Disentangling Signal propagation and Noise-related Effects in the Presence of High Permittivity Materials via Ideal Current Patterns

Manushka V. Vaidya^{1,2,3}, Christopher M. Collins^{1,2,3}, Daniel K. Sodickson^{1,2,3}, Giuseppe Carluccio^{1,2}, and Riccardo Lattanzi^{1,2,3}

1) Ideal
current patterns: An in-house simulation framework based on dyadic Green’s
functions (DGF) was used to calculate the ideal current patterns^{3} corresponding
to the UISNR at a voxel 3.4cm from the center of a sphere at 7T (Fig. 1). A
mode expansion order of 60 was used to ensure convergence. Calculations were
repeated in the presence and absence of a HPM layer surrounding the object with
εr = 1000.

2) Signal-only
propagation model: A
circularly polarized local magnetic field source at the operating frequency
(Fig. 1) was modeled to simulate a precessing spin at the voxel of interest using
numerical simulation software (CST, 2015). The corresponding tangential *E* field, which may be associated with a putative
detector current pattern well matched to the precessing spin’s field, and hence
well suited for efficient signal reception, was calculated on a curved
spherical surface (Fig. 1) to investigate the effects of signal propagation
through HPMs. Approximately one million mesh cells were used. An accuracy of
-50 dB was used to ensure convergence.

3) Optimal E fields: The optimal net E field generated by the ideal current patterns was calculated (Fig.5) and its spatial distribution was investigated to test the hypothesis that reduced E field penetration, and consequently reduced sample noise is associated with larger ideal current patterns.

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2.Yang QX, Wang J, Wang J, Collins CM, Wang C, Smith MB. Reducing SAR and enhancing cerebral signal-to-noise ratio with high permittivity padding at 3 T. Magnetic Resonance in Medicine 2011;65(2):358-362.

3. Lattanzi R, Sodickson DK. Ideal current patterns yielding optimal signal-to-noise ratio and specific absorption rate in magnetic resonance imaging: computational methods and physical insights. Magn Reson Med 2012;68(1):286-304.

4. Vaidya MV, Haemer G, Carluccio G, Novikov DS, Sodickson DK, Collins CM, Wiggins GC, Lattanzi R. Ideal current patterns correspond to larger surface coils with use of high permittivity materials Proc Intl Soc Mag Reson Med 2015:p.3109.

5. King SB, Ryner LN, Tomanek B, Sharp JC, Smith ICP. MR spectroscopy using multi-ring surface coils. Magnetic Resonance in Medicine 1999;42(4):655-664.

6. Haemer GG, Collins CM, Sodickson DK, Wiggins GC. Discovering and working around effects of unwanted resonant modes in high permittivity materials placed near RF coils. Proc Intl Soc Mag Reson Med 2015:p.0859.

Figure 1: Voxel
of interest (red X) is located 3.4cm from the center of spherical sample (gray)
surrounded by HPM (blue)(A). HPM thickness ranged from 0.8cm to 3.2cm (λ/4-λ in
HPM). Ideal current patterns and tangential E fields of a synthetic dipole (B) were
calculated on a spherical surface (dotted line).

Figure 2: Ideal current patterns for a voxel of interest change in size and direction (red) for different thicknesses of the HPM. In D, concentric
loops with opposite direction are observed. Ideal current patterns in B, C are
out of phase and E,F are in phase with A.

Figure 3: Tangential
E fields produced by a local circularly-polarized field source at the voxel of interest demonstrate a phase delay for cases with the HPM layer. Tangential
E fields in Fig E are phase delayed by approximately 90^{o} w.r.t A,
and fields in Fig H are in-phase with A.

Figure 4: The
size of the distributed loops in the tangential E field plots does not change noticeably
for cases with and without an HPM. Tangential E fields in Fig B were manually advanced
in phase by approximately 90^{o} in order to align the loop at the same
position as in Fig A, for visual comparison.

Figure 5: The optimal E fields, which are the weighted
combination of the DGF basis fields using the same weights that result in UISNR
(matrix size of 128x128; slice x = 0), demonstrate that cases with less E field
penetration (B,D,E) correspond to larger ideal current patterns in Fig 2:B,D,E.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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