Available online at www.sciencedirect.com

Magnetic Resonance Imagi

ng 28 (2010) 777–783

Recovery of signal loss due to an in-plane susceptibility gradient in thegradient echo EPI through acquisition of extended phase-encoding lines

Kwan-Jin Junga,b,⁎, Hua Penga, Tiejun Zhaoc, Galia Avidand, Marlene BehrmanneaBrain Imaging Research Center, University of Pittsburgh, Pittsburgh, PA 15203, USA

bBioengineering Department, University of Pittsburgh, Pittsburgh, PA 15261, USAcSiemens Healthcare, Siemens Medical Solutions USA, Inc., University of Pittsburgh, Pittsburgh, PA 15213, USAdDepartment of Behavioral Sciences, Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel

eDepartment of Psychology, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

Received 8 September 2009; revised 20 January 2010; accepted 5 March 2010

Abstract

In gradient echo imaging the in-plane susceptibility gradient causes an echo shift which results in signal loss. The loss of signal becomesmore severe in gradient echo EPI, due to the low amplitude of the gradient which is applied in the phase-encoding direction during a longecho train. As the readout gradient amplitude is set to be very high in gradient echo EPI, the echo shift in the readout direction is negligiblecompared to that in the phase-encoding direction. Traditionally, a z-shimming technique has been applied to the phase-encoding direction ofgradient echo EPI to restore the lost signal. This technique, however, requires a significant increase of scan time, as is also the case with thethrough-plane z-shimming technique. A new approach that allows one to restore the lost signal is to acquire additional phase-encoding linesbeyond the regular phase-encoding range. The extension of the phase-encoding lines prior to the regular phase-encoding range exploits thedelay time for optimum echo time of the BOLD sensitivity. Therefore, scan time is increased only for the extended phase-encoding linesposterior to the regular phase-encoding range. This technique has been confirmed experimentally by imaging human subject's heads at 3T.© 2010 Elsevier Inc. All rights reserved.

Keywords: EPI; Susceptibility artifact; Susceptibility gradient; Phase-encoding; Echo shift

1. Introduction

Local variations in magnetic susceptibility induce amagnetic field which can have a field gradient in thethrough-plane and in-plane directions. The through-planesusceptibility gradient (TSG) reduces the signal in gradientecho imaging due to phase dispersion in the through-planedirection within the slice.

The in-plane susceptibility gradient (ISG) can be dividedinto two orthogonal directions along the readout and phase-encoding (PE) directions, i.e., ISGRO and ISGPE, respective-ly. In conventional gradient echo imaging sequences, ISGRO

shifts the echo center in the data acquisition window, whichresults in partial loss of the echo signal in the readoutdirection as in partial Fourier imaging [1,2]. The partial

⁎ Corresponding author. Brain Imaging Research Center, PittsburghPA 15203, USA. Tel.: +1 412 383 8014; fax: +1 412 383 6799.

E-mail address: kjj1@pitt.edu (K.-J. Jung).

0730-725X/$ – see front matter © 2010 Elsevier Inc. All rights reserved.doi:10.1016/j.mri.2010.03.016

,

acquisition of the echo signal can cause image artifacts suchas a signal drop and ripple in the readout direction. The shifttime of the echo center is inversely proportional to theamplitude of the readout gradient [3].

In EPI, the amplitude of the readout gradient is set to bevery high (about 10 times higher than that of conventionalimaging sequences) in order to shorten the echo spacing.Therefore, the echo shift in the readout direction can beignored. In contrast, the train of PE gradient blips can beinterpreted as a readout or frequency-encoding gradient withsmall amplitude. As a result, the echo center can be shiftedsignificantly in the PE direction due to ISGPE. When the echotrains are acquired for the PE lines that cover the full k-spaceas in conventional EPI, the echoes shifted outside the regularPE range will be lost as in the partial Fourier acquisition in thePE direction. The lost signal can cause signal loss and rippleartifacts in the PE direction on the reconstructed image [4–6].

