(2–4); and finally, gradient eddy currents related to thecoupling between the object and gradient coils (5). Theintensity nonuniformities caused by these factors strongly

affect the quantitative and qualitative analyses of MR im-ages. The effects are primarily manifest as smoothly vary-ing signal changes across tissue regions that should beuniform and these effects become more pronounced athigher field strengths. Such intensity nonuniformities canreduce the diagnostic quality of the images and also maketissue segmentation difficult (6,7).

The approaches developed to date to address this prob-lem can be divided into two categories: those that measureor calculate the RF field maps and those that rely onpostprocessing alone. The RF field map approaches arebased on the experimentally measured or numerically cal-culated RF field distributions (8–12). In these approaches,the transmit RF field B1

� is typically measured in a homo-geneous phantom. The primary limitation of this approachis that the B1

� field distribution in vivo can differ signifi-cantly from that of the phantoms because of the differencesin geometry and electromagnetic properties. Methodsbased on measurements obtained in uniform phantomscannot account for the effect of in vivo coil loading on theSI inhomogeneity (9). In addition, the RF coil perturbs thefield distribution of the whole system and this is often notconsidered in these approaches. Another approach is todetermine the B1

� and reception sensitivity theoretically(13–15). Such theoretical methods must necessarily ignorethe effect of detailed factors on field distribution, such asimperfect coil configurations and current distributionswithin the coils at high frequency. Additionally, the Biot–Savart law is not applicable when the frequency is above20 MHz (about 0.5 T for protons), and the wave behavior ofelectromagnetic field must be considered. Instead of usingthe Biot–Savart law, finite element approaches, or finitedifference time domain methods, are used to calculate theRF field (16). These calculations are expensive and slow,and the result depends strongly on the correct modeling.Moreover, these approaches cannot correct the nonunifor-mities arising from non-RF field factors. To date, no singleapproach has been developed that can correct the nonuni-formities arising from transmitter and receiver effects invivo.

The second line of attack for reducing the B1 problem,intensity-based postprocessing methods, includes digitalfiltering, parametric, nonparametric approaches, and low-pass filtering (17–20). In low-pass filtering, the signal in-homogeneity is assumed to be smoothly varying across theimage and this assumption is generally true (17–20). Morerecently, such filtering approaches have been extendedusing the wavelet transform, and these have been shown tobe effective in correcting intensity inhomogeneities in dataobtained with surface coils and phase array coils (21,22).Both the low-pass filtering and wavelet analysis methodslead to a loss of fine detail and can introduce local edge

1Department of Diagnostic Radiology, Yale University School Medical Center,The Anlyan Center, New Haven, Connecticut.2Center for NMR Research, Department of Radiology, Pennsylvania StateUniversity College of Medicine, Hershey, Pennsylvania.3Department of Biomedical Engineering, Yale University, New Haven, Con-necticut.4Department of Neurosurgery, Yale University School of Medicine, New Ha-ven, Connecticut.Grant numbers: NS40497, NS38467, EB00473, and EB00454.*Correspondence to: Jinghua Wang, Department of Diagnostic Radiology,Yale University, 300 Cedar Street, TAC-MRRC, New Haven, CT 06520.E-mail: Jinghua.wang@yale.eduReceived 29 March 2004; revised 2 August 2004; accepted 22 September2004.DOI 10.1002/mrm.20354Published online in Wiley InterScience (www.interscience.wiley.com).

Magnetic Resonance in Medicine 53:408–417 (2005)

© 2005 Wiley-Liss, Inc. 408

artifacts. The parametric methods assume that a singletype of tissue does not vary significantly in a particularslice and fit a signal intensity correction image accordingto the class of chosen tissue (23,24). These methods re-quire expert supervision to choose reference points foreach tissue for the fitting process before the correctionimage is obtained. Furthermore, the nonparametric algo-rithm assumes that coil heterogeneity results in smoothshifts in intensity, which can be detected within a singlehomogeneous tissue (25,26). Although these postprocess-ing techniques are attractive and work well in many situ-ations, the corrections are independent of coil geometryand tissue content, most of them rely on some level ofexpert supervision, and they only provide an approximatecorrection of intensity nonuniformities.

