A half-Fourier gradient echo technique for dynamic MR imaging

I I, pp.357-366.

Magnetic Resonance Imaging, Vol. Printed in the USA. All rights reserved.

1993 Copyright 0

0730-725X/93 16.00 + .OO I!993 Pergamon Press Ltd.

0 Original Contribution A HALF-FOURIER GRADIENT ECHO TECHNIQUE FOR DYNAMIC MR IMAGING W~LIAM H. PERMAN,* KENNETH

0~ EL-GHAZZAWY,~ MOKHTAR H. GADO,~ B. LARSON,$[[ JOEL S. PERLMUTTER]~

*Department of Radiology, Saint Louis University School of Medicine, St. Louis, MO 63 110-0250, USA; TDepartment of Chemistry, Washington University, St. Louis, MO, USA; SMallinckrodt Institute of Radiology, $Institute for Biomedical Computing, I(Department of Neurology and Neurological Surgery, Washington University School of Medicine, St. Louis, MO, USA Recently we developed the simultaneous dual FLASH (SDFLASH) pulse sequence that simultaneously obtains sequential images from the brain and the internal-carotid arteries in the neck with 1-set temporal resolution using a standard MR scanner. The high temporal resolution (1 set) of the SDFLASH technique was achieved partly by using a low number of phase-encoding views which thereby limited our in-plane spatial resolution to 6.25 x 3.12 mm pixels. To overcome this limitation we have developed a calibration technique which corrects distortions in signal intensity and object shape when using gradient echo half-Fourier spin warp imaging. Using this calibration technique, the operator can use the 41% decrease in scan time to either double the spatial or temporal resolution. We have successfully used this technique to acquire SDFLASH images of the head and neck with 1.0 set temporal resolution and 3.12 x 1.6 mm spatial resolution.

Keywords: Reconstruction algorithms; Perfusion imaging; Rapid imaging. INTRODUCTION

either increase the temporal resolution by nearly a factor of two for the same spatial resolution, or increase the spatial resolution in the phase-encoding direction by a factor of two while maintaining almost the same temporal resolution. As with all half-Fourier techniques, the penalty for doubling spatial or temporal resolution is a decrease in the signal-to-noise ratio (SNR) by a factor of a.

Important information about local neuronal functional and cerebrovascular status can be provided by the measurement of regional cerebral blood flow (rCBF) and regional cerebral blood volume (rCBV). Determination of rCBF and rCBV using MR imaging and intravascular paramagnetic contrast agents (e.g., Magnevist GdDTPA, Berlex Laboratories Inc., Wayne, New Jersey) requires rapid sequential measurements of contrastagent concentration in arterial blood and in brain tissue. Recently we developed the simultaneous dual FLASH (SDFLASH) pulse sequence1y2that simultaneously obtains sequential images from the brain and the internal carotid arteries in the neck with 1-set temporal resolution using a standard MR scanner. The high temporal resolution (1 set) of the SDFLASH technique was achieved partly by using a low number of phaseencoding views which limited our in-plane spatial resolution to 6.25 x 3.12 mm pixels. The purpose of this article is to present the implementation of a gradient echo half-Fourier technique, which allows the user to

Background The temporal resolution of FLASH-based dynamic MR imaging methods depends on the repetition time (TR) and the number of phase-encodings that are acquired for image reconstruction. Selection of the echo time of the 2nd echo (TE2) in the SDFLASH sequence determines the minimum TR available. We have chosen TE2 = 27 msec and TR = 34 msec in the SDFLASH sequence as the best compromise between providing adequate susceptibility weighting and minimizing image acquisition time. Therefore the only way to further reduce the SDFLASH scan time is to decrease the

RECENED 7/2/92; ACCEPTED 1 l/6/92. Address correspondence to William H. Perman, PhD, Department of Radiology, Saint Louis University Medical

Center, 3635 Vista Ave. at Grand Blvd., P.O. Box 15250, St. Louis, MO 63110-0250. 351

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number of phase-encoding views acquired for image reconstruction. Consider the typical spin warp3 imaging experiment shown in Fig. 1 where the raw data is obtained for M,,

views or phase-encodings, with N, sampled frequencyencoded points for each view. We denote the signal of the N, x MY sampled complex raw data set (time domain) as S(kx,ky), where S(kx,ky) = re(kx,ky) +

,ky= 1

I

Measure S(kxo+q, kyo-e)” -

ky, = My/2 + I

G,=O /

I

I I

Calculate S( kxo-q, kyo+e)

I I

I

I ..

