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

Performance of receive head arrays versus ultimate intrinsic SNR at 7 T and 10.5 T

PURPOSE

We examined magnetic field dependent SNR gains and ability to capture them with multichannel receive arrays for human head imaging in going from 7 T, the most commonly used ultrahigh magnetic field (UHF) platform at the present, to 10.5 T, which represents the emerging new frontier of >10 T in UHFs.

METHODS

Electromagnetic (EM) models of 31-channel and 63-channel multichannel arrays built for 10.5 T were developed for 10.5 T and 7 T simulations. A 7 T version of the 63-channel array with an identical coil layout was also built. Array performance was evaluated in the EM model using a phantom mimicking the size and electrical properties of the human head and a digital human head model. Experimental data was obtained at 7 T and 10.5 T with the 63-channel array. Ultimate intrinsic SNR (uiSNR) was calculated for the two field strengths using a voxelized cloud of dipoles enclosing the phantom or the digital human head model as a reference to assess the performance of the two arrays and field depended SNR gains.

RESULTS

uiSNR calculations in both the phantom and the digital human head model demonstrated SNR gains at 10.5 T relative to 7 T of 2.6 centrally, ˜2 at the location corresponding to the edge of the brain, ˜1.4 at the periphery. The EM models demonstrated that, centrally, both arrays captured ˜90% of the uiSNR at 7 T, but only ˜65% at 10.5 T, leading only to ˜2-fold gain in array SNR in going from 7 to 10.5 T. This trend was also observed experimentally with the 63-channel array capturing a larger fraction of the uiSNR at 7 T compared to 10.5 T, although the percentage of uiSNR captured were slightly lower at both field strengths compared to EM simulation results.

CONCLUSIONS

Major uiSNR gains are predicted for human head imaging in going from 7 T to 10.5 T, ranging from ˜2-fold at locations corresponding to the edge of the brain to 2.6-fold at the center, corresponding to approximately quadratic increase with the magnetic field. Realistic 31- and 63-channel receive arrays, however, approach the central uiSNR at 7 T, but fail to do so at 10.5 T, suggesting that more coils and/or different type of coils will be needed at 10.5 T and higher magnetic fields.

A theoretical framework to investigate the effect of high permittivity materials in MRI using anatomy-mimicking cylinders

PURPOSE

Recent numerical and empirical results proved that high permittivity materials (HPM) used in pads placed near the subject or directly integrated with coils can increase the SNR and reduce the specific absorption rate (SAR) in MRI. In this paper, we propose an analytical investigation of the effect on the magnetic field distribution of a layer of HPM surrounding an anatomy-mimicking cylindrical sample.

METHODS

The study is based on a reformulation of the Mie scattering for cylindrical geometry, following an approach recently introduced for spherical samples. The total field in each medium is decomposed in terms of inward and outward electromagnetic waves, and the fields are expressed as series of cylindrical harmonics, whose coefficients can be interpreted as classical reflection and transmission coefficients.

RESULTS

Our new formulation allows a quantitative evaluation of the effect of the HPM layer for varying permittivity and thickness, and it provides an intuitive understanding of such effect in terms of propagation and scattering of the RF field.

CONCLUSION

We show how HPM can filter out the modes that only contribute to the noise or RF power deposition, resulting in higher SNR or lower SAR, respectively. Our proposed framework provides physical insight on how to properly design HPM for MRI applications.

RF coil design strategies for improving SNR at the ultrahigh magnetic field of 10.5 Tesla

Purpose

To develop multichannel transmit and receive arrays towards capturing the ultimate-intrinsic-SNR (uiSNR) at 10.5 Tesla (T) and to demonstrate the feasibility and potential of whole-brain, high-resolution human brain imaging at this high field strength.

Methods

A dual row 16-channel self-decoupled transmit (Tx) array was converted to a 16Tx/Rx transceiver using custom transmit/receive switches. A 64-channel receive-only (64Rx) array was built to fit into the 16Tx/Rx array. Electromagnetic modeling and experiments were employed to define safe operation limits of the resulting 16Tx/80Rx array and obtain FDA approval for human use.

Results

The 64Rx array alone captured approximately 50% of the central uiSNR at 10.5T while the identical 7T 64Rx array captured ∼76% of uiSNR at this lower field strength. The 16Tx/80Rx configuration brought the fraction of uiSNR captured at 10.5T to levels comparable to the performance of the 64Rx array at 7T. SNR data obtained at the two field strengths with these arrays displayed dependent increases over a large central region. Whole-brain high resolution T 2 * and T 1 weighted anatomical and gradient-recalled echo EPI BOLD fMRI images were obtained at 10.5T for the first time with such an advanced array, illustrating the promise of >10T fields in studying the human brain.

Conclusion

We demonstrated the ability to approach the uiSNR at 10.5T over the human brain with a novel, high channel count array, achieving large SNR gains over 7T, currently the most commonly employed ultrahigh field platform, and demonstrate high resolution and high contrast anatomical and functional imaging at 10.5T.

