Multicoil Dixon chemical species separation with an iterative least-squares estimation method

Dixon techniques for water and fat imaging

In 1984, Dixon published a first paper on a simple spectroscopic imaging technique for water and fat separation. The technique acquires two separate images with a modified spin echo pulse sequence. One is a conventional spin echo image with water and fat signals in-phase and the other is acquired with the readout gradient slightly shifted so that the water and fat signals are 180 degrees out-of-phase. Dixon showed that from these two images, a water-only image and a fat-only image can be generated. The water-only image by the Dixon's technique can serve the purpose of fat suppression, an important and widely used imaging option for clinical MRI. Additionally, the availability of both the water-only and fat-only images allows direct image-based water and fat quantitation. These applications, as well as the potential that the technique can be made highly insensitive to magnetic field inhomogeneity, have generated substantial research interests and efforts from many investigators. As a result, significant improvement to the original technique has been made in the last 2 decades. The following article reviews the underlying physical principles and describes some major technical aspects in the development of these Dixon techniques.

Noise considerations of three-point water-fat separation imaging methods

Separation of water from fat tissues in magnetic resonance imaging is important for many applications because signals from fat tissues often interfere with diagnoses that are usually based on water signal characteristics. Water and fat can be separated with images acquired at different echo time shifts. The three-point method solves for the unknown off-resonance frequency together with the water and fat densities. Noise performance of the method, quantified by the effective number of signals averaged (NSA), is an important metric of the water and fat images. The authors use error propagation theory and Monte Carlo simulation to investigate two common reconstructive approaches: an analytic-solution based estimation and a least-squares estimation. Two water-fat chemical shift (CS) encoding strategies, the symmetric (-theta, 0, theta) and the shifted (0, theta, 2theta) schemes are studied and compared. Results show that NSAs of water and fat can be different and they are dependent on the ratio of intensities of the two species and each of the echo time shifts. The NSA is particularly poor for the symmetric (-theta, 0, theta) CS encoding when the water and fat signals are comparable. This anomaly with equal amounts of water and fat is analyzed in a more intuitive geometric illustration. Theoretical prediction of NSA matches well with simulation results at high signal-to-noise ratio (SNR), while deviation arises at low SNR, which suggests that Monte Carlo simulation may be more appropriate to accurately predict noise performance of the algorithm when SNR is low.

Cartilage imaging at 3.0T with gradient refocused acquisition in the steady-state (GRASS) and IDEAL fat-water separation

PURPOSE

To demonstrate the feasibility of evaluating the articular cartilage of the knee joint at 3.0T using gradient refocused acquisition in the steady-state (GRASS) and iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) fat-water separation.

MATERIALS AND METHODS

Bloch equation simulations and a clinical pilot study (n = 10 knees) were performed to determine the influence of flip angle of the IDEAL-GRASS sequence on the signal-to-noise ratio (SNR) of cartilage and synovial fluid and the contrast-to-noise ratio (CNR) between cartilage and synovial fluid at 3.0T. The optimized IDEAL-GRASS sequence was then performed on 30 symptomatic patients as part of the routine 3.0T knee MRI examination at our institution.

RESULTS

The optimal flip angle was 50 degrees for IDEAL-GRASS cartilage imaging, which maximized contrast between cartilage and synovial fluid. The IDEAL-GRASS sequence consistently produced high-quality fat- and water-separated images of the knee with bright synovial fluid and 0.39 x 0.67 x 1.0 mm resolution in 5 minutes. IDEAL-GRASS images had high cartilage SNR and high contrast between cartilage and adjacent joint structures. The IDEAL-GRASS sequence provided excellent visualization of cartilage lesions in all patients.

CONCLUSION

The IDEAL-GRASS sequence shows promise for use as a morphologic cartilage imaging sequence at 3.0T.

Multiresolution field map estimation using golden section search for water-fat separation

Many diagnostic MRI sequences demand reliable and uniform fat suppression. Multipoint water-fat separation methods, which are based on chemical-shift induced phase differences, have shown great success in the presence of field inhomogeneities. This work presents a computationally efficient and robust field map estimation method. The method begins with subsampling image data into a multiresolution image pyramidal structure, and then utilizes a golden section search to directly locate possible field map values at the coarsest level of the pyramidal structure. The field map estimate is refined and propagated to increasingly finer resolutions in an efficient manner until the full-resolution field map is obtained for final water-fat separation. The proposed method is validated with multiecho sequences where long echo-spacings normally impose great challenges on reliable field map estimation.

Simultaneous estimation of tongue volume and fat fraction using IDEAL-FSE

PURPOSE

To determine whether high-resolution, high signal-to-noise ratio (SNR) images of the tongue acquired with IDEAL-FSE (iterative decomposition of water and fat with echo asymmetry and least squares estimation) will provide comparable volumetric measures to conventional nonfat-suppressed FSE imaging and to determine the feasibility of estimating the proportion of lingual fat in adults using IDEAL-FSE imaging.

MATERIALS AND METHODS

Healthy volunteers underwent magnetic resonance imaging of the tongue using both IDEAL-FSE and conventional FSE sequences. The tongue was manually outlined to derive both volumetric and fat fraction measures. Intraclass correlation coefficients (ICCs) were computed for intrarater measurement reliability and Spearman's rank correlation tested the relationship between IDEAL-FSE and conventional volumetric measures of the tongue.

RESULTS

IDEAL-FSE imaging yielded almost identical volumetric measures to that of conventional FSE imaging in the same amount of scan time (IDEAL-FSE mean 64.1 cm(3); conventional mean 63.3 cm(3); r = 0.988, P < or = 0.01). The average fat signal fraction across participants was 26.5%. Intrarater reliability was excellent for all measures (ICC > or = 0.92).

CONCLUSION

Our results indicate that IDEAL-FSE provided similar lingual volume estimates to conventional FSE imaging obtained in both the current and previous studies. IDEAL-FSE measures of lingual fat composition may be useful in studies that aim to increase lingual muscle strength and volume in swallowing and speech-disordered populations.

A single-point Dixon technique for fat-suppressed fast 3D gradient-echo imaging with a flexible echo time

PURPOSE

To develop a single-point Dixon (SPD) technique that requires only data of a single echo with a flexible echo time, and to demonstrate its use for fat-suppressed, T1-weighted contrast agent enhancement studies.

