A new design and rationale for 3D orthogonally oversampled k -space trajectories

Multipulse sodium magnetic resonance imaging for multicompartment quantification: Proof-of-concept

We present a feasibility study of sodium quantification in a multicompartment model of the brain using sodium (²³Na) magnetic resonance imaging. The proposed method is based on a multipulse sequence acquisition and simulation at 7 T, which allows to differentiate the ²³Na signals emanating from three compartments in human brain in vivo: intracellular (compartment 1), extracellular (compartment 2), and cerebrospinal fluid (compartment 3). The intracellular sodium concentration C₁ and the volume fractions α₁, α₂, and α₃ of all respective three brain compartments can be estimated. Simulations of the sodium spin 3/2 dynamics during a 15-pulse sequence were used to optimize the acquisition sequence by minimizing the correlation between the signal evolutions from the three compartments. The method was first tested on a three-compartment phantom as proof-of-concept. Average values of the ²³Na quantifications in four healthy volunteer brains were α₁ = 0.54 ± 0.01, α₂ = 0.23 ± 0.01, α₃ = 1.03 ± 0.01, and C₁ = 23 ± 3 mM, which are comparable to the expected physiological values \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\alpha }}}_{{\bf{1}}}^{{\boldsymbol{theory}}}$$\end{document}α1theory ∼ 0.6, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\alpha }}}_{{\bf{2}}}^{{\boldsymbol{theory}}}$$\end{document}α2theory ∼ 0.2, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{\alpha }}}_{{\bf{3}}}^{{\boldsymbol{theory}}}$$\end{document}α3theory ∼ 1, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{C}}}_{{\bf{1}}}^{{\boldsymbol{theory}}}$$\end{document}C1theory ∼ 10–30 mM. The proposed method may allow a quantitative assessment of the metabolic role of sodium ions in cellular processes and their malfunctions in brain in vivo.

Rapid anatomical brain imaging using spiral acquisition and an expanded signal model

We report the deployment of spiral acquisition for high-resolution structural imaging at 7T. Long spiral readouts are rendered manageable by an expanded signal model including static off-resonance and B₀ dynamics along with k-space trajectories and coil sensitivity maps. Image reconstruction is accomplished by inversion of the signal model using an extension of the iterative non-Cartesian SENSE algorithm. Spiral readouts up to 25 ms are shown to permit whole-brain 2D imaging at 0.5 mm in-plane resolution in less than a minute. A range of options is explored, including proton-density and T₂* contrast, acceleration by parallel imaging, different readout orientations, and the extraction of phase images. Results are shown to exhibit competitive image quality along with high geometric consistency.

Longitudinal study of sodium MRI of articular cartilage in patients with knee osteoarthritis: initial experience with 16-month follow-up

OBJECTIVES

To evaluate the potential of sodium MRI to detect changes over time of apparent sodium concentration (ASC) in articular cartilage in patients with knee osteoarthritis (OA).

METHODS

The cartilage of 12 patients with knee OA were scanned twice over a period of approximately 16 months with two sodium MRI sequences at 7 T: without fluid suppression (radial 3D) and with fluid suppression by adiabatic inversion recovery (IR). Changes between baseline and follow-up of mean and standard deviation of ASC (in mM), and their rate of change (in mM/day), were measured in the patellar, femorotibial medial and lateral cartilage regions for each subject. A matched-pair Wilcoxon signed rank test was used to assess significance of the changes.

RESULTS

Changes in mean and in standard deviation of ASC, and in their respective rate of change over time, were only statistically different when data was acquired with the fluid-suppressed sequence. A significant decrease (p = 0.001) of approximately 70 mM in mean ASC was measured between the two IR scans.

CONCLUSION

Quantitative sodium MRI with fluid suppression by adiabatic IR at 7 T has the potential to detect a decrease of ASC over time in articular cartilage of patients with knee osteoarthritis.

KEY POINTS

• Sodium MRI can detect apparent sodium concentration (ASC) in cartilage • Longitudinal study: sodium MRI can detect changes in ASC over time • Potential for follow-up studies of cartilage degradation in knee osteoarthritis.