In this work, a simple method is proposed for measuringin vivo the homogeneity of the B1

� transmission and thereception sensitivity, and existing methods are adapted tocorrect the images. The B1

� map of the loaded volume coilis obtained using a spin echo sequence in vivo. The in vivosensitivity of a loaded coil can be obtained if the imagingparameters are chosen to make the heterogeneous objectappear homogeneous by choosing TE and TR to minimizetissue contrast. If the image contains only three primarytissues (such as gray matter (GM), white matter (WM), andcerebrospinal fluid (CSF) in the brain), tissue contrast iseasily nulled and the reception sensitivity of the systemdirectly measured. Once the B1

� map and the receptionsensitivity are determined, the intensity nonuniformitiescan be corrected for different RF flip angles and pulsesequences in vivo. Although a volume coil is used in thework presented here, this approach can be extended tosurface coils and separate transmit and receive coil sys-tems.

THEORY

Transmission Field

For a spin echo (SE) sequence, the signal intensity can beobtained by solving the Bloch equation as follows (27),

SISE(x) � M0

sin�SE�x)� �1 � cos�SE(x) � E1 � (1 � cos�SE(x)) � E1 � eTE/2T1�

1 � cos�SE(x) � cos�SE(x) � E1

� eTE/T2� S(x), [1]

where �SE(x), �SE(x) are the flip angles (FA) of the excita-tion and refocusing pulses, and S(x) represents the recep-tion sensitivity at position x. M0 is the equilibrium longi-tudinal magnetization, E1 � exp(�TRT1), and T1 is thelongitudinal relaxation time. When T1 TE and TR T1, Eq. [1] can be simplified to (28)

SISE(x) � CSE(x) � S�x� � sin�SE(x) � sin2�SE(x)

2, [2]

where the variable, CSE(x), depends on the properties oftissue (proton density, T1, and T2) and imaging parameters

such as TE, TR, and flip angles. If �SE(x) � 2�SE(x) forconventional SE, the SI can be written as

SISE(x) � CSE(x) � S�x� � sin3�SE(x)

� CSE(x) � S(x) � sin3(� � B1�(x) � ), [3]

where � is the magnetogyric ratio, is the duration of theRF pulse, and B1

� is a positive circularly polarized RFfield component that rotates in the same direction as nu-clear spins precession. Equation [3] shows that signal in-tensity is dependent on a sin3� flip angle term, whichmakes 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; thus atthese angles the B1

� map has maximal sensitivity to smallchanges in the B1 field.

To measure the B1� and reception field distributions,

two SE images are acquired with different excitation flipangles such that �2,SE(x) � 2�1,SE(x) while the other imag-ing parameters remain fixed. Using two such SE se-quences, with excitation and refocusing flip angles of 60/120o and 120/240o, respectively, the B1

� distribution cor-responding to the flip angle of 60o can be determined (8).The ratio of the two images is given by (5)

�SE �SI2,SE(x)SI1,SE(x)

�sin3�2,SE(x)sin3�1,SE(x)

. [4]

Then, according to Eq. [3],

B1� �

1�

� arccos��SE8�1/3. [5]

Similarly, the signal intensity of the ideal steady-stategradient-echo (SSGE) sequence with excitation FA of �GE

can be approximated as (29)

SIGE(x) � M0 �(1�E1) � sin�GE(x)

1�E1 � E2 � (E1 � E2) � cos�GE(x)

� eTE/T2 � S�x�, [6]

where E2 � exp(�TRT2*). For TR T2*, E2 � 0, and the

ideal SSGE signal model equation can be simplified as

SIGE(x) � M0 � sin�GE(x) �(1 � E1)

1 � E1 � cos�GE(x)

� eTE/T2 � S�x�, [7]

When TR T1, E1 � 0, and the signal intensity is given by

SIGE(x) � CGE(x) � S�x� � sin�GE(x). [8]

The ratio of signal intensities of two GE images with dif-ferent flip angles �1,GE(x) and �2,GE(x) is given by