MATERIALS AND METHODS

Raw data were collected using a product fast 3D gradient-echo pulse sequence. Phase-error removal and fat-suppression (FS) were achieved using a fully-automated region-growing algorithm. A water and fat phantom and the abdomen and breast of cancer patients before and after injection of gadolinium contrast agent were imaged at varying echo times. Scan time efficiency and overall FS quality were compared to those by the product fast 3D gradient-echo technique with conventional FS.

RESULTS

In phantom, the SPD technique achieved uniform FS for a wide range of echo times corresponding to the water and fat relative phase angles between 100 degrees and 160 degrees. In patients, the technique was able to achieve approximately 30% scan time reduction and more uniform FS when compared to using the conventional FS technique but otherwise identical scan parameters.

CONCLUSION

The SPD technique compares favorably in scan time efficiency and FS uniformity and can be useful for fast T1-weighted and fat-suppressed imaging with contrast agent administration.

Generalized k-space decomposition with chemical shift correction for non-Cartesian water-fat imaging

Chemical-shift artifacts associated with non-Cartesian imaging are more complex to model and less clinically acceptable than the bulk fat shift that occurs with conventional spin-warp Cartesian imaging. A novel k-space based iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) approach is introduced that decomposes multiple species while simultaneously correcting distortion of off-resonant species. The new signal model accounts for the additional phase accumulated by off-resonant spins at each point in the k-space acquisition trajectory. This phase can then be corrected by adjusting the decomposition matrix for each k-space point during the final IDEAL processing step with little increase in reconstruction time. The technique is demonstrated with water-fat decomposition using projection reconstruction (PR)/radial, spiral, and Cartesian spin-warp imaging of phantoms and human subjects, in each case achieving substantial correction of chemical-shift artifacts. Simulations of the point-spread-function (PSF) for off-resonant spins are examined to show the nature of the chemical-shift distortion for each acquisition. Also introduced is an approach to improve the signal model for species which have multiple resonant peaks. Many chemical species, including fat, have multiple resonant peaks, although such species are often approximated as a single peak. The improved multipeak decomposition is demonstrated with water-fat imaging, showing a substantial improvement in water-fat separation.

Improving fat-suppressed T2-weighted imaging of the head and neck with 2 fast spin-echo dixon techniques: initial experiences

Two modified fast spin-echo (FSE) techniques (a 2-point and a single-scan triple-echo Dixon) were used for T2-weighted imaging of the head and neck in 7 patients along with conventional FSE with fat saturation. Both Dixon techniques provided consistent and more uniform fat suppression (FS) than conventional FSE. The 2-point Dixon technique was noted to be more susceptible to motion artifacts. The triple-echo Dixon technique offered the best scan time efficiency and overall image quality.

Comparative MR study of hepatic fat quantification using single-voxel proton spectroscopy, two-point dixon and three-point IDEAL

Hepatic fat fraction (HFF) was measured in 28 lean/obese humans by single-voxel proton spectroscopy (MRS), a two-point Dixon (2PD), and a three-point iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) method (3PI). For the lean, obese, and total subject groups, the range of HFF measured by MRS was 0.3-3.5% (1.1 +/- 1.4%), 0.3-41.5% (11.7 +/- 12.1), and 0.3-41.5% (10.1 +/- 11.6%), respectively. For the same groups, the HFF measured by 2PD was -6.3-2.2% (-2.0 +/- 3.7%), -2.4-42.9% (12.9 +/- 13.8%), and -6.3-42.9% (10.5 +/- 13.7%), respectively, and for 3PI they were 7.9-12.8% (10.1 +/- 2.0%), 11.1-49.3% (22.0 +/- 12.2%), and 7.9-49.3% (20.0 +/- 11.8%), respectively. The HFF measured by MRS was highly correlated with those measured by 2PD (r = 0.954, P < 0.001) and 3PI (r = 0.973, P < 0.001). With the MRS data as a reference, the percentages of correct differentiation between normal and fatty liver with the MRI methods ranged from 68-93% for 2PD and 64-89% for 3PI. Our study demonstrates that the apparent HFF measured by the MRI methods can significantly vary depending on the choice of water-fat separation methods and sequences. Such variability may limit the clinical application of the MRI methods, particularly when a diagnosis of early fatty liver needs to be performed. Therefore, protocol-specific establishment of cutoffs for liver fat content may be necessary.

Joint estimation of water/fat images and field inhomogeneity map

Water/fat separation in the presence of B 0 field inhomogeneity is a problem of considerable practical importance in MRI. This article describes two complementary methods for estimating the water/fat images and the field inhomogeneity map from Dixon-type acquisitions. One is based on variable projection (VARPRO) and the other on linear prediction (LP). The VARPRO method is very robust and can be used in low signal-to-noise ratio conditions because of its ability to achieve the maximum-likelihood solution. The LP method is computationally more efficient, and is shown to perform well under moderate levels of noise and field inhomogeneity. These methods have been extended to handle multicoil acquisitions by jointly solving the estimation problem for all the coils. Both methods are analyzed and compared and results from several experiments are included to demonstrate their performance.

Relaxation effects in the quantification of fat using gradient echo imaging

Quantification of fat has been investigated using images acquired from multiple gradient echoes. The evolution of the signal with echo time and flip angle was measured in phantoms of known fat and water composition and in 21 research subjects with fatty liver. Data were compared to different models of the signal equation, in which each model makes different assumptions about the T1 and/or T2* relaxation effects. A range of T1, T2*, fat fraction and number of echoes was investigated to cover situations of relevance to clinical imaging. Results indicate that quantification is most accurate at low flip angles (to minimize T1 effects) with a small number of echoes (to minimize spectral broadening effects). At short echo times, the spectral broadening effects manifest as a short apparent T2 for the fat component.

SENSE phase-constrained magnitude reconstruction with iterative phase refinement

Conventional sensitivity encoding (SENSE) reconstruction is based on equations in the complex domain. However, for many MRI applications only the magnitude is relevant. If there exists an estimate of the underlying phase information, a magnitude-only phase-constrained reconstruction can help to improve the conditioning of the SENSE reconstruction problem. Consequently, this reduces g-factor-related noise enhancement. In previous attempts at phase-constrained SENSE reconstruction, image quality was hampered by strong aliasing artifacts resulting from inadequate phase estimates and high sensitivity to phase errors. If a full-resolution phase image is used, a significant reduction in aliasing errors and better noise properties compared to SENSE can be obtained. An iterative scheme that improves the phase estimate to better approximate the phase is presented. The mathematical framework of the new approach is provided together with comparisons of conventional SENSE, phase-constrained SENSE, and the new phase-refinement method. Both theory and experimental verification demonstrate significantly better noise performance at high reduction factors, i.e., close to the theoretical limit. For applications that need only magnitude data, an iterative phase-constrained SENSE reconstruction can provide substantial SNR improvement over SENSE reconstruction and less artifacts than phase-constrained SENSE.