Dynamic phosphocreatine imaging with unlocalized pH assessment of the human lower leg muscle following exercise at 3T

PURPOSE

To develop a high temporal resolution imaging method that measures muscle-specific phosphocreatine (PCr) resynthesis time constant (τ_PCr ) and pH changes in muscles of the lower leg following exercise on a clinical 3T MRI scanner.

METHODS

We developed a frequency-selective 3D non-Cartesian FLORET sequence to measure PCr with 17-mm nominal isotropic resolution (28 mm actual resolution) and 6-s temporal resolution to capture dynamic metabolic muscle activity. The sequence was designed to additionally collect inorganic phosphate spectra for pH quantification, which were localized using sensitivity profiles of individual coil elements. Nineteen healthy volunteers were scanned while performing a plantar flexion exercise on an in-house developed ergometer. Data were acquired with a dual-tuned multichannel coil array that enabled phosphorus imaging and proton localization for muscle segmentation.

RESULTS

After a 90-s plantar flexion exercise at 0.66 Hz with resistance set to 40% of the maximum voluntary contraction, τ_PCr was estimated at 22.9 ± 8.8 s (mean ± standard deviation) with statistical coefficient of determination r²  = 0.89 ± 0.05. The corresponding pH values after exercise were in the range of 6.9-7.1 in the gastrocnemius muscle.

CONCLUSION

The developed technique allows measurement of muscle-specific PCr resynthesis kinetics and pH changes following exercise, with a temporal resolution and accuracy comparable to that of single voxel ³¹ P-MRS sequences. Magn Reson Med 79:974-980, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

Quantitative sodium magnetic resonance imaging of cartilage, muscle, and tendon

Sodium magnetic resonance imaging (MRI), or imaging of the 23Na nucleus, has been under exploration for several decades, and holds promise for potentially revealing additional biochemical information about the health of tissues that cannot currently be obtained from conventional hydrogen (or proton) MRI. This additional information could serve as an important complement to conventional MRI for many applications. However, despite these exciting possibilities, sodium MRI is not yet used routinely in clinical practice, and will likely remain strictly in the domain of exploratory research for the coming decade. This paper begins with a technical overview of sodium MRI, including the nuclear magnetic resonance (NMR) signal characteristics of the sodium nucleus, the challenges associated with sodium MRI, and the specialized pulse sequences, hardware, and reconstruction techniques required. Various applications of sodium MRI for quantitative analysis of the musculoskeletal system are then reviewed, including the non-invasive assessment of cartilage degeneration in vivo, imaging of tendinopathy, applications in the assessment of various muscular pathologies, and assessment of muscle response to exercise.

Three-dimensional ultrashort echo-time imaging using a FLORET trajectory

PURPOSE

Three-dimensional ultrashort echo-time (UTE) imaging commonly makes use of an isotropic 3D radial projection acquisition. The FLORET sequence is proposed and evaluated as a more efficient alternative.

METHODS

The properties of the FLORET trajectory are contrasted with those of a 3D radial projection trajectory. The theoretical advantages of FLORET, including greater sampling and SNR efficiency, are evaluated based upon experimental data. The effect of T2* decay on FLORET is analyzed in comparison to the 3D radial, Cones, and Density Adapted Radial trajectories. FLORET UTE image quality is compared with 3D radial UTE image quality.

RESULTS

FLORET is shown to have several advantages over 3D radial acquisitions with respect to image quality, scan time, signal-to-noise, and off-resonance blurring for UTE data. The signal and resolution losses from T2* decay for a FLORET acquisition are shown to be comparable to those of Density Adapted Radial and Density Compensated Cones trajectories.