�GE � sin�2,GE(x)sin�1,GE(x). [9]

Transmitter and Receiver Induced Nonuniformities 409

When �2,GE(x), the B1� for GE sequence can be written as

B1� � 1 � � arccos(�GE/2). [10]

The corrected flip angle �(x) of both the SE and the GEacquisitions can be calculated by

�(x) � �nom � ��B1� ref

�ref�, [11]

where �nom is the nominal flip angle (the flip angle enteredat the console) used for acquiring the image to be cor-rected, (�B1

� ref/�ref) is the scaling flip angle distributiondetermined from field mapping, where �ref and ref are thenominal input excitation flip angle and pulse length of theradiofrequency pulse used for determining B1

�. The cal-culated flip angles are based on the assumption of a linearrelationship between flip angle and B1

� map. Deviationsfrom this linear relationship can be neglected up to ap-proximately 140o, but must be taken into account for largerflip angles (19).

Reception Sensitivity

The reception sensitivity can be obtained as follows (9),

S�x� � SISE(x)/(CSE � sin3�SEMCI(x)) [12]

S�x� � SIGE(x)/(CGE � sin�GEMCI(x)), [13]

for spin echo (12) and gradient echo (13) acquisitions,where �SEMCI(x) and �GEMCI(x) are the corrected flip angles(given by Eq. [11]) of the minimal contrast images, corre-sponding to signal intensities of the spin echo, SISE(x), andgradient echo, SIGE(x), sequences, respectively. The calcu-lations are based on the B1

� map and the assumption of alinear relationship between the B1

� map and the flip angleobtained. The factors CSE and CGE are constant for homo-geneous objects or variables related to the tissue contrast ofthe SE and GE sequence, respectively. In the brain, thecontrast among the primary tissues of interest, GM, WM,and CSF, can be minimized by 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. That is, withthe appropriate TE and TR, the heterogeneous region ofinterest (ROI) can be made to have uniform signal intensityby minimizing the equation

Cij � ��i � �1 � exp��TRTli � exp(� TE/T2i) � �j

� (1 � exp�� TR/Tlj) � exp(� TE/T2j), [14]

where Cij represents the contrast between tissues i and j.The parameters T1, T2, and PD of tissues i and j are T1i, T2i,and �i, T1j, T2j, and �j, respectively. If the ROI includesthree tissues, the optimized TE and TR can be derivedfrom the condition of zero contrast among these tissues. Ifmore than three tissues are present, TE and TR can bechosen to minimize the contrast among all the tissues,although in this case some contrast will remain. The re-

ception sensitivity is given by either Eq. [12] or [13], whichcan then be used to correct any image using the expression

SIcorrected,k � SImeasured,k SIcorrection,k, [15]

where k � SE or GE. The correction matrix is given bySIcorrection,SE � sin3�(x) � S(x), where �(x) is the excitationflip angle of the image to be corrected and this flip anglehas been corrected using Eq. [11], and S(x) is given by Eq.[12], with excitation and refocusing flip angles of �SEMCI(x)and 2�SEMCI(x). The correction matrix for the gradient echoscheme is similar and is given by SIcorrection,GE � sin �(x)� S(x).

With this background the procedure for mapping andcorrecting images in vivo is to collect two multishot spinecho EPI acquisitions with excitation and refocusing flipangles of 60/120o and 120/240o and a TR of 2.2 sec, fol-lowed by a third acquisition with the contrast between thetissues of interest minimized and an excitation flip angleof 90o and refocusing flip angle of 180o. With a seven-shotEPI sequence the imaging time for these three image ac-quisitions is less than 2 min. The correction proceduredescribed above can then be applied to any subsequentacquisitions.

