PULSAR: A MATLAB Toolbox for Parallel Magnetic Resonance Imaging Using Array Coils and Multiple Channel Receivers

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1 PULSA: A MATLAB Toolbox for Parallel Magnetic esonance Imaging Using Array Coils and Multiple Channel eceivers JIM X. JI, 1 JOG BUM SO, 1 SWATI D. AE 2 1 Department of Electrical and Computer Engineering, Texas A&M University, College Station, Texas Department of Bioengineering, Georgia Institute of Technology, Atlanta, Georgia ABSTACT: Partial parallel imaging (PPI) techniques using array coils and multichannel receivers have become an effective approach to achieving fast magnetic resonance imaging (MI). This article presents a Matlab toolbox called PULSA (Parallel imaging Utilizing Localized Surface-coil Acquisition and econstruction) that can simulate the data acquisition and image reconstruction, and analyze performance of five common PPI techniques. PULSA can simulate sensitivity functions of rectangular loop coils using a quasi-static model based on Biot-Savart s Law and undersampled multichannel data acquisition on a rectilinear k-space grid. In addition, PULSA provides performance evaluation of the techniques based on artifact power (AP), signal-to-noise ratio (S), and computational complexity. In this article, the structure and functionality of the PULSA toolbox are described. Examples using both the simulated and real four-channel and eight-channel data were used to demonstrate the utilities of the toolbox and to show that PULSA is a convenient and effective means to study the PPI under different coil geometries, acquisition strategies, and reconstruction methods Wiley Periodicals, Inc. Concepts Magn eson Part B (Magn eson Engineering) 31B: 24 36, 2007 KEY WODS: parallel imaging; magnetic resonance imaging; image reconstruction; toolbox; SESE; SMASH; GAPPA; PILS; SPACE-IP ITODUCTIO eceived 16 August 2006; revised 13 October 2006; accepted 13 October 2006 Correspondence to: Jim Ji, Ph.D.; jimji@tamu.edu Concepts in Magnetic esonance Part B (Magnetic esonance Engineering), Vol. 31B(1) (2007) Published online in Wiley InterScience ( com). DOI /cmr.b Wiley Periodicals, Inc. Technical developments of partial parallel imaging (PPI) techniques using array coils and multichannel receivers in the past decade provide an effective approach to achieving fast magnetic resonance imaging (MI). A number of data acquisition and image reconstruction strategies have been proposed and adopted for clinical MI applications such as realtime cardiovascular imaging, functional MI, and contrast-enhanced M studies (1 5). This article presents a Matlab Toolbox called PULSA (Parallel imaging Utilizing Localized Surface-coil Acquisition and econstruction) that can simulate and analyze the data acquisition, image reconstruction, and performance of five widely used PPI techniques. In a parallel MI system (illustrated in Fig. 1), multiple-channel receivers acquire k-space data simultaneous in parallel. The acquired data are encoded by both the gradient-induced encodings (e.g., phase and frequency encodings) and the coil sensitivities. Because the coil elements have different sensitivity functions, the data acquired from L channels, d 1 (k), d 2 (k),...,d L (k), are not the same but contain complementary information. As a result, phase encodings in MI can be reduced to save imaging time. However, to reconstruct desirable images from the reduced k- 24

2 PULSA: A MATLAB TOOLBOX FO PAALLEL MI 25 Channel Information Coil 1 Coil 3 Coil L eceiver 1 d1 eceiver 2 d2 d3 d4 Image econstruction Image Figure 1 Illustration of a parallel MI system using array coils and multichannel receivers. space data, special reconstruction algorithms must be used to fuse the k-space data from multiple channels. A partial list of the previously proposed PPI techniques includes SESE (Sensitivity Encoding), GAPPA (Genealized Autocalibrating Partially Parallel Acquisitions), SMASH (Simultaneous Acquisition of Spatial Harmonics), PILS (Parallel Imaging with Localized Sensitivity), and SPACE-IP (Sensitivity Profiles from an Array of Coils for Encoding and econstruction In Parallel) (6 10). Although the mathematical foundation of the various reconstruction methods is the same, they involve different assumptions and approximations. Consequently, each method performs differently under given imaging conditions (e.g., array geometry and k-space data sampling scheme). Methods also vary in terms of numerical