Multiecho reconstruction for simultaneous water-fat decomposition and T2* estimation

PURPOSE

To describe and demonstrate the feasibility of a novel multiecho reconstruction technique that achieves simultaneous water-fat decomposition and T2* estimation. The method removes interference of water-fat separation with iron-induced T2* effects and therefore has potential for the simultaneous characterization of hepatic steatosis (fatty infiltration) and iron overload.

MATERIALS AND METHODS

The algorithm called "T2*-IDEAL" is based on the IDEAL water-fat decomposition method. A novel "complex field map" construct is used to estimate both R2* (1/T2*) and local B(0) field inhomogeneities using an iterative least-squares estimation method. Water and fat are then decomposed from source images that are corrected for both T2* and B(0) field inhomogeneity.

RESULTS

It was found that a six-echo multiecho acquisition using the shortest possible echo times achieves an excellent balance of short scan and reliable R2* measurement. Phantom experiments demonstrate the feasibility with high accuracy in R2* measurement. Promising preliminary in vivo results are also shown.

CONCLUSION

The T2*-IDEAL technique has potential applications in imaging of diffuse liver disease for evaluation of both hepatic steatosis and iron overload in a single breath-hold.

Least-squares chemical shift separation for (13)C metabolic imaging

PURPOSE

To describe a new least-squares chemical shift (LSCSI) method for separation of chemical species with widely spaced peaks in a sparse spectrum. The ability to account for species with multiple peaks is addressed.

MATERIALS AND METHODS

This method is applied to imaging of (13)C-labeled pyruvate and its metabolites alanine, pyruvate, and lactate. The method relies on a priori knowledge of the resonant frequencies of the different chemical species, as well as the relative signal from the two pyruvate peaks, one of which lies near the alanine peak. With this information a least-squares method was utilized for separation of signal from the three metabolites, facilitating tremendous reductions in the amount of data required to decompose the different chemical species. Optimization of echo spacing for maximum noise performance of the signal separation is also described.

RESULTS

Imaging an enriched (13)C phantom at 3.0T, the LSCSI method demonstrates excellent metabolite separation, very similar to echo planar spectroscopic imaging (EPSI), while only using 1/16th as much data.

CONCLUSION

This approach may be advantageous for in vivo hyperpolarized (13)C metabolic applications for reduced scan time compared with EPSI.

On the application of chemical shift-based multipoint water-fat separation methods in balanced SSFP imaging

Chemical shift-based multipoint water-fat separation methods have been applied in balanced steady-state free precession (bSSFP) sequences because of the high signal-to-noise-ratio (SNR) attainable. In this approach the echo formation is approximated to occur concurrently for both water and fat at an echo time (TE) equal to half the repetition time (TR/2 approximation). However, the degree to which the imaging conditions underlying the TR/2 approximation are satisfied can significantly vary in vivo depending upon the imaging region of interest (ROI) and the pixels across a field of view (FOV). The consequence of the TR/2 approximation on chemical shift-based multipoint water-fat separation was investigated. The influence of a mismatch between the pass-band profiles of water and fat (pass-band mismatch) on fat quantification was also examined. Theoretical and experimental results demonstrate that the TR/2 approximation can result in spatially dependent noise performance of multipoint water-fat separation methods, and the pass-band mismatch can render the precision of fat quantification spatially dependent. Given that local tissue characteristics in affected liver can be substantially variable, this study is of particular importance in liver imaging.

Optimization of fast spiral chemical shift imaging using least squares reconstruction: application for hyperpolarized (13)C metabolic imaging

A least-squares-based optimization and reconstruction algorithm has been developed for rapid metabolic imaging in the context of hyperpolarized (13)C. The algorithm uses a priori knowledge of resonance frequencies, J-coupling constants, and T(2)* values to enable acquisition of high-quality metabolic images with imaging times of approximately 100 ms for an 8-cm field of view (FOV) and 0.5 cm isotropic resolution. A root-mean-square error (rMSE) analysis is introduced to optimize metabolic image quality by appropriate choice of pulse sequence parameters, echo times, and signal model. By performing the reconstruction in k-space, the algorithm also allows the inclusion of the effect of chemical shift evolution during the readout period. Single-interleaf multiecho spiral chemical shift imaging (spCSI) is analyzed in detail as an illustrative example for the use of the new reconstruction and optimization algorithm. Simulation of the in vivo spectrum following the bolus injection of hyperpolarized (13)C(1) pyruvate shows that single-interleaf spiral spectroscopic imaging can achieve image quality in 100 ms, comparable to the performance of a 13-s phase-encoded chemical shift imaging (FIDCSI) experiment. Single-interleaf spCSI was also tested at a 3-T MR scanner using a phantom containing approximately 0.5-M solutions of alanine, lactate, and a pyruvate-pyruvate hydrate C(1)-C(2) ester at thermal equilibrium polarization, all enriched to 99% (13)C in the C(1) carbonyl positions. Upon reconstruction using the k-space-based least-squares technique, metabolite ratios obtained using the spCSI method were comparable to those obtained using a reference FIDCSI acquisition.

Referenceless MR thermometry for monitoring thermal ablation in the prostate

Referenceless proton resonance frequency (PRF) shift thermometry provides a means to measure temperature changes during minimally invasive thermotherapy that is inherently robust to motion and tissue displacement. However, if the referenceless method is used to determine temperature changes during prostate ablation, phase gaps between water and fat in image regions used to determine the background phase can confound the phase estimation. We demonstrate an extension to referenceless thermometry which eliminates this problem by allowing background phase estimation in the presence of phase discontinuities between aqueous and fatty tissue. In this method, images are acquired with a multiecho sequence and binary water and fat maps are generated from a Dixon reconstruction. For the background phase estimation, water and fat regions are treated separately and the phase offset between the two tissue types is determined. The method is demonstrated feasibile in phantoms and during in vivo thermal ablation of canine prostate.