METHODS

B1� map for phantom at TR 5T1 and 5T2

All phantom and human brain images were obtained on aSiemens 3.0-T Trio system with a Siemens head coil. TheSiemens phantom is a cylinder (15 cm diameter, 36 cmlength) filled with distilled water, NiSO4 (1.24 g/liter) andNaCl (2.62 g/liter). Axial images of the phantom wereobtained with TR/TE � 6000/15 msec, FOV 200 �200 mm2, matrix 256 � 256, slice thickness of 5 mm, withflip angles of 10, 30, 45, 60, 75, and 90o for the GE se-quence and excitation flip angles of 50, 60, 80, 90, 110, and120o for the SE sequence. The refocusing flip angles for theSE sequence are double the corresponding excitation flipangles for the SE sequence. The total acquisition time foreach image was approximately 16 min due to the long TRnecessary for the longitudinal magnetization of the phan-tom to completely recover between excitations (this longacquisition time is not needed in vivo as will be shownbelow). The B1

� and reception sensitivity maps of thephantom measured for the SE method were obtained withexcitation flip angles of 60 and 120o and refocusing flipangles of 120 and 240o, respectively. The B1

� and recep-tion sensitivity maps of the phantom were also measuredwith a GE sequence using the two images with the flipangles of 30 and 60o, respectively.

Variation of B1� Map for Phantom with TR Comparable to

T1

In the phantom studies in the previous section, the B1�

maps are calculated using both the SE and the GE se-quences, with TR T1, but this long TR leads to prohib-itively long scan times that would be impractical for clin-ical applications. To study the effect of TR on the B1

� map,a cylindrical phantom with 15-cm diameter was filled with

410 Wang et al.

1% low fat milk (Deerfield farms) with T1 and T2 of 1500and 86 msec, respectively. Single-slice images were ac-quired over a range of TRs from 150 to 9000 msec withconventional spin echo and multishot spin echo EPI se-quences. The flip angles for both the conventional andmultishot EPI spin echo sequences are 60 and 120o forexcitation and 120 and 240o for refocusing. The otheracquisition parameters are as in the previous phantomstudy above: FOV 200 � 200 mm2, matrix 256 � 256, slicethickness 5 mm. A term to quantify the error of the B1

�

map due to TR is defined as

FracErrorTR ��Xmeasured � Xtrue��Xmeasured � Xtrue�

� 200, [16]

where Xmeasured is the measured value of parameter Xobtained with reduced TRs. Xtrueis the true value obtainedusing the mean value at TR � 9000 msec, which is six timesas long as T1 of the milk phantom. In order to quantify thesignal nonuniformities, we introduce a parameter

� �SD

mean� 100, [17]

where SD is the standard deviation of ROI, which shouldhave uniform intensity, and mean is the mean intensity inthis same region.

B1� and Reception Sensitivity Maps in Vivo

For heterogeneous objects such as those found in vivo, itis important that the transmission field and receptionsensitivity maps are obtained with the tissue contrastminimized. At 3.0 T, the measured relative PD, T1, andT2 are 1, 3050 msec, 323 msec for CSF; 0.867, 1300 msec,99 msec for GM; and 0.807, 830 msec, 82 msec for WM(30). For conventional spin echo sequences with excita-tion flip angle of 90o and refocusing flip angle of 180o,the optimized TR/TE � 1720/50 msec can be calculated,and plots of the contrasts between these tissues areshown in Fig. 1a. Minimal contrast images from normalvolunteers were acquired with these optimal parame-ters, an example of which is shown in Fig. 1b. The otherimaging parameters were FOV 220 � 220 mm2, matrix256 � 256, slice thickness 2 mm, 1 slice. Two imageswere acquired to estimate the in vivo B1

� map, usingexcitation flip angles of 60 and 120o and refocusing flip

angles of 120 and 240o, respectively. The other param-eters were the same as those used for the image with theminimal contrast. Both the B1

� and the reception sensi-tivity maps were obtained using slice-selective pulses.The images to be corrected were acquired using an in-version recovery spin echo sequence with TR/TI/TE �2000/700/15 msec and a flip angle of 90o, and all otherimaging parameters, such as FOV, matrix, and slicethickness, identical to the previous acquisition. Themultislice in vivo B1

� maps were calculated using twospin echo segmented EPI acquisitions with nominal ex-citation/refocusing flip angles of 60/120o, and 120/240o,at TR/TE 2000/16 msec, FOV 240 � 180 mm2, matrix128 � 96, slice thickness of 5 mm, 18 slices, 1-mm gap,bandwidth 752 Hz per pixel, 7 segments, and a totalacquisition time of 70 sec for both acquisitions com-bined. The reception sensitivity map is calculated usingthe minimal contrast image and the B1