This study aims to restore the signal that has been lost dueto the ISGPE in slice-selective EPI, especially for gradient

Fig. 1. An extended EPI pulse sequence with 96 PE lines for 64x64 matrix acquisition. The slice selection gradient (GSS) remains the same, while the readougradient (GRO) and PE gradient (GPE) are extended as shown in the red waveform. Note that the magnitude of the dephasing lobe of the PE gradient is increasedto compensate for the additional 16 PE lines. The time scale is matched to the scan parameters of GE EPI imaging in the experiment.

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echo (GE) EPI. One approach, in which the through-plane z-shimming technique [7,8] was applied to the PE direction,was previously developed [5]. However, that techniqueincreased the scan time significantly. Another approach hasbeen to optimize the slice orientation to minimize the ISG[9,10]. For biological objects, however, it is difficult tooptimize the slice orientation over the whole region of interestdue to the complicated pattern of the susceptibility gradientwhich is dependent on the shape and orientation of the object.The view-angle tilting technique can correct an inhomoge-neity artifact in conventional imaging [11]. However, thistechnique cannot be directly applied to the EPI sequence andits effect is limited to a certain slice angle relative to theorientation of an object with susceptibility [12].

Here, we offer a new approach that involves extending thePE lines and acquiring the echoes that are shifted outside theregular PE range. This technique allows us to recover signalsthat would otherwise be lost and thereby prevent a rippleartifact, without significantly increasing the scan time. A GEEPI sequence with extended PE lines was developed andtested at 3T. It has been experimentally confirmed to beeffective in recovering signal loss through scans of humansubjects' heads.

2. Materials and methods

The magnetic field applied to the sample consists of theuniform field B0 and an inhomogeneous field ΔB0 (x,y,z)which is time independent and varies spatially [1]. Thespatial gradient of ΔB0 (x,y,z) in the PE direction y, i.e.,ISGPE can be defined as

Ry =ADB0

Ay

1

gyð1Þ

in units of the applied PE gradient gy. In EPI the PE gradientis applied as a triangle blip at the bipolar switch of thereadout gradient (Fig. 1). For simplicity of analysis, the PE

t

gradient blip can be considered to be a constant gradient gyapplied during the echo spacing time TESP. Therefore, gy isthe area of the PE gradient blip divided by TESP.

The ISGPE will affect the effective PE gradient, gy⁎, whichis a superposition of gy and ISGPE, i.e.,

g⁎y = gyð1 + RyÞ: ð2Þ

The zeroth order moment of the PE directional gradient,my, can be obtained as a function of the PE k-space variableky (-Ny/2 ≤ kybNy/2) as follows:

my ky� �

= g⁎y TESPky + RygyTE: ð3Þ

Ny is the number of PE steps. The echo is formed when

my ky� �

= 0: ð4Þ

Therefore, the echo shift from the center (ky = 0) of theregular PE range, i.e., Δky can be calculated from Eqs. (3)and (4) as follows:

Dky =−TETESP

Ry

1 + Ry

� �: ð5Þ

In order to compensate for the change of the effective PEgradient in Eq. (2), the range of the PE lines (Ny⁎) needs to beadjusted for ISGPE as follows:

N ⁎y ¼ −Ny

11 + Ry

� �: ð6Þ

The effect of ISGPE on the echo center and PE rangefor Ny = 64 are illustrated in Fig. 2 for the case of TE/TESP = Ny as a 2-D map. At 3 Tesla the optimum TE isabout 30 ms [13] and TESP may be about 450 μs for Ny = 64for a whole body MRI scanner. As ISGPE increases in thepositive or negative direction relative to gy, the required PErange extends in the prior or posterior side of the regular PErange, respectively.

Fig. 2. The effect of ISGPE (in-plane susceptibility gradient in the PEdirection) on the echo center (red line) and PE range (white strip) for TE/TESP=Ny. The regular PE range is for 64 PE lines and its boundary is markedby two cyan horizontal lines at ky = ± 32. The ISGPE has the units of the PEgradient amplitude gy.

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The lost signal can be recovered by acquiring signalsoutside the regular PE range by extending the PE linesbeyond the regular PE range. To compensate for bothpolarities of ISGPE, the PE lines need to be extended to boththe prior and posterior sides of the regular PE range. Anextended GE EPI sequence with 16 additional PE lines oneach side is shown in Fig. 1 for Ny = 64 and the image matrixof 64x64. The amplitude of the PE dephasing lobe needs tobe increased by 48/32 to keep the echo center at ky = 0.