Comparison of tight-fitting 7T parallel-transmit head array designs using excitation uniformity and local specific absorption rate metrics

PURPOSE

We model the performance of parallel transmission (pTx) arrays with 8, 16, 24, and 32 channels and varying loop sizes built on a close-fitting helmet for brain imaging at 7 T and compare their local specific absorption rate (SAR) and flip-angle performances to that of birdcage coil (used as a baseline) and cylindrical 8-channel and 16-channel pTx coils (single-row and dual-row).

METHODS

We use the co-simulation approach along with MATLAB scripting for batch-mode simulation of the coils. For each coil, we extracted B1 + maps and SAR matrices, which we compressed using the virtual observation points algorithm, and designed slice-selective RF shimming pTx pulses with multiple local SAR and peak power constraints to generate L-curves in the transverse, coronal, and sagittal orientations.

RESULTS

Helmet designs outperformed cylindrical pTx arrays at a constant number of channels in the flip-angle uniformity at a constant local SAR metric: up to 29% for 8-channel arrays, and up to 34% for 16-channel arrays, depending on the slice orientation. For all helmet arrays, increasing the loop diameter led to better local SAR versus flip-angle uniformity tradeoffs, although this effect was more pronounced for the 8-channel and 16-channel systems than the 24-channel and 32-channel systems, as the former have more limited degrees of freedom and therefore benefit more from loop-size optimization.

CONCLUSION

Helmet pTx arrays significantly outperformed cylindrical arrays with the same number of channels in local SAR and flip-angle uniformity metrics. This improvement was especially pronounced for non-transverse slice excitations. Loop diameter optimization for helmets appears to favor large loops, compatible with nearest-neighbor decoupling by overlap.

A 128-channel receive array for cortical brain imaging at 7 T

PURPOSE

A 128-channel receive-only array for brain imaging at 7 T was simulated, designed, constructed, and tested within a high-performance head gradient designed for high-resolution functional imaging.

METHODS

The coil used a tight-fitting helmet geometry populated with 128 loop elements and preamplifiers to fit into a 39 cm diameter space inside a built-in gradient. The signal-to-noise ratio (SNR) and parallel imaging performance (1/g) were measured in vivo and simulated using electromagnetic modeling. The histogram of 1/g factors was analyzed to assess the range of performance. The array's performance was compared to the industry-standard 32-channel receive array and a 64-channel research array.

RESULTS

It was possible to construct the 128-channel array with body noise-dominated loops producing an average noise correlation of 5.4%. Measurements showed increased sensitivity compared with the 32-channel and 64-channel array through a combination of higher intrinsic SNR and g-factor improvements. For unaccelerated imaging, the 128-channel array showed SNR gains of 17.6% and 9.3% compared to the 32-channel and 64-channel array, respectively, at the center of the brain and 42% and 18% higher SNR in the peripheral brain regions including the cortex. For R = 5 accelerated imaging, these gains were 44.2% and 24.3% at the brain center and 86.7% and 48.7% in the cortex. The 1/g-factor histograms show both an improved mean and a tighter distribution by increasing the channel count, with both effects becoming more pronounced at higher accelerations.

CONCLUSION

The experimental results confirm that increasing the channel count to 128 channels is beneficial for 7T brain imaging, both for increasing SNR in peripheral brain regions and for accelerated imaging.

Novel Numerical Basis Sets for Electromagnetic Field Expansion in Arbitrary Inhomogeneous Objects

We investigated how to construct low-order subspace basis sets to accurately represent electromagnetic fields generated within inhomogeneous arbitrary objects by radio-frequency sources external to a Huygen's surface. The basis generation relies on the singular value decomposition of Green's functions integro-differential operators which makes it feasible to derive a reduced-order yet stable model. We present a detailed study of the theoretical and numerical requisites for generating such basis, and show how it can be used to calculate performance limits in magnetic resonance imaging applications. Finally, we propose a novel numerical framework for the computation of characteristic modes of arbitrary inhomogeneous objects. We validated accuracy and convergence properties of the numerical basis against a complete analytical basis in the case of a uniform spherical object. We showed that the discretization of the Huygens's surface has a minimal effect on the accuracy of the calculations, which mainly depended on the electromagnetic solver resolution and order of approximation.

Magnetic field strength dependent SNR gain at the center of a spherical phantom and up to 11.7T

PURPOSE

The SNR at the center of a spherical phantom of known electrical properties was measured in quasi-identical experimental conditions as a function of magnetic field strength between 3 T and 11.7 T.

METHODS

The SNR was measured at the center of a spherical water saline phantom with a gradient recalled echo sequence. Measurements were performed at NeuroSpin at 3, 7, and 11.7 T. The phantom was then shipped to Maastricht University and then to the University of Minnesota for additional data points at 7, 9.4, and 10.5 T. Experiments were carried out with the exact same type of birdcage volume coil (except at 3 T, where a similar coil was used) to attempt at isolating the evolution of SNR with field strength alone. Phantom electrical properties were characterized over the corresponding frequency range.

