Synopsis

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.

Introduction

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.

Methods

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.

Results

Discussion and conclusion

Acknowledgements

References

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