I

I

Opa=-%a:

I

I

f-J=

‘MY

kx,=N,/2+1 (A)

0

w=%ax

.

“‘Y-

ky,=M,f2+1

G,=O

Calculate

I

I I $e=

’

-%a:

I I

I I .

I

Kx,=N,/2+1

1 MY

0)

Fig. 1. Cartesian representation of a typical spin warp imaging experiment where raw data is obtained for MY = 64 views or phase-encodings, with N, = 64 frequency-encoded points for each view. G,, is the maximum amplitude of the phaseencoding gradient, G,,. The central phase-encoding view (G, = 0) is given by /cv = ky, = MY/2 + 1. (A) When the calibra-

tion constants are determined before taking the Fourier transform along the frequency-encoding direction, the complex conjugate of point S(kx o+,, ,ky,_,) is point S(kx,_, ,kyo+J. (B) When the calibration constants are determined after taking the Fourier transform along the frequency-encoding direction, the complex conjugate of point S( kxo+h, ky,_, ) is point S(kx,+,,kY,+,

).

Half-Fourier gradient echo 0 W.H. PERMANETAL.

j im (kx, ky), where j = J-i. We also Let G,, be the maximum amplitude of the phase-encoding gradient (G,,) as determined by selected field-of-view and number of phase-encoding steps.4 During the scan the phase-encoding gradient amplitude is decreased in discrete steps from + G,, to -G,, . The central phaseencoding view or line number index (where G,, = 0) is given by ky, = ky, = MY/2 + 1. Since the subject undergoing MR scanning is real, it is theoretically possible to reduce the number of phase-encodings and thus the scan time, without loss of spatial resolution, by using partial or half-Fourier methods4-6 of data collection. In theory these methods collect only half of the necessary phase-encodings, that is, from ky, = 1 to ky, (phase-encoding gradient amplitudes G,, to 0), or from ky, = ky, to MY (phase-encoding amplitudes 0 to -G,,), and then invoke the Hermitian symmetry of real objects to obtain the missing views from the sampled views for image reconstruction. Half-Fourier imaging has been successfully applied to spin warp imaging&i’ using radiofrequency (RF) spin echoes. However, it was discovered that simple complex conjugation of the measured half of the raw data to produce the

359

missing phase-encoding views did not produce acceptable images due to constant, linear, and quadratic phase-error terms present in the MR raw data.6*‘2 Although several algorithms’2T’3 were proposed to decrease the phase errors, the current implementation of spin echo half-Fourier imaging provides acceptable image quality by collecting several additional phaseencoding views (m) following ky, (i.e., m = 9 for a nominal 256 phase-encoding acquisitior#‘) to directly measure the lower order phase terms. When this same oversampling technique is applied to gradient echo half-Fourier spin warp imaging, asymmetries in the static magnetic field and susceptibility heterogeneity within the subject produce significant phase errors in the raw data which severely degrade image quality, even for moderate values of m as shown in Fig. 2. We have developed a calibration technique based upon obtaining a full-Fourier set of baseline SDFLASH dynamic scans (20 scans at 2 set per scan) which then enable calculation of magnitude and phase calibration constants for each Hermitian pair in the raw data. These calibration constants then are applied to the half-Fourier dynamic raw data during recon-

Fig. 2. The full-Fourier (My = 64 and IV, = 128) (A) image of a kite spatial-resolution phantom contained in a homogeneous medium. The uncorrected (B), corrected using the Pre-FFT method (C), and corrected using the Post-FFT method (D) halfFourier images with m = 3.

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struction to substantially remove phase artifacts, thereby allowing the use of half-Fourier gradient echo data collection for dynamic MR imaging.