stability, needs for accurate sensitivity estimate, and computational complexity. To develop and deploy PPI techniques for a specific application, it is desirable to qualitatively and quantitatively characterize and analyze the techniques. Currently, M engineers and researchers often have to implement PPI data processing and reconstructions from scratches based on the literatures. Though the applications of PPI technique and numbers of related publications keep increasing, more efforts are needed eceiver 3 eceiver 4 eceiver L dl to make useful research and education tools for parallel MI accessible to the general M community (11). PULSA is an open-source toolbox developed in our lab to serve as a research and educational platform for parallel MI. The software toolbox was written in MATLAB to provide data simulation, image reconstruction, and performance analysis for parallel imaging techniques. The toolbox consists of three main modules: (1) simulation of coil sensitivities and multichannel k-space data; (2) image reconstruction using five well-known PPI methods; and (3) performance evaluation based on artifact power (AP), signal-tonoise ratio (S), and computational complexity. In this article, we describe the structure and functionality of the PULSA toolbox and demonstrate how to use PULSA to study and explore PPI techniques using a set of experiments with simulated and real parallel MI data. STUCTUE AD FUCTIOS OF THE PULSA TOOLBOX As illustrated in Fig. 2, PULSA consists of three major parts: (1) data acquisition and simulation; (2) image reconstruction, and (3) performance analysis. Data Acquisition and Simulation As shown in Fig. 2, parallel MI image reconstruction generally requires two sets of data: undersampled k-space data ( d 1 (k), d 2 (k),...,d L (k), ) and additional calibration data (used for channel sensitivity estimate or for autocalibrated reconstructions). In practical applications, raw data acquired by M systems can be read into Matlab data file and then PULSA can be used to process the data. In simulations, PULSA can synthesize multichannel data for a given coil geometry, object image function, and sampling scheme. The data organization convention in PULSA (for 2D experiments) is defined in Table 1. Figure 2 Overview of the structure and data flow of the PULSA Toolbox.

3 26 JI, SO, AD AE Table 1 The Data Organization Convention in the PULSA Toolbox Dimension 1 st 2 nd 3 rd k-space domain k y (i.e., phase-encoding direction) k x (i.e., frequency-encoding direction) coil Image domain y x coil Coil Sensitivity Simulation. In the present implementation, PULSA models array coils made of rectangular loops based on a quasi-static assumption. Specifically, it assumes that the wavelength at the Larmor frequency is large compared with the size of the object to be imaged. In this case, the B1 field can be calculated based on the Biot-Savart Law: B r 4 l I r dl â 2 [1] where r is the vector from a point on the wire to an observation point at the image grid r, I is the current in the wire (assumed to be uniform on the wire), dl is the differential directional path along the wire, and â is the unit vector along r r (12 15). Here, B (B x, B y, B z ) is a 3D vector field. Because in MI only the transverse magnetization produces significant signals, the complex coil sensitivity function can be conveniently defined as S(r) B x (r) jb y (r). In PULSA, it is assumed that the coils are placed in space such that the coil loop plane is parallel to the B0 field. The array can be planar or wrapped around. Given the orientations of each coil element, and length and width of each loop, the program can compute the complex sensitivity of each coil on a specified voxel grid in the field of view (FOV). In its current implementation, PULSA does not simulate the noise correlation matrix. Interested readers are referred to (12, 13, 16) for further discussion on the topic. Simulation of k-space Data. Given a test phantom image with the desired FOV and voxel size and coil sensitivity functions, PULSA program can simulate k-space data with different sampling schemes. To do so, the image and each coil sensitivity function are multiplied in a point-by-point fashion, then a 2D discrete Fourier transform is applied to produce a fully encoded k-space data. To simulate acquisition data noise, zero-mean, circularly symmetric, complex Gaussian noise is added to the k-space data. In addition, noise from different channels or at different data points is