The magnetic field maps were measured through the useof the gradient echo sequence with echo times (TE) of 10 and12.46 ms at the same slice location as the EPI images. Thesusceptibility gradients were calculated for x (readout), y(PE), and z (slice selection) directions and displayed in color-coded 2D maps.

The GE EPI sequence shown in Fig. 1 was programmedbased on the conventional GE EPI sequence for Ny = 64.A volunteer's head was scanned at 3T (Siemens, Allegra)using a quadrature birdcage RF coil. The imagingparameters were: slice thickness = 3.5 mm, in-planeresolution = 3.5 mm, pixel bandwidth = 3004 Hz, TESP =0.38 ms, TE = 30 ms, TR = 5 sec, flip angle = 90°, numberof slices = 64, slice orientation = transverse, and PEdirection = AP (y axis). The echo shift was expected to beincreased beyond that shown in Fig. 2 because TE/TESP inEq. (5) was larger than Ny (= 64) due to a faster gradientsystem of the head-dedicated MRI scanner.

The effect of ISGPE on the echo shift and PE range wasdemonstrated on the 2D k-space map as a change in themagnitude of the EPI echo trains. In addition, the PEdirectional profiles of the k-space map were obtained byintegrating the signal in the readout direction to demonstratethe shifted echo in the PE direction.

The images were reconstructed offline in four differentcombinations of the PE lines: (i) including only the middle64 lines as in the conventional sequence (reg), (ii) includingthe prior 16 lines in addition to the middle 64 lines (pre), and(iii) including the posterior 16 lines in addition to the middle64 lines (post), and (iv) including 96PE lines (full). Theimages obtained with additional PE lines were comparedwith images obtained from the regular PE lines.

The included k-space data was configured into a 96x96matrix by padding zeros in the excluded region in the PEdirection. The images were reconstructed into a 96x96matrix and then interpolated down to a 64x64 matrix.

The reproducibility of the proposed method was testedby functional MRI scans of four additional subjects. Thesescans were obtained at a typical transverse sliceorientation with a variation of echo time ( = 25 and 30ms), pixel bandwidth (2605 to 3125 Hz/pixel), and voxelsize (3.2 and 3.5 mm3). The volunteers consented toparticipate in the study, whose protocol was approved bythe University IRB.

3. Results

The measured TSG and ISG were not zero neardiscontinuities at the ear canal and the inferior frontal sinusas shown in Fig. 3, which were similar to publishedsimulation and measurement results [14–16]. In the PEdirection (y), a positive and negative ISGPE were observed atthe anterior side of the ear canal and at the superior side ofthe frontal sinus, respectively.

In the k-space maps of the selected slices acquired withGE EPI, the echoes were indeed observed to be shifted andextended outside the regular PE range (Fig. 4A), which wasbetter demonstrated through the PE directional profile of thek-space map (Fig. 4B). In the 1st slice group (slice number23 - 25), the signals in the prior (left) side were higher thanthose in the posterior (right) side. In the 2nd slice group (slicenumber 29 - 31), by contrast, the signals in the posterior sidewere higher than those in the prior side. The direction of theecho shift agreed with the expected direction from Eq. (5)and the polarity of ISGPE in Fig. 3. It was observed that theamplitude of the shifted echo signals was reduced in theposterior side relative to that in the prior side, which could beattributed to the T2⁎ weighting.

The signal distribution in the echo trains of the k-spacemap was directly translated into the reconstructed imagesas expected (Fig. 5). The 1st slice group experiencedsignal loss around the ear canal when the prior 16 echoeswere excluded. In contrast, the 2nd slice group had signal

Fig. 3. Susceptibility gradient maps at the selected slices obtained from a human head. ISGRO, ISGPE, and TSG were in the x, y and z direction, respectively. The1st row is the inverted-intensity gradient echo images. The color bar unit is 7.57 μT/m and therefore 18 on the color bar is equal to 136 μT/m, which was abouthalf of gy ( = 276 μT/m).

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loss near the frontal sinus when the posterior 16 echoeswere excluded.