Therefore,

after measuring

the half-Fourier

views

ky, = 1 to ku, + m, the real and imaginary parts of views ku, = ky, + m + 1 to MY were calculated from

the measured views by MATERIALS AND METHODS

re(kx,-,&+,) MR scanning of normal human subjects and MR phantoms was performed on a 1.O T whole-body imaging system (Siemens Medical Systems, Inc., Iselin, New Jersey). Unless otherwise noted, 20 trans-axial reference full-Fourier raw data sets (2.18 set/data set) were obtained for two separate slice locations using the SDFLASH pulse sequence with TR = 34 msec, TE = lo,27 msec, FOV = 200 mm, thickness = 10 mm, echosampling time of 5.12 msec, and an acquisition matrix of 64 phase-encoded by 128 frequency-encoded points, giving in-plane spatial resolution of 3.12 x 1.56 mm. The raw data was saved on the MR system disk at the end of the scanning. The uncorrected gradient echo half-Fourier image is obtained by measuring the views from ky, = 1 to kYo+m3 and then performing a 2-dimensional Fourier transform on the raw data with zero filling of the raw data matrix. The corrected half-Fourier image is obtained by measuring the views from ky, = 1 to kyo+m, then calculating the missing views from ky, = m + 1 to MY using calibration constants determined from the average full-Fourier raw data set. We investigated two methods for calculating and applying the magnitude, si (kx,, ky,,,), and phase, 4i (kx,, ky,), calibration factors. In one method the average full-Fourier raw data set was determined by averaging the real and imaginary values of 10 raw data sets before performing the Fourier transform along the rows in the frequencyencoding direction (Pre-FFT method). The calibration constants for ku, = ku, + m + 1 to MY were determined by taking the ratio of the magnitude values, s1 (kx,, , ky,), of the Hermitian pairs ~1 (kwv,kyo+,)

=

mag(kx,-,, ky,+, )

X COS[4i(kXo-,,kYo+c)l, (24 and im(kx,-,,ky,+,)

= mag(kx,+,,ky,-,) x SI (kx,-,,kyo+,) x sin[9i(kxo-,,kyo+,)1

,

(2b)

where E takes on values from m + 1 to M,/2, and T,Jtakes the values of 1 to N,/2. Following determination of the missing views of the raw data matrix, the rows and columns were sequentially Fourier-transformed to form a magnitude image. The receiver gain and image scale factor were kept constant for all image reconstructions, allowing direct comparison of magnitude-image values. In the second method, the Fourier transform of the averaged raw data set (10 data files) is taken along the rows in the frequency-encoding direction (Post-FFT method) before the calibration constants are determined. Since the first FFT has already been performed the calibration constants are determined as above, except that each view is not reversed before finding the calibration value

~=m+

1,. ..M,/2;

9 = l,.. .N,

,

W

and

7 = 1,. . .N,/2

.

(la)

The & (kx,, ku,) calibration constants for views ky, = ky, + m + 1 to MYwere determined by the phase relationship of the full-Fourier data point to be estimated from a half-Fourier data collection. For example,

e=m+l,...

x ~1(kx,-,,kyo+,)

mag(kx,+,,ky,-,) ’

E = m + 1, M,/2;

cbi(kX~_,,ky,+,)

= mag(kx,+,,ky,-,)

= atan-’

im(kx,-,,ky,+,) re(kxO-,,k.vO+,)

A4__/2; 17=1,...

N,/2.

(lb)

&WX,,~Y,+,) = atan-’ e=m+

l,...

M/2;

v=l,...

N, .

(3b)

Note that we use Kx,, instead of kx, to denote that the data have been Fourier-transformed along the frequency-encoding direction. Similar to Method 1, views ky, = ky, + m + 1 to My were determined by applying the calibration constants determined using Eqs. (3a) and (3b) to the measured views such that

Half-Fourier gradient echo 0 W.H. PERMANET

361

AL.

RESULTS

x cc)S bb2Wx,,,~~,+,)1 ,

W

and imWx,,~~,+,)

= ma ( Q,,ky,-6) x

s2

(.Kx.,9kyo+,1

x sin[42Wx7,kyo+c)1 ,

(4b)

where E takes on values from m + 1 to MJ2. The raw data for the uncorrected and corrected halfFourier images was derived from the same set of fullFourier raw data. The magnitude image reconstructed using the full raw data set and standard 2-dimensional Fourier reconstruction then serves as a reference standard for quantitative evaluation of the half-Fourier reconstruction methods.

