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Exploring dynamic RF shimming for labelling in PCASL at 7T1Sir Peter Mansfield Imaging Centre, School of Physics & Astronomy, University of Nottingham, Nottingham, United Kingdom
Synopsis
Despite the intrinsic SNR gains at 7T, pseudo-continuous arterial spin labeling (PCASL) is limited by poor $$$|B_1^+|$$$ coverage in the labelling plane and the associated high local SAR of the sequence. In this work we perform simulations to consider the usefulness of dynamic RF shimming using a commercially available head-only RF coil equipped with 8-transmit channels, for labelling in PCASL.
Introduction
In static RF shimming, RF of different fixed amplitude and relative phase is applied to multiple RF transmitter elements so as to control the spatial distribution of the electromagnetic fields in the subject, usually to homogenise the effective $$$|B_1^+|$$$ or minimise the maximum local specific absorption rate (SAR). Dynamic RF shimming$$$^{1-3}$$$, in which the phase and amplitude settings are modified over time provides additional degrees of freedom with which to shape both the spatiotemporal distribution of the electromagnetic fields.
Despite the intrinsic SNR gains at 7T, pseudo-continuous arterial spin labeling (PCASL) is limited by poor $$$|B_1^+|$$$ coverage in the labelling plane and the associated high local SAR of the sequence. In this work we consider the usefulness of dynamic RF shimming using a commercially available head-only RF coil equipped with 8-transmit channels, for labelling in PCASL.
Theory
The basic PCASL labelling sequence consists of $$$N_p$$$-repeated Hanning pulses separated by a gap of $$$\Delta t$$$; alongside an unbalanced gradient with average strength $$$G_{\text{av}}$$$. We introduce a dynamic RF shim complex-valued weighting matrix $$$\mathbf{W}$$$ of size $$$(N_{c}\times N_p)$$$, where $$$N_c$$$ is the number of transmit channels available. We express the design problem as a constrained magnitude least squares optimisation$$$^4$$$ over the entire labelling sequence. The target magnetisation $$$\mathbf{D}$$$ is a matrix of size $$$(N_{v}\times N_p)$$$ where $$$N_v$$$ is the number of intravessel voxels at the labelling volume of interest and $$$\mathbf{S}$$$ are the concatenated coil sensitivities.
$$\begin{split}\min_{\mathbf{W}\in\mathbb{C}^{N_c\times N_p}}|||\mathbf{SW}| - &\mathbf{D}||_{F}^2\\ \text{s.t.} |w_{cn}|^2 &< p_{\text{peak}} \quad \forall c\in\{1,...,N_c\}, n\in\{1,...,N_p\}\\ ||\mathbf{w_{c}}||^2 &< p_{\text{av}}\Delta t \quad \forall c\in\{1,...,N_c\}\\ ||\overline{\mathbf{W}}\circ\mathbf{Q}_{\text{v}}\mathbf{W}||&< \text{SAR}_{\text{local}}, \quad \forall \text{v}\in\{1,...,N_\text{VOPs}\}\\ \end{split}$$
where $$$||.||_F^2$$$ is the squared Frobenious norm and $$$\circ$$$ represents the Hadamard product. The variable exchange method can be used to minimise the above equation, whereby the cost function is reformulated as $$$||\mathbf{SW-D\circ Z}||_{F}^2$$$, where $$$\mathbf{Z}$$$ is iteratively replaced as $$$\exp{(i\measuredangle SW)}$$$. Importantly, a smoothing Gaussian filter (std. dev. $$$\sigma$$$) can be applied to each row of $$$\mathbf{Z}$$$, to produce temporal smoothing of the phase. The motivation here is that the flowing spins will still be inverted through the labelling plane as long as the average effective field varies slowly relative to the average effective frequency sweep. An interior-point method was used to solve each inner iteration of the variation exchange method. Analytical gradient and Hessian derivatives were used to exploit the sparsity and quadratic nature of the problem and constraints.
Methods
134 Virtual observation points (VOPs) were calculated with an overestimation factor of epsilon = 5 for both the Hugo head model, from electromagnetic simulations provided by the coil manufacturer (Nova Medical Inc.). The left and right carotid arteries (LCA and RCA) and left and right vertebral arteries (LVA and RVA) were extracted.
A basic PCASL
labelling train was defined consisting of 1000 Hanning pulses of width 0.5 ms,
with a pulse gap of 1.5 ms. The optimisation described above was repeated over a range of smoothing factors $$$\sigma\in[0.1,100]$$$. Bloch simulations were used to verify the behaviour of the magnetisation under the influence of the modified labelling
sequences. (T1 = $$$\infty$$$, T2 = 50 ms, stepsize = 1$$$\mu$$$s, flow rate 0.3 ms$$$^{-1}$$$). All computation was carried out on a Apple MacBook (2.2GHz quad-core Intel Core i7 processor).
Results
All optimisations converged within 5 minutes. Static RF shimming improves the magnitude and uniformity as compared to quadrature mode by a factor of 140%, similar to previous work$$$^{5}$$$. Introducing dynamic RF shimming can be seen to have an additional small improvement of up to 15% (see Figure 1). The standard deviation of the $$$|B_1^+|$$$ distribution across all vessels was also reduced by 24% in the best case. Bloch simulations (Figure 2) show the inversion performance of the PCASL sequence breaks down in the regime of minimal phase smoothing $$$(\sigma < 1)$$$, but is maintained or slightly improved for values larger than this.Discussion
We considered the application of dynamic RF shimming to improve PCASL labelling by maximising the effective $$$|B_1^+|$$$ distribution at the labelling plane under constrained power and local SAR limits. Allowing the RF shims to vary over the entire PCASL labelling sequence has allowed a greater degree of freedom for the optimisation, as local SAR limits can be exceeded instantaneously (but stay below the time averaged limit). Allowing a greater degree of phase variation over the labelling sequence can acheive a higher average $$$|B_1^+|$$$, although at a point this degrade the inversion performance. We empirically found $$$\sigma=1$$$ to be a good trade off in this case. Consideration of off-resonance effects was neglected and would need to be included in any experimental implementation.Acknowledgements
This work was supported by funding from the Engineering and Physical Sciences Research Council (EPSRC) and Medical Research Council (MRC) [grant number EP/L016052/1].References
[1] Sbrizzi, A. et al. (2017): Magn Reson Med. 77: 361-373
[2] Malik, S.J. et al. (2015): Magn Reson Med. 73: 951-963
[3] Sbrizzi, A. et al. (2017): Proc. Intl. Soc. Mag. Reson. Med. 25 #1326
[4] Setsompop, K. et al. (2008): Magn Reson Med. 59(4): 908-915
[5] Tong, Y. et al. (2018): Proc. Intl. Soc. Mag. Reson. Med. 26 #3399
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