Ultimate intrinsic signal-to-noise ratio in MRI

An analytic expression for the ultimate intrinsic SNR in a uniform sphere

PURPOSE

The ultimate intrinsic signal-to-noise ratio (UISNR) is normally calculated using electrodynamic simulations with a complete basis of modes. Here, we provide an exact solution for the UISNR at the center of a dielectric sphere and assess how accurately this solution approximates UISNR away from the center.

METHODS

We performed a mode analysis to determine which modes contribute to central UISNR - ζ(r→0). We then derived an analytic expression to calculate ζ(r→0) and analyzed its dependence on main magnetic field strength, sample geometry, and electrical properties. We validated the proposed solution against an established method based on dyadic Green's function simulations.

RESULTS

Only one divergence-free mode contributes to ζ(r→0). The UISNR given by the exact solution matched the full simulation results for various parameter settings, whereas calculation speed was approximately 1000 times faster. We showed that the analytic expression can approximate the UISNR with <5% error at positions as much as 10-20% of the radius away from the center.

CONCLUSION

The proposed formula enables rapid and direct calculation of UISNR in the central region of a sphere. The resulting UISNR value may be used, for example, as an absolute reference to assess the performance of head coils with spherical phantoms.

The ultimate intrinsic signal-to-noise ratio of loop- and dipole-like current patterns in a realistic human head model

PURPOSE

The ultimate intrinsic signal-to-noise ratio (UISNR) represents an upper bound for the achievable SNR of any receive coil. To reach this threshold a complete basis set of equivalent surface currents is required. This study systematically investigated to what extent either loop- or dipole-like current patterns are able to reach the UISNR threshold in a realistic human head model between 1.5 T and 11.7 T. Based on this analysis, we derived guidelines for coil designers to choose the best array element at a given field strength. Moreover, we present ideal current patterns yielding the UISNR in a realistic body model.

METHODS

We distributed generic current patterns on a cylindrical and helmet-shaped surface around a realistic human head model. We excited electromagnetic fields in the human head by using eigenfunctions of the spherical and cylindrical Helmholtz operator. The electromagnetic field problem was solved by a fast volume integral equation solver.

RESULTS

At 7 T and above, adding curl-free current patterns to divergence-free current patterns substantially increased the SNR in the human head (locally >20%). This was true for the helmet-shaped and the cylindrical surface. On the cylindrical surface, dipole-like current patterns had high SNR performance in central regions at ultra-high field strength. The UISNR increased superlinearly with B0 in most parts of the cerebrum but only sublinearly in the periphery of the human head.

CONCLUSION

The combination of loop and dipole elements could enhance the SNR performance in the human head at ultra-high field strength.

Computation of ultimate SAR amplification factors for radiofrequency hyperthermia in non-uniform body models: impact of frequency and tumour location

PURPOSE

We introduce a method for calculation of the ultimate specific absorption rate (SAR) amplification factors (uSAF) in non-uniform body models. The uSAF is the greatest possible SAF achievable by any hyperthermia (HT) phased array for a given frequency, body model and target heating volume.

METHODS

First, we generate a basis-set of solutions to Maxwell's equations inside the body model. We place a large number of electric and magnetic dipoles around the body model and excite them with random amplitudes and phases. We then compute the electric fields created in the body model by these excitations using an ultra-fast volume integral solver called MARIE. We express the field pattern that maximises the SAF in the target tumour as a linear combination of these basis fields and optimise the combination weights so as to maximise SAF (concave problem). We compute the uSAFs in the Duke body models at 10 frequencies in the 20-900 MHz range and for twelve 3 cm-diameter tumours located at various depths in the head and neck.

RESULTS

For both shallow and deep tumours, the frequency yielding the greatest uSAF was ∼900 MHz. Since this is the greatest frequency that we simulated, we hypothesise that the globally optimal frequency is actually greater.

CONCLUSIONS

The uSAFs computed in this work are very large (40-100 for shallow tumours and 4-17 for deep tumours), indicating that there is a large room for improvement of the current state-of-the-art head and neck HT devices.

An EM Simulation-Based Design Flow for Custom-Built MR Coils Incorporating Signal and Noise

Developing custom-built MR coils is a cumbersome task, in which an a priori prediction of the coils' SNR performance, their sensitivity pattern, and their depth of penetration helps to greatly speed up the design process by reducing the required hardware manufacturing iterations. The simulation-based design flow presented in this paper takes the entire MR imaging process into account. That is, it includes all geometric and material properties of the coil and the phantom, the thermal noise as well as the target MR sequences. The proposed simulation-driven design flow is validated using a manufactured prototype coil, whose performance was optimized regarding its SNR performance, based on the presented design flow, by comparing the coil's measured performance against the simulated results. In these experiments, the mean and the standard deviation of the relative error between the simulated and measured coil sensitivity pattern were found to be and . Moreover, the peak deviation between the simulated and measured voxel SNR was found to be less than 4%, indicating that simulations are in good accordance with the measured results, validating the proposed software-based design approach.