The full-Fourier magnitude image of a homogeneous phantom containing a lucite spatial-resolution insert is shown in Fig. 2A; the half-Fourier magnitude image derived from the same raw data with an oversampling of m = 3 views, but without completion of the raw data matrix, is shown in Fig. 2B. Note the significant degradation of image quality in Fig. 2B caused by asymmetries in the raw data resulting from susceptibility and static field induced variations in magnetic-field homogeneity. The signal intensity of the medium surrounding the resolution insert has significant peaks and valleys in the phase-encoding direction, and the holes of the resolution insert are elliptically distorted in the phase-encoding direction as described by Ludeke.r4 The corrected half-Fourier magnitude images obtained by completing the raw-data matrix using the Pre-FFT method and the Post-FPT method are shown in Figs. 2C and 2D, respectively. These figures demonstrate that both Pre- and Post-FFTcalibration techniques eliminate

m = 3 (A), the corrected using the Pre-FFT method (B), and corrected using the Post-FFT method (C) half-Fourier images. Profiles through the PMD images A-C are taken along the line shown in (D).

Fig. 3. The percent magnitude difference (PMD) of the full-Fourier image and the uncorrected image with

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the signal intensity variations which are apparent age (Fig. 2B).

and hole shape distortions in the uncorrected half-Fourier im-

One method of quantifying the effect of completing the raw-data matrix using the calibration factors before performing image reconstruction is to examine the percent magnitude difference (PMD) between the full-Fourier image (Fig. 2A) and the half-Fourier images (Figs. 2B-D). The full- versus half-Fourier PMD images for the uncorrected, corrected using the PreFFT method, and corrected using the Post-FFT method, are shown in Figs. 3A-C. Profiles taken along a representative line through the phantom in the phaseencoding direction (Fig. 3D) avoiding the resolution pattern are shown in Fig. 4A for the uncorrected and Post-FPT corrected PMD images. The PMD profile for the uncorrected half-Fourier reconstruction oscillates with excursions of 15% for positions 6-80, then increases to a maximum of 90% for positions 81-125.

The PMD profile for the half-Fourier image corrected using the Post-FFT method has a maximum excursion of less than 4% across the object. Profiles from the PMD images corrected using the Pre- and Post-FFT methods are plotted together in Fig. 4B. Note that both half-Fourier correction methods give similar results with a maximum PMD excursion of less than 4%. The results of using m = 0,3,6,9, 12, and 16 oversampled views for half-Fourier image reconstruction without completion of the raw data matrix are shown in Fig. 5. Significant (PMD > 10%) artifacts in signal intensity and hole distortion are present in the images until the view oversampling is such that 75% of the fullFourier phase-encoding lines have been sampled (49 of 64 possible phase-encodings were used for m = 16). Profiles through the PMD images for m = 0, 3, and 6 are shown in Fig. 6A, and for m = 9, 12 and 16 in Fig. 6B. The PMD profiles of the m = 16 uncorrected half-Fourier image and the Post-FFT corrected image

d ‘;I 12.0

POSITION (4

24.0

38.0

48.0

60.0

I

I

72.0

84.0

I

96.0

108.0

120.0

POSITION (B)

Fig. 4. (A) PMD profiles obtained from the uncorrected (dotted line) and corrected images using the Post-FFT method (dashed line) taken along the line shown in Fig. 3D. (B) PMD profiles obtained from half-Fourier images corrected using the Pre- (dotted line) and Post-FFT (dashed line) methods.

Half-Fourier gradient echo 0 W .H. PERMANET

Fig. 5. Uncorrected half-Fourier images reconstructed viewfs without completion of the raw-data matrix.

AL.

363

using m = 0 (A),3 (B),6 (C),9 (D), 12 (E), and 16 (F) oversampled

are shown in Fig. 6C. The Post-FFT corrected PMD profile demonstrates consistently lower values than the m = 16 PMD profile, especially at positions 66-126. The full-Fourier, uncorrected, and corrected halfFourier images of a normal subject are shown in Fig. 7 for a slice taken through the neck. Although the corrected half-Fourier images (Figs. 7B and 7C) do not display the large phase errors present in the uncorrected half-Fourier image (Fig. 7A), the image produced using

the Post-FFT correction method (Fig. 1D) displays lines of artifact running through the half-Fourier image. DISCUSSION It is evident in Fig. 2B that the uncorrected gradient echo haIf-Fourier image contains significant artifactual errors in image signal intensity and in apparent object shape. The effect of increasing the number of

Magnetic Resonance Imaging 0 Volume 11, Number 3, 1993

9

:

12. 0

24.0

30.0

48.0

I

60.0

72.0

,

34.0

es.0

1

108.0

1

120.0

s, ’

12.0

I

24.0

I 36.0

I 48.0

80.0

I 72.0

, 84.0

I 88.0

, 108.0

I 120.0

POSITION

POSITION

Fig. 6. PMD profiles of the uncorrected half-Fourier reconstructions having (A) m = 0 (dotted line), 3 (dashed line), and 6 (chain-dot line), and (B) m = 9 (dotted line), 12 (dashed line), and 16 (chain-dot line). The profiles were taken along the line shown in Fig. 3D. (C) The PMD profiles for the m = 16 uncorrected (dashed line) and corrected using the Post-FFT method (dotted line) half-Fourier reconstructions.

