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Journal of Magnetic Resonance 230 (2013) 111–116

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Journal of Magnetic Resonance journal homepage: www.elsevier.com/locate/jmr

Multi-Frame SPRITE: A method for resolution enhancement of multiple-point SPRITE data Joachim B. Kaffanke a,1, Sandro Romanzetti a,1, Thomas Dierkes a,b, Martin O. Leach c, Bruce J. Balcom d, N. Jon Shah a,e,⇑ a

Institute of Neuroscience and Medicine – 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany Institute for Biomagnetism and Biosignalanalysis, University of Muenster, 48149 Muenster, Germany Cancer Research UK Clinical Magnetic Resonance Research Group, The Institute of Cancer Research and The Royal Marsden NHS Foundation Trust, Downs Road, Sutton, Surrey SM2 5PT, United Kingdom d Department of Physics, MRI Centre, P.O. Box 4400, University of New Brunswick, Fredericton, NB, Canada E3B 5A3 e Department of Neurology, JARA, RWTH Aachen University, 52074 Aachen, Germany b c

a r t i c l e

i n f o

Article history: Received 26 September 2012 Revised 24 January 2013 Available online 9 February 2013 Keywords: Magnetic resonance imaging (MRI) Single point imaging (SPI) SPRITE Resolution enhancement Multi-Frame SPRITE Chirp z-transform (CZT) Multiple point acquisition Data processing Image reconstruction

a b s t r a c t The Single Point Ramped Imaging with T1 Enhancement (SPRITE) sequence is well suited for the acquisition of magnetic resonance signals from fast relaxing nuclei and from heterogeneous materials. However, it is time inefficient compared to sequences that are based on frequency encoding because only one single point is acquired per excitation. Multiple-point SPRITE (mSPRITE) mitigates this problem with the acquisition of multiple FID points. mSPRITE images reconstructed from early FID samples suffer from reduced spatial resolution due to the limited extent of its corresponding k-space. In this work we present a new reconstruction algorithm for spatial resolution enhancement that solves this problem without changes to the mSPRITE sequence. The method, called Multi-Frame mSPRITE, substitutes high spatial frequencies from late FID points into k-spaces of limited extent constructed from early FID points. In this way, images of high quality and resolution can be obtained despite a large range of zoom factors used to reconstruct images with the same FOV and resolution. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction The Single Point Ramped Imaging with T1 Enhancement (SPRITE) sequence has been extensively used for imaging studies of systems such as concrete, cement, polymers, and compact bone, in which relaxation times are very short [1]. Recently, it has also been used for in vivo imaging of sodium in the brain [2,3]. Other applications, characterised by short relaxation times, such as the imaging of bound water protons and the direct detection of oxygen and phosphorus in brain and muscles, may be rendered feasible by SPRITE. In the SPRITE sequence, spatial localisation is achieved by phase encoding spins at individual k-space locations prior to sampling the magnetisation at a single time point. Therefore, the time evolution of the magnetisation is not measured. This has the beneficial result, particularly for heterogeneous materials, that magnetic sus-

⇑ Corresponding author at: Institute of Neuroscience and Medicine – 4, Forschungszentrum Jülich GmbH, 52425 Jülich, Germany. Fax: +49 2461 61 8294. E-mail address: [email protected] (N. Jon Shah). 1 These authors contributed equally to the manuscript. 1090-7807/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2013.01.008

ceptibility, chemical shift, dipolar and quadrupolar effects are not measured and do not contribute to image artefacts. Furthermore, the strength of applied magnetic field gradients affects, excluding diffusion, only the final image resolution [4]. The major drawback of the SPRITE sequence is that the acquisition of one single sample per k-space point causes long acquisition times and reduces the sequence efficiency, making it particularly unsuitable for in vivo applications. With the introduction of multiple point SPRITE (mSPRITE) [5,6], the sequence efficiency improved significantly. In the mSPRITE sequence (Fig. 1A), multiple, M, data points are sampled after each RF excitation pulse. Since data acquisition is performed in the presence of active phase encode gradients, each of the M data samples can be used to construct M k-spaces of varying FOV (Fig. 1B). The M images can be combined, for example to obtain a signal-to-noise ratio (SNR) enhancement, but their FOVs must be matched beforehand. The chirp z-transform algorithm (CZT) can be employed for this purpose as suggested for reconstruction in multiple point Constant Time Imaging [7]. The CZT operates on spatial frequency data and computes the discrete Fourier transform (DFT) of arbitrary size [8]. Its effect is similar to a sinc interpolation [9,10], but it has the

