Clare McElcheran^{1}, Laleh Golestanirad^{2}, Maria Iacono^{3}, Benson Yang^{4}, Kevan Anderson^{5}, Giorgio Bonmassar^{2}, and Simon Graham^{4}

Deep
brain stimulators and other elongated implants interact with the RF
transmission fields used in MRI, potentially causing unsafe levels of localized
tissue heating. It may be possible to
suppress these heating effects using parallel RF transmission (pTx) methods,
but a practical approach still remains to be implemented. Toward this goal, we present a method that
combines intra-operative computed tomography (CT) data, electromagnetic
simulations, and low-SAR B_{1}-mapping to determine pTx
input parameters for suppressing heating effects in DBS patients.

Conceptually, the proposed method has two main stages. Stage 1 uses existing patient data and
simulation-based optimization to determine solutions with “safe” pTx inputs (RF
shim settings that enable B_{1}-mapping with low local SAR
at the tip of the DBS implant) which span all possible EM field distributions,
without B_{1}^{+} homogeneity constraints.
Stage 2 involves pTx calibration with B_{1}-mapping using
the N “safe” pTx inputs similar to the method of Brunner et al^{5}.
This reduces the risk of heating at the implant tip, compared to the technique
of mapping B_{1}-fields of individual coil elements which does not
protect against RF coupling. The resulting B_{1}-maps are then used in
an additional optimization step to determine pTx inputs that minimize local SAR
while maintaining B_{1}-homogeneity, similar to standard pTx
techniques.

Specifically, stage 1 involves a constrained optimization via simplex algorithm to determine N linearly independent complex signal inputs to each channel of an N-element pTx coil which produce minimal 1g local SAR in the region of minimization (ROM) surrounding the implant tip and are linearly independent (Eq. 1):

$$ \min_{A_n^{(j)},\phi_n^{(j)}}(\mu_{tip}(\frac{\mid E_{tot}\mid^2}{\mid E_{quad}\mid^2})) (1) $$

$$s.t. \{(A_1^{(j)}e^{\phi_1^{(j)}},...,A_N^{(j)}e^{\phi_N^{(j)}}),(A_1^{(j-1)}e^{\phi_1^{(j-1)}}, ..., A_N^{(j-1)}e^{\phi_N^{(j-1)}}), ..., (A_1^{(0)}e^{\phi_1^{(0)}},..., A_N^{(0)}e^{\phi_N^{(0)}})\}\ is\ linearly\ independent$$

where A_{n
}and Φ_{n }are the input amplitude and phase of the n^{th}
channel, μ_{ROM}(·) is the mean in the ROM, E_{quad} is the electric (E) field in
pTx quadrature mode (A_{n}=1, Φ_{n}=2π/N) and is the E-field generated by the optimal inputs. E-fields are obtained from EM simulations of
patient-specific models including DBS lead trajectories segmented from standard
post-operative CT scans.

Stage 2 involves standard B_{1}-mapping of
the DBS patient using the set of “safe” inputs determined in Stage 1. The B_{1}-maps are then used
in a second optimization which determines the input amplitude and phase for
each pTx channel to maximize B_{1}^{+}-field homogeneity for
high quality imaging in a volume of interest (VOI), and to minimize the B_{1}^{+}
artifact in the ROM to avoid elevated local SAR (Eq. 2):

$$ \min_{A_n, \phi_n}(\frac{\sigma_{VOI}(\mid B_{1,tot}^+\mid)}{\mu_{VOI}(\mid B_{1,quad}^+\mid)}+\lambda\cdot\frac{B_{1,tot}^{art}}{B_{1,quad}^{art}}) (2)$$

$$ B_{(\cdot)}^{art}=(\frac{\max_{ROM}\mid B_{(\cdot)}^{+}\mid)}{\mu_{ROM}(\mid B_{(\cdot)}^+\mid)} $$

where σ_{VOI}(·) is the spatial standard deviation over the VOI,
and max_{ROM} (·) is the spatial maximum over the ROM.

For initial evaluation, realistic DBS lead trajectories and
head models were semi-automatically segmented from intra-operative CT images of
6 patients who received sub-thalamic nucleus DBS at Massachusetts General
Hospital (MGH). Secondary use of patient data was approved by the MGH Internal
Review Board. EM simulations were
performed using FEKO (Atlair, MI, USA) and optimization was completed using
Matlab (Mathworks, Natick, MA). “Safe” B_{1}-mapping
inputs were calculated for each patient with 4- and 8-element pTx coil
configurations at 3 T. A random rigid-body
transformation was applied to emulate possible positioning errors between Stage
1 and Stage 2 (Fig. 1). B_{1}^{+}-fields
were calculated via simulation to represent B_{1}^{+}-mapping
in Stage 2. The simulated B_{1}^{+}-field
and SAR patterns for the final set of optimized inputs for each pTx
configuration were then obtained, and compared with a transmit/receive
quadrature birdcage coil.

1. Rezai AR, Phillips M, Baker KB, Sharan AD, Nyenhuis J, Tkach J, Henderson J, Shellock FG. Neurostimulation system used for deep brain stimulation (DBS): MR safety issues and implications of failing to follow safety recommendations. Invest Radiol 2004; 39(5):300-303.

2. Eryaman Y, Guerin B, Akgun C, Herraiz JL, Martin A, Torrado-Carvajal A, Malpica N, Hernandez-Tamames JA, Schiavi E, Adalsteinsson E, et al. Parallel transmit pulse design for patients with deep brain stimulation implants. Magn Reson Med 2015; 73(5):1896-903.

3. McElcheran CE, Yang B, Anderson KJ, Golenstani-Rad L, Graham SJ. Investigation of Parallel Radiofrequency Transmission for the Reduction of Heating in Long conductive Leads in 3 Tesla Magnetic Resonance Imaging. PLoS One 2015; 10(8):e0134379.

4. Katscher U, Bornert P, Leussler C, van den Brink JS. Transmit SENSE. Magn Reson Med 2003; 49(1):144-50.

5.
Brunner DO, Pruessmann, KP. B_{1}^{+} Interferometry
for the Calibration of RF Transmitter Arrays. Magn Reson Med 2009;
61:1480-1488.

Figure 1: Example patient head model (a) original
orientation and (b) after random transformation (Δx = -1.5 cm, Δy = 0.1 cm, Δz = -1.7 cm, rot_{x} = -5°, rot_{y} = -5°, rot_{z} = 1°). Inset: insulated DBS implant with four
electrodes.

Figure 2: Example of linearly independent “safe” inputs for
4-channel pTx (a) B_{1}^{+}-field (b) raw SAR (resolution 0.39 cm
x 0.45 cm). Arrow indicates wire location.

Figure 3: Median and inter-quartile range of six patients
excited with the birdcage coil, and optimized 4-element and 8-element pTx: (a)
local 1 g SAR at implant tip; (b) coefficient of variation (COV) of B_{1}^{+}-field
in the volume of interest.

Figure 5: Example patient raw SAR (resolution 0.39cm x
0.45cm) for (a) birdcage excitation; (b) optimized 4-element pTx; and (c) 8-element
pTx.

Figure 4: Example patient B_{1}^{+}-field
for (a) birdcage excitation; (b) optimized 4-element pTx; and (c) 8-element
pTx.