� map. The min-imal contrast images are acquired with excitation flipangle of 90o and the refocusing flip angle of 180o, TR/TE � 2200/16 msec, and all other imaging parametersthe same as for the B1

� mapping. 3D volume T1-weighted images of the brain of normal volunteers wereacquired using MPRAGE with TR/TI/TE � 2000/700/15 msec and flip angle 12o, FOV 220 � 220 mm2, matrix256 � 256, slice thickness 1 mm, 160 slices. Note thatthis 3D MPRAGE acquisition to be corrected was ob-tained using non-slice-selective pulses, whereas allother acquisitions were with slice-selective pulses.

To reduce noise sensitivity and take into account thefact that the B1

� and reception sensitivity vary smoothlywithin MR images, the calculated B1

� and reception sen-sitivity maps were filtered using a Gaussian low-pass filter.Tissue contrast cannot be eliminated completely becausethe actual tissue relaxation parameters vary spatially andthe contrast is minimized only for the averaged relaxationand nominal flip angle of the tissues of interest. In mostcases, the contribution of the residual contrast on thereception sensitivity can be ignored. However, if the resid-ual contrast is large, low-pass filtering can reduce thisresidual contrast. Here the calculated B1

� and receptionsensitivity maps were filtered using a Gaussian low-passfilter with a 10 � 10 mm2 window width and a SD of 2 mmto reduce both residual contrast and noise. Although thetransmission and reception maps are filtered, the fine de-tails of image are not affected by the correction.

FIG. 1. Theoretical dependence of contrastamong CSF, gray matter, and white matter in thebrain on the acquisition parameters (TR and TE) (a)and the minimal contrast image (b) under the opti-mal TR � 1720 msec and TE � 50 msec for mini-mal contrast.

Transmitter and Receiver Induced Nonuniformities 411

RESULTS

An example of the B1� and reception sensitivity maps

measured in vivo is shown in Fig. 2. The � of the B1� and

reception sensitivity maps in Fig. 2a and b of the braintissues are 9.7 and 11.9%, respectively. These measuredB1

� and reception sensitivity maps were then used tocorrect a T1-weighted brain image of the same subject andthe results are shown in Fig. 2d along with the originalimage in Fig. 2c. The intensity variations indicated by thearrows in Fig. 2c are corrected well, as shown in Fig. 2d.The corrected image exhibits significant improvement inthe signal uniformity among individual tissues: CSF, WM,and GM. This example illustrates the effectiveness of using2D in vivo measures of the B1

� and reception sensitivity tocorrect 2D images.

For practical applications, the additional imaging timefor estimating the B1

� and reception sensitivity maps mustbe minimized. Since the B1

� and reception sensitivityprofiles vary slowly spatially, B1

� and reception sensitiv-ity maps with low resolution can be obtained (reducingimaging time) and these can be interpolated and registeredto the high-resolution acquisitions to be corrected. Heresuch maps covering the entire human brain with the lowresolution were obtained using a segmented spin echo EPIsequence with a total acquisition time for transmit andreceiver mapping of less than 2 min. Figure 3 shows a setof three slices from an MPRAGE 3D volume, before (Fig.3a–c) and after (Fig. 3d–f) correction with the B1

� andreception sensitivity maps acquired using EPI. The bottomrow of corrected images demonstrates better tissue signal

FIG. 2. The transmitted field map (a) and receiversensitivity map (b) calculated using the SE method.An uncorrected T1-weighted image is shown in (c),and the corrected image is shown in (d), obtainedusing the maps of (a) and (b).

FIG. 3. Three slices from a 120-slice high-resolution 3D MPRAGE acquisition showinguncorrected images (a–c) and the corre-sponding corrected images (d–f).

