Background

Highly effective water-excitation radiofrequency (RF) pulses that enable lipid suppression have recently been reported^1,2. These pulses have mostly been designed analytically and optimized experimentally, and are thus limited to low-dimensional parameter optimization (i.e. fewer than 4 parameters). These constraints limit the optimization process to a small domain of solutions that may not necessarily include the optimum. In the case of high-resolution gradient-recalled-echo (GRE) imaging, short RF pulses are mandatory to reach short scan duration.

We therefore propose a flexible and efficient method for optimizing water-selective RF pulses using up to at least 10 pulse parameters (OptiPulse). We exploit simplicial homology global optimization (SHGO³) to optimize the parameters of the pulses with respect to a loss function that is computed from the frequency response simulated with the Bloch equations. The goal of this study was thus to test the optimization framework by designing several pulses with an increasing number of optimizable parameters and to compare the resulting images to those obtained with an analytically optimized RF pulse (LIBRE²) in a phantom, in the knee and the heart.

Methods

The optimization of binomial and B-splines⁴ interpolated pulses is performed at 3T for a RF excitation angle of 8° (Figure 1). In the case of binomial pulses, each sub-pulse (2, 3, or 4 sub-pulses in total) has two optimization parameters: the phase and offset frequency. The B-splines pulse has 10 optimization parameters: five for the amplitude and five for the phase. Third-order B-splines are used to interpolate a curve between optimized parameter values. The transverse magnetization frequency response Mxy is then computed using a Bloch-equation simulation of 200 isochromats with offset frequencies uniformly distributed between –1000Hz to 1000Hz⁵. The pulse performance is assessed with a composite loss function 𝓛:

$$\mathcal{L} = \frac{[\|M_{xy}\|_2]_f}{[\|M_{xy}\|_2]_w} + \frac{\lambda_1}{[\|M_{xy}\|_2]_w} + \lambda_2 ([\|M_{xy}\|_2]_f)^2 \hspace{30pt} (Eq.1)$$

where P is the vector containing the pulse parameters, λ₁=0.01 and λ₂=400 are regularization coefficients, and ||...||₂ is the L2 norm. The norms are averaged over the water ([...]_w: -50 to 50 Hz) or fat ([...]_f: -540 to -340 Hz) frequencies. By minimizing Eq. 1, the maximum fat-water contrast is enforced by the ratio of the fat magnetization over water magnetization, while λ₁ enforces water excitation and λ₂ imposes a minimum around fat. The minimization is performed with SHGO³, an optimizer for black-box and derivative-free problems.

Four pulses with a 1ms duration each were optimized: a 1-1, a 1-2-1, and a 1-3-3-1 binomial pulse, and a 10-point B-splines interpolated pulse. The pulses were implemented on a 3T clinical scanner (Siemens Prisma) in a 3D radial GRE pulse sequence with TE=2.13ms. The simulated pulses were validated in a three-compartment phantom containing agar gels and lipids that simulate blood, muscle, and fat, by comparing the obtained images to acquisitions without fat suppression and to those acquired with a LIBRE water-excitation pulse⁶. The knees of five healthy volunteers (31±7y) were scanned using the same pulses, and the fat and muscle SNR as well as the muscle-fat CNR were measured. ANOVA with post-hoc Tukey tests were used for comparison. Finally, the two best performing pulses were used to acquire ECG-triggered respiratory-motion-corrected GRE⁷ images of a heathy volunteer’s heart.

Results

The simulations resulted in high water-fat contrast, full lipid suppression and robustness to variation in B1 for all investigated pulses (Figure 2 and 3). The simulated frequency responses are very similar among all water-selective pulses. However, the 1-2-1, 1-3-3-1 and B-splines pulses have a suppression “valley” shifted towards the water peak, which is useful considering that lipids also have a significant resonance at 3.11 ppm⁸.

The phantom images show near-complete fat suppression for all four optimized pulses and the suppression is similar to the one of LIBRE (Figure 3C). The 1-1 binomial and the B-splines pulse appear to outperform the LIBRE pulse near the edge of the phantom.

In vivo, each pulse resulted in fat suppression that was comparable to the LIBRE pulse (Figure 4). The optimized pulses were all able to highlight the cartilage by suppressing bone fat while also maintaining high muscle signal. The 1-1 and B-splines pulses images show a more homogeneous suppression of the bone fat across all volunteers, their respective CNRs are comparable to those of LIBRE pulse (Figure 2). Interestingly, the B-splines and 1-3-3-1 pulses standard deviations (SD) are significantly lower than the one of the other pulses.

Additionally, the heart scans show that the pulses transfer well to the thorax, where larger B0 inhomogeneities are encountered. The 1-1 and B-Splines scans results in similar fat suppression as the scan using LIBRE, while the B-Splines pulse results in the complete suppression of epicardial fat signal (Figure 5).

Conclusion

The RF pulses presented here performed well in simulation, phantom and in vivo studies, and matched the performance of the analytically optimized LIBRE water excitation pulse. This demonstrates that the OptiPulse framework can find at least a local optimum in many different parameters spaces, making the framework physically sound.

In conclusion, the simplicity and flexibility of the OptiPulse framework opens avenues in RF pulse design for many applications and could be expanded to help address more challenging problems such as spatial selectivity or low field strength fat suppression.

Acknowledgements

This research was supported by the Swiss National Science Foundation (32003B_182615 to MS).