CONCLUSION

The FLORET sequence is recommended as an alternative to 3D radial projection sequences for musculoskeletal UTE imaging as well as other UTE applications that accommodate modest to long per shot sampling times. FLORET is not recommended for imaging extremely short T₂ species such as dentin. Magn Reson Med 78:1038-1049, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Magnetic Resonance Imaging of Phosphocreatine and Determination of BOLD Kinetics in Lower Extremity Muscles using a Dual-Frequency Coil Array

Magnetic resonance imaging (MRI) provides the unique ability to study metabolic and microvasculature functions in skeletal muscle using phosphorus and proton measurements. However, the low sensitivity of these techniques can make it difficult to capture dynamic muscle activity due to the temporal resolution required for kinetic measurements during and after exercise tasks. Here, we report the design of a dual-nuclei coil array that enables proton and phosphorus MRI of the human lower extremities with high spatial and temporal resolution. We developed an array with whole-volume coverage of the calf and a phosphorus signal-to-noise ratio of more than double that of a birdcage coil in the gastrocnemius muscles. This enabled the local assessment of phosphocreatine recovery kinetics following a plantar flexion exercise using an efficient sampling scheme with a 6 s temporal resolution. The integrated proton array demonstrated image quality approximately equal to that of a clinical state-of-the-art knee coil, which enabled fat quantification and dynamic blood oxygen level-dependent measurements that reflect microvasculature function. The developed array and time-efficient pulse sequences were combined to create a localized assessment of calf metabolism using phosphorus measurements and vasculature function using proton measurements, which could provide new insights into muscle function.

3D image-based navigators for coronary MR angiography

PURPOSE

To develop a method for acquiring whole-heart 3D image-based navigators (iNAVs) with isotropic resolution for tracking and correction of localized motion in coronary magnetic resonance angiography (CMRA).

METHODS

To monitor motion in all regions of the heart during a free-breathing scan, a variable-density cones trajectory was designed to collect a 3D iNAV every heartbeat in 176 ms with 4.4 mm isotropic spatial resolution. The undersampled 3D iNAV data were reconstructed with efficient self-consistent parallel imaging reconstruction (ESPIRiT). 3D translational and nonrigid motion-correction methods using 3D iNAVs were compared to previous translational and nonrigid methods using 2D iNAVs.

RESULTS

Five subjects were scanned with a 3D cones CMRA sequence, accompanied by both 2D and 3D iNAVs. The quality of the right and left anterior descending coronary arteries was assessed on 2D and 3D iNAV-based motion-corrected images using a vessel sharpness metric and qualitative reader scoring. This assessment showed that nonrigid motion correction based on 3D iNAVs produced results that were noninferior to correction based on 2D iNAVs.

CONCLUSION

The ability to acquire isotropic-resolution 3D iNAVs every heartbeat during a CMRA scan was demonstrated. Such iNAVs enabled direct measurement of localized motion for nonrigid motion correction in free-breathing whole-heart CMRA. Magn Reson Med 77:1874-1883, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

A radial sampling strategy for uniform k-space coverage with retrospective respiratory gating in 3D ultrashort-echo-time lung imaging

The purpose of this work was to develop a 3D radial-sampling strategy which maintains uniform k-space sample density after retrospective respiratory gating, and demonstrate its feasibility in free-breathing ultrashort-echo-time lung MRI. A multi-shot, interleaved 3D radial sampling function was designed by segmenting a single-shot trajectory of projection views such that each interleaf samples k-space in an incoherent fashion. An optimal segmentation factor for the interleaved acquisition was derived based on an approximate model of respiratory patterns such that radial interleaves are evenly accepted during the retrospective gating. The optimality of the proposed sampling scheme was tested by numerical simulations and phantom experiments using human respiratory waveforms. Retrospectively, respiratory-gated, free-breathing lung MRI with the proposed sampling strategy was performed in healthy subjects. The simulation yielded the most uniform k-space sample density with the optimal segmentation factor, as evidenced by the smallest standard deviation of the number of neighboring samples as well as minimal side-lobe energy in the point spread function. The optimality of the proposed scheme was also confirmed by minimal image artifacts in phantom images. Human lung images showed that the proposed sampling scheme significantly reduced streak and ring artifacts compared with the conventional retrospective respiratory gating while suppressing motion-related blurring compared with full sampling without respiratory gating. In conclusion, the proposed 3D radial-sampling scheme can effectively suppress the image artifacts due to non-uniform k-space sample density in retrospectively respiratory-gated lung MRI by uniformly distributing gated radial views across the k-space.

Hybrid radial-cones trajectory for accelerated MRI

PURPOSE

To design and develop a series of ultrashort echo time k-space sampling schemes, termed radial-cones, which enables high sampling efficiency while maintaining compatibility with parallel imaging and compressed sensing reconstructions.