Water-fat separation with IDEAL gradient-echo imaging

PURPOSE

To combine gradient-echo (GRE) imaging with a multipoint water-fat separation method known as "iterative decomposition of water and fat with echo asymmetry and least squares estimation" (IDEAL) for uniform water-fat separation. Robust fat suppression is necessary for many GRE imaging applications; unfortunately, uniform fat suppression is challenging in the presence of B(0) inhomogeneities. These challenges are addressed with the IDEAL technique.

MATERIALS AND METHODS

Echo shifts for three-point IDEAL were chosen to optimize noise performance of the water-fat estimation, which is dependent on the relative proportion of water and fat within a voxel. Phantom experiments were performed to validate theoretical SNR predictions. Theoretical echo combinations that maximize noise performance are discussed, and examples of clinical applications at 1.5T and 3.0T are shown.

RESULTS

The measured SNR performance validated theoretical predictions and demonstrated improved image quality compared to unoptimized echo combinations. Clinical examples of the liver, breast, heart, knee, and ankle are shown, including the combination of IDEAL with parallel imaging. Excellent water-fat separation was achieved in all cases. The utility of recombining water and fat images into "in-phase," "out-of-phase," and "fat signal fraction" images is also discussed.

CONCLUSION

IDEAL-SPGR provides robust water-fat separation with optimized SNR performance at both 1.5T and 3.0T with multicoil acquisitions and parallel imaging in multiple regions of the body.

Balanced SSFP imaging of the musculoskeletal system

Magnetic resonance imaging (MRI), with its unique ability to image and characterize soft tissue noninvasively, has emerged as one of the most accurate imaging methods available to diagnose bone and joint pathology. Currently, most evaluation of musculoskeletal pathology is done with two-dimensional acquisition techniques such as fast spin echo (FSE) imaging. The development of three-dimensional fast imaging methods based on balanced steady-state free precession (SSFP) shows great promise to improve MRI of the musculoskeletal system. These methods may allow acquisition of fluid sensitive isotropic data that can be reformatted into arbitrary planes for improved detection and visualization of pathology. Sensitivity to fluid and fat suppression are important issues in these techniques to improve delineation of cartilage contours, for detection of marrow edema and derangement of other joint structures.

Fast spin-echo triple-echo dixon (fTED) technique for efficientT2-weighted water and fat imaging

Previously published fast spin-echo (FSE) implementations of a Dixon method for water and fat separation all require multiple scans and thus a relatively long scan time. Further, the minimum echo spacing (esp), a time critical for FSE image quality and scan efficiency, often needs to be increased in order to bring about the required phase shift between the water and fat signals. This work proposes and implements a novel FSE triple-echo Dixon (fTED) technique that can address these limitations. In the new technique, three raw images are acquired in a single FSE scan by replacing each frequency-encoding gradient in a conventional FSE with three consecutive gradients of alternating polarity. The timing of the three gradients is adjusted by selecting an appropriate receiver bandwidth (RBW) so that the water and fat signals for the three corresponding echoes have a relative phase shift of -180 degrees , 0 degrees , and 180 degrees , respectively. A fully automated postprocessing algorithm is then used to generate separate water-only and fat-only images for each slice. The technique was implemented with and without parallel imaging. We demonstrate that the new fTED technique enables both uniform water/fat separation and fast scanning with uncompromised scan parameters, including applications such as T(2)-weighted separate water and fat imaging of the abdomen during breath-holding.

Interleaved water and fat imaging and applications to lipid quantitation using the gradient reversal technique

PURPOSE

To implement and evaluate the gradient reversal-based chemical shift imaging technique to obtain qualitative and quantitative spatially-registered fat and water images with high imaging efficiency at very high field.

MATERIALS AND METHODS

A multiecho gradient reversal-based sequence allowing interleaved water-fat imaging during a single acquisition and quantitation of fat/water content is presented. The sequence was optimized and implemented at 11.7T. The quantitation was verified with water-fat phantoms and applied to lipid measurement in an in vivo mouse model.

RESULTS

Results from phantoms, in vivo lipid measurement in mouse liver and hind limb muscle, and ex vivo rat knee imaging experiments demonstrated the robustness and high selectivity of this technique for interleaved and quantitative water and fat imaging at very high field.

CONCLUSION

The proposed MRI technique permits interleaved water and fat imaging, with which spectrally well-separated water and fat images at the identical slice locations could be obtained in a single acquisition without increasing scan time. The technique could be used for in vivo quantitative mapping of lipid content and applied to investigations using small animal experiment models.

Fat quantification with IDEAL gradient echo imaging: Correction of bias fromT1 and noise

Quantification of hepatic steatosis is a significant unmet need for the diagnosis and treatment of patients with nonalcoholic fatty liver disease (NAFLD). MRI is capable of separating water and fat signals in order to quantify fatty infiltration of the liver (hepatic steatosis). Unfortunately, fat signal has confounding T(1) effects and the nonzero mean noise in low signal-to-noise ratio (SNR) magnitude images can lead to incorrect estimation of the true lipid percentage. In this study, the effects of bias from T(1) effects and image noise were investigated. An oil/water phantom with volume fat-fractions ranging linearly from 0% to 100% was designed and validated using a spoiled gradient echo (SPGR) sequence in combination with a chemical-shift based fat-water separation method known as iterative decomposition of water and fat with echo asymmetry and least squares estimation (IDEAL). We demonstrated two approaches to reduce the effects of T(1): small flip angle (flip angle) and dual flip angle methods. Both methods were shown to effectively minimize deviation of the measured fat-fraction from its true value. We also demonstrated two methods to reduce noise bias: magnitude discrimination and phase-constrained reconstruction. Both methods were shown to reduce this noise bias effectively from 15% to less than 1%.

Fast decomposition of water and lipid using a GRASE technique with the IDEAL algorithm

Three-point Dixon techniques achieve good lipid-water separation by estimating the phase due to field inhomogeneities. Recently it was demonstrated that the combination of an iterative algorithm (iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL)) with a fast spin-echo (FSE) three-point Dixon method yielded robust lipid-water decomposition. As an alternative to FSE, the gradient- and spin-echo (GRASE) technique has been developed for efficient data collection. In this work we present a method for lipid-water separation by combining IDEAL with the GRASE technique. An approach to correct for errors in the lipid-water decomposition caused by phase distortions due to the switching of the readout gradient polarities inherent to GRASE is presented. The IDEAL-GRASE technique is demonstrated in phantoms and in vivo for various applications, including pelvic, musculoskeletal, and (breath-hold) cardiac imaging.