412 Wang et al.

homogeneity than the uncorrected images in the top row.Even though low-resolution maps are used to correct thetransmit and receiver nonuniformities, signal uniformityfor a given tissue is improved, leading to better depictionof fine details in the white matter. These results demon-strate that low-resolution B1

� and reception sensitivitymaps can markedly reduce the signal intensity nonunifor-mities in vivo.

Equation [5] was derived with the assumption that theacquisition TR satisfies the relation: TR 5T1. Such longTRs are impractical and thus we investigated the impact ofTR on these calculations. Figure 4a shows an in vivo B1

�

map of a volunteer’s brain acquired with TR of 1720 msec,which is very similar to the B1

� map acquired with a TR of9000 msec (and all other imaging parameters identical), asshown in Fig. 4b. The difference between these maps isless than 4%, suggesting that shorter TRs can be usedeffectively.

Since the transmit field and receive sensitivity maps canbe obtained using either spin echo or gradient echo se-quences, phantom studies were performed to comparethese two approaches. The B1

� and reception sensitivitymaps of the homogeneous phantom are shown in Fig. 5.Figure 5a and b shows B1

� maps measured by the SEsequence with excitation flip angles of 60 and 120o and theGE method with flip angles of 30 and 60o, respectively.The reception sensitivity maps obtained using SE and GEimaging and using Eqs. [11] and [12] are shown in Fig. 5dand e, respectively. The B1

� and reception sensitivitymaps are normalized by their means and their difference isshown in Fig. 5c and f. The standard deviations of thesetwo difference maps are less than 0.02, indicating that themeasurements obtained using the spin echo and gradientecho methods are similar. The � of the B1

� and receptionsensitivity maps in Fig. 5 are 18.6 and 19.7% for the SEmethod and 20.6 and 21.0% for the GE method, respec-tively. This indicates that the B1

� and reception sensitivitymaps measured by both methods have significant nonuni-formities.

The images corrected using these maps are shown in Fig.5g–l. Figure 5g shows the original SE phantom image andit’s correction via the spin echo transmit and receive maps(Fig. 5h) and by the gradient echo transmit and receivemaps (Fig. 5i). Similar results are shown in the bottom rowfor a GE phantom image before (Fig. 5j) and after correction

using SE maps (Fig. 5k) and GE maps (Fig. 5l). In theoriginal images (Fig. 5g and j), intensity nonuniformitiesare observed as a center bright pattern due to the RF fieldwave behavior. With our correction method, this artifact isparticularly well compensated using the spin echo fieldmaps (Fig. 5h and k).

Histogram analysis was used to experimentally evaluatethe ability of the spin and gradient echo field mappingapproaches to correct spin and gradient echo images ac-quired with a range of flip angles. The results are shown inFig. 6 for the correction of gradient echo phantom imagesobtained with flip angles of 10, 45, 75, and 90o, Figs. 6a–d,respectively, and for spin echo phantom images obtainedwith excitation flip angles of 50, 80, 90, and 110o, Fig.6e–h. These results demonstrate that over this wide rangeof acquisitions the spin echo field map approach providesexcellent results as indicated by the narrow distribution ofintensities in the histograms. Quantitative results obtainedmeasuring the � parameter are summarized in Table 1. Itcan also be observed that both the spin echo and thegradient echo methods are more effective at correctingimages acquired with low flip angles, possibly because thedeviation from a linear relationship between B1

� and flipangle is minimal with lower nominal flip angles. It is alsopossible that slice profile effects on intensity nonunifor-mities become more important for larger nominal flip an-gles. The � in Table 1 indicates that the SE method im-proves the RF inhomogeneity to a greater extent than theGE method when applied to spin echo images. � is re-duced from around 30% for the original images to around6% for the images corrected using the SE method and toaround 9% for the images corrected using the GE method.Thus, the spin echo approach was used in the human brainexample shown.