also assumed to be independent. The noise variance of each data point contains contributions from both the real and imaginary noise. If the noise in the real and imaginary parts is assumed to be mutually independent, it is easy to show that 2 2 real 2 image. Because the Fourier transform reconstruction used in MI is an orthogonal operation, it follows that the average S per data point in k-space equals the average S per pixel in the image. Using the S definition in Eq. [5], it is straightforward to show that the noise variance real image 1 2 d exp S 20 [2] where the 2 counts for the complex noise factor, d is the mean square signal intensity defined as d (1/) n 1 d(n) 2, and S is the preferred average signal-to-noise ratio in decibels. To simulate undersampled dataset, data from all channels are decimated according to the desirable sampling scheme of a particular imaging method and reduction factors (). PULSA offers a flexible way to define the acquired phase-encoding lines, which can be centered, uniformly undersampled, or undersampled with variable density along the phase-encoding dimension. Image econstruction PULSA implements five commonly used reconstruction algorithms, namely, SESE, SMASH, PILS, GAPPA, and SPACE-IP. The current implementation of the algorithms works with rectilinear k-space data undersampled along one phase-encoding dimension. Among the methods, SESE, SMASH, and SPACE-IP require explicit channel sensitivity maps, PILS requires one-dimension sensitivity profile along the phase-encoding direction, and GAPPA is an autocalibrated method that does not require explicit sensitivity maps but nevertheless needs channel calibration data. Sensitivity Estimation. The sensitivity can be estimated by dividing individual coil images (which carry the channel sensitivity weighting) with a uniform image (6). The uniform image can be an image acquired using a body coil or a SOS (sum of squares) image of all coil images (14). Because the sensitivity

4 PULSA: A MATLAB TOOLBOX FO PAALLEL MI 27 maps are usually smooth functions, it often suffices to use low-resolution coil image reconstruction using zero-padded FFT from some central k-space data. In addition, PULSA implements several postfiltering algorithms to improve the sensitivity estimate, including polynomial fitting (6), singular value decomposition (svd) (18), wavelet filtering (19, 20), median filtering, and hamming filtering. For PILS reconstruction, PULSA supplies a 1D Gaussian profile fitting algorithm where the magnitude of the estimated sensitivity maps is projected to the phase-encoding direction and is used to fit a Gaussian function (9). SESE. The PULSA implements the basic Cartesian SESE algorithm and the improved SESE reconstructions with Tikhonov regularization and svd regularization (18, 19, 21, 22). The input to the function is the uniformly undersampled k-space data and estimated channel sensitivity functions. egularizations improve numerical condition of the SESE unfolding matrix, which is particularly useful when large undersampling factors are used. A regularization parameter is used to control the degree of regularization. For Tikhonov regularization, a regularization image can also be supplied. This image may be obtained from low-resolution calibration scan as in (19, 22). When it is not available (i.e., a zero image is used as regularization image), the regularization is degraded to the simple matrix regularization by adding positive constant to the diagonal elements (23, 39). PILS. PILS is a cut-and-paste parallel imaging reconstruction technique. It assumes that individual coil has localized sensitivity. As each coil just sees the partial image in the whole FOV, there is no significant aliasing even the k-space is undersampled (9). With this assumption, PILS reconstructs images by composing individual coil images according to the coil center locations using SOS recon. PILS works well with localized coils but may suffer from artifacts if the assumption of coil localization is invalid. To find central locations of coils, PULSA implements 1D Gaussian profile fitting, where the coil center is assumed to be the peak of the fitted Gaussian profile. SPACE-IP. SPACE-IP is a reconstruction method that can work with variable density sampling along phase-encoding direction in k-space (10). The method directly relates the coil sensitivity, gradientinduced encodings, and desirable image function with a set of linear equations. Image reconstruction can