12.0

24.0

38.0

48.0

60.0 72.0 -_-_.-..

84.0

80.0

108.0

120.0

Half-Fouriergradientecho 0 W.H. PERMANET AL.

365

Fig. 7. The full-Fourier (A), uncorrected half-Fourier (B), Pre-FFT corrected half-Fourier (C), and Post-FFT corrected (D) half -Fourier images obtained through the neck of a normal subject.

oversampled phase-encoding views is to decrease these errors, but as shown in Fig. 6B, the oversampling needs to be on the order of 75% of the full-Fourier phaseencodings in order to decrease the errors to less than 10% for the case shown. The reduction in scan time for this case is then only 25% when view oversampling is used to correct the phase errors in a gradient echo halfFourier image. Since the artifact pattern is a function of the spatial magnetic-field homogeneity across the object, the number of oversampled views necessary to decrease the artifacts below 10% may vary for other objects or subjects due to object or subject specific susceptibility changes in the local magnetic field. The signal-intensity and object-shape distortions can be minimized to less than 4% in the case shown by applying the half-Fourier gradient-echo correction procedure. Since this technique directly measures calibration factors for each imaging situation, it is able to routinely produce good quality half-Fourier gradient echo images at a savings of 41% of the scan time regardless of the object or subject scanned. Although conceptually the same, the Pre- and PostFFT methods for calculating and applying the correc-

tion factors have different sensitivities to inconsistencies in the raw data. In the Pre-FPT method, in which calculation and application of the correction factors occurs before the Fourier transform along the frequencyencoding direction, inconsistencies in phase and amplitude that occur in the raw data appear as increased noise throughout the reconstructed half-Fourier gradient echo image, as is shown in Fig. 7C. When the correction factors are calculated and applied after performing the Fourier transform along the frequencyencoding direction (Post-FFT method), the inconsistencies in phase and amplitude of the single raw-data set with respect to the averaged calibration raw data cause local distortions which when Fourier transformed in the second direction appear as “lines” of artifact in the reconstructed half-Fourier gradient echo image as shown in Fig. 7D. Therefore, when amplitude and phase inconsistencies are present in the raw data the Pre-FFT method produces the most acceptable image quality by smearing the artifact across the entire image. Although the artifact lines appear to be associated with arterial or venous blood flow, their appearance in nonflowing phantoms (not shown), and the fact

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Magnetic Resonance Imaging 0 Volume

that a line of artifact is not associated with each vessel, argue that these artifacts result from magnitude and phase inconsistencies in the raw data. We have also found that the location of the artifacts changes for the same phantom from day to day and from scanner to scanner. The additional fact that the relative artifact locations change with the orientation selected for the scan would imply that these artifacts are a result of gradient and associated eddy-current instabilities. A further application of this technique would be the correction of a long TR (TR > 200 msec) gradient echo half-Fourier acquisition using a short TR (TR = 25 msec) calibration scan acquired with the same pulse sequence. If the imaging system is linear and stationary (i.e., both eddy currents and receiver phase shifts are constant between the two different TR scans) then the calibration factors determined from the short TR scan can be directly applied to the long TR scan since the calibration factors depend on the ratio of the amplitudes of the Kx,,+* and Kx,_,, views, and not on the actual amplitude values. In summary, we present a calibration technique that corrects distortions in signal intensity and in object shape when using gradient echo half-Fourier spin warp imaging. Using this technique, the operator can use the 41% decrease in scan time to either double spatial or temporal resolution. We have successfully used this technique to acquire SDFLASH images of the head and neck with 1.0 set temporal resolution and 3.12 x 1.6 mm spatial resolution. We are currently further reducing the spatial resolution in the phase-encoding direction by using an asymmetric field-of-view of 160 mm in the phase-encoding direction to obtain 2.5 x 1.6 mm spatial resolution. REFERENCES . Perman, W.H.; Gado, M.; Perlmutter,

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