The impact of vessel size, orientation and intravascular contribution on the neurovascular fingerprint of BOLD bSSFP fMRI

Monte Carlo simulations have been used to analyze oxygenation-related signal changes in pass-band balanced steady state free precession (bSSFP) as well as in gradient echo (GE) and spin echo (SE) sequences. Signal changes were calculated for artificial cylinders and neurovascular networks acquired from the mouse parietal cortex by two-photon laser scanning microscopy at 1 μm isotropic resolution. Signal changes as a function of vessel size, blood volume, vessel orientation to the main magnetic field B₀ as well as relations of intra- and extravascular and of micro- and macrovascular contributions have been analyzed. The results show that bSSFP is highly sensitive to extravascular and microvascular components. Furthermore, GE and bSSFP, and to a lesser extent SE, exhibit a strong dependence of their signal change on the orientation of the vessel network to B₀.

Approaching ultimate intrinsic signal-to-noise ratio with loop and dipole antennas

PURPOSE

Previous work with body-size objects suggested that loops are optimal MR detectors at low fields, whereas electric dipoles are required to maximize signal-to-noise ratio (SNR) at ultrahigh fields ( ≥ 7 T). Here we investigated how many loops and/or dipoles are needed to approach the ultimate intrinsic SNR (UISNR) at various field strengths.

METHODS

We calculated the UISNR inside dielectric cylinders mimicking different anatomical regions. We assessed the performance of various arrays with respect to the UISNR. We validated our results by comparing simulated and experimental coil performance maps.

RESULTS

Arrays with an increasing number of loops can rapidly approach the UISNR at fields up to 3 T, but are suboptimal at ultrahigh fields for body-size objects. The opposite is true for dipole arrays. At 7 T and above, 16 dipoles provide considerably larger central SNR than any possible loop array, and minimal g factor penalty for parallel imaging.

CONCLUSIONS

Electric dipoles can be advantageous at ultrahigh fields because they can produce both curl-free and divergence-free currents, whereas loops are limited to divergence-free contributions only. Combining loops and dipoles may be optimal for body imaging at 3 T, whereas arrays of loops or dipoles alone may perform better at lower or higher field strengths, respectively. Magn Reson Med 79:1789-1803, 2018. © 2017 International Society for Magnetic Resonance in Medicine.

On the Contribution of Curl-Free Current Patterns to the Ultimate Intrinsic Signal-to-Noise Ratio at Ultra-High Field Strength

The ultimate intrinsic signal-to-noise ratio (SNR) is a coil independent performance measure to compare different receive coil designs. To evaluate this benchmark in a sample, a complete electromagnetic basis set is required. The basis set can be obtained by curl-free and divergence-free surface current distributions, which excite linearly independent solutions to Maxwell's equations. In this work, we quantitatively investigate the contribution of curl-free current patterns to the ultimate intrinsic SNR in a spherical head-sized model at 9.4 T. Therefore, we compare the ultimate intrinsic SNR obtained with having only curl-free or divergence-free current patterns, with the ultimate intrinsic SNR obtained from a combination of curl-free and divergence-free current patterns. The influence of parallel imaging is studied for various acceleration factors. Moreover results for different field strengths (1.5 T up to 11.7 T) are presented at specific voxel positions and acceleration factors. The full-wave electromagnetic problem is analytically solved using dyadic Green's functions. We show, that at ultra-high field strength (B₀ ⩾7T) a combination of curl-free and divergence-free current patterns is required to achieve the best possible SNR at any position in a spherical head-sized model. On 1.5- and 3T platforms, divergence-free current patterns are sufficient to cover more than 90% of the ultimate intrinsic SNR.

Electromagnetic computation and modeling in MRI

Electromagnetic (EM) computational modeling is used extensively during the development of a Magnetic Resonance Imaging (MRI) scanner, its installation, and use. MRI, which relies on interactions between nuclear magnetic moments and the applied magnetic fields, uses a range of EM tools to optimize all of the magnetic fields required to produce the image. The main field magnet is designed to exacting specifications but challenges in manufacturing, installation, and use require additional tools to maintain target operational performance. The gradient magnetic fields, which provide the primary signal localization mechanism, are designed under another set of complex design trade-offs which include conflicting imaging performance specifications and patient physiology. Gradients are largely impervious to external influences, but are also used to enhance main field operational performance. The radiofrequency (RF) magnetic fields, which are used to elicit the signals fundamental to the MR image, are a challenge to optimize for a host of reasons that include patient safety, image quality, cost optimization, and secondary signal localization capabilities. This review outlines these issues and the EM modeling used to optimize MRI system performance.

The ultimate signal-to-noise ratio in realistic body models

PURPOSE

We compute the ultimate signal-to-noise ratio (uSNR) and G-factor (uGF) in a realistic head model from 0.5 to 21 Tesla.

METHODS

We excite the head model and a uniform sphere with a large number of electric and magnetic dipoles placed at 3 cm from the object. The resulting electromagnetic fields are computed using an ultrafast volume integral solver, which are used as basis functions for the uSNR and uGF computations.

RESULTS

Our generalized uSNR calculation shows good convergence in the sphere and the head and is in close agreement with the dyadic Green's function approach in the uniform sphere. In both models, the uSNR versus B₀ trend was linear at shallow depths and supralinear at deeper locations. At equivalent positions, the rate of increase of the uSNR with B₀ was greater in the sphere than in the head model. The uGFs were lower in the realistic head than in the sphere for acceleration in the anterior-posterior direction, but similar for the left-right direction.

CONCLUSION

The uSNR and uGFs are computable in nonuniform body models and provide fundamental performance limits for human imaging with close-fitting MRI array coils. Magn Reson Med 78:1969-1980, 2017. © 2016 International Society for Magnetic Resonance in Medicine.

