BEEEP: B1-robust Energy Efficient Excitation Pulses
Eric Van Reeth1, Hélène Ratiney1, Olivier Beuf1, Soukaina Kanice1, Steffen J Glaser2, and Dominique Sugny3

1CREATIS, Villerubanne, France, 2Department of Chemistry, Technical University of Munich, Garching, Germany, 3Laboratoire Interdisciplinaire Carnot de Bourgogne, Dijon, France


This study introduces a new family of broadband B1-robust excitation (90°) pulses for MRI with large enough bandwidth (+/- 1 kHz) to account for static field inhomogeneities, and minimal energy deposition. RF pulses are designed with a regularized optimal control algorithm, which is able to adapt the pulse B1-robustness range to fit the coil limits in terms of peak amplitude and energy. In vitro acquisitions using an endoluminal-shaped RF transmit coil show comparable excitation profiles than BIR4 pulses, although BEEEP pulses deposit 5.2 times less energy.


Adiabatic excitation pulses are known for their high immunity to RF inhomogeneity. Once the adiabatic threshold is reached, such pulses guarantee a uniform flip of the magnetization [1]. Their performance is generally limited by the available peak pulse amplitude and/or maximal energy deposition (SAR) authorized by clinical systems. For this reason, robust and energy-efficient pulses have been investigated, in the context of NMR spectroscopy [2] and high-field MRI [3, 4].

This study introduces a new family of broadband B1-robust excitation (90°) pulses for MRI with large enough bandwidth (+/- 1 kHz) to account for static field inhomogeneities, and minimal energy deposition. The objective is to provide uniform excitation in the context of single loop surface RF transmission coil (e.g. with endoluminal coils), although they can be applied in any context willing to limit excitation energy deposition.


RF pulses are designed with a regularized optimal control algorithm, which is able to adapt the pulse B1-robustness range to fit the coil limits in terms of peak amplitude and energy. Optimal control is a well known pulse design tool in MRI [5]. It iteratively computes the pulse that optimizes a user-defined cost function, usually set to minimize the distance to a given magnetization target state. In this context, energy minimization can be performed by fixing hard constraints [2, 4], or penalty terms [3]. The cost function is regularized by a term proportional to the pulse energy ($$$||\omega||^2$$$):

$$C(\omega) = \frac{1}{I\times J}\sum_{i=1}^I \sum_{j=1}^J\Vert \overrightarrow{M_{i,j}}(t_f) - \overrightarrow{T_{i,j}}\Vert^2 + \lambda ||\omega||^2$$

where $$$i$$$ and $$$j$$$$ represent the indexes of the considered B0 and B1 inhomogeneity range, $$$\overrightarrow{T_{i,j}}$$$ the magnetization target state, and $$$\lambda$$$ a positive scalar. The optimal pulse thus balances the minimization of the average error norm between the magnetization state at the end of the pulse ($$$t_f$$$) and its target, and the energy deposition.

Our implementation is based on a second order GRAPE optimal control algorithm for cost minimization [6]. Taking advantage of the fact that symmetric pulses have shown to perform equally well as non-symmetric pulses in terms of robustness to B1 inhomogeneities [7], our optimization is performed only on 25 cosine Fourier series coefficients of the real and imaginary parts of the pulse, to ensure symmetry [8]. Therefore, this implies that isochromats with frequency offsets of opposite signs will have symmetric trajectories. As a result, only the positive resonance frequency offsets need to be considered in the optimization process which reduces the computation time.

The characteristics of the pulse were assessed on a pre-clinical 4.7T Bruker MRI on homogeneous agar phantoms. In a first study, a quadrature coil (inner diameter 40mm) was used to acquire the magnetization map with respect to B0 and B1 variations. Two pulses were compared, namely the optimized BEEEP pulse and a tanh/tan BIR4 pulse of the same duration, whose frequency modulation parameters were set to optimize the ratio between the adiabatic threshold and the targeted bandwidth ($$$\Delta \omega$$$ = 15kHz ; $$$\beta$$$ = 10 ; $$$\kappa$$$ = 1.5).

Finally, in vitro experiments were performed using a simple prototype of endoluminal-shaped RF transmit/receive coil [9], to compare both pulse performances. The coil was sealed inside a tube, and immersed into a nickel sulfate doped solution. A fast spin-echo sequence is used with a turbo factor of 2, TE = 11.7ms, TR = 1.5s. No gradient was applied during excitation, meaning that the signal from the whole tube is integrated.


Figure 1 shows the resulting amplitude and phase of the optimized BEEEP pulse. Both amplitude and phase are modulated to ensure robustness to B1 variations, and only the central part has a quadratic phase pattern. Figure 2 compares the acquired magnetization maps of both pulses with respect to frequency offsets and peak RF amplitude. The relation between peak amplitude and the pulse energy is given in Figure 3, showing an energy ratio of 5.2 between both pulses. Figures 4 and 5 compares the results obtained in the context of endoluminal RF transmission coil.

Discussion and conclusion

The results show that BEEEP pulses are able to compete with BIR4 in terms of robustness to large B1 variations (+/- ~50%), which is needed in the context of surface coil RF transmission. The proposed strategy allows to adapt B0 and B1 robustness ranges to the coil and the sample, resulting in a valuable compromise regarding RF peak amplitude and energy deposition, compared to adiabatic strategies. This will be further exploited in the context of endoluminal imaging, for which the combined use of receive coils with transmit body coil often raise safety issues not trivial to handle.


This work is supported by the ANR-DFG research program Explosys (GrantNo. ANR-14-CE35-0013-01; GL203/9-1) and from the TUM Institute for Advanced Study, funded by the German Excellence Initiative and the E. U. Seventh Framework Program under Grant No.291763. This work was performed within the framework of the LABEX PRIMES (ANR-11-LABX-0063/ ANR-11-IDEX-0007).


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Amplitude (a) and unwrapped phase (b) of the BEEEP pulse. It has a constant time-bandwidth product of 4.5 (unitless). This pulse is energy efficient because unlike BIR4 pulses, only the central part of the pulse has high amplitude coefficients. The central part features an adiabatic behavior with a quadratic phase pattern, which is completed by non-adiabatic patterns at the pulse extremities.

Comparison of acquired magnetization maps for similar resonance offsets and B1 peak amplitude ranges. Dotted lines illustrate the targeted bandwidth (+/- 1 kHz). Both pulses ensure an homogeneous excitation inside the targeted bandwidth. Notice how the BEEEP pulse is able to preserve the signal coherence at low B1 peak amplitudes.

Evolution of the pulse energy as a function of the B1 peak amplitude. As expected, the BEEEP pulse induces several times (5.2) less energy deposition than BIR4 for a given peak amplitude value.

Axial images acquired when RF pulses are transmitted by the endoluminal coil. Images are shown on the same intensity scale. Dashed green lines indicated the line along which the intensity profiles are plotted (Figure 5). At high transmission gain (7dB), BIR4 produces slightly more signal close to the coil, but presents a faster decay. At low transmission gain (11dB), the adiabatic threshold is quickly reached, which induces a quick signal drop, while the BEEEP pulse preserves more signal away from the coil.

Intensity profiles derived from raw data shown in Figure 4. At higher pulse amplitudes (amplifier attenuation of 7dB), BIR4 produces slightly more signal close to the coil but slightly less further away. At low transmission amplitudes (11dB), the BIR4 pulse induces a much quicker signal drop than the BEEEP pulse. This could be anticipated from the magnetization maps, which show that BEEEP pulses produce a much more homogeneous signal at low peak amplitudes.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)