Figure 7 shows the impact of short TR in vivo in a plotof the fractional error in the B1

� map as a function of theratio TR/T1. B1

� maps were estimated using a conven-tional spin echo (Fig. 7a) and segmented spin echo EPI(Fig. 7b) sequence with nominal excitation flip angles of 60and 120o and nominal spin echo flip angles of 120 and240o, respectively. The fractional error in the B1

� maps isless than 4% when the ratio (TR/T1) 1, for both the SEand the segmented EPI SE sequences, in comparison withTR � 6T1. This suggests that a rapid B1

� mapping acqui-

FIG. 4. The in vivo B1� maps of a volunteer brain

obtained with relative short TR (a) TR � 1740 msecand very long TR (b), TR � 9000 msec. This resultdemonstrates that relatively short TR can be usedto produce accurate B1

� maps rapidly.

Transmitter and Receiver Induced Nonuniformities 413

sition using a TR � 2200msec provides sufficient accuracyto correct the intensity nonuniformities.

DISCUSSION

Akoka et al. (10) used two stimulated echo images tocalculate B1

� in vivo. However, they did not correct thesignal intensities based on these in vivo B1

� maps. Barkeret al. proposed a method for measuring the B1

� maps usingboth uniform phantoms and heterogeneous objects in vivo.They did not minimize tissue contrast in the in vivo im-ages and thus were unable to determine the receptionsensitivity map, nor could they correct for the receptionsensitivity profile (9). To correct for these effects, we havepresented a method for determining the appropriate inten-sity correction matrix calculated using the Bloch equationwith the B1

� map and reception sensitivity profiles mea-sured in vivo. The in vivo B1

� map can be estimated usingEqs. [5] and [10]. The reception sensitivity can be calcu-lated using Eqs. [12] and [13] and the minimal contrast

image and B1� map. Generally, the B1

� map is not influ-enced by tissue parameters T1, T2, or PD of brain tissues asshown in Fig. 2 for long TR ( 5T1), and even when theratio TR/T1 is approximately 2, the contribution of TR tothe error in the measured B1

� map is less than 5% for bothconventional spin echo and segmented spin echo EPI se-quences (Fig. 7). These results indicate the feasibility ofperforming transmit/receive mapping with reasonable TRsin vivo.

Slice profile effects should also be considered in B1�

mapping. We measured the effect of slice profile on theB1

� map, data not shown, using selective (2D acquisition)versus nonselective (3D acquisition) RF pulses, and foundless than 4% mean deviation in the B1

� maps. Because ofthis consistency, B1

� maps from acquisitions using slice-selective pulses can be used to correct intensity nonuni-formities in 3D acquisitions obtained using non-slice-se-lective pulse as shown in Fig. 3. However, if high accuracyis required it is preferable to match the RF pulse for B1

mapping with the RF pulse of the image to be corrected.

FIG. 5. The transmitted field and receptionsensitivity maps of homogeneous phantommeasured by the spin echo (a, d) and gra-dient echo (b, e) sequences and the differ-ence between these two methods (c, f), re-spectively. Uncorrected phantom image ac-quired using a GE sequence (g) with flipangle of 45o and SE (j) sequence with theexcitation flip angle of 90o, as well as thecorrected images using SE method (h, k)and GE methods (i, l), respectively.

414 Wang et al.

For example, perform field mapping with nonselectivepulses if the acquisition to be corrected uses a nonselectivepulse. Slice profile effects that arise due to the finite lengthof RF pulses are not corrected by field mapping, and theseeffects can be significant between 2D and 3D acquisitions,depending on the shape and duration of the specific pulsesused.

The minimal contrast image at the optimized TR/TE isused to measure the reception sensitivity profile. In prac-tice, however, some residual contrast is inevitably presentas relaxation times very spatially even within the sametissue. It is important therefore to examine the impact ofthe residual contrast on the measurement of the receptionsensitivity. In the Bloch equations presented above, thesignal is proportional to C(x) and reception sensitivityS(x). For a given intensity, the error in C(x) must give rise

FIG. 6. Histogram of the images acquiredby the conventional GE sequence with flipangles of 10o (a), 30o (b), 60o (c), and 90o (d)and by a conventional SE sequence withexcitation flip angles of 50o (e), 80o (f), 90o

(g), and 110o (h), respectively. Each includeshistograms of the uncorrected and cor-rected images with the SE and GE methods.

