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

Abstract

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 (B ⩾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.

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

“…in Ref. . The radius of the spherical cap was set to = 12.2 cm, which is the same radius as in our previous work .…”

“…. The radius of the spherical cap was set to = 12.2 cm, which is the same radius as in our previous work . To study the effect of the cap angle on the UISNR, we monotonously increased in discrete steps from to .…”

“…and in Ref. . The boundary coefficients , and are specified in the supporting information in Equations S17‐S20.…”

“…In electromagnetic theory, loop‐only arrays can be modeled by a divergence‐free surface current distribution. Divergence‐free current patterns must be complemented by curl‐free current patterns to form a complete electromagnetic basis yielding the UISNR . Straight, Z‐directed dipoles positioned on a cylindrical former are characterized by a Z‐directed current distribution (Figure C).…”

“…Randomly excite a large number of elementary electric and magnetic dipoles lying on a Huygen's surface and solve the Helmholtz equation Use the analytically known eigenfunctions of the Helmholtz operator in spherical or cylindrical coordinate systems. Equivalent surface current patterns, which surround the sample, can be used to excite these eigenfunctions. …”