THEORY AND METHODS

Radial-cones is a trajectory that samples three-dimensional (3D) k-space using a single base cone distributed along radial dimensions through a cost function-based optimization. Trajectories were generated for highly undersampled, short readout sampling and compared with 3D radial sampling in point spread function (PSF) analysis, digital and physical phantoms, and initial human volunteers. Parallel imaging reconstructions were evaluated with and without the use of compressed sensing-based regularization.

RESULTS

Compared with 3D radial sampling, radial-cones reduced the peak value and energy of PSF aliasing. In both digital and physical phantoms, this improved sampling behavior corresponded to a reduction in the root mean square error with a further reduction using compressed sensing. A slight increase in noise and a corresponding increase in apparent resolution was observed with radial-cones. In in vivo feasibility testing, radial-cones reconstructed images have a markedly lower number of apparent artifacts. Ultimate gains in imaging performance were limited by off-resonance blurring.

CONCLUSION

Radial-cones is an efficient non-Cartesian sampling scheme enabling short echo readout with a high level of compatibility with parallel imaging and compressed sensing. Magn Reson Med 77:1068-1081, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

Quantitative sodium MRI of kidney

One of the main tasks of the human kidneys is to maintain the homeostasis of the body's fluid and electrolyte balance by filtration of the plasma and excretion of the end products. Herein, the regulation of extracellular sodium in the kidney is of particular importance. Sodium MRI ((23)Na MRI) allows for the absolute quantification of the tissue sodium concentration (TSC) and thereby provides a direct link between TSC and tissue viability. Renal (23)Na MRI can provide new insights into physiological tissue function and viability thought to differ from the information obtained by standard (1)H MRI. Sodium imaging has the potential to become an independent surrogate biomarker not only for renal imaging, but also for oncology indications. However, this technique is now on the threshold of clinical implementation. Numerous, initial pre-clinical and clinical studies have already outlined the potential of this technique; however, future studies need to be extended to larger patient groups to show the diagnostic outcome. In conclusion, (23)Na MRI is seen as a powerful technique with the option to establish a non-invasive renal biomarker for tissue viability, but is still a long way from real clinical implementation.

High-performance radiofrequency coils for (23)Na MRI: brain and musculoskeletal applications

(23)Na RF coil design for brain and MSK applications presents a number of challenges, including poor coil loading for arrays of small coils and SNR penalties associated with providing (1)H capability with the same coil. The basics of RF coil design are described, as well as a review of historical approaches to dual tuning. There follows a review of published high performance coil designs for MSK and brain imaging. Several coil designs have been demonstrated at 7T and 3T which incorporate close-fitting receive arrays and in some cases design features which provide (1)H imaging with little penalty to (23)Na sensitivity. The "nested coplanar loop" approach is examined, in which small transmit-receive (1)H elements are placed within each (23)Na loop, presenting only a small perturbation to (23)Na performance and minimizing RF shielding issues. Other designs incorporating transmit-receive arrays for (23)Na and (1)H are discussed including a 9.4 T (23)Na/(1)H brain coil. Great gains in (23)Na SNR have been made with many of these designs, but simultaneously achieving high performance for 1H remains elusive.

Evaluation of cartilage repair and osteoarthritis with sodium MRI

The growing need for early diagnosis and higher specificity than that which can be achieved with morphological MRI is a driving force in the application of methods capable of probing the biochemical composition of cartilage tissue, such as sodium imaging. Unlike morphological imaging, sodium MRI is sensitive to even small changes in cartilage glycosaminoglycan content, which plays a key role in cartilage homeostasis. Recent advances in high- and ultrahigh-field MR systems, gradient technology, phase-array radiofrequency coils, parallel imaging approaches, MRI acquisition strategies and post-processing developments have resulted in many clinical in vivo sodium MRI studies of cartilage, even at 3 T. Sodium MRI has great promise as a non-invasive tool for cartilage evaluation. However, further hardware and software improvements are necessary to complete the translation of sodium MRI into a clinically feasible method for 3-T systems. This review is divided into three parts: (i) cartilage composition, pathology and treatment; (ii) sodium MRI; and (iii) clinical sodium MRI studies of cartilage with a focus on the evaluation of cartilage repair tissue and osteoarthritis.