The noise factor of receiver coil matching networks in MRI

In typical MRI applications the dominant noise sources in the received signal are the sample, the coil loop and the preamplifier. We hypothesize that in some cases (e.g. for very small receiver coils) the matching network noise has to be considered explicitly. Considering the difficulties of direct experimental determinations of the noise factor of matching networks with sufficient accuracy, it is helpful to estimate the noise factor by calculation. A useful formula of the coil matching network is obtained by separating commonly used coil matching network into different stages and calculating their noise factor analytically by a combination of the noise from these stages. A useful formula of the coil matching network is obtained. ADS simulations are performed to verify the theoretical predictions. Thereafter carefully-designed proof-of-concept phantom experiments are carried out to qualitatively confirm the predicted SNR behavior. The matching network noise behavior is further theoretically investigated for a variety of scenarios. It is found that in practice the coil matching network noise can be improved by adjusting the coil open port resonant frequency.

Simulation verification of SNR and parallel imaging improvements by ICE-decoupled loop array in MRI

Transmit/receive L/C loop arrays with the induced current elimination (ICE) or magnetic wall decoupling method has shown high signal-to-noise (SNR) and excellent parallel imaging ability for MR imaging at ultrahigh fields, e.g., 7 T. In this study, we aim to numerically analyze the performance of an eight-channel ICE-decoupled loop array at 7 T. Three dimensional (3-D) electromagnetic (EM) and radiofrequency (RF) circuit co-simulation approach was employed. The values of all capacitors were obtained by optimizing the S-parameters of all coil elements. The EM simulation accurately modeled the coil structure, the phantom and the excitation. All coil elements were well matched to 50 ohm and the isolation between any two coil elements was better -15 dB. The simulated S parameters were exactly similar with the experimental results, indicating the simulation results were reliable. Compared with the conventional capacitively decoupled array, the ICE-decoupled array had higher sensitivity at the peripheral areas of the image subjects due to the shielding effect of the decoupling loops. The increased receive sensitivity resulted in an improvement of signal intensity and SNR for the ICE-decoupled array.

Screen-printed flexible MRI receive coils

Magnetic resonance imaging is an inherently signal-to-noise-starved technique that limits the spatial resolution, diagnostic image quality and results in typically long acquisition times that are prone to motion artefacts. This limitation is exacerbated when receive coils have poor fit due to lack of flexibility or need for padding for patient comfort. Here, we report a new approach that uses printing for fabricating receive coils. Our approach enables highly flexible, extremely lightweight conforming devices. We show that these devices exhibit similar to higher signal-to-noise ratio than conventional ones, in clinical scenarios when coils could be displaced more than 18 mm away from the body. In addition, we provide detailed material properties and components performance analysis. Prototype arrays are incorporated within infant blankets for in vivo studies. This work presents the first fully functional, printed coils for 1.5- and 3-T clinical scanners.

Signal-to-noise ratio is one of the key factors that currently limit the diagnostic image quality and patient conditions of magnetic resonance imaging. Here, Corea et al. use fully printed flexible receive coils, conforming to patient bodies, to improve signals and patient comfort in clinical scanners.

Experimental verification of SNR and parallel imaging improvements using composite arrays

Composite MRI arrays consist of triplets where two orthogonal upright loops are placed over the same imaging area as a standard surface coil. The optimal height of the upright coils is approximately half the width for the 7 cm coils used in this work. Resistive and magnetic coupling is shown to be negligible within each coil triplet. Experimental evaluation of imaging performance was carried out on a Philips 3 T Achieva scanner using an eight-coil composite array consisting of three surface coils and five upright loops, as well as an array of eight surface coils for comparison. The composite array offers lower overall coupling than the traditional array. The sensitivities of upright coils are complementary to those of the surface coils and therefore provide SNR gains in regions where surface coil sensitivity is low, and additional spatial information for improved parallel imaging performance. Near the surface of the phantom the eight-channel surface coil array provides higher overall SNR than the composite array, but this advantage disappears beyond a depth of approximately one coil diameter, where it is typically more challenging to improve SNR. Furthermore, parallel imaging performance is better with the composite array compared with the surface coil array, especially at high accelerations and in locations deep in the phantom. Composite arrays offer an attractive means of improving imaging performance and channel density without reducing the size, and therefore the loading regime, of surface coil elements. Additional advantages of composite arrays include minimal SNR loss using root-sum-of-squares combination compared with optimal, and the ability to switch from high to low channel density by merely selecting only the surface elements, unlike surface coil arrays, which require additional hardware.

Approaching Ultimate Intrinsic SNR in a Uniform Spherical Sample with Finite Arrays of Loop Coils

We investigated to what degree and at what rate the ultimate intrinsic (UI) signal-to-noise ratio (SNR) may be approached using finite radiofrequency detector arrays. We used full-wave electromagnetic field simulations based on dyadic Green's functions to compare the SNR of arrays of loops surrounding a uniform sphere with the ultimate intrinsic SNR (UISNR), for increasing numbers of elements over a range of magnetic field strengths, voxel positions, sphere sizes, and acceleration factors. We evaluated the effect of coil conductor losses and the performance of a variety of distinct geometrical arrangements such as "helmet" and "open-pole" configurations in multiple imaging planes. Our results indicate that UISNR at the center is rapidly approached with encircling arrays and performance is substantially lower near the surface, where a quadrature detection configuration tailored to voxel position is optimal. Coil noise is negligible at high field, where sample noise dominates. Central SNR for practical array configurations such as the helmet is similar to that of close-packed arrangements. The observed trends can provide physical insights to improve coil design.

Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI

PURPOSE

Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error.

THEORY AND METHODS

The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z(2) strength within 30% of the nominal value and demonstrated on a human 3T scanner.

RESULTS

Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method.

CONCLUSION

Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.

Numerical evaluation of image homogeneity, signal-to-noise ratio, and specific absorption rate for human brain imaging at 1.5, 3, 7, 10.5, and 14T in an 8-channel transmit/receive array

PURPOSE

To predict signal-to-noise ratio (SNR) trends and absorbed energy in magnetic resonance imaging (MRI) of the brain up to 14T.

MATERIALS AND METHODS

A human head in an eight-channel transmit/receive coil was simulated with Maxwell and Bloch equations to determine excitation homogeneity with radiofrequency (RF) shimming, image homogeneity, SNR, and absorbed energy in MRI from 1.5 to 14T considering realistic field distributions and relaxation properties.

RESULTS

RF shimming alone achieved a standard deviation in excitation flip angle less than 10° in mid-brain up to 14T, but produced a small region with low excitation on a lower slice. Current reconstruction methods may produce shading artifacts at 14T. SNR increases with a greater-than-linear rate for gradient recalled echo (GRE) sequences having short (2 msec) echo time (TE) and long relaxation time (TR) (∼2.3-fold increase from 7T to 14T), but a less-than-linear rate if TE is 10 msec (∼1.6-fold increase from 7T to 14T). Depending on the sequence, SNR per square root of imaging time may produce a less-than-linear increase with B0 . Whole-head absorbed energy shows a less-than-quadratic increase with B0 (1.7-fold increase from 7T to 14T).

CONCLUSION

Numerical simulations indicate that with proper preparation and precautions, imaging of the human brain at up to 14T could be performed safely, with advantages in SNR.

MRI at 7 Tesla and above: demonstrated and potential capabilities

With more than 40 installed MR systems worldwide operating at 7 Tesla or higher, ultra-high-field (UHF) imaging has been established as a platform for clinically oriented research in recent years. Along with technical developments that, in part, have also been successfully transferred to lower field strengths, MR imaging and spectroscopy at UHF have demonstrated capabilities and potentials for clinical diagnostics in a variety of studies. In terms of applications, this overview article focuses on already achieved advantages for in vivo imaging, i.e., in imaging the brain and joints of the musculoskeletal system, but also considers developments in body imaging, which is particularly challenging. Furthermore, new applications for clinical diagnostics such as X-nuclei imaging and spectroscopy, which only really become feasible at ultra-high magnetic fields, will be presented.

[Problems and chances of high field magnetic resonance imaging]

CLINICAL/METHODICAL ISSUE

The spatial, temporal and spectral resolution in magnetic resonance imaging (MRI) is in many cases currently not sufficient to detect submillimeter lesions or to image the dynamics of the beating heart.

STANDARD RADIOLOGICAL METHODS

At present MRI systems at 1.5 T and 3 T are the standard units for clinical imaging.

METHODICAL INNOVATIONS

The use of ultrahigh magnetic fields of 7 T and higher increases the signal-to-noise ratio, which holds promise for a significant improvement of the spatial and/or temporal resolution as well as for new contrast mechanisms.

PERFORMANCE

With 7 T MRI, images of the brain have been acquired routinely with a spatial resolution of 0.3 mm. The theoretical improvement of the signal-to-noise ratio is often not fully realized due to B1 inhomogeneities and contrast variations.

ACHIEVEMENTS

With MRI at 7 T a notable increase in spatial resolution can be achieved. Methods such as time-of-flight MR angiography and susceptibility-weighted imaging (e.g. neurofunctional MRI, fMRI) profit especially from the higher field strengths. Transmission field inhomogeneities are still a major challenge for ultrahigh field (UHF) MRI and are also a partially unsolved safety problem.

PRACTICAL RECOMMENDATIONS

The use of UHF MRI is currently limited to special applications and the expected gain of the high field must be weighed against technical limitations in both image acquisition and interpretation.

Massively parallel MRI detector arrays

Originally proposed as a method to increase sensitivity by extending the locally high-sensitivity of small surface coil elements to larger areas via reception, the term parallel imaging now includes the use of array coils to perform image encoding. This methodology has impacted clinical imaging to the point where many examinations are performed with an array comprising multiple smaller surface coil elements as the detector of the MR signal. This article reviews the theoretical and experimental basis for the trend towards higher channel counts relying on insights gained from modeling and experimental studies as well as the theoretical analysis of the so-called "ultimate" SNR and g-factor. We also review the methods for optimally combining array data and changes in RF methodology needed to construct massively parallel MRI detector arrays and show some examples of state-of-the-art for highly accelerated imaging with the resulting highly parallel arrays.

High-field magnetic resonance imaging using solenoid radiofrequency coils

High-resolution magnetic resonance imaging using dedicated high-field radiofrequency micro-coils at 16.4 T (700 MHz) was investigated. Specific solenoid coils primarily using silver and copper as conductors with enamel and polyurethane coatings were built to establish which coil configuration produces the best image. Image quality was quantified using signal-to-noise ratio and signal variation over regions of interest. Benchmarking was conducted using 5-mm diameter coils, as this size is comparable to an established coil of the same size. Our 1.4-mm-diameter coils were compared directly to each other, from which we deduce performance as a function of conductor material and coating. A variety of materials and conductor coatings allowed us to choose an optimal design, which we used to image a kidney section at 10-micron resolution. We applied zero-fill extrapolation to achieve 5-micron resolution.