Iterative Decomposition of Water and Fat with Echo Asymmetry and Least-Squares Estimation (IDEAL) Fast Spin-Echo Imaging of the Ankle: Initial Clinical Experience

OBJECTIVE

Reliable, uniform fat suppression is important. Multiple approaches currently exist, many of which suffer from either suboptimal signal-to-noise ratio (SNR), or the inability to obtain consistent fat suppression around the ankle joint. Our purpose was to test iterative decomposition of water and fat with echo asymmetry and the least-squares estimation (IDEAL) method in combination with fast spin-echo imaging, which is able to achieve reliable high SNR images with uniform fat-water separation.

SUBJECTS AND METHODS

We compared IDEAL fast spin-echo with conventional fat-suppressed fast spin-echo imaging in 33 ankles in 32 patients. Quantitative measurements of SNR and contrast-to-noise ratio efficiency were made, and qualitative diagnostic image quality and fat-suppression scores were determined.

RESULTS

We found that the SNR efficiency for both cartilage and fluid was similar for both techniques, and fluid/cartilage contrast-to-noise ratio efficiency was higher with IDEAL fast spin-echo imaging. Fat suppression and diagnostic quality scores using the IDEAL method were superior (p < 0.01) to fat-suppressed fast spin-echo imaging.

CONCLUSION

IDEAL fast spin-echo imaging is a promising technique for MRI of the ankle.

Dual-contrast single breath-hold 3D abdominal MR imaging

OBJECT

Multiple contrasts are often helpful for a comprehensive diagnosis. In 3D abdominal MRI, breath-hold techniques are preferred for single contrast acquisitions to avoid respiratory artifacts. In this paper, highly accelerated parallel MRI is used to acquire large 3D abdominal volumes with two different contrasts within a single breath-hold.

MATERIAL AND METHODS

In vivo studies have been performed on six healthy volunteers, combining T (1)- and T (2)-weighted, gradient- or spin-echo based scans, as well as water/fat resolved imaging in a single breath-hold. These 3D scans were acquired with an acceleration factor of six, using a prototype 32-element receive array.

RESULTS

The presented approach was tested successfully on all volunteers. The whole liver area was covered by a FOV of 350 x 250 x 200 mm(3) for all scans with reasonable spatial resolution. Arbitrary scan protocols generating different contrasts have been shown to be combinable in this single breath-hold approach. Good spatial correspondence with negligible spatial offset was achieved for all different scan combinations acquired in overall breath-hold times between 15 and 25 s.

CONCLUSION

Enabled by highly parallel imaging technology, this study demonstrates the technical feasibility and the promising image quality of single breath-hold dual contrast MRI.

Fast chemical shift mapping with multiecho balanced SSFP

OBJECT

A method is proposed that provides spectroscopic images with high spatial resolution and moderate spectral resolution at very short total data acquisition times.

MATERIALS AND METHODS

Balanced steady-state free precession (bSSFP, TrueFISP, FIESTA, b-FFE) is combined with a multiecho readout gradient and frequency-sensitive reconstruction such as Fourier reconstruction known from echo-planar spectroscopic imaging (EPSI) or matrix inversion. Balanced SSFP imaging requires short repetition times to minimize banding artefacts, thereby restricting the achievable frequency resolution.

RESULTS

Two-dimensional (2D) high-resolution spectroscopic images were produced of three 1H resonances (water, acetone and fat) on phantoms and water/fat separation in vivo within 1-2 s. Additionally, fast 31P spectroscopic images were acquired from a phantom consisting of two resonances within 195 ms.

CONCLUSION

Frequency-sensitive reconstruction of multiecho bSSFP data can provide spectroscopic images with high spatial and temporal resolution while the frequency resolution is moderate at around 100 Hz. The method can also separate more than three resonances, allowing for hetero-nuclei metabolite mapping, for example 13C and 31P.

T1- and T2-weighted fast spin-echo imaging of the brachial plexus and cervical spine with IDEAL water–fat separation

PURPOSE

To compare the iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) method with fat-saturated T1-weighted (T1W) and T2W fast spin-echo (FSE) and short-TI inversion recovery (STIR) imaging of the brachial plexus and cervical spine.

MATERIALS AND METHODS

Images acquired at 1.5T in five volunteers using fat-saturated T1W and T2W FSE imaging and STIR were compared with T1W and T2W IDEAL-FSE images. Examples of T1W and T2W IDEAL-FSE images acquired in patients are also shown.

RESULTS

T1W and T2W IDEAL-FSE demonstrated superior fat suppression (P<0.05) and image quality (P<0.05), compared to T1W and T2W fat-saturated FSE, respectively. SNR performance of T1W-IDEAL-FSE was similar to T1W FSE in the spinal cord (P=0.250) and paraspinous muscles (P=0.78), while T2W IDEAL-FSE had superior SNR in muscle (P=0.02) and CSF (P=0.02), and marginally higher cord SNR (P=0.09). Compared to STIR, T2W IDEAL-FSE demonstrated superior image quality (P<0.05), comparable fat suppression (excellent, P=1.0), and higher SNR performance (P<0.001).

CONCLUSION

IDEAL-FSE is a promising method for T1W and T2W imaging of the brachial plexus and cervical spine.

Two-point water-fat imaging with partially-opposed-phase (POP) acquisition: An asymmetric Dixon method

A novel two-point water-fat imaging method is introduced. In addition to the in-phase acquisition, water and fat magnetization vectors are sampled at partially-opposed-phase (POP) rather than exactly antiparallel as in the original Dixon method. This asymmetric sampling encodes more valuable phase information for identifying water and fat. From the magnitudes of the two complex images, a big and a small chemical component are first robustly obtained pixel by pixel and then used to form two possible error phasor candidates. The true error phasor is extracted from the two error phasor candidates through a simple procedure of regional iterative phasor extraction (RIPE). Finally, least-squares solutions of water and fat are obtained after the extracted error phasor is smoothed and removed from the complex images. For noise behavior, the effective number of signal averages NSA* is typically in the range of 1.87-1.96, very close to the maximum possible value of 2. Compared to earlier approaches, the proposed method is more efficient in data acquisition and straightforward in processing, and the final results are more robust. At both 1.5T and 0.3T, well separated and identified in vivo water and fat images covering a broad range of anatomical regions have been obtained, supporting the clinical utility of the method.