Sodium inversion recovery MRI on the knee joint at 7 T with an optimal control pulse

In the field of sodium magnetic resonance imaging (MRI), inversion recovery (IR) is a convenient and popular method to select sodium in different environments. For the knee joint, IR has been used to suppress the signal from synovial fluids, which improves the correlation between the sodium signal and the concentration of glycosaminoglycans (GAGs) in cartilage tissues. For the better inversion of the magnetization vector under the spatial variations of the B0 and B1 fields, the IR sequence usually employ adiabatic pulses as the inversion pulse. On the other hand, it has been shown that RF shapes robust against the variations of the B0 and B1 fields can be generated by numerical optimization based on optimal control theory. In this work, we compare the performance of fluid-suppressed sodium MRI on the knee joint in vivo, between one implemented with an adiabatic pulse in the IR sequence and the other with the adiabatic pulse replaced by an optimal-control shaped pulse. While the optimal-control pulse reduces the RF power deposited to the body by 58%, the quality of fluid suppression and the signal level of sodium within cartilage are similar between two implementations.

A nested phosphorus and proton coil array for brain magnetic resonance imaging and spectroscopy

A dual-nuclei radiofrequency coil array was constructed for phosphorus and proton magnetic resonance imaging and spectroscopy of the human brain at 7T. An eight-channel transceive degenerate birdcage phosphorus module was implemented to provide whole-brain coverage and significant sensitivity improvement over a standard dual-tuned loop coil. A nested eight-channel proton module provided adequate sensitivity for anatomical localization without substantially sacrificing performance on the phosphorus module. The developed array enabled phosphorus spectroscopy, a saturation transfer technique to calculate the global creatine kinase forward reaction rate, and single-metabolite whole-brain imaging with 1.4cm nominal isotropic resolution in 15min (2.3cm actual resolution), while additionally enabling 1mm isotropic proton imaging. This study demonstrates that a multi-channel array can be utilized for phosphorus and proton applications with improved coverage and/or sensitivity over traditional single-channel coils. The efficient multi-channel coil array, time-efficient pulse sequences, and the enhanced signal strength available at ultra-high fields can be combined to allow volumetric assessment of the brain and could provide new insights into the underlying energy metabolism impairment in several neurodegenerative conditions, such as Alzheimer's and Parkinson's diseases, as well as mental disorders such as schizophrenia.

A flexible nested sodium and proton coil array with wideband matching for knee cartilage MRI at 3T

PURPOSE

We describe a 2 × 6 channel sodium/proton array for knee MRI at 3T. Multielement coil arrays are desirable because of well-known signal-to-noise ratio advantages over volume and single-element coils. However, low tissue-coil coupling that is characteristic of coils operating at low frequency can make the potential gains from a phased array difficult to realize.

METHODS

The issue of low tissue-coil coupling in the developed six-channel sodium receive array was addressed by implementing 1) a mechanically flexible former to minimize the coil-to-tissue distance and reduce the overall diameter of the array and 2) a wideband matching scheme that counteracts preamplifier noise degradation caused by coil coupling and a high-quality factor. The sodium array was complemented with a nested proton array to enable standard MRI.

RESULTS

The wideband matching scheme and tight-fitting mechanical design contributed to >30% central signal-to-noise ratio gain on the sodium module over a mononuclear sodium birdcage coil, and the performance of the proton module was sufficient for clinical imaging.

CONCLUSION

We expect the strategies presented in this study to be generally relevant in high-density receive arrays, particularly in x-nuclei or small animal applications. Magn Reson Med 76:1325-1334, 2016. © 2015 Wiley Periodicals, Inc.

Variable density randomized stack of spirals (VDR-SoS) for compressive sensing MRI

PURPOSE

To develop a 3D sampling strategy based on a stack of variable density spirals for compressive sensing MRI.