be achieved solving the equations. To overcome the possible ill conditions, SPACE-IP uses svd regularization in solving the linear system equations. Current implementation of the PULSA supports variable density sampling along the phase-encoding direction, though other sampling patterns and regularization schemes exist (10). As in SESE, SPACE-IP may suffer from artifacts coming from inaccurate sensitivity estimation. In general, SPACE-IP also requires solving a large linear system, which is time consuming. SMASH. SMASH is an early PPI technique significantly different from the three methods described above. In SMASH, a full k-space data set is synthesized from the acquired undersampled data from all channels (8). PULSA implements the original SMASH algorithm, including harmonic fitting from the estimated coil-sensitivity functions and data synthesis. It also contains an algorithm to extract object contours from the low-resolution sensitivity maps for tailored-smash method where the harmonic fitting excludes the background areas (21). PULSA does not include implementations of the AUTO-SMASH and VD-AUTO-SMASH algorithms as they are the predecessors of the GAPPA method, a widely used autocalibration technique (22, 23). GAPPA. GAPPA, similar to SMASH, recovers the missing k-space data using a linear interpolation model. However, it reproduces a set of k-space data for each channel and reconstructs the desirable image using an SOS operation. The generic GAPPA interpolation model uses neighboring undersampled k- space phase-encoding lines (blocks) and channels as input. The interpolation coefficients are uniform over all k-space regions and can be determined from a set of autocalibration signal (ACS) lines in the central k-space using least-squares fitting (7). MCMLI (multicolumn multiline interpolation) is a generalized GAPPA technique that includes blocks, channels, and adjacent frequency encodings (columns) in the interpolation model (24). Park s method performs adaptive fitting with ACS lines at different parts of the k-space, which can further improve reconstruction quality (25). In addition, the GAPPA operation can be performed in a hybrid k-x space where the frequency encoding direction is resolved using inverse Fourier transform. To accommodate these variations, PULSA implements a general multidimensional linear interpolation model that allows users to select blocks (phase encodings), columns (frequency encodings), neighboring channels (coils), ACS lines, localized/global fitting, and hybrid k-x space fitting.

5 28 JI, SO, AD AE Performance Evaluation Quantitative performance evaluation is an important aspect of parallel imaging. PULSA provides three quantitative criteria for evaluating PPI technique namely, artifact power, S, and computational complexity. These parameters may not accurately reflect the true performance, such as those from OC (receiver operating characteristic) evaluation, but in practical applications they are widely accepted and used by the M engineers because of the convenience (26). Artifact Power. Artifact power (AP) is directly related to the well-known square difference error. Assume that a fully encoded k-space data set is available. An SOS image can be reconstructed from such data and used as a reference to evaluate the reconstructed image from the undersampled k-space data (14). Specifically, the AP in PULSA is defined as (19, 27, 28) AP I reference x, y c I recon x, y 2 x,y OI [3] I reference x, y 2 x,y OI where I recon and I reference are the reconstructed image and the reference image, respectively. OI is the region of interest. Because a variety of scaling factors may be introduced during the reconstruction process, a constant c is introduced to minimize the scaling effect. This constant can be calculated by solving the equation I reference c I recon where I reference is a vector containing all pixels within the OI of the reference image and I recon is the corresponding vector of the reconstructed image. The denominator is a normalization factor corresponding to the total energy of the reference image. The evaluation is performed over the selected OI only, which can be a partial or whole image. ote that the AP definition in the above equation relies on the magnitude reconstruction only (i.e., any phase difference will not affect the quantity of the AP). This definition, in general, works for most applications. However, for phase-contrast imaging and other phase-sensitive applications, magnitude