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A RF

G TR

B

Fig. 1. The mSPRITE acquisition scheme. A non-selective broad band RF-pulse, a, is applied in presence of phase-encoding gradients, G, and the magnetisation is sampled at several encoding times, t0, t1, t2, . . . (A). Each of these points is used to form independent k-spaces, each with a different Dk. This leads to images that have different FOVs (B).

advantage of being able to accurately control the phase of the reconstructed images [11]. The CZT algorithm cannot improve the resolution of images of limited spatial frequency bandwidth. Therefore, images reconstructed using the CZT of data points acquired soon after the excitation have low resolution and suffer from strong Gibbs ringing artefacts. As a result, zoom factors have to be kept above a minimum value (e.g. >0.8), which limits the maximum number of collected data samples, and ultimately the sequence efficiency [6]. In this work we propose a new method, called Multi-Frame (MF), for the reconstruction of mSPRITE data. This method is based on the observation that each k-space dataset contains spatial frequency information of all the preceding ones. If the dwell time,

Dt, is kept short compared to the sample magnetisation relaxation time, the difference in signal intensity between consecutive datasets can be neglected and high spatial frequencies from late datasets can be used to enhance the resolution of early ones. The MF method should not be confused with standard keyhole imaging schemes. Keyhole methods sample the central portion of k-space which is then combined with high spatial frequency data from a base-line high-resolution measurement [12,13] to increase the temporal resolution of dynamic imaging. MF reconstruction of mSPRITE data is not intended for dynamic imaging but rather aims to average data acquired with different FOVs of samples with short relaxation times in an optimal way; this method is thus entirely distinct from standard keyhole imaging.

A

W0

W1

W2

W3

R1 = W1 - W0

R2 = W2 - W1

R3 = W3 - W2

W1 + R 2 + R 3

W2 + R 3

W3

B

C

W0 + R 1 + R 2 + R 3

Fig. 2. Schematic representation of the scaled k-space datasets and their use in the MF method: (A) k-spaces scaled to the common FOV represented by the solid square around the windows W, (B) frames of k-space data, (C) composite k-spaces.

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l = 0, 1, . . . M  1) location in the presence of phase-encode gradients (Fig. 1A). Samples acquired at each tl are combined to produce M independent k-space datasets. The integral of the phase encoding gradients is larger for later tl (Fig. 1B) which increases the kspace sampling rates, Dkl, proportional to the encoding time [4]:

Dkl ¼

c 2p

Z

tl

DGds ¼

0

c 2p

tl DG ¼ t l Dg;

ð1Þ

where DG is the amplitude of the gradient steps, and Dg = cDG/2p. Each independent k-space dataset is expressed as a function of the encoding time:

b Sðt l ; nDkl Þ ¼ b F ðnDkl ÞX l ðnDkl Þ;

n ¼ N=2; . . . ; N=2  1;

ð2Þ

where N is the size of the acquisition matrix, b F ðnDkl Þ is the discrete spectral representation of the real object F(x), and Xl(nDkl) is the kspace support defined as:

 X l ðnDkl Þ ¼

1 if  t l DgN=2 6 nDkl 6 t l DgðN=2  1Þ 0

otherwise

ð3Þ

From Eq. (1) is easy to recognise that the FOV of k-spaces obtained from early FID points (early k-spaces) is larger than the FOV of k-spaces obtained from late FID points (late k-spaces). Furthermore, Eqs. (2) and (3) show that the maximum extent of early k-spaces is smaller than of late k-spaces (Fig. 1B). Therefore, early images have lower resolution than late images. The standard reconstruction of mSPRITE data is based on the chirp z-transform algorithm (CZT) [6]. The CZT can be used to compute discrete Fourier transforms (DFT) of arbitrary size [8]. Using the CZT is possible to reconstruct k-space datasets directly into images of chosen FOV. The FOV used is that of the final k-space dataset to avoid aliasing artefacts in mSPRITE:

FOV ¼

1 1 ¼ DkM1 Dk

ð4Þ

with this choice, a zoom factor, Zl, for the lth k-space is defined as:

