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

Lee, Hong-Hsi; Sodickson, Daniel K.; Lattanzi, Riccardo

doi:10.1002/mrm.27207

Cited by 12 publications

(22 citation statements)

References 17 publications

(72 reference statements)

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“…Our results demonstrated that the signal‐only optimal and ideal current patterns were equivalent for a central voxel (Figure ). The absence of dark mode current patterns (Figure ) can be explained by the fact that only a single current mode contributes to the signal sensitivity at the center of a sphere, limiting the degrees of freedom to simultaneously minimize sample noise. Phase advancement in the ideal and signal‐only current patterns in the presence of HPM (Figures and ) indicate that the current pattern optimization has accounted and compensated for the phase delay encountered by the signal propagating through the HPM layer.…”

Section: Discussionmentioning

confidence: 99%

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

Vaidya

Sodickson

Collins

et al. 2018

Magnetic Resonance in Med

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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.

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Section: Discussionmentioning

confidence: 99%

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

Vaidya

Sodickson

Collins

et al. 2018

Magnetic Resonance in Med

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“…Approaching the problem from the point of view of determining uiSNR, Lee et al 13 demonstrated that only one divergence‐free mode contributes to the MR signal at the center of a sphere with uniform electrical properties, which led to the derivation of a precise analytical expression for the uiSNR in the center of a sphere. The returned expression is identical to the previous Hoult's result (Equations 48 and 6 in the two articles, respectively), thus proving that this SNR formula in fact can be considered the uiSNR at the center of a sphere of uniform properties.…”

Section: Methodsmentioning

confidence: 99%

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

Ster

Grant

Moortele

et al. 2022

Magnetic Resonance in Med

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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 B01.94 ± 0.16 compared with B02.13 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.

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“…In particular, their shape was identical for the central voxel, consisting of distributed current loops precessing at the Larmor frequency around the direction of the main magnetic field (Video S1). This was expected, since only one mode survives at the center of the sphere, 24 and in both cases its role is to closely track spins precessing at the voxel of interest. The only difference is the opposite direction of the precession of the current loops, which accounts for the fact that for OPTXE it is the transmit sensitivity that is maximized, whereas for UISNR it is the receive sensitivity.…”

Section: Discussionmentioning

confidence: 93%

“…As a result, the optimal RF shimming weights are not equal in the two cases, yielding different distributions of the net magnetic and electric field. The shape and amplitude of the ICP associated with OPTXE and UISNR for the same voxel are also different, except at the center of the object, where they are dominated by one mode 24 …”

Section: Discussionmentioning

confidence: 99%

“…It has been shown that theoretical performance limits could be used as absolute references against which to evaluate RF coil performance and to derive guidelines for optimal coil design 1,17–25 . For example, the ultimate intrinsic signal‐to‐noise ratio (UISNR) could be used to assess receive arrays, 26–29 while the associated ideal current patterns could be employed to guide coil design 30–33 .…”

Section: Introductionmentioning

confidence: 99%

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A formalism to investigate the optimal transmit efficiency in radiofrequency shimming

2020

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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.

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

Abstract: 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.

Cited by 12 publications

References 17 publications

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

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

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

A formalism to investigate the optimal transmit efficiency in radiofrequency shimming

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