AP can be replaced by a more general MAE parameter (mean angular error) (29 31): MAE 1 arg e j recon x,y e j reference x,y [4] x,y OI where recon and reference are phase angles in reconstructed complex image and the reference image, respectively, is the total number of pixels in the OI, and arg{ } returns phase angle values in [, ). S. Image S in parallel imaging is unique in that it is location-dependent due to the coil geometry factor. As described in (6), S in parallel imaging depends on both the undersampling factors and the geometry-factor (a numerical indicator of numerical condition of the reconstruction). Depending on the number of image acquisitions (or simulations) available, PULSA provides three S performance evaluating criteria: two-region S, two-acquisition S, and pixel-wise S. The two-region S method can be applied to a signal image. Specifically, the two-region S is calculated from an OS (region of signal) and an O (region of noise) by (16): Mean of OS S 1 20 log Standard Deviation of O db [5] The O can usually be selected from the background areas where no object features present. This S strongly depends on where the OS and O are defined. An improved S evaluation is possible when two identical image acquisitions are available (28). Specifically, S 2 20 log 2 Mean of OI in any one acquisition Standard Deviation of OI in the subtracted image db [6] This definition assumes that the image features in the two acquisitions are identical, whereas the noise is independent. The scaling factor of 2 is necessary to balance subtraction operation in the denominator. The pixel-wise S provide an S map (i.e., spatial distributions of S over the FOV). Specifically, the S at any particular point is defined as (12) S 3 Mean of signals at a pixel over reconstructions 20 log Standard Deviation of signals at the pixel over reconstructions db [7]

6 PULSA: A MATLAB TOOLBOX FO PAALLEL MI 29 Table 2 Computational Complexity of Four Fundamental Algebraic Operations Operation Matrix Size Computational Complexity Matrix inversion O( 3 ) Matrix pseudoinversion M O(M 3 2M 2 ) Matrix multiplication P and P M O(MP) 2D FFT M O 1 2 log M log M where is the number of the identical acquisitions. The criterion requires multiple acquisitions but provides the most accurate and comprehensive S information. Particularly when using data simulation tools provided by PULSA, it is straightforward to repeat the simulations for times (using the same parameters but with random noise) to obtain the pixelwise S map. Computational Complexity. As PPI techniques are used to speed up image formation processes, their computational complexity is an important factor to consider. The computational complexity can be evaluated based on the number of complex multiplication operation required (ignoring the potential of parallel computing). Table 2 shows the number of complex multiplications for the four most common algebraic operations in parallel image reconstruction (32). Table 3 lists the necessary operations for channel/ sensitivity calibration and image reconstruction operation in each of the five PPI techniques. It shows only the operations in the generic algorithms. Some improved algorithms may have better reconstruction result at the price of more computational cost. ESULTS Data Simulation and Acquisition Two sets of simulated data were presented to demonstrate the utilities of PULSA for simulating multichannel MI data. The data sets correspond to a four-channel linear planar array and an eight-channel head array, respectively. The phantom images used in simulation are shown in Figure 3. Each coil-element in the four-channel linear array is assumed to have a size of 23 7 cm. Two neighboring coils are placed 6 cm apart (partially overlapped). Figure 4 illustrates the simulated sensitivity maps using the quasi-static model. The field of view of this plot is cm. Table 3 Typical Computation Complexity of the Five Generic PPI Algorithms Matrix Inversion Matrix Multiplication FFT Size o. Size o. Size o. SESE: Calib EG EG EG EG M C econ C M C, C 1 M M C PILS: Calib EG EG EG EG M C econ EG EG EG EG M C SPACE-IP: Calib EG EG EG EG M C C econ C C M, C 1 M M 1 C SMASH: Calib C EG EG M C econ EG EG C, C 1 M M 1 GAPPA: Calib MA BC C( 1) EG EG EG EG econ EG EG M CB, BC 1 CM( 1) M C : number of phase encodings; M: number of frequency encodings; : undersampling factor; C: number of channels; A: number of calibration lines; B: number of blocks in GAPPA; EG: negligible.