RESULTS

Electrical properties were found to barely vary over the frequency range. Removing the influence of the flip-angle excitation inhomogeneity was crucial, as expected. After such correction, measurements revealed a gain of SNR growing as B₀ ^{1.94 ± 0.16} compared with B₀ ^2.13 according to ultimate intrinsic SNR theory.

CONCLUSIONS

By using quasi-identical experimental setups (RF volume coil, phantom, electrical properties, and protocol), this work reports experimental data between 3 T and 11.7 T, enabling the comparison with SNR theories in which conductivity and permittivity can be assumed to be constant with respect to field strength. According to ultimate SNR theory, these results can be reasonably extrapolated to the performance of receive arrays with greater than about 32 elements for central SNR in the same spherical phantom.

Scattering from Spheres: A New Look into an Old Problem

In this work, we introduce a theoretical framework to describe the scattering from spheres. In our proposed framework, the total field in the outer medium is decomposed in terms of inward and outward electromagnetic fields, rather than in terms of incident and scattered fields, as in the classical Lorenz–Mie formulation. The fields are expressed as series of spherical harmonics, whose combination weights can be interpreted as reflection and transmission coefficients, which provides an intuitive understanding of the propagation and scattering phenomena. Our formulation extends the previously proposed theory of non-uniform transmission lines by introducing an expression for impedance transfer, which yields a closed-form solution for the fields inside and outside the sphere. The power transmitted in and scattered by the sphere can be also evaluated with a simple closed-form expression and related with the modulus of the reflection coefficient. We showed that our method is fully consistent with the classical Mie scattering theory. We also showed that our method can provide an intuitive physical interpretation of electromagnetic scattering in terms of impedance matching and resonances, and that it is especially useful for the case of inward traveling spherical waves generated by sources surrounding the scatterer.

A formalism to investigate the optimal transmit efficiency in radiofrequency shimming

Transmit efficiency specifies the amplitude of the magnetic resonance excitation field produced over a region of interest with respect to the radiofrequency (RF) power deposited in the sample. This metric is highly important at ultra-high field magnetic resonance imaging (≥7 T), where excitation inhomogeneities and electric field interference effects could prevent achieving the desired flip angle distribution while satisfying the power safety limits. The aim of this work was to introduce an approach to calculate a theoretical upper bound on the transmit efficiency (OPTXE) for RF shimming, independent from any particular coil design. We computed the OPTXE for head-mimicking uniform spherical samples and a realistic heterogeneous head model by maximizing the square of the net transmit field per unit power deposition. The corresponding RF shimming weights were used to combine the analytical surface current modes into ideal current patterns. OPTXE grew monotonically as the target excitation voxel approached the surface of the object, and overall decreased at higher field strengths, presenting similar trends in both the uniform sphere and heterogeneous head model. Arrays with an increasing number of loops could closely approach OPTXE in the central region of the object, but performance decreased closer to the surface and at higher magnetic field strengths. The performance of 32 loops for a two-dimensional excitation region at 7 T increased from 34% to 93% when they were arranged based on the shape of the ideal current patterns. OPTXE provides an absolute reference to evaluate coil designs and RF shimming algorithms, whereas ideal current patterns could serve as guidelines for novel coil designs at ultra-high field. The uniform sphere model enables rapid analytic simulations and provides a good approximation of the OPTXE distribution in a realistic heterogeneous head model with comparable dimensions.

Disentangling the effects of high permittivity materials on signal optimization and sample noise reduction via ideal current patterns

PURPOSE

To investigate how high-permittivity materials (HPMs) can improve SNR when placed between MR detectors and the imaged body.

METHODS

We used a simulation framework based on dyadic Green's functions to calculate the electromagnetic field inside a uniform dielectric sphere at 7 Tesla, with and without a surrounding layer of HPM. SNR-optimizing (ideal) current patterns were expressed as the sum of signal-optimizing (signal-only) current patterns and dark mode current patterns that minimize sample noise while contributing nothing to signal. We investigated how HPM affects the shape and amplitude of these current patterns, sample noise, and array SNR.

RESULTS

Ideal and signal-only current patterns were identical for a central voxel. HPMs introduced a phase shift into these patterns, compensating for signal propagation delay in the HPMs. For an intermediate location within the sphere, dark mode current patterns were present and illustrated the mechanisms by which HPMs can reduce sample noise. High-amplitude signal-only current patterns were observed for HPM configurations that shield the electromagnetic field from the sample. For coil arrays, these configurations corresponded to poor SNR in deep regions but resulted in large SNR gains near the surface due to enhanced fields in the vicinity of the HPM. For very high relative permittivity values, HPM thicknesses corresponding to even multiples of λ/4 resulted in coil SNR gains throughout the sample.

CONCLUSION

HPMs affect both signal sensitivity and sample noise. Lower amplitude signal-only optimal currents corresponded to higher array SNR performance and could guide the design of coils integrated with HPM.