Zl ¼

tl : tM1

ð5Þ

Application of the CZT to the lth k-space dataset with final FOV and zoom factor results in the images Cl,m [8]:

C l;m ¼ ðZ l DkÞ

N=2 X

^Sl;n e2piZl mn=N

ð6Þ

n¼N=2

Fast Fourier Transformation (FFT) of these CZT-reconstructed b l: images reveals their spatial frequency spectrum, C

F ðjDkÞX Zl ðjDkÞ; Cbl ðjDkÞ ¼ FFTðC l Þ ¼ b where Fig. 3. Flow chart of the MF SPRITE method showing Fourier and image spaces at different stages of the data processing. After k-space acquisition with the mSPRITE sequence, a standard FFT produces images with different FOVs. (1) Images of common FOV, but different resolutions are reconstructed by the CZT. (2) The CZTreconstructed images are transformed back to k-space by using an inverse FFT. At this stage, acquired data have a different support in each k-space dataset but a common Dk. (3–4) Windows for relevant data and frames that extend the data of preceding k-spaces are calculated. (5) Application of the windows and frames to the following datasets, extending the high-frequency information to build up the composite k-spaces. (6) The resolution-enhanced images are finally calculated with a standard FFT.

2. Theory The equations given in this section are linearly independent in each spatial dimension. Therefore, for simplicity and without loss of generality, we describe the properties of the datasets and data processing only in one dimension. In an mSPRITE sequence, M samples of the MR signal are acquired at times tl after excitation (where tl = t0 + lDt;

X Zl ðjDkÞ ¼



j ¼ N=2 . . . N=2  1

1 if  Z l DkN=2 6 jDk 6 Z l DkðN=2  1Þ 0

otherwise

ð7Þ ð8Þ

The extents of the k-space supports of Eq. (8), XZl, and Eq. (3), XZ, are equal. The CZT leaves the spatial frequency spectra, b F , of the original datasets unchanged (Fig. 2A). The resolution of early CZT-reconstructed images can be enhanced if their supporting bandwidth is extended. To achieve this we introduce the concept of windows and frames, Wl and Rl respectively, that are defined as follows and represented schematically in Fig. 2A and B:

Wl ¼ b F ðjDkÞX Zl ðjDkÞ Rl ¼ W l  W l1

ð9Þ

The missing parts of the k-space of low-resolution early datasets are extended by the frames obtained from later datasets (Fig. 2C). Resolution-enhanced images, Il, are obtained after IFFT transform:

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" Il ¼ IFFT½ b Il  ¼ IFFT W l þ

M 1 X

# Ri

ð10Þ

i¼lþ1

This iterative widening method, called Multi-Frame (MF), improves the resolution without adversely effecting the signal intensity, as long as consecutive datasets have minimal variations of signal intensity. A complete flow-chart of the algorithm is shown in Fig. 3. 3. Experimental To characterise the MF method, computer simulations and mSPRITE MR measurements were performed. A synthetic 3D phantom composed of two concentric spheres of different T 2 was used to investigate the method in the presence of signal relaxation. The k-space signal of this phantom was synthesised by sampling two concentric Bessel functions on a 64  64  32 grid and modulating it with two exponential decays of T 2 ¼ 0:3 and 0.15 ms for the outer shell and inner sphere, respectively. 17 time points were simulated for each k-space point from 0.2 to 1.0 ms with constant interval, Dt, of 50 ls. This gave rise to zoom factors between 0.2 and 1.0. MR measurements were carried out on a 4 T whole-body scanner equipped with a Varian (Palo Alto, USA) Unity INOVA console and Siemens (Erlangen, Germany) Sonata gradients (40 mT/m maximum gradient strength and 200 mT/m/s maximum slew rate). A resolution phantom filled with transformer oil was used for the MR measurements in order to avoid B1 field inhomogeneity. The T1 of the phantom, measured with a standard inversion-recovery pulse sequence, was 200 ± 5 ms. T 2 was estimated from a pulse-acquire sequence to be 1.25 ± 0.05 ms. The repetition time, TR, of mSPRITE was set to 6 ms to supress residual magnetisation effects. The same 17 time points as the simulation were measured from 0.2 to 1.0 ms with a Dt of 50 ls. The zoom factors ranged from 0.2 to 1.0. The acquisition matrix size was 64  64  32 and the FOV of the M-th dataset was 256  256  256 mm3. To excite the whole FOV, a broadband RF pulse of 6.25 ls duration and a flip angle of 1° was used [4]. A filter bandwidth of 80 kHz was used. Simulations and measurement were processed with the same software programmed with IDL 6.0 (Boulder, USA) on an Apple MAC OSX 10.7 (Apple Inc., Cupertino, California, USA). 4. Results Fig. 4 shows the results of the standard CZT and the MF reconstruction methods applied to the simulated phantom. In this figure,