METHODS

A random sampling pattern was obtained by rotating each spiral by a random angle and by delaying for few time steps the gradient waveforms of the different interleaves. A three-dimensional (3D) variable sampling density was obtained by designing different variable density spirals for each slice encoding. The proposed approach was tested with phantom simulations up to a five-fold undersampling factor. Fully sampled 3D dataset of a human knee, and of a human brain, were obtained from a healthy volunteer. The proposed approach was tested with off-line reconstructions of the knee dataset up to a four-fold acceleration and compared with other noncoherent trajectories.

RESULTS

The proposed approach outperformed the standard stack of spirals for various undersampling factors. The level of coherence and the reconstruction quality of the proposed approach were similar to those of other trajectories that, however, require 3D gridding for the reconstruction.

CONCLUSION

The variable density randomized stack of spirals (VDR-SoS) is an easily implementable trajectory that could represent a valid sampling strategy for 3D compressive sensing MRI. It guarantees low levels of coherence without requiring 3D gridding. Magn Reson Med 76:59-69, 2016. © 2015 Wiley Periodicals, Inc.

Repeatability of quantitative sodium magnetic resonance imaging for estimating pseudo-intracellular sodium concentration and pseudo-extracellular volume fraction in brain at 3 T

The purpose of this study is to assess the repeatability of the quantification of pseudo-intracellular sodium concentration (C1) and pseudo-extracellular volume fraction (α) estimated in brain in vivo using sodium magnetic resonance (MRI) at 3 T. Eleven healthy subjects were scanned twice, with two sodium MRI acquisitions (with and without fluid suppression by inversion recovery), and two double inversion recovery (DIR) proton MRI. DIR MRIs were used to create masks of gray and white matter (GM, WM), that were subsequently applied to the C1 and α maps calculated from sodium MRI and a tissue three-compartment model, in order to measure the distributions of these two parameters in GM, WM or full brain (GM+WM) separately. The mean, median, mode, standard deviation (std), skewness and kurtosis of the C1 and α distributions in whole GM, WM and full brain were calculated for each subject, averaged over all data, and used as parameters for the repeatability assessment. The coefficient of variation (CV) was calculated as a measure of reliability for the detection of intra-subject changes in C1 and αfor each parameter, while intraclass correlation (ICC) was used as a measure of repeatability. It was found that the CV of most of the parameters was around 10-20% (except for C1 kurtosis which is about 40%) for C1 and α measurements, and that ICC was moderate to very good (0.4 to 0.9) for C1 parameters and for some of the α parameters (mainly skewness and kurtosis). In conclusion, the proposed method could allow to reliably detect changes of 50% and above of the different measurement parameters of C1 and αin neuropathologies (multiple sclerosis, tumor, stroke, Alzheimer's disease) compared to healthy subjects, and that skewness and kurtosis of the distributions of C1 and αseem to be the more sensitive parameters to these changes.

Graphical programming interface: A development environment for MRI methods

PURPOSE

To introduce a multiplatform, Python language-based, development environment called graphical programming interface for prototyping MRI techniques.

METHODS

The interface allows developers to interact with their scientific algorithm prototypes visually in an event-driven environment making tasks such as parameterization, algorithm testing, data manipulation, and visualization an integrated part of the work-flow. Algorithm developers extend the built-in functionality through simple code interfaces designed to facilitate rapid implementation.

RESULTS

This article shows several examples of algorithms developed in graphical programming interface including the non-Cartesian MR reconstruction algorithms for PROPELLER and spiral as well as spin simulation and trajectory visualization of a FLORET example.

CONCLUSION

The graphical programming interface framework is shown to be a versatile prototyping environment for developing numeric algorithms used in the latest MR techniques.

Classification of sodium MRI data of cartilage using machine learning

PURPOSE

To assess the possible utility of machine learning for classifying subjects with and subjects without osteoarthritis using sodium magnetic resonance imaging data. Theory: Support vector machine, k-nearest neighbors, naïve Bayes, discriminant analysis, linear regression, logistic regression, neural networks, decision tree, and tree bagging were tested.