Parallel-transmission-enabled magnetization-prepared rapid gradient-echo T1-weighted imaging of the human brain at 7 T

One of the promises of Ultra High Field (UHF) MRI scanners is to bring finer spatial resolution in the human brain images due to an increased signal to noise ratio. However, at such field strengths, the spatial non-uniformity of the Radio Frequency (RF) transmit profiles challenges the applicability of most MRI sequences, where the signal and contrast levels strongly depend on the flip angle (FA) homogeneity. In particular, the MP-RAGE sequence, one of the most commonly employed 3D sequences to obtain T1-weighted anatomical images of the brain, is highly sensitive to these spatial variations. These cause deterioration in image quality and complicate subsequent image post-processing such as automated tissue segmentation at UHF. In this work, we evaluate the potential of parallel-transmission (pTx) to obtain high-quality MP-RAGE images of the human brain at 7 T. To this end, non-selective transmit-SENSE pulses were individually tailored for each of 8 subjects under study, and applied to an 8-channel transmit-array. Such RF pulses were designed both for the low-FA excitation train and the 180° inversion preparation involved in the sequence, both utilizing the recently introduced k(T)-point trajectory. The resulting images were compared with those obtained from the conventional method and from subject-specific RF-shimmed excitations. In addition, four of the volunteers were scanned at 3 T for benchmarking purposes (clinical setup without pTx). Subsequently, automated tissue classification was performed to provide a more quantitative measure of the final image quality. Results indicated that pTx could already significantly improve image quality at 7 T by adopting a suitable RF-Shim. Exploiting the full potential of the pTx-setup, the proposed k(T)-point method provided excellent inversion fidelity, comparable to what is commonly only achievable at 3 T with energy intensive adiabatic pulses. Furthermore, the cumulative energy deposition was simultaneously reduced by over 40% compared to the conventional adiabatic inversions. Regarding the low-FA k(T)-point based excitations, the FA uniformity achieved at 7 T surpassed what is typically obtained at 3 T. Subsequently, automated white and gray matter segmentation not only confirmed the expected improvements in image quality, but also suggests that care should be taken to properly account for the strong local susceptibility effects near cranial cavities. Overall, these findings indicate that the k(T)-point-based pTx solution is an excellent candidate for UHF 3D imaging, where patient safety is a major concern due to the increase of specific absorption rates.

Ideal current patterns yielding optimal signal-to-noise ratio and specific absorption rate in magnetic resonance imaging: computational methods and physical insights

At high and ultra-high magnetic field strengths, understanding interactions between tissues and the electromagnetic fields generated by radiofrequency coils becomes crucial for safe and effective coil design as well as for insight into limits of performance. In this work, we present a rigorous electrodynamic modeling framework, using dyadic Green's functions, to derive the electromagnetic field in homogeneous spherical and cylindrical samples resulting from arbitrary surface currents in the presence or absence of a surrounding radiofrequency shield. We show how to calculate ideal current patterns that result in the highest possible signal-to-noise ratio (ultimate intrinsic signal-to-noise ratio) or the lowest possible radiofrequency power deposition (ultimate intrinsic specific absorption rate) compatible with electrodynamic principles. We identify familiar coil designs within optimal current patterns at low to moderate field strength, thereby establishing and explaining graphically the near-optimality of traditional surface and volume quadrature designs. We also document the emergence of less familiar patterns, e.g., involving substantial electric--as well as magnetic-dipole contributions, at high field strength. Performance comparisons with particular coil array configurations demonstrate that optimal performance may be approached with finite arrays if ideal current patterns are used as a guide for coil design.

The future of ultra-high field MRI and fMRI for study of the human brain

MRI and fMRI have been used for about three and two decades respectively and much has changed over this time period, both in the quality of the data and in the range of applications for studying the brain. Apart from resolution improvements from around 4mm in the early days to below 0.5mm with modern technology, novel uses of contrast have led to the ability to sensitize images to some of the brain's structural properties at the cellular scale as well as study the localization and organization of brain function at the level of cortical columns. These developments have in part been facilitated by a continuing drive to increase the magnetic field strength. Will the next few decades see similar improvements? Here we will discuss current state of high field MRI, expected further increases in field strength, and improvements expected with these increases.

Parallel traveling-wave MRI: a feasibility study

Traveling-wave magnetic resonance imaging utilizes far fields of a single-piece patch antenna in the magnet bore to generate radio frequency fields for imaging large-size samples, such as the human body. In this work, the feasibility of applying the "traveling-wave" technique to parallel imaging is studied using microstrip patch antenna arrays with both the numerical analysis and experimental tests. A specific patch array model is built and each array element is a microstrip patch antenna. Bench tests show that decoupling between two adjacent elements is better than -26-dB while matching of each element reaches -36-dB, demonstrating excellent isolation performance and impedance match capability. The sensitivity patterns are simulated and g-factors are calculated for both unloaded and loaded cases. The results on B 1- sensitivity patterns and g-factors demonstrate the feasibility of the traveling-wave parallel imaging. Simulations also suggest that different array configuration such as patch shape, position and orientation leads to different sensitivity patterns and g-factor maps, which provides a way to manipulate B(1) fields and improve the parallel imaging performance. The proposed method is also validated by using 7T MR imaging experiments.