7 30 JI, SO, AD AE (a) (b) Figure 3 Phantom images used for simulation of (a) fourchannel linear array data and (b) eight-channel head array data. The simulation parameters of the eight-channel head array are: size of 22 7 cm, coils are uniformlly wrapped around a 25-cm-diameter cylinder. The axis of cylinder is parallel to the B0 field and the FOV is cm. Figure 5 displays the simulated sensitivity maps (magnitude only). Multichannel images were then created by multiplying the phantom images with the simulated sensitivity profiles. Data were added with complex Gaussian noise to make an S level of 25 db after these images are Fourier transformed to generate the multichannel k-space data. For testing the reconstruction algorithms in PUL- SA with in-vivo M data, two sets of real data were acquired using M systems with coil array and multichannel receiver. The first is a spine data set acquired on a 3 Tesla whole-body GE scanner (GE Healthcare, Waukesha, WI) from a healthy male volunteer using a four-channel CTL spine array with fast spoiled gradient-echo sequence, T/TE 300/12 ms, BW 62.5 khz, matrix size , tip angle 15, and FOV cm. The second is a brain data set acquired using an eight-channel head array with similar parameters except that T/TE 300/10 ms, BW 16 khz, and FOV cm. One fully sampled data set was acquired in each study. The multichannel images are shown in Fig. 6. To simulate undersampled datasets, k-space data were decimated using reduction factors of 2 and 3 for the four-channel spine dataset and 2 and 4 for the eight-channel brain dataset, respectively. Additionally, central 64 frequency-encoding lines were preserved to be used for coil sensitivity estimation or channel calibration. Image econstruction and Performance Evaluation using PULSA Channel sensitivity functions were estimated from 64 central k-space phase-encoding lines and processed using various filtering techniques. Figure 7 shows the estimated four-channel array sensitivity with various postprocessing. Artifact Power and S. The AP of PPI reconstructions of the in-vivo spine and brain experiments were evaluated using the OIs as defined in Fig. 8. The S of the images was evaluated using the tworegion S method because multiple identical data acquisitions as required by other S criteria are not available in these studies. The OS and OI definitions used for the S evaluation are also shown in Fig. 8. The obtained AP and S numbers are shown under the reconstructed images in Figs. 9 and Fig. 10. The reconstructed in-vivo spine and brain images are shown in Figs. 9 and 10, respectively. Except for the autocalibrating GAPPA method, channel sensitivity functions estimated from the 64 central k-space lines were postprocessed using a 5 5 median filter on the magnitude part. The phase was preserved. The coil-center locations for PILS were estimated using 1D Gaussian fitting. The same 64 k-space lines were used as ACS lines in GAPPA. The GAPPA reconstruction uses all channels and a block size of four. Coil 1 Coil 2 Coil 3 Coil 4 1 (a) π (b) 0 π Figure 4 Simulated sensitivity maps of the four-channel array: (a) magnitude and (b) phase.

8 PULSA: A MATLAB TOOLBOX FO PAALLEL MI Figure 5 Simulated sensitivity maps of the eight-channel head array. Due to the space limit, only the magnitude parts of the complex sensitivity maps are shown. As shown in both examples, GAPPA resulted in the high S and low AP. PILS and SMASH contain visually aliasing artifacts (arrows). The results show that the coil sensitivities in these experiments are not sufficiently localized for the PILS method, and the PILS method may show banding artifacts at high undersampling factors. It also shows that SMASH works better with linear spine array than with the head array for which the spatial harmonics are difficult to synthesize. GAPPA yields slightly better reconstruction quality than SPACE-IP and SESE in these examples because all methods performed sensitivity estimation using self-calibrated data. Computational Complexity. The overall computational complexity of the five reconstruction methods is shown in Fig. 11. As an example, the number of required complex multiplications is shown using the (a) Coil 1 Coil 2 Coil 3 Coil 4 (b) Coil 1 Coil 2 Coil 3 Coil 4 Coil 5 Coil 6 Coil 7 Coil 8 Figure 6 In-vivo M images acquired using (a) four-channel spine array and (b) eight-channel head array.