only images corresponding to the acquisition times of 0.2, 0.4, 0.6 and 0.8 ms are shown (from left to right) for both methods because 1 ms images are identical. The zoom factors of these images were 0.2, 0.4, 0.6 and 0.8. Images reconstructed with CZT (top row) show decreasing blurring with increasing zoom factors. At low zoom factors (Zl = 0.2–0.4), low resolution and Gibbs ringing combine in such a way that even the simple two-compartment homogeneous structure is not reproduced. Images obtained with a zoom factor of 0.6 show moderate blurring, but Gibbs ringing is still clearly visible. Images of the same datasets reconstructed with the MF method are shown on the bottom row. In this images, the structure of the phantom is well separated already for the low zoom factor Zl = 0.2. Fig. 5 shows profile plots through the centre of the simulated phantoms. The incremented k-space bandwidth shows both the effects of higher image resolution and reduction of Gibbs ringing. Fig. 6 shows the application of the method to real MR data of a resolution phantom filled with transformer oil. For comparison with the simulated data, images have the same zoom factors (0.2, 0.4, 0.6, 0.8). The images reconstructed using the CZT are shown on the top row. Results of the MF method are shown in the bottom row. Here, the performance of the proposed MF method on the image resolution is clearly visible. In particular, Gibbs ringing is greatly reduced. Fig. 6 also shows that considerable image improvement is obtained already for zoom factors of 0.6–0.8. For example, the resolution rods of the sixth row of (counting from top to bottom) are barely discernible in the CZT image with zoom factor, Zl = 0.8. In the images reconstructed with the MF method the same rods are visible and with high contrast for all zoom factors used. Fig. 7 shows the profile plots through the 5th row of resolution rods (from top to bottom). These plots show that Gibbs ringing artefacts are consistently reduced and that structures that were lost by standard CZT reconstruction appear sharp. 5. Discussion The standard reconstruction of mSPRITE data is based on the CZT algorithm. This reconstruction, however, limits the maximum number of data points that can be acquired during each FID, because images reconstructed from early points have low resolution and suffer from strong Gibbs ringing artefacts. In this note we have demonstrated that the proposed MF method largely solves this problem. The CZT and MF reconstruction methods were applied on the same simulated and real MR data. Images reconstructed with the MF method surpassed the standard reconstruction both in terms

Fig. 4. Simulated phantom images of two concentric spheres with relaxation times of 0.15 ms (inner sphere) and 0.3 ms (outer sphere) reconstructed with the CZT (top row) and the MF methods (bottom row). The zoom factors, from left to right, of 0.2, 0.4, 0.6 and 0.8, corresponded to acquisition times of 0.2, 0.4, 0.6 and 0.8 ms, respectively.

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Fig. 5. Intensity profiles of the CZT (red) and the MF method (blue) through the centres of the simulated images in Fig. 4.

Fig. 6. Images of a resolution phantom filled with transformer oil acquired with the mSPRITE sequence. The encoding times were: 0.2, 0.4, 0.6 and 0.8 ms. The corresponding zoom factors, the same as for the simulated data, were (from left to right): 0.2, 0.4, 0.6 and 0.8.

Fig. 7. Intensity profiles of the CZT (red) and the MF method (blue) through the 5th row (counting from top) of the resolution phantom in Fig. 6.