METHODS

Sodium magnetic resonance imaging with and without fluid suppression by inversion recovery was acquired on the knee cartilage of 19 controls and 28 osteoarthritis patients. Sodium concentrations were measured in regions of interests in the knee for both acquisitions. Mean (MEAN) and standard deviation (STD) of these concentrations were measured in each regions of interest, and the minimum, maximum, and mean of these two measurements were calculated over all regions of interests for each subject. The resulting 12 variables per subject were used as predictors for classification.

RESULTS

Either Min [STD] alone, or in combination with Mean [MEAN] or Min [MEAN], all from fluid suppressed data, were the best predictors with an accuracy >74%, mainly with linear logistic regression and linear support vector machine. Other good classifiers include discriminant analysis, linear regression, and naïve Bayes.

CONCLUSION

Machine learning is a promising technique for classifying osteoarthritis patients and controls from sodium magnetic resonance imaging data.

Sodium MRI: methods and applications

Sodium NMR spectroscopy and MRI have become popular in recent years through the increased availability of high-field MRI scanners, advanced scanner hardware and improved methodology. Sodium MRI is being evaluated for stroke and tumor detection, for breast cancer studies, and for the assessment of osteoarthritis and muscle and kidney functions, to name just a few. In this article, we aim to present an up-to-date review of the theoretical background, the methodology, the challenges, limitations, and current and potential new applications of sodium MRI.

A method for estimating intracellular sodium concentration and extracellular volume fraction in brain in vivo using sodium magnetic resonance imaging

In this feasibility study we propose a method based on sodium magnetic resonance imaging (MRI) for estimating simultaneously the intracellular sodium concentration (C₁, in mM) and the extracellular volume fraction (α) in grey and white matters (GM, WM) in brain in vivo. Mean C₁ over five healthy volunteers was measured ~11 mM in both GM and WM, mean α was measured ~0.22 in GM and ~0.18 in WM, which are in close agreement with standard values for healthy brain tissue (C₁ ~ 10–15 mM, α ~ 0.2). Simulation of ‘fluid’ and ‘solid’ inclusions were accurately detected on both the C₁ and α 3D maps and in the C₁ and α distributions over whole GM and WM. This non-invasive and quantitative method could provide new biochemical information for assessing ion homeostasis and cell integrity in brain and help the diagnosis of early signs of neuropathologies such as multiple sclerosis, Alzheimer's disease, brain tumors or stroke.

Sodium MR Imaging of Articular Cartilage Pathologies

Many studies have proved that noninvasive sodium MR imaging can directly determine the cartilage GAG content, which plays a central role in cartilage homeostasis. New technical developments in the recent decade have helped to transfer this method from in vitro to pre-clinical in vivo studies. Sodium imaging has already been applied for the evaluation of cartilage and repair tissue in patients after various cartilage repair surgery techniques and in patients with osteoarthritis. These studies showed that this technique could be helpful not only for assessment of the cartilage status, but also predictive for osteoarthritis. However, due to the low detectable sodium MR signal in cartilage, sodium imaging is still challenging, and further hardware and software improvements are necessary for translating sodium MR imaging into clinical practice, preferably to 3T MR systems.

Biomedical applications of sodium MRI in vivo

In this article we present an up-to-date overview of the potential biomedical applications of sodium magnetic resonance imaging (MRI) in vivo. Sodium MRI is a subject of increasing interest in translational imaging research as it can give some direct and quantitative biochemical information on the tissue viability, cell integrity and function, and therefore not only help the diagnosis but also the prognosis of diseases and treatment outcomes. It has already been applied in vivo in most human tissues, such as brain for stroke or tumor detection and therapeutic response, in breast cancer, in articular cartilage, in muscle, and in kidney, and it was shown in some studies that it could provide very useful new information not available through standard proton MRI. However, this technique is still very challenging due to the low detectable sodium signal in biological tissue with MRI and hardware/software limitations of the clinical scanners. The article is divided in three parts: 1) the role of sodium in biological tissues, 2) a short review on sodium magnetic resonance, and 3) a review of some studies on sodium MRI on different organs/diseases to date.

Spiral trajectory design: a flexible numerical algorithm and base analytical equations

PURPOSE

Spiral-based trajectories for magnetic resonance imaging can be advantageous, but are often cumbersome to design or create. This work presents a flexible numerical algorithm for designing trajectories based on explicit definition of radial undersampling, and also gives several analytical expressions for charactering the base (critically sampled) class of these trajectories.