9 32 JI, SO, AD AE Coil 1 Coil 2 Coil 3 Coil 4 (a) (b) (c) (d) (e) Figure 7 Sensitivity estimation of the four-channel simulated array coils by (a) dividing coil images with the SOS image (64 central k-space lines used for estimation); (b) svd method by Walsh with a mask; (c) median filtering of (a) with 5 5 window; (d) filtering (a) with the first-order polynomial fitting; and (e) 1D Gaussian model fitting. Only the magnitudes of sensitivity functions are shown. following set of parameters: 256, M 256, C 8, B 2, and A 32 and 64 for various reduction factors. The graph shows that SMASH and PILS have relatively low computational complexity, although the reconstruction qualities by these methods are not as good as those by the other methods. SPACE-IP has the highest computational complexity, and SESE and GAPPA have comparable intermediate complexity. In PULSA, the computational time can also be tracked using the built-in timer in Matlab. DISCUSSIO The PULSA toolbox is not designed to be a comprehensive package of every known algorithm but rather as a basic set of reconstruction tools and a platform for continued development. There are a number of possible extensions to the current implementations. First, non-cartesian SESE and PAS (parallel magnetic resonance imaging with adaptive radius in k-space) can work with nonrectilinear k- space trajectories such as spirals to achieve highspeed imaging with array coils (33, 34). Second, in 3D acquisitions, 2D SESE and 3D GAPPA (i.e., undersampling along two phase encoding dimensions) can achieve better numerical conditions and therefore higher overall undersampling factors (35, 36). For dynamic imaging studies, joint undersampling along the temporal and phase encoding dimensions (e.g., T-SESE, k-t SESE and TGAPPA) can further

10 PULSA: A MATLAB TOOLBOX FO PAALLEL MI 33 O I O S O O S O I O Figure 8 The definitions of region of interest (OI), region of signal (OS), and region of noise (O) used for measuring artifact powers and signal-to-noise ratios. improve the efficiency for sensitivity estimation or channel calibration, or reconstruction quality (37, 38). Finally, the parallel excitation technique such as transmit-sese is a recent, active research area (40). These aspects of parallel imaging are expected to be incorporated in the toolbox when PULSA will be further developed. SUMMAY PULSA is a Matlab-based open source software toolbox for simulating data acquisition, image reconstruction, and performance analysis of parallel MI methods using multichannel receivers. In addition to functioning as an offline reconstruction tool, PULSA allows users to study parallel imaging under various coil geometry, undersampling factors, and reconstruction strategies. Signal-to-noise ratio, artifact power, and computational complexity were used to characterize the reconstruction methods. We demonstrated the utilities of PULSA using computer simulations and in-vivo data sets collected using array coils and multichannel receivers. The quantitative performance agrees well with visual inspections of the reconstructed images. The PULSA toolbox is expected to be useful for evaluating current PPI meth- SESE PILS SPACE-IP SMASH GAPPA =2 S AP =3 S AP Figure 9 Images reconstructed using PULSA from the four-channel in-vivo spine data. The AP and S are shown under each image.

11 34 JI, SO, AD AE SESE PILS SPACE-IP SMASH GAPPA =2 S AP =4 S AP Figure 10 Images reconstructed using PULSA from the eight-channel in-vivo head data. The AP and S are shown under each image. ods, developing new imaging methods, or learning the different parallel imaging methods. Moreover, we hope PULSA would provide a platform and basis for M engineers to expedite learning and research in parallel magnetic resonance imaging. The PULSA toolbox can be accessed at jimji. Calibration econstruction A = 16 A = 64 (a) (b) Figure 11 The representative numbers of complex multiplications of different reconstruction methods: (a) sensitivity estimation or channel calibration; (b) image reconstruction.

