Christopher J. Mirfin^{1}, Stephen Bawden^{1}, Paul Glover^{1}, Penny A. Gowland^{1}, and Richard Bowtell^{1}

We investigate the performance that can be achieved by applying volume and slice shimming on the commonly-used Nova 8-channel transmit/32-channel receive head coil, whilst controlling the total transmit power, as a proxy for global SAR. Under this constraint, our results suggest that shimming on individual axial slices can significantly improve the achievable B1 field uniformity (39.0% ± 3.9%) for the same transmit power as normal quadrature mode.

Static RF shimming through parallel transmission is a
crucial tool for the mitigation of B1 inhomogeneities at high-field^{1,2}. Multi-slice
acquisitions allow shimming to be performed separately on each slice, and this
approach has previously been shown to outperform standard volume shimming at
the expense of increased global SAR on a specially-designed, 15-channel
transceiver coil^{3}.

In this work, we investigate the performance that can be achieved by applying volume and slice shimming on the commonly-used Nova 8-channel transmit/32-channel receive head coil (Nova Medical Inc., Wilmington, USA), whilst controlling the total transmit power, as a proxy for global SAR. Under this constraint, our results suggest that shimming on individual axial slices can significantly improve the achievable B1-field uniformity for the same transmit power as normal quadrature mode.

B1 mapping was performed on six volunteers using the actual flip-angle
imaging method^{4} on a Philips (Eindhoven, Netherlands) 7T Achieva scanner
equipped with 8 transmit channels . The mapping of the B1-fields due to all
8-elements of the Nova transmit coil with an isotropic voxel size of 7mm and whole
brain coverage took less than 5 minutes (TR_{1}= 40ms; TR_{2}= 160ms; TE= 4.6ms; FA= 40^{o}).

The coil can be driven in quadrature mode by applying a set of equal transmit amplitudes with differing phase offsets on each of the eight channels, yielding a B1-field with characteristic central brightening. The quadrature-mode B1-field was also mapped on the same six volunteers.

To achieve improved uniformity via B1-shimming, the complex transmit
channel weights ($$$w\in\mathbb{C}$$$) were optimised using a magnitude least squares approach with Tikhonov regularisation (see equation 1, where $$$S_i$$$ represents the coil sensitivities at location $$$i$$$), and solved
using a variable exchange method^{5}. The channel amplitudes were subsequently scaled to yield a mean B1 field equal
to the target field $$$b$$$.

$$\min_{w}\bigg( \sum_{i\in ROI}|||S_i w|-b||^2 + \beta ||w||^2 \bigg)\quad\quad(1)$$

To match the transmit power between a B1-shim selected for B1 uniformity (uniform shim) and quadrature mode, the regularisation parameter $$$\beta$$$ in Eq. [1] was suitably adjusted. In effect, the L-curve of solutions (see Figure 1) was traversed until the nearest power-matched solution was found. For the extreme case of no power regularisation, $$$\beta$$$ was set to zero. The total optimisation time was less than one-minute in all cases.

Numerical simulations (FDTD) of electromagnetic fields produced by the coil elements in human head models (male and female) were provided by the coil manufacturer for an isotropic voxel size of 2mm. These were used to generate 10-gram average SAR maps in order to quantify local and global SAR for different sets of shim weights.

Calculations on the in vivo data showed that RF shimming over the whole volume provided no significant reduction in the standard deviation of the B1 field compared to quadrature mode (Figure 2). For the same total power as quadrature mode, axial slice-by-slice shimming provided the largest improvement in uniformity, with a change in standard deviation of 39.0% ± 3.9% from volume quadrature mode. Coronal and sagittal slice-by-slice shimming also gave improvements of 31.1% ± 4.6% and 23.3% ± 8.7% respectively.

It can be seen that removing power regularisation can slightly reduce the standard deviation further (standard deviation improvement over volume quadrature mode: axial: 46.0% ± 4.4%, coronal: 36.4% ± 6.1%, sagittal: 28.8% ± 6.8%), but this improvement comes at the expense of a dramatic increase in the transmit power, particularly for coronal and sagittal slice shimming (Figure 2).

For the numerical simulations, with power regularisation, shimming over the axial slices again resulted in the greatest improvement (73.0% improvement in uniformity, as compared to quadrature volume mode). Global and local (Figure 4) SAR increased in this instance by 12.0% and 21.3% respectively. Without power regularisation, these values rise to 87.2% and 72.3%.

These results show the sub-optimal performance of quadrature volume mode for head imaging. Slice-by-slice shimming (even in quadrature mode) provides substantial improvements in the B1-field uniformity, which can be further improved at the same transmit power by use of a shimming optimisation algorithm.

Shimming on axial slices is preferential for the Nova 8-channel coil due to its rotational symmetry, whereby each channel provides an equal contribution to the total B1 field in an axial plane. Coronal and sagittal slices experience poorer channel coverage when unit power is defined for each coil, with fewer than 8 coils dominating (Figure 3). In the unlimited power scenario– the optimisation seeks to increase the power through these other channels, resulting in the large total transmit power (and hence SAR) observed in Figure 2 for coronal and sagittal slices.

1. Katscher U. et al. (2006): NMR in Biomedicine. 19(3): 393-400

2. Van de Moortele PF. et al. (2005): MRM. 54(6): 1503-1518

3. Curtis A. et al. (2012): MRM. 68(4): 1109-1116

4. Yarnykh VL. (2007): MRM. 57(1): 192-200

5. Setsompop K. et al. (2008): MRM. 59: 908-915

Figure 1: L-curve
of solutions produced by decreasing the value of the regularisation parameter β
(range shown 10-0.001). When the equivalent
transmit power to quadrature mode is found, the search is terminated (vertical
line). The extended L-curve is shown to illustrate how higher transmit power can
further improve B1-field uniformity.

Figure 2: Relative
standard deviation of |B1|-field and total transmit power, normalised by values
for quadrature volume mode. Top row – numerically simulated B1 maps.
Bottom row – experimental results for 6 participants (error bars demonstrate
variation between participants).

Figure 3: Relative |B1| (normalised to peak value) for 1 volunteer at 7T for each transmit channel
individually. Top row – axial centre slice. Centre row – coronal centre slice.
Bottom row – sagittal centre slice.

Figure 4: 10-gram
averaged SAR maps (centre axial slice). Left: quadrature axial volume mode. Centre:
uniform shim (power matched) – displaying larger maximum local SAR ‘hotspot’. Right:
uniform shim (no power regularisation) with higher average (global) SAR and
maximum local SAR.