A critical appraisal of radiographic scoring systems for assessment of juvenile idiopathic arthritis

Assessing structural damage to joints over time is essential for evaluating the effectiveness of therapeutic interventions for patients with inflammatory arthritis. Although radiography is able to quantify joint damage, the changes found with conventional radiography early in the disease course are nonspecific, and late radiographic changes are often irreversible. Although many clinical trials on drug development for children still use radiographic scales as endpoints for the study, more specific therapies have been developed for juvenile idiopathic arthritis (JIA) that would enable imaging to "fine-tune" patients to placement into specific treatment algorithms. As a result, new imaging scales to identify early abnormalities are clearly needed. Many pediatric rheumatology centers around the world persistently apply adult-designed radiographic scoring systems to evaluate the progression of JIA. Few pediatric-targeted radiographic scales are available for assessment of progression of JIA in growing joints, and the clinimetric and psychometric properties of such scales have been poorly investigated. We present a critique to the evaluative, discriminative, and predictive roles of the van der Heijde modification of Sharp's radiographic method, a scale originally designed to assess damage to joints of adults with rheumatoid arthritis, when it is applied to a pediatric population. We discuss the advantages and drawbacks of this radiographic scoring system for assessing growing joints and the ability of MRI to overcome inadequacies of conventional radiography.

Advanced magnetic resonance imaging of articular cartilage

MRI is one of the most accurate imaging methods available to diagnose disorders of articular cartilage. Conventional two-dimensional and three-dimensional approaches show changes in cartilage morphology. Newer and substantially faster three-dimensional imaging methods show great promise to improve MRI of cartilage. These methods may allow acquisition of fluid-sensitive isotropic data that can be reformatted into arbitrary planes for improved detection and visualization of pathology. Unique MRI contrast mechanisms also allow clinicians to probe cartilage physiology and detect early changes in cartilage macromolecules.

Articular cartilage of the knee: rapid three-dimensional MR imaging at 3.0 T with IDEAL balanced steady-state free precession--initial experience

Institutional review board approval and informed consent were obtained for this HIPAA-compliant study. In this study, iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL) balanced steady-state free precession (bSSFP), fat-suppressed bSSFP, and fat-suppressed spoiled gradient-echo (GRE) sequences for 3.0-T magnetic resonance (MR) imaging of articular knee cartilage were prospectively compared in five healthy volunteers. Cartilage and fluid signal-to-noise ratio (SNR), cartilage-fluid contrast-to-noise ratio (CNR), SNR efficiency, CNR efficiency, image quality, and fat suppression were compared. Fat-suppressed bSSFP and IDEAL bSSFP had higher SNR efficiency of cartilage (P < .01) than did GRE. IDEAL bSSFP had higher cartilage-fluid CNR efficiency than did fat-suppressed bSSFP or GRE (P < .01). Fat-suppressed bSSFP and IDEAL bSSFP had higher image quality than did GRE (P < .01). GRE and IDEAL bSSFP had significantly better fat-water separation or fat saturation than did fat-suppressed bSSFP (P < .05). IDEAL bSSFP is a promising method for imaging articular knee cartilage.

Noise reduction in multiple-echo data sets using singular value decomposition

A method is described for denoising multiple-echo data sets using singular value decomposition (SVD). Images are acquired using a multiple gradient- or spin-echo sequence, and the variation of the signal with echo time (TE) in all pixels is subjected to SVD analysis to determine the components of the signal variation. The least significant components are associated with small singular values and tend to characterize the noise variation. Applying a "minimum variance" filter to the singular values suppresses the noise components in a way that optimally approximates the underlying noise-free images. The result is a reduction in noise in the individual TE images with minimal degradation of the spatial resolution and contrast. Phantom and in vivo results are presented.

MRI of articular cartilage in OA: novel pulse sequences and compositional/functional markers

Osteoarthritis (OA) is a leading cause of disability worldwide. Magnetic resonance imaging (MRI), with its unique ability to image and characterize soft tissue non-invasively, has proven valuable in assessing cartilage in OA. The development of new, fast imaging methods with high contrast show promise to improve the magnetic resonance (MR) evaluation of this disease. In addition to morphologic MRI methods, MRI contrast mechanisms under development may reveal detailed information about the physiology of cartilage. It is anticipated that these and other MRI techniques will play an increasingly important role in assessing the success or failure of therapies for OA. On December 5 and 6, 2002, OMERACT (Outcome Measures in Rheumatology Clinical Trials) and OARSI (Osteoarthritis Research Society International) held a workshop in Bethesda, MD aiming at providing a state-of-the-art review of imaging outcome measures for OA of the knee to help guide scientists and pharmaceutical companies in the use of MRI in multi-site studies of OA. Applications of MRI were initially reviewed by a multidisciplinary, international panel of expert scientists and physicians from academia, the pharmaceutical industry and regulatory agencies. The findings of the panel were then presented to a wider group of participants for open discussion. The following report summarizes the results of these discussions with respect to novel MRI pulse sequences for evaluating articular cartilage of the knee in OA and notes any additional advances that have been made since.

Phased array ghost elimination

Parallel imaging may be applied to cancel ghosts caused by a variety of distortion mechanisms, including distortions such as off-resonance or local flow, which are space variant. Phased array combining coefficients may be calculated that null ghost artifacts at known locations based on a constrained optimization, which optimizes SNR subject to the nulling constraint. The resultant phased array ghost elimination (PAGE) technique is similar to the method known as sensitivity encoding (SENSE) used for accelerated imaging; however, in this formulation is applied to full field-of-view (FOV) images. The phased array method for ghost elimination may result in greater flexibility in designing acquisition strategies. For example, in multi-shot EPI applications ghosts are typically mitigated by the use of an interleaved phase encode acquisition order. An alternative strategy is to use a sequential, non-interleaved phase encode order and cancel the resultant ghosts using PAGE parallel imaging. Cancellation of ghosts by means of phased array processing makes sequential, non-interleaved phase encode acquisition order practical, and permits a reduction in repetition time, TR, by eliminating the need for echo-shifting. Sequential, non-interleaved phase encode order has benefits of reduced distortion due to off-resonance, in-plane flow and EPI delay misalignment. Furthermore, the use of EPI with PAGE has inherent fat-water separation and has been used to provide off-resonance correction using a technique referred to as lipid elimination with an echo-shifting N/2-ghost acquisition (LEENA), and may further generalized using the multi-point Dixon method. Other applications of PAGE include cancelling ghosts which arise due to amplitude or phase variation during the approach to steady state. Parallel imaging requires estimates of the complex coil sensitivities. In vivo estimates may be derived by temporally varying the phase encode ordering to obtain a full k-space dataset in a scheme similar to the autocalibrating TSENSE method. This scheme is a generalization of the UNFOLD method used for removing aliasing in undersampled acquisitions. The more general scheme may be used to modulate each EPI ghost image to a separate temporal frequency as described in this paper.