of final resolution and reduced Gibbs ringing. A direct comparison of these images clearly showed their differences. CZT images of early FID points have a limited spectral support. Therefore, the early images have low resolution and suffer from strong Gibbs ringing. This combination is particularly undesirable in presence of structures, even simple ones, characterised by different T 2 values such as in the case of our simulated phantom. The MF method, however, shows increased image quality in terms of Gibbs ringing reduction and consequently it allows for better image interpretation. Images reconstructed from real MR data acquired with the mSPRITE sequence on a resolution phantom confirmed the previous findings. In particular, at small zoom factors the resolution rods

that were not visible in the CZT images could be easily differentiated in the MF images. Compared to previous works, the MF method allows the acquisition of images with smaller zoom factors. This was previously found to be limited to Zl = 0.8 [5]. The extension to zoom factors as low as Zl = 0.2 demonstrated here might be exploited, for example, to acquire more data for signal averaging and to further improve the efficiency of the mSPRITE sequence. A limitation of this method is that it only performs optimally if the image reconstructed from the last FID point has sufficient SNR. If this condition is not fulfilled, significant noise may be introduced in the final images. As a consequence, the acquisition interval cannot be stretched until the noise level is reached. This means that

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mapping short T 2 distributions, an interesting potential application of the proposed MF method, may not be accurate. Further investigations are required to fully assess the applicability of the proposed MF mSPRITE method for T 2 measurements. 6. Conclusion In this note, a method for mSPRITE reconstruction based on an iterative k-space bandwidth extension has been described. Both phantom and MRI experiments demonstrate that the proposed method provides better image quality than the standard CZT methods. References [1] B.J. Balcom, R.P. MacGregor, S.D. Beyea, D.P. Green, R.L. Armstrong, T.W. Bremner, Single-point ramped imaging with T1 enhancement (SPRITE), J. Magn. Reson. A 123 (1996) 131–134. [2] S. Romanzetti, M. Halse, J. Kaffanke, K. Zilles, B.J. Balcom, N.J. Shah, A comparison of three SPRITE techniques for the quantitative 3D imaging of the 23Na spin density on a 4T whole-body machine, J. Magn. Reson. 179 (2006) 56–64. [3] K. Reetz, S. Romanzetti, I. Dogan, C. Saß, C. Werner, J. Schiefer, et al., Increased brain tissue sodium concentration in Huntington’s disease – a sodium imaging study at 4 Tesla, NeuroImage (2012) 517–524.

[4] S. Gravina, D.G. Cory, Sensitivity and resolution of constant-time imaging, J. Magn. Reson. A 104 (1994) 53–61. [5] M. Halse, D.J. Goodyear, B. MacMillan, P. Szomolanyi, D. Matheson, B.J. Balcom, Centric scan SPRITE magnetic resonance imaging, J. Magn. Reson. 165 (2003) 219–229. [6] M. Halse, J. Rioux, S. Romanzetti, J.B. Kaffanke, B. MacMillan, I. Mastikhin, N.J. Shah, E. Aubanel, B.J. Balcom, Centric scan SPRITE magnetic resonance imaging: optimization of SNR, resolution, and relaxation time mapping, J. Magn. Reson. 169 (2004) 102–117. [7] O. Heid, Sensitivity Enhanced Single Point Imaging, Abstract ISMRM 1998, 2186. [8] L.R. Rabiner, R.W. Schafer, C.M. Rader, The chirp z-transform algorithm and its application, Bell Syst. Tech. J. 48 (1969) 1249–1292. [9] J. Kaffanke, T. Dierkes, S. Romanzetti, M. Halse, J. Rioux, M.O. Leach, B. Balcom, N.J. Shah, Application of chirp z-transform to MRI data, J. Magn. Reson. 178 (2006) 121–128. [10] L. Yaroslavsky, Boundary effect free and adaptive discrete signal sincinterpolation algorithms for signal and image resampling, Appl. Opt. 42 (2003) 4166–4175. [11] J. Rioux, M. Halse, E. Aubanel, B.J. Balcom, J.B. Kaffanke, S. Romanzetti, T. Dierkes, N.J. Shah, An accurate nonuniform fourier transform for SPRITE magnetic resonance imaging data, ACM Trans. Math. Softw. 33 (2007) 13–37. [12] J.J. van Waals, M.E. Brummer, W.T. Dixon, H.H. Tuithof, H. Engels, R.C. Nelson, B.M. Gerety, J.L. Chezmar, J.A. Denboer, KEYHOLE method for accelerating imaging of contrast agent uptake, J. Magn. Reson. Imag. 3 (1993) 671–675. [13] R.A. Jones, O. Haraldseth, T.B. Müller, P.A. Rinck, A.N. Oksendal, K-space substitution: a novel dynamic imaging technique, Magn. Reson. Med. 29 (6) (1993) 830–834.