Analytic expressions for the ultimate intrinsic signal-to-noise ratio and ultimate intrinsic specific absorption rate in MRI

The ultimate intrinsic signal-to-noise ratio is the highest possible signal-to-noise ratio, and the ultimate intrinsic specific absorption rate provides the lowest limit of the specific absorption rate for a given flip angle distribution. Analytic expressions for ultimate intrinsic signal-to-noise ratio and ultimate intrinsic specific absorption rate are obtained for arbitrary sample geometries. These expressions are valid when the distance between the point of interest and the sample surface is smaller than the wavelength, and the sample is homogeneous. The dependence on the sample permittivity, conductivity, temperature, size, and the static magnetic field strength is given in analytic form, which enables the easy evaluation of the change in signal-to-noise ratio and specific absorption rate when the sample is scaled in size or when any of its geometrical or electrical parameters is altered. Furthermore, it is shown that signal-to-noise ratio and specific absorption rate are independent of the permeability of the sample. As a practical case and a solution example, a uniform, circular cylindrically shaped sample is studied.

Calculation of radiofrequency electromagnetic fields and their effects in MRI of human subjects

Radiofrequency magnetic fields are critical to nuclear excitation and signal reception in magnetic resonance imaging. The interactions between these fields and human tissues in anatomical geometries results in a variety of effects regarding image integrity and safety of the human subject. In recent decades, numerical methods of calculation have been used increasingly to understand the effects of these interactions and aid in engineering better, faster, and safer equipment and methods. As magnetic resonance imaging techniques and technology have evolved through the years, so to have the requirements for meaningful interpretation of calculation results. Here, we review the basic physics of radiofrequency electromagnetics in magnetic resonance imaging and discuss a variety of ways radiofrequency field calculations are used in magnetic resonance imaging in engineering and safety assurance from simple systems and sequences through advanced methods of development for the future.

Traveling-wave RF shimming and parallel MRI

At sufficiently high Larmor frequencies, traveling electromagnetic waves along a magnet bore can be used for remote magnetic resonance excitation and detection, effectively using the bore as a waveguide. So far, this approach has relied only on the lowest waveguide modes and thus has not supported multiple-channel operation for radiofrequency shimming and parallel imaging. In this work, this limitation is addressed by establishing a larger number of propagating modes and tapping their spatial field diversity with multiple waveguide ports. The number of available modes is increased by loading with dielectric inserts; the ports are implemented by stub and loop couplers at the end of a waveguide extension. The resulting traveling-wave array, operated at 298 MHz in a 7T whole-body magnet, is shown to enable radiofrequency shimming as well as parallel imaging with commonly used acceleration factors. The last part of the study concerns the amount of dielectric loading that is required. For the given Larmor frequency and bore dimensions, it is found that rather few water-filled inserts, occupying ∼5% of the bore cross-section, are sufficient for effective parallel imaging.

Reconstruction of MRI data encoded with arbitrarily shaped, curvilinear, nonbijective magnetic fields

A basic framework for image reconstruction from spatial encoding by curvilinear, nonbijective magnetic encoding fields in combination with multiple receivers is presented. The theory was developed in the context of the recently introduced parallel imaging technique using localized gradients (PatLoc) approach. In this new imaging modality, the linear gradient fields are generalized to arbitrarily shaped, nonbijective spatial encoding magnetic fields, which lead to ambiguous encoding. Ambiguities are resolved by adaptation of concepts developed for parallel imaging. Based on theoretical considerations, a practical algorithm for Cartesian trajectories is derived in the case that the conventional gradient coils are replaced by coils for PatLoc. The reconstruction method extends Cartesian sensitivity encoding (SENSE) reconstruction with an additional voxelwise intensity-correction step. Spatially varying resolution, signal-to-noise ratio, and truncation artifacts are described and analyzed. Theoretical considerations are validated by two-dimensional simulations based on multipolar encoding fields and they are confirmed by applying the reconstruction algorithm to initial experimental data.

Cardiac chamber quantification using magnetic resonance imaging at 7 Tesla--a pilot study

OBJECTIVES

Interest in cardiovascular magnetic resonance (CMR) at 7 T is motivated by the expected increase in spatial and temporal resolution, but the method is technically challenging. We examined the feasibility of cardiac chamber quantification at 7 T.

METHODS

A stack of short axes covering the left ventricle was obtained in nine healthy male volunteers. At 1.5 T, steady-state free precession (SSFP) and fast gradient echo (FGRE) cine imaging with 7 mm slice thickness (STH) were used. At 7 T, FGRE with 7 mm and 4 mm STH were applied. End-diastolic volume, end-systolic volume, ejection fraction and mass were calculated.

RESULTS

All 7 T examinations provided excellent blood/myocardium contrast for all slice directions. No significant difference was found regarding ejection fraction and cardiac volumes between SSFP at 1.5 T and FGRE at 7 T, while volumes obtained from FGRE at 1.5 T were underestimated. Cardiac mass derived from FGRE at 1.5 and 7 T was larger than obtained from SSFP at 1.5 T. Agreement of volumes and mass between SSFP at 1.5 T and FGRE improved for FGRE at 7 T when combined with an STH reduction to 4 mm.

CONCLUSIONS

This pilot study demonstrates that cardiac chamber quantification at 7 T using FGRE is feasible and agrees closely with SSFP at 1.5 T.