Single acquisition water-fat separation: Feasibility study for dynamic imaging

Water-fat separation can be challenging in the presence of field inhomogeneities. Three-point (3-pt) water-fat separation methods achieve robust performance by measuring and compensating for field inhomogeneities; however, they triple the scan time. The "1+-pt" water-fat separation method proposed in this article for dynamic or repetitive imaging situations combines 3-pt methods' ability to correct for field inhomogeneities with the scan efficiency of a single acquisition method to achieve high temporal and spatial resolutions and robust water-fat separation. Single-echo data are collected with water and fat at a relative phase shift of an odd multiple of pi/2. To correct for undesired phase modulation, phase maps are estimated from a 3-pt calibration scan acquired prior to dynamic imaging. The phase maps are assumed to be slowly varying in time, so they may be used for correcting the phase of the subsequent single-echo signals at the same imaging location. Noise performance was investigated and shown to be equivalent to a single excitation acquisition. The 1+-pt method can also be used in conjunction with parallel imaging. In this situation, the calibration scans required by both methods can be integrated into a shared calibration scan. Promising results were obtained in breast, abdominal, and cardiac imaging applications.

S5FP: spectrally selective suppression with steady state free precession

A method is presented that employs the inherent spectral selectivity of the Steady-State Free Precession (SSFP) pulse sequence to provide a spectral band of suppression. At TE = TR/2, SSFP partitions the magnetization into two phase-opposed spectral components. Z-storing one of these components simultaneously further excites the other, which is then suppressed by gradient crushing and RF spoiling. The Spectrally Selective Suppression with SSFP (S(5)FP) method is shown to provide significant attenuation of fat signals, while the water signals are essentially unaffected and provide the normal SSFP contrast. Fat suppression is achieved with relatively little temporal overhead (less than 10% reduction in temporal resolution). S(5)FP was validated using simulations, phantoms, and human studies.

Fat/water separation in single acquisition steady-state free precession using multiple echo radial trajectories

Phase detection in fully refocused SSFP imaging has recently allowed fat/water separation without preparing the magnetization or using multiple acquisitions. Instead, it exploits the phase difference between fat and water at an echo time at the midpoint of the TR. To minimize the TR for improved robustness to B0 inhomogeneity, a 3D projection acquisition collecting two half echoes at the beginning and end of each excitation was previously implemented. Since echoes are not formed at the midpoint of the TR, this method still requires two passes of k-space for fat/water separation. A new method is presented to linearly combine the half echoes to separate fat and water in a single acquisition. Separation using phase detection provides superior contrast between fat and water voxels. Results from high resolution angiography and musculoskeletal studies with improved robustness to inhomogeneity and a 50% scan time reduction compared to the two pass method are presented.

Intrinsic fat suppression in TIDE balanced steady-state free precession imaging

A novel fat-suppressed balanced steady-state free precession (b-SSFP) imaging method based on the transition into driven equilibrium (TIDE) sequence with variable flip angles is presented. The new method, called fat-saturated (FS)-TIDE, exploits the special behavior of TIDE signals from off-resonance spins during the flip angle ramp. As shown by simulations and experimental data, the TIDE signal evolution for off-resonant isochromats during the transition from turbo spin-echo (TSE)-like behavior to the true fast imaging with steady precession (TrueFISP) mode undergoes a zero crossing. The resulting signal notch for off-resonant spins is then used for fat suppression. The efficiency of FS-TIDE is demonstrated in phantoms and healthy volunteers on a 1.5T system. The resulting images are compared with standard TrueFISP data with and without fat suppression. It is demonstrated that FS-TIDE provides a fast and stable means for homogenous fat suppression in abdominal imaging while maintaining balanced SSFP-like image contrast and signal-to-noise ratio (SNR). The scan time of FS-TIDE is not increased compared to normal TrueFISP imaging without fat suppression and identical k-space trajectories. Because of the intrinsic fat suppression, no additional preparation is needed. Possible repetition times (TRs) are not firmly limited to special values and are nearly arbitrary.

Alternating repetition time balanced steady state free precession

A novel balanced SSFP technique for the separation or suppression of different resonance frequencies (e.g., fat suppression) is presented. The method is based on applying two alternating and different repetition times, TR(1) and TR(2). This RF scheme manipulates the sensitivity of balanced SSFP to off-resonance effects by a modification of the frequency response profile. Starting from a general approach, an optimally broadened stopband within the frequency response function is designed. This is achieved with a TR(2) being one third of TR(1) and an RF-pulse phase increment of 90 degrees . With this approach TR(2) is too short ( approximately 1 ms) to switch imaging gradients and is only used to change the frequency sensitivity. Without a significant change of the spectral position of the stopband, TR(1) can be varied over a range of values ( approximately 2.5-4.5 ms) while TR(2) and phase cycling is kept constant. On-resonance spins show a magnetization behavior similar to balanced SSFP, but with maximal magnetization at flip angles about 10 degrees lower than in balanced SSFP. The total scan time is increased by about 30% compared to conventional balanced SSFP. The new technique was applied on phantoms and volunteers to produce rapid, fat suppressed images.

