Introduction

The complex infrastructure needed for high-field MR scanners has relegated this very safe, and remarkably revealing, clinical tool to high-end hospital care. But for many potential applications of MR, point-of-care diagnostics, routine screening or classroom experimentation, image quality is far less critical than portability and low cost. Emphasizing cost and portability over image quality has led researchers to focus on low-field MR, of the order of tens to hundreds of millitesla, generated using arrays of inexpensive permanent magnets.^1-3 In this paper, we describe our approach to achieving a commensurate cost reduction in the RF subsystem, while still generating RF signals needed for the higher B₀ inhomogeneity associated with magnet arrays. We propose a low-cost (<$100) signal chain consisting of a Teensy 4.0 microcontroller and 8-channel STHV800 ultrasound pulser chip. The Teensy's ARM Cortex-M7 processor can generate pulses with a timing resolution of 3.3ns that the ultrasound pulser can drive transmitter coils. We use MATLAB’s genetic algorithm to optimize broadband 90 and 180° RF pulses based on solving the Bloch equation, and demonstrate these tools in our spokes-and-hub permanent magnet.⁴

Methods

Ultrasound and low-field MR share a similar range of center frequencies (1-8MHz), but thanks to the large portable-ultrasound market, there are a number of low-cost ICs for generating ultrasound pulses. For example, we used the 8-channel STHV800 ultrasound pulser ($30, STMicroelectronics) to create programmable, high-voltage pulses as well as receiving low-amplitude signals through its T/R switch. Because each channel is driven by 2 digital bits, the chip can be enabled by digital square-wave outputs. Teensy 4.0 ($20, PJRC), with its ARM Cortex-M7 processor and dynamic clock scaling functionality, allows for reliable generation of pulse width modulated (PWM) RF pulses. This allows for careful control of the RF output from the Teensy through amplitude and frequency modulation to created dithered-pulses. These two degrees of freedom, amplitude and frequency, can be easily modulated by adjusting duty cycle and period of square-wave oscillation on the microcontroller. This allows us to set up an optimization of 90 and 180° pulses to satisfy the Bloch equations over a specified bandwidth of frequencies. Given the limited number of degrees of freedom and short pulse durations required when driving at higher amplitudes, computing and optimizing a discrete time solution to the Bloch equation in the rotating frame can be done within minutes on a CPU using MATLAB’s constrained optimization genetic algorithm.

From our Bloch simulation, we designed dithered-pulses optimized across a frequency band of 8.05 - 8.17MHz (~100kHz bandwidth). As shown by the transverse magnetizations, M_x and M_y in Fig. 1, the optimizer was able to produce well-aligned frequency isochrones for the 90 and 180° pulses. In the longitudinal direction M_z, for the 90° pulse, the simulated pulse was able to get all the frequency lines to converge at 0, and for the 180° pulse, the was able to produce the appropriate flip. Figure 2 shows that the simulated pulse and measurement from the Teensy output are in close alignment in both time and frequency.

With the Teensy generating gating and optimized Bloch RF pulses, these signals are modulated by the STHV800 ultrasound pulser for bipolar RF drive up to ±90V as detailed by the schematic in Fig. 3. We recorded spin echoes (SEs) in three permanent magnets with nominal B0 around 191 mT with center frequency at 8.13MHz. The magnets also covered a wide range of homogeneity — 50ppm homogeneity over 10mm from the MIT-MGH ‘tabletop scanners’, 1000ppm over 2.5 and 10mm from two different equivalent-charge-optimized ‘spokes-and-hub’ magnets.^4,5

Results

With the signal chain described above, we have demonstrated the use of our broadband RF pulse in several permanent magnet topologies. Figure 4 shows that, when using the same excitation pulse on three magnets of varying B₀ and homogeneity, reproducible SEs can be obtained from each magnet. A shorter echo time was used for the spokes-and-hub magnet due to the inhomogeneity within the magnet. The pulses can be used even when a permanent gradient is applied to the magnets during both excitation and readout (Fig. 5). For the tabletop magnet, we drove up to 2A on existing gradient coils from the setup to create the constant x-directed gradient field; in the spokes-and-hub magnets, additional bar magnets were placed along one side as shown in Fig. 5. The gradient produces broadening of SEs in frequency and narrowing in time. Since the spokes-and-hub topology is inherently less homogeneous than the carefully-shimmed tabletop magnets, when the permanent magnet gradient is applied, our 100kHz broadband RF pulse is indeed able to excite that bandwidth within the volume of fluid in the phantom. Furthermore, the spread-spectrum excitation can enable 1D-projection imaging as shown by the distinct frequency peaks when gradients were applied to the two separate tubes within Phantom B in Fig. 5.

Conclusion

By using the Teensy 4.0 and STHV800 to produce Bloch-optimized dithered pulses, we have demonstrated a low-cost signal chain for broadband excitation of hand-held MR magnets that is forgiving to the large inhomogeneities within these magnets. Furthermore, with the 8 channels available on the STHV800 chip, there is an opportunity to explore avenues in parallel transmission or PWM drive of gradient coils.

Acknowledgements

Funding support from NIH NIBIB R01EB018976, MIT-MGH seed grant, Skolkovo Institute of Science and Technology Next Generation Program, and MIT EECS department.