Interventional MRI: tapering improves the distal sensitivity of the loopless antenna

The "loopless antenna" is an interventional MRI detector consisting of a tuned coaxial cable and an extended inner conductor or "whip". A limitation is the poor sensitivity afforded at, and immediately proximal to, its distal end, which is exacerbated by the extended whip length when the whip is uniformly insulated. It is shown here that tapered insulation dramatically improves the distal sensitivity of the loopless antenna by pushing the current sensitivity toward the tip. The absolute signal-to-noise ratio is numerically computed by the electromagnetic method-of-moments for three resonant 3-T antennae with no insulation, uniform insulation, and with linearly tapered insulation. The analysis shows that tapered insulation provides an approximately 400% increase in signal-to-noise ratio in trans-axial planes 1 cm from the tip and a 16-fold increase in the sensitive area as compared to an equivalent, uniformly insulated antenna. These findings are directly confirmed by phantom experiments and by MRI of an aorta specimen. The results demonstrate that numerical electromagnetic signal-to-noise ratio analysis can accurately predict the loopless detector's signal-to-noise ratio and play a central role in optimizing its design. The manifold improvement in distal signal-to-noise ratio afforded by redistributing the insulation should improve the loopless antenna's utility for interventional MRI.

Performance evaluation of a 32-element head array with respect to the ultimate intrinsic SNR

The quality of an RF detector coil design is commonly judged on how it compares with other coil configurations. The aim of this article is to develop a tool for evaluating the absolute performance of RF coil arrays. An algorithm to calculate the ultimate intrinsic signal-to-noise ratio (SNR) was implemented for a spherical geometry. The same imaging tasks modeled in the calculations were reproduced experimentally using a 32-element head array. Coil performance maps were then generated based on the ratio of experimentally measured SNR to the ultimate intrinsic SNR, for different acceleration factors associated with different degrees of parallel imaging. The relative performance in all cases was highest near the center of the samples (where the absolute SNR was lowest). The highest performance was found in the unaccelerated case and a maximum of 85% was observed with a phantom whose electrical properties are consistent with values in the human brain. The performance remained almost constant for 2-fold acceleration, but deteriorated at higher acceleration factors, suggesting that larger arrays are needed for effective highly-accelerated parallel imaging. The method proposed here can serve as a tool for the evaluation of coil designs, as well as a tool to guide the development of original designs which may begin to approach the optimal performance.

In vivo 1H NMR spectroscopy of the human brain at high magnetic fields: metabolite quantification at 4T vs. 7T

A comprehensive comparative study of metabolite quantification from the human brain was performed on the same 10 subjects at 4T and 7T using MR scanners with identical consoles, the same type of RF coils, and identical pulse sequences and data analysis. Signal-to-noise ratio (SNR) was increased by a factor of 2 at 7T relative to 4T in a volume of interest selected in the occipital cortex using half-volume quadrature radio frequency (RF) coils. Spectral linewidth was increased by 50% at 7T, which resulted in a 14% increase in spectral resolution at 7T relative to 4T. Seventeen brain metabolites were reliably quantified at both field strengths. Metabolite quantification at 7T was less sensitive to reduced SNR than at 4T. The precision of metabolite quantification and detectability of weakly represented metabolites were substantially increased at 7T relative to 4T. Because of the increased spectral resolution at 7T, only one-half of the SNR of a 4T spectrum was required to obtain the same quantification precision. The Cramér-Rao lower bounds (CRLB), a measure of quantification precision, of several metabolites were lower at both field strengths than the intersubject variation in metabolite concentrations, which resulted in a strong correlation between metabolite concentrations of individual subjects measured at 4T and 7T.

Understanding and manipulating the RF fields at high field MRI

This paper presents a complete overview of the electromagnetics (radiofrequency aspect) of MRI at low and high fields. Using analytical formulations, numerical modeling (computational electromagnetics), and ultrahigh field imaging experiments, the physics that impacts the electromagnetic quantities associated with MRI, namely (1) the transmit field, (2) receive field, and (3) total electromagnetic power absorption, is analyzed. The physical interpretation of the above-mentioned quantities is investigated by electromagnetic theory, to understand 'What happens, in terms of electromagnetics, when operating at different static field strengths?' Using experimental studies and numerical simulations, this paper also examines the physical and technological feasibilities by which all or any of these specified electromagnetic quantities can be manipulated through techniques such as B(1) shimming (phased array excitation) and signal combination using a receive array in order to advance MRI at high field strengths. Pertinent to this subject and with highly coupled coils operating at 7 T, this paper also presents the first phantom work on B(1) shimming without B(1) measurements.

Improving SNR of RF coils using composite coil elements

A composite coil element consists of up to three independent orthogonal loops. It improves the flexibility in shaping the radio frequency (RF) field in its vicinity, compared with a single-loop coil element. Computer simulations were conducted to explore the potential advantages of this type of coil configuration for improving the signal-to- noise ratio (SNR), including the intrinsic SNR (ISNR) and the realistic SNR, when the effects of resistive loss of the coil were included. A 'half-space' model was considered, with a variable B(0) direction relative to the surface of a large conductive medium. The SNR performance of a square single-loop coil parallel to the surface of the medium was compared with that of a composite coil element where up to two additional orthogonal square loops of the same size were added to the single coil loop. The SNR performances of coil arrays consisting of single-loop elements and composite elements were also evaluated. The RF field was calculated using the finite-difference time-domain method. The results show that the composite coil element has a substantially better ISNR at all depths from the surface than that of a single-loop element covering the same surface area. Furthermore, the ISNR of a composite element is not sensitive to the surface orientation relative to the B(0) field. The computer simulation also revealed that at 128 MHz, the resistive loss from the copper coil loops standing upright on the surface at room temperature is substantial compared to the loss in the medium. Consequently, the realistic SNR is significantly lower than ISNR at 128 MHz for a composite coil element. The coil loading by the medium becomes more dominant at 170 and 298 MHz, and the differences between the realistic SNR and ISNR become smaller at these higher frequencies.

