RF engineers, MR physicists, ultra-high field practitioners.

To evaluate the impact of coil coverage for brain imaging at 3 T and 7 T using the ultimate SNR metric.Dipoles and head model: We simulated the Virtual Family Duke body model (head only, the body was cut off below the neck) [1]. The head model had a resolution of 3 mm isotropic (63×80×85 pixels). In order to compute the ultimate SNR (uSNR), we placed a cloud of dipoles around the model at a distance no less than D=3 cm (there were >10⁵ dipoles per coil coverage simulation). Three coil coverages were simulated (Fig. 1a). The “All around” dipole distribution corresponds to the true uSNR as it allows simulation of incident electromagnetic (EM) fields impinging the head model from all directions in space. The “All around but neck” is a more realistic situation since in practice no coils can be placed below the neck and therefore corresponds to the “achievable ultimate SNR”. The Helmet distribution corresponds to modern multi-channel coil geometries. Basis calculation: Unlike in uniform spheres and cylinders [2-4], a basis of EM fields in non-uniform realistic body models such as Duke cannot be computed analytically. Instead, we compute a numerical EM basis in Duke using a three-step process. First, we place a large number of dipoles (>10⁵) around the body model at a distance no less than D=3 cm. Note that there are 6 dipoles per sampled spatial position: Three X, Y and Z electric dipoles and three X, Y and Z magnetic dipoles. Second, we compute the incident E and H fields (i.e., in free space without the body model) created by random excitations of the dipole cloud. This is done by (i) exciting all the dipoles simultaneously using random excitations and (ii) computing the resulting E and H fields using the free-space Maxwell Green function. Finally, we compute the scattered E and H fields in the body model using the ultra-fast “MARIE” EM solver that we have described previously [5,6] (https://github.com/thanospol/MARIE). SNR calculation: We compute the SNR at all head locations using an increasing number of random basis vectors and stop adding basis vectors when the SNR converges to the ultimate value (Fig. 2). To compute the SNR, we compute the optimal combination of the basis vector x as follows: min{x^HCx} s.t. B^Tx=1, where C is the noise correlation matrix computed from the E fields and the conductivity map [3-4,7] and B is a column vector concatenating the values of B1- for every basis vector at the location considered. This optimization is performed at every location in the head model. The SNR is then computed as: SNR=B₀²B^Tx/sqrt(x^HCx), where B0 is the field strength in Tesla. We also compute the accelerated SNR as one over the G-factor for SENSE acceleration in the A-P direction.Fig. 2 shows that SNR converged to the ultimate at all locations in the head when using 2500 random basis excitations. The uSNR is, as expected, greater at 7 T than at 3 T because our SNR metric reflects the B0² dependence due to increased density of the “spin-up” population as well as increased induced current in the received elements with B0. The sagittal SNR maps (Fig. 2b&c) clearly show that not placing coil elements above the eyes/nose/mouth dramatically decreases SNR in this region but has little effect on SNR in the brain, except for a small patch in the frontal lobe. This means that adding coil elements above the eye and nose is not an effective strategy for increasing the SNR in the brain, but one must be careful to place coil elements as close as possible to the eyes in order to cover the frontal lobe. Finally, the ultimate retained-SNR in SENSE accelerated imaging was close to 100% for R≤6 and then decreased rapidly for greater acceleration factors. There does not seem to be a dramatic worsening of the retained-SNR when using a helmet coil design compared to the ultimate “All around” dipole configuration. Similar results (uSNR maps and retained-SNR) were obtained at 7 T.