The brain regions without susceptibility gradients main-tained the same image intensity among the different

Fig. 4. The k-space maps (A) and their profiles (B), acquired with GE EPI at the sedenote the echo center and boundary of the regular PE range, i.e., at ky = ± 32, respecin (B). The contrast of the k-space map was enhanced by taking the logarithm and

reconstruction schemes since the signal was contained withinthe regular PE range, as seen in Fig. 4. The inclusion of bothsides clearly recovered the signals that had been shifted intothe extended PE lines from the regular PE range. Extending

lected head slices. In each slice of (A), the red and blue dashed vertical linestively. The signal difference at the PE range boundary is marked by an arrowapplying a gamma correction with a parameter of 0.5.

Fig. 5. Reconstructed and subtracted images acquired with GE EPI at selected head slices. The inclusion of the PE lines for each reconstruction was as follows:Reg = middle 64, Pre = pre 16 + middle 64, Post = middle 64 + post 16, and Full = pre 16 + middle 64 + post 16. The intensity of the subtraction images wasamplified 4-fold to enhance the difference.

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the PE lines in the posterior side of the PE range increased thescan time less than 10%.

The recovery of the signal loss demonstrated in Fig. 4 andFig. 5 was reproduced on additional four subjects. Therecovered regions and signal amount were very similar (datanot shown).

4. Discussion

The extension of the PE lines from 64 to 96 for the imagematrix of 64x64 is different from the signal acquisition forthe image matrix of 96x96. The echo spacing between twoadjacent PE blips is longer in the 96x96 matrix acquisitionthan in the 64x64 matrix acquisition due to the increasedreadout sample number. Therefore, the phase shift inducedby ISGPE on the spins will develop more during the increased

echo spacing of the 96x96 matrix acquisition than during the64x64 matrix acquisition.

The extended EPI is also different from oversampling inthe PE direction. Oversampling is done in order to avoidimage wrap-around in the PE direction through the increaseof the field-of-view in the PE direction. The increased field-of-view in the PE direction is achieved by sampling the PEdirection more finely with reduced amplitude of each PEincrement, as well as, by increasing the PE line numbers. Thedephasing lobe of the PE gradient remains the same as that inthe absence of oversampling. In contrast, the dephasing lobeneeds to be increased in the proposed extended EPI sequence.

In contrast to the GE EPI sequence, there was nonoticeable shift of the echo center in the spin echo (SE) EPIsequence (data not shown). A susceptibility-induced gradientwill not shift the echo center in the SE EPI as the refocusingof spins by the 180° RF pulse balances such inhomogeneities.

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Therefore, the signals were condensed near the echo centerand decayed quickly near the boundary of the regular PErange. As a result, the signals outside the regular PE rangewere smaller than those of GE EPI, and the signals recoveredby the extended acquisition of PE lines were not aspronounced as those of GE EPI.

The method of partial Fourier imaging cannot be appliedto GE EPI because of the shift of the echo center. The shiftedecho center can violate the assumed conjugate symmetry ofthe k-space data in reference to ky = 0 [17]. Therefore, theshifted echo center must be considered for each region withthe ISGPE in the partial Fourier reconstruction, which mightbe too complicated [18]. As the signal loss was notsignificant in SE EPI, the partial Fourier imaging can stillbe applied to the SE EPI as in diffusion weighted imaging.

The optimum echo time for BOLD sensitivity isproportional to the T2⁎ relaxation time of the gray matter[5]. At 3T the optimum echo time is greater than 30 ms [13].Therefore, the extension of the PE lines prior to the regularPE range does not increase the scan time. The extended PElines posterior to the regular PE range can be customized tominimize the increase in scan time. However, due to thepronounced T2⁎ decay at the posterior side as shown in Fig.4B, the extended PE lines in the posterior side can bereduced to minimize the increase in scan time. In addition,parallel imaging could further minimize the scan time.

The extended EPI method can be combined with othertechniques to recover signal loss due to the TSG gradientsuch as the z-shimming technique and optimization of sliceorientation. The slice orientation can be optimized tominimize the TSG at the region-of-interest [9,18,19]. Sincethe TSG can vary depending on the object shape andorientation relative to the main magnetic field direction, theoptimum slice orientation may need to be found experimen-tally for each subject [14,15,20]. However, the scan to findthe optimum slice orientation can be acquired before therepetitive scans of fMRI. The optimum slice orientation canbe found by comparing the image intensities obtained by theproposed extended GE EPI at each slice.