Noise figure limits for circular loop MR coils

Circular loops are the most common MR detectors. Loop arrays offer improved signal-to-noise ratios (SNRs) and spatial resolution, and enable parallel imaging. As loop size decreases, loop noise increases relative to sample noise, ultimately dominating the SNR. Here, relative noise contributions from the sample and the coil are quantified by a coil noise figure (NF), NF(coil), which adds to the conventional system NF. NF(coil) is determined from the ratio of unloaded-to-loaded coil quality factors Q. Losses from conductors, capacitors, solder joints, eddy currents in overlapped array coils, and the sample are measured and/or computed from 40 to 400 MHz using analytical and full-wave numerical electromagnetic analysis. The Qs are measured for round wire and tape loops tuned from 50 to 400 MHz. NF(coil) is determined as a function of the radius, frequency, and number of tuning capacitors. The computed and experimental Qs and NF(coil)s agree within approximately 10%. The NF(coil) values for 3 cm-diameter wire coils are 3 dB, 1.9 dB, 0.8 dB, 0.2 dB, and 0.1 dB, at 1T, 1.5T, 3T, 7T, and 9.4T, respectively. Wire and tape perform similarly, but tape coils in arrays have substantial eddy current losses. The ability to characterize and reliably predict component- and geometry-associated coil losses is key to designing SNR-optimized loop and phased-array detectors.

MRI endoscopy using intrinsically localized probes

Magnetic resonance imaging (MRI) is traditionally performed with fixed externally applied gradient magnetic fields and is hence intrinsically locked to the laboratory frame of reference (FoR). Here a method for high-resolution MRI that employs active, catheter-based, tiny internal probes that utilize the spatial properties of the probe itself for localization is proposed and demonstrated at 3 T. Because these properties are intrinsic to the probe, they move with it, transforming MRI from the laboratory FoR to the FoR of the device itself, analogous to an endoscope. The "MRI endoscope" can utilize loop coils and loopless antennas with modified sensitivity, in combination with adiabatic excitation by the device itself, to restrict the MRI sensitivity to a disk-shaped plane a few mm thick. Excitation with the MRI endoscope limits the eddy currents induced in the sample to an excited volume whose size is orders of magnitude below that excited by a conventional body MRI coil. Heat testing shows maximum local temperature increases of <1 degrees C during MRI, within regulatory guidelines. The method is demonstrated in a kiwifruit, in intact porcine and rabbit aortas, and in an atherosclerotic human iliac artery specimen, with in-plane resolution as small as 80 microm and 1.5-5 mm slice thickness.

Electrodynamic constraints on homogeneity and radiofrequency power deposition in multiple coil excitations

The promise of increased signal-to-noise ratio and spatial/spectral resolution continues to drive MR technology toward higher magnetic field strengths. SAR management and B1 inhomogeneity correction become critical issues at the high frequencies associated with high field MR. In recent years, multiple coil excitation techniques have been recognized as potentially powerful tools for controlling specific absorption rate (SAR) while simultaneously compensating for B1 inhomogeneities. This work explores electrodynamic constraints on transmit homogeneity and SAR, for both fully parallel transmission and its time-independent special case known as radiofrequency shimming. Ultimate intrinsic SAR--the lowest possible SAR consistent with electrodynamics for a particular excitation profile but independent of transmit coil design--is studied for different field strengths, object sizes, and pulse acceleration factors. The approach to the ultimate intrinsic limit with increasing numbers of finite transmit coils is also studied, and the tradeoff between homogeneity and SAR is explored for various excitation strategies. In the case of fully parallel transmission, ultimate intrinsic SAR shows flattening or slight reduction with increasing field strength, in contradiction to the traditionally cited quadratic dependency, but consistent with established electrodynamic principles.

128-channel body MRI with a flexible high-density receiver-coil array

PURPOSE

To determine whether the promise of high-density many-coil MRI receiver arrays for enabling highly accelerated parallel imaging can be realized in practice.

MATERIALS AND METHODS

A 128-channel body receiver-coil array and custom MRI system were developed. The array comprises two clamshells containing 64 coils each, with the posterior array built to maximize signal-to-noise ratio (SNR) and the anterior array design incorporating considerations of weight and flexibility as well. Phantom imaging and human body imaging were performed using a variety of reduction factors and 2D and 3D pulse sequences.

RESULTS

The ratio of SNR relative to a 32-element array of similar footprint was 1.03 in the center of an elliptical loading phantom and 1.7 on average in the outer regions. Maximum g-factors dropped from 5.5 (for 32 channels) to 2.0 (for 128 channels) for 4x4 acceleration and from 25 to 3.3 for 5x5 acceleration. Residual aliasing artifacts for a right/left (R/L) reduction factor of 8 in human body imaging were significantly reduced relative to the 32-channel array.

CONCLUSION

MRI with a large number of receiver channels enables significantly higher acceleration factors for parallel imaging and improved SNR, provided losses from the coils and electronics are kept negligible.