Table 1Uniformity of Signal in Phantom Study

�(Original)

�(SE method)

�(GE method)

SE-50 0.5738 0.0417 0.2131SE-80 0.3553 0.0427 0.0751SE-90 0.3089 0.0455 0.0710SE-110 0.1842 0.0662 0.1783GE-10 0.3293 0.0528 0.0528GE-45 0.3109 0.0624 0.0446GE-75 0.2643 0.0825 0.0951GE-90 0.2327 0.1017 0.1376

Transmitter and Receiver Induced Nonuniformities 415

to the same percentage error in S(x), which will result inthe same error in the corrected SI. To quantify the residualcontrast we applied the approach of Cohen et al. (18) andsmoothed minimal contrast image using a Gaussian kernelof 256 � 256 mm2 with a default full width at half-maxi-mum of 96 mm. The residual error can then be determinedby dividing the image with minimal contrast by thesmoothed image to eliminate the contribution of inhomo-geneous field to SI (18). In the ideal case, the contrastamong the tissues in the corrected image reduces to theSNR at the optimum TR/TE. In this comparison, the mea-sured ratio (�) of mean and SD in a Gaussian smoothedminimal contrast image is 8.2%. This implies that theresidual average contrast between tissues plus noise is8.2% and suggests that the assumption of a homogeneousbrain at the optimum TR/TE is in error by this amount orless. The phantom studies showed that our method canimprove � from around 30% before correction to 6% aftercorrection for a uniform phantom with TR 5T1. Theresidual error after correction in vivo is only 8.2%; com-parable to the 6% residual in the phantom studies, indi-cating that the residual contrast in the minimal contrastimage does not have a major effect on the ability to correctin vivo images.

The theory and simulations presented above indicatethat the errors are small for TR T1 and nominal exci-tation flip angles greater than 60o (assuming a refocusingflip angle of 180o for spin echo). The error in the B1

�

map can be large, however, for TR � T1 and nominalexcitation flip angles less than 60o. In this case, thedenominator in Eqs. [1] and [7] will yield a large error inthe calculation of B1

�. It should be noted that evenunder these conditions the reception sensitivity can stillbe measured accurately and the nonuniformities in thereception sensitivity maps are of the same order as theB1

� maps. Thus substantial improvements in signal ho-mogeneity can still be obtained using this method evenwithout the transmission inhomogeneity correction us-ing the B1

� maps. However, for the small increase inimaging time required for both transmit field and re-ceiver sensitivity mapping, we recommend acquiringthe three acquisitions in order to perform both correc-tions.

The phantom studies were unable to completely elimi-nate the intensity inhomogeneity because of severalsources of residual error. The first is that the flip angleprescribed at the console is often not exactly that which isproduced in the image (ignoring B1

� inhomogeneity is-sues, but simply considering amplitude scaling issues).Second, residual error arises from slice profile effects (dueto the use of finite RF pulses, not B1

� inhomogeneities),which, while small, do add errors to the signal intensitynonuniformity correction. Finally, intrinsic SNR limita-tions also will lead to nonzero residuals in the correctionof intensity inhomogeneities.

CONCLUSIONS

Two methods, a spin echo based and a gradient echo basedmethod, have been described to measure transmission andreception uniformity profiles for a volume coil. Resultsdemonstrate improvements in signal uniformity across ahomogeneous phantom using both gradient echo and spinecho sequences with a range of flip angles. Although bothmethods are able to correct intensity variations, the spinecho method provides better results than the gradient echomethod. By minimizing the contrast among CSF, GM, andWM, the reception sensitivity profile of the coil can becalculated using in vivo data, allowing image intensities tobe appropriately corrected. It is shown that segmented EPIcan be used to obtain the transmission and reception sen-sitivity maps in less than 2 min, making this approachapplicable to routine MR imaging. It is also shown thatrapidly acquired maps with low resolution can be used tocorrect high-resolution 3D brain images. The short acqui-sition time needed for measuring the correction matrix invivo suggests that this approach is amenable to routineclinical application. Finally, this approach is not limitedto applications using transmit/receive coils but can beextended to systems that use separate transmit and receivecoils.

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