The inclusion of the extended PE lines to the imagereconstruction can degrade the signal-to-noise ratio (SNR) inbrain regions with negligible ISGPE, as the extra PE linescontain mostly noise without signal [21]. The SNR penaltycan be reduced either by adaptive filtering in the PE directionor by reconstruction methods other than the direct Fouriertransformation. Considering that the polarity of the ISGPE isconstant at each voxel, the shifted echo signal of a voxel canbe included in images with either the prior or posterior sideof the extended PE lines. Therefore, the image intensity ofeach voxel can be chosen between the regular and one of thepre or posterior extended PE ranges by comparing the imageintensity at each voxel.

The technique that applies z-shimming to the PE gradientincreases the scan time in proportion to the iteration of z-shimming [7,8]. In order to cover both the positive andnegative ISGPE, this technique requires at least 3 iterations,

resulting in a 3-fold increase of scan time. However, it is notclear how many iterations are necessary to cover the widerrange of ISGPE. The scan time penalty can be reduced byapplying the z-shimming only to the slices affected by ISGPE

at the cost of variation of the image intensity due to the timedifference of spin relaxation of the selected slices [22]. Onthe other hand, the repeated acquisitions will contribute to anincrease of SNR.

The method for recovery of signal, as described here,has the potential to benefit many individuals whose interestis in imaging regions that are subject to signal loss. Oneconcrete example is the recent interest in imaging theanterior inferior region of human temporal cortex which isactivated during tasks requiring face identification. Impor-tantly, the anterior temporal lobe, especially in the righthemisphere, is thought to play a key role in the ‘extended'face network [23] and to be involved in discriminatingbetween individual faces (i.e. Sally's face versus Jane'sface) [24,25]. This cortex is near the anterior side of the earcanal where the signal is restored by the proposed EPIsequence and improving data acquisition in this region willassist cognitive neuroscientists in their pursuit of the neuralcorrelate of individual face recognition.

5. Conclusions

The shift direction of the echo center and the effective PErange depend on the polarity of the ISGPE. The shift of theecho center and variation of the PE range resulted in atruncation of the signal in the PE direction when only theconventional PE range was sampled. The truncation of thesignal in the PE direction resulted in signal loss near theregion with the ISGPE.

The proposed extended sampling of the PE lines was ableto restore the lost signal that was shifted outside the regularPE range due to the ISGPE. Depending on the polarity of theISGPE, either the prior or posterior side of the extended PErange could contain the shifted echo signals. The scan timewas moderately increased when the posterior side of theextended PE lines was included.

With the proposed extended EPI sequence, the effect ofthe TSG can be minimized by optimizing the sliceorientation to reduce only the TSG without concernsabout the ISG. Furthermore, the proposed extended EPIcan be combined with other techniques to reduce the effectof the TSG.

References

[1] Hutchison JM, Sutherland RJ, Mallard JR. NMR imaging: imagerecovery under magnetic fields with large non-uniformities. J Phys [E]1978;11:217–21.

[2] Posse S. Direct imaging of magnetic field gradients by group spin-echoselection. Magn Reson Med 1992;25:12–29.

[3] Reichenbach JR, Venkatesan R, Yablonskiy DA, Thompson MR, LaiS, Haacke EM. Theory and application of static field inhomogeneity

783K.-J. Jung et al. / Magnetic Resonance Imaging 28 (2010) 777–783

effects in gradient-echo imaging. J Magn Reson Imaging 1997;7:266–79.

[4] Turner R, Ordidge RJ. Technical challenges of functional magneticresonance imaging. IEEE Eng Med Biol Mag 2000;19:42–54.

[5] Deichmann R, Josephs O, Hutton C, Corfield DR, Turner R.Compensation of susceptibility-induced BOLD sensitivity losses inecho-planar fMRI imaging. Neuroimage 2002;15:120–35.

[6] Chen NK, Oshio K, Panych LP. Application of k-space energyspectrum analysis to susceptibility field mapping and distortioncorrection in gradient-echo EPI. Neuroimage 2006;31:609–22.