12 PULSA: A MATLAB TOOLBOX FO PAALLEL MI 35 ACKOWLEDGMETS The authors thank Dr. Dan K. Spence for providing coil modeling routines and Dr. Jingfei Ma for assistance in data acquisition. Support from the ational Institutes of Health (121EB A1) is gratefully acknowledged. EFEECES 1. Weiger M, Pruessmann KP, Boesiger P Cardiac real-time imaging using SESE. SESitivity Encoding scheme. Magn eson Med 43(2): Kostler H, Beer M, itter C, Hahn D, Sandstede J Auto-SESE view-sharing cine cardiac imaging. MAGMA 17: Huber M, Kozerke S, Pruessmann K, Smink J, Boesiger P Sensitivity-encoded coronary MA at 3T. Magn eson Med 52: van den Brink JS, Watanabe Y, Kuhl CK, Chung T, Muthupillai, Van Cauteren M, et al Implications of SESE M in routine clinical practice. Eur J adiol 46(1): Park J, McCarthy, Li D Feasibility and performance of breath-hold 3D TUE-FISP coronary MA using self-calibrating parallel acquisition. Magn eson Med 52: Pruessmann KP, Weiger M, Scheidegger MB, Boesiger P SESE: sensitivity encoding for fast MI. Magn eson Med 42(5): Griswold MA, Jakob PM, Heidemann M, ittka M, Jellus V, Wang J, et al Generalized autocalibrating partially parallel acquisitions (GAPPA). Magn eson Med 47(6): Sodickson DK, Griswold MA, Jakob PM SMASH imaging. Magn eson Imaging Clin orth Am 7(2): Griswold MA, Jakob PM, ittka M, Goldfarb JW, Haase A Partially parallel imaging with localized sensitivities (PILS). Magn eson Med 44(4): Kyriakos WE, Panych LP, Kacher DF, Westin CF, Bao SM, Mulkern V, et al Sensitivity profiles from an array of coils for encoding and reconstruction in parallel (SPACE IP). Magn eson Med 44(2): ane S, Ji J A MATLAB toolbox for parallel imaging using multiple phased-array coils. Proc 13th Int Soc Magn eson Med Wright SM, Wald LL Theory and application of array coils in M spectroscopy. M Biomed 10(8): Kellman P, Schnermann M, McVeigh E Comparison of 1-D and 2-D surface coil arrays for accelerated volume M imaging using sensitivity encoding. Biomed Imaging Proc 2002 IEEE International Symposium. p oemer PB, Edelstein WA, Hayes CE, Souza SP, Mueller OM The M phased array. Magn eson Med 16(2): ayfeh M, Brussel M Electricity and magnetism. ew York: Wiley. 16. Macovski A oise in MI. Magn eson Med 36: Walsh DO, Gmitro AF, Marcellin MW Adaptive reconstruction of phased array M imagery. Magn eson Med 43(5): Liang Z, Mammer, Ji J, Pelc, Glover G Improved image reconstruction from sensitivity-encoded data by wavelet denoising and Tikhonov regularization. Biomed Imaging 5th IEEE EMBS International Summer School. p Ji J, Son J Highly accelerated parallel imaging methods for localized massive array coils: comparison using 64-channel phased-array data. Proc IEEE Intl Symp Biomed Imaging. p Katscher U, Kohler T Underdetermined SESE. In: Workshop on minimum M data acquisition methods: making more with less. p McKenzie CA, Yeh E, Sodickson DK Improved spatial harmonic selection for SMASH image reconstructions. Magn eson Med 46(4): Jakob PM, Griswold MA, Edelman, Sodickson DK AUTO-SMASH: a self-calibrating technique for SMASH imaging. Simultaneous acquisition of spatial harmonics. MAGMA 7(1): Heidemann M, Griswold MA, Haase A, Jakob PM VD-AUTO-SMASH imaging. Magn eson Med 45(6): Wang Z, Wang J, Detre J Improved data reconstruction method for GAPPA. Magn eson Med 54: Park J, Zhang Q, Jellus V, Simonetti O, Li D Artifact and noise suppression in GAPPA imaging using improved k-space coil calibration and variable density sampling. Magn eson Med 53: Obuchowski A eceiver operating characteristic curves and their use in radiology. adiology 229: McGibney G, Smith M, ichols ST, Crawley A Quantitative evaluation of several partial Fourier reconstruction algorithms used in MI. Magn eson Med 30(1): Madore B, Pelc J SMASH and SESE: experimental and numerical comparisons. Magn eson Med 45(6): Bankson J, Stafford J, Hazle JD Partially parallel imaging with phase-sensitive data: increased temporal resolution for magnetic resonance temperature imaging. Magn eson Med 53: Willig-Onwuachi J, Yeh E, Grant A, Ohliger M, McKenzie C, Sodickson D Phase-constrained parallel M image reconstruction. J Magn eson 176: Son J, Ji J Auto-calibrated phase-sensitive partially parallel MI. Paper presented at the Proc of the

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