THEORY AND METHODS

Expressions for the gradient waveform, based on slew and amplitude limits, are developed such that a desired pitch in the spiral k-space trajectory is followed. The source code for this algorithm, written in C, is publicly available. Analytical expressions approximating the spiral trajectory (ignoring the radial component) are given to characterize measurement time, gradient heating, maximum gradient amplitude, and off-resonance phase for slew-limited and gradient amplitude-limited cases. Several numerically calculated trajectories are illustrated, and base Archimedean spirals are compared with analytically obtained results.

RESULTS

Several different waveforms illustrate that the desired slew and amplitude limits are reached, as are the desired undersampling patterns, using the numerical method. For base Archimedean spirals, the results of the numerical and analytical approaches are in good agreement.

CONCLUSION

A versatile numerical algorithm was developed, and was written in publicly available code. Approximate analytical formulas are given that help characterize spiral trajectories.

Distributed spirals: a new class of three-dimensional k-space trajectories

This work presents a new class of three-dimensional spiral based-trajectories for sampling magnetic resonance data. The distributed spirals trajectory efficiently traverses a cylinder or sphere or intermediate shape in k-space. The trajectory is shown to be nearly as efficient as a conventional stack of spirals trajectory in terms of scan time and signal-to-noise ratio, while reducing coherent aliasing in all three spatial directions and reducing Gibbs ringing due to the nature of collecting data from a sphere in k-space. The trajectory uses a single two-dimensional spiral waveform with the addition of a single orthogonal waveform which is scaled with each repetition, making it relatively easy to implement. Blurring from off-resonance only occurs in two dimensions due to the temporal nature of the sampling.

Multidirectional high-moment encoding in phase contrast MRI

The use of phase contrast MRI to measure vascular flow provides a unique method for acquiring quantitative estimates of flow as well as morphological imaging. The quantitative aspects of phase contrast magnetic resonance angiography (PC-MRA) provide unique relationships between measurement parameters and resulting signal to noise ratio of the velocity measurements. This article introduces a new method to exploit these relationships providing increased efficiency, and therefore, higher vessel conspicuity. Signal to noise ratio gains in high-moment PC-MRA are limited by the ability to unalias phase measurements that fall outside the -π to π interval. Unaliasing phase on a per pixel basis is limited by errors in the measurements due to noise and intravoxel flow distributions. Current dual-VENC methods have been shown to be robust to these errors and provide high velocity to noise ratio gains, however, the collection of a required high-VENC set can be inefficient. The presented method provides more time efficient gains in velocity to noise ratio compared to a dual-VENC approach by eliminating the high-VENC acquisitions and using shared information between nonorthogonal measurements. Simulations, phantom, and in vivo angiography are used to characterize the noise performance of each method. The velocity to noise ratio efficiency of the proposed method is shown to be ∼1.7 times greater than the dual-VENC method at the same gradient moment.

Efficient sample density estimation by combining gridding and an optimized kernel

The reconstruction of non-Cartesian k-space trajectories often requires the estimation of nonuniform sampling density. Particularly for 3D, this calculation can be computationally expensive. The method proposed in this work combines an iterative algorithm previously proposed by Pipe and Menon (Magn Reson Med 1999;41:179-186) with the optimal kernel design previously proposed by Johnson and Pipe (Magn Reson Med 2009;61:439-447). The proposed method shows substantial time reductions in estimating the densities of center-out trajectories, when compared with that of Johnson. It is demonstrated that, depending on the trajectory, the proposed method can provide reductions in execution time by factors of 12 to 85. The method is also shown to be robust in areas of high trajectory overlap, when compared with two analytical density estimation methods, producing a 10-fold increase in accuracy in one case. Initial conditions allow the proposed method to converge in fewer iterations and are shown to be flexible in terms of the accuracy of information supplied. The proposed method is not only one of the fastest and most accurate algorithms, it is also completely generic, allowing any arbitrary trajectory to be density compensated extemporaneously. The proposed method is also simple and can be implemented on parallel computing platforms in a straightforward manner.