[7] Frahm J, Merboldt KD, Hanicke W. Direct FLASH MR imaging ofmagnetic field inhomogeneities by gradient compensation. MagnReson Med 1988;6:474–80.

[8] Yang QX, Williams GD, Demeure RJ, Mosher TJ, Smith MB.Removal of local field gradient artifacts in T2⁎-weighted images athigh fields by gradient-echo slice excitation profile imaging. MagnReson Med 1998;39:402–9.

[9] Deichmann R, Gottfried JA, Hutton C, Turner R. Optimized EPI forfMRI studies of the orbitofrontal cortex. Neuroimage 2003;19:430–41.

[10] Ojemann JG, Akbudak E, Snyder AZ, McKinstry RC, Raichle ME,Conturo TE. Anatomic localization and quantitative analysis ofgradient refocused echo-planar fMRI susceptibility artifacts. Neuro-image 1997;6:156–67.

[11] Cho ZH, Kim DJ, Kim YK. Total inhomogeneity correction includingchemical shifts and susceptibility by view angle tilting. Med Phys1988;15:7–11.

[12] Jung KJ, Moon CH. Effect of slice angle on inhomogeneity artifact andits correction in slice-selective MR imaging. Concepts Magn ResonPart A 2009;34(A):238–48.

[13] Fera F, Yongbi MN, van Gelderen P, Frank JA, Mattay VS, Duyn JH.EPI-BOLD fMRI of human motor cortex at 1.5 T and 3.0 T: sensitivitydependence on echo time and acquisition bandwidth. J Magn ResonImaging 2004;19:19–26.

[14] Truong TK, Clymer BD, Chakeres DW, Schmalbrock P. Three-dimensional numerical simulations of susceptibility-induced magnetic

field inhomogeneities in the human head. Magn Reson Imaging2002;20:759–70.

[15] Li S, Dardzinski BJ, Collins CM, Yang QX, Smith MB. Three-dimensional mapping of the static magnetic field inside the humanhead. Magn Reson Med 1996;36:705–14.

[16] Koch KM, Papademetris X, Rothman DL, de Graaf RA. Rapidcalculations of susceptibility-induced magnetostatic field perturbationsfor in vivo magnetic resonance. Phys Med Biol 2006;51:6381–402.

[17] Jesmanowicz A, Bandettini PA, Hyde JS. Single-shot half k-spacehigh-resolution gradient-recalled EPI for fMRI at 3 Tesla. Magn ResonMed 1998;40:754–62.

[18] Chen NK, Oshio K, Panych LP. Improved image reconstruction forpartial Fourier gradient-echo echo-planar imaging (EPI). Magn ResonMed 2008;59:916–24.

[19] Speck O, Stadler J, Zaitsev M. High resolution single-shot EPI at 7T.MAGMA 2008;21:73–86.

[20] Xu N, Li Y, Paschal CB, Gatenby JC, Morgan VL, Pickens DR,Dawant BM, Fitzpatrick JM. Simulation of Susceptibility-InducedDistortions in fMRI. Proc. SPIE Medical Imaging. San Diego, CA:SPIE; 2006. p. 614461.

[21] Windischberger C, Moser E. Spatial resolution in echo planar imaging:shifting the acquisition window in k-space. Magn Reson Imaging2000;18:825–34.

[22] Du YP, Dalwani M, Wylie K, Claus E, Tregellas JR. Reducingsusceptibility artifacts in fMRI using volume-selective z-shimcompensation. Magn Reson Med 2007;57:396–404.

[23] Avidan G, Behrmann M. Functional MRI reveals compromised neuralintegrity of the face processing network in congenital prosopagnosia.Curr Biol 2009;19(13):1–5.

[24] Kriegeskorte N, Formisano E, Sorger B, Goebel R. Individual faceselicit distinct response patterns in human anterior temporal cortex. ProcNatl Acad Sci U S A 2007;104:20600–5.

[25] Rajimehr R, Young JC, Tootell RB. An anterior temporal face patch inhuman cortex, predicted by macaque maps. Proc Natl Acad Sci U S A2009;106:1995–2000.