Iterative decomposition of water and fat with echo asymmetry and least-squares estimation (IDEAL): application with fast spin-echo imaging

Chemical shift based methods are often used to achieve uniform water-fat separation that is insensitive to Bo inhomogeneities. Many spin-echo (SE) or fast SE (FSE) approaches acquire three echoes shifted symmetrically about the SE, creating time-dependent phase shifts caused by water-fat chemical shift. This work demonstrates that symmetrically acquired echoes cause artifacts that degrade image quality. According to theory, the noise performance of any water-fat separation method is dependent on the proportion of water and fat within a voxel, and the position of echoes relative to the SE. To address this problem, we propose a method termed "iterative decomposition of water and fat with echo asymmetric and least-squares estimation" (IDEAL). This technique combines asymmetrically acquired echoes with an iterative least-squares decomposition algorithm to maximize noise performance. Theoretical calculations predict that the optimal echo combination occurs when the relative phase of the echoes is separated by 2pi/3, with the middle echo centered at pi/2+pik (k=any integer), i.e., (-pi/6+pik, pi/2+pik, 7pi/6+pik). Only with these echo combinations can noise performance reach the maximum possible and be independent of the proportion of water and fat. Close agreement between theoretical and experimental results obtained from an oil-water phantom was observed, demonstrating that the iterative least-squares decomposition method is an efficient estimator.

A fast spin echo two-point Dixon technique and its combination with sensitivity encoding for efficient T2-weighted imaging

A fast spin echo two-point Dixon (fast 2PD) technique was developed for efficient T2-weighted imaging with uniform water and fat separation. The technique acquires two interleaved fast spin echo images with water and fat in-phase and 180 degrees out-of-phase, respectively, and generates automatically separate water and fat images for each slice. The image reconstruction algorithm uses an improved and robust region-growing scheme for phase correction and achieves consistency in water and fat identification between different slices by exploiting the intrinsic correlation between the complex images from two neighboring slices. To further lower the acquisition time to that of a regular fast spin echo acquisition with a single signal average, we combined the fast 2PD technique with sensitivity encoding (SENSE). Phantom experiments show that the fast 2PD and SENSE are complementary in scan efficiency and signal-to-noise ratio (SNR). In vivo data from scanning of clinical patients demonstrate that T2-weighted imaging with uniform and consistent fat separation, including breath-hold abdominal examinations, can be readily performed with the fast 2PD technique or its combination with SENSE.

Cardiac CINE imaging with IDEAL water-fat separation and steady-state free precession

PURPOSE

To decompose multicoil CINE steady-state free precession (SSFP) cardiac images acquired at short echo time (TE) increments into separate water and fat images, using an iterative least-squares "Dixon" (IDEAL) method.

MATERIALS AND METHODS

Multicoil CINE IDEAL-SSFP cardiac imaging was performed in three volunteers and 15 patients at 1.5 T.

RESULTS

Measurements of signal-to-noise ratio (SNR) matched theoretical expectations and were used to optimize acquisition parameters. TE increments of 0.9-1.0 msec permitted the use of repetition times (TRs) of 5 msec or less, and provided good SNR performance of the water-fat decomposition, while maintaining good image quality with a minimum of banding artifacts. Images from all studies were evaluated for fat separation and image quality by two experienced radiologists. Uniform fat separation and diagnostic image quality was achieved in all images from all studies. Examples from volunteers and patients are shown.

CONCLUSION

Multicoil IDEAL-SSFP imaging can produce high quality CINE cardiac images with uniform water-fat separation, insensitive to Bo inhomogeneities. This approach provides a new method for reliable fat-suppression in cardiac imaging.

MR imaging of articular cartilage at 1.5T and 3.0T: comparison of SPGR and SSFP sequences

OBJECTIVE

To compare articular cartilage signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and thickness measurements on a 1.5 T and a 3.0 T magnetic resonance (MR) scanner using three-dimensional spoiled gradient recalled echo (3D-SPGR) and two 3D steady-state free precession (SSFP) sequences.

METHODS

Both knees of five volunteers were scanned at 1.5 T and at 3.0 T using a transmit-receive quadrature extremity coil. Each examination consisted of a sagittal 3D-SPGR sequence, a sagittal fat suppressed 3D-SSFP (FS-SSFP) sequence, and a sagittal Dixon 3D-SSFP sequence. For quantitative analysis, we compared cartilage SNR and CNR efficiencies, as well as average cartilage thickness measurements.

RESULTS

For 3D-SPGR, cartilage SNR efficiencies at 3.0 T increased compared to those at 1.5 T by a factor of 1.83 (range: 1.40-2.09). In comparison to 3D-SPGR, the SNR efficiency of FS-SSFP increased by a factor of 2.13 (range: 1.81-2.39) and for Dixon SSFP by a factor of 2.39 (range: 1.95-2.99). For 3D-SPGR, CNR efficiencies between cartilage and its surrounding tissue increased compared to those at 1.5 T by a factor of 2.12 (range: 1.75-2.47), for FS-SSFP by a factor 2.11 (range: 1.58-2.80) and for Dixon SSFP by a factor 2.39 (range 2.09-2.83). Average cartilage thicknesses of load bearing regions were not different at both field strengths or between sequences (P>0.05). Mean average cartilage thickness measured in all knees was 2.28 mm.

CONCLUSION

Articular cartilage imaging of the knee on a 3.0 T MR scanner shows increased SNR and CNR efficiencies compared to a 1.5 T scanner, where SSFP-based techniques show the highest increase in SNR and CNR efficiency. There was no difference between average cartilage thickness measurements performed at the 1.5 T and 3.0 T scanners or between the three different sequences.

Cramér-Rao bounds for three-point decomposition of water and fat

The noise analysis for three-point decomposition of water and fat was extended to account for the uncertainty in the field map. This generalization leads to a nonlinear estimation problem. The Crámer-Rao bound (CRB) was used to study the variance of the estimates of the magnitude, phase, and field map by computing the maximum effective number of signals averaged (NSA) for any choice of echo time shifts. The analysis shows that the noise properties of the reconstructed magnitude, phase, and field map depend not only on the choice of echo time shifts but also on the amount of fat and water in each voxel and their alignment at the echo. The choice of echo time shifts for spin-echo, spoiled gradient echo, and steady-state free precession imaging techniques were optimized using the CRB. The noise analysis for the magnitude explains rough interfaces seen clinically in the boundary of fat and water with source images obtained symmetrically about the spin-echo. It also provides a solution by choosing appropriate echo time shifts (-pi/6+pik, pi/2+pik, 7pi/6+pik), with k an integer. With this choice of echo time shifts it is possible to achieve the maximum NSA uniformly across all fat:water ratios. The optimization is also carried out for the estimation of phase and field map. These theoretical results were verified using Monte Carlo simulations with a newly developed nonlinear least-squares reconstruction algorithm that achieves the CRB.