Introduction

High acoustic noise from MRI systems can lead to a patient anxiety and discomfort [1]. The primary source of this acoustic noise is from vibrations due to gradient coil activity, so designing pulse sequences to minimize noise can help with this problem.
Previous work in the field of acoustic noise minimization has utilized lowpass filtering techniques to lower the spectral frequency of the acoustic noise where typical MRI systems usually have a weaker response [2]. Another proposed technique modifies gradient lobe timings relative to each other to avoid certain frequency ranges [3].
In this work, we aim to apply a numerically optimal design approach that acoustically minimizes the gradient waveforms while considering the entire frequency range and response of the MRI system. We do this by measuring the acoustic frequency response function [4,5] of a given MRI system, and then using an open source gradient optimization framework (GrOpt [6]) to design gradient waveforms that have a minimal predicted acoustic noise output based on the response function.

Methods

Frequency Response Function
The frequency response of the MRI system was measured by playing a series of short, different gradient waveforms subsequently on all three gradient axes. The audio from the sequence was measured with a microphone. Assuming a linear impulse response, we can describe the expected acoustic output: $$$a(t)=g(t)*h(t)$$$, where $$$g(t)$$$ is the gradient waveform and $$$h(t)$$$ is the acoustic impulse response. In the frequency domain this gives $$$A(f)=G(f)H(f)$$$ , where $$$H(f)$$$ is the desired acoustic frequency response function, which we obtained with an average of Weiner deconvolutions across all gradient pulses measured in the calibration scan.

Imaging Gradients and Optimization
A spoiled echo gradient sequence was designed using four different methods: (1) A traditionally “fast” waveform utilizing high slew rates (s_max) and maximum gradient amplitude (g_max); and (2) A conventional “slow” sequence obtained by reducing the s_max and g_max, with a corresponding increase in TE and TR (Figure 2). For (3) and (4), GrOpt was used to numerically optimize waveforms that minimized either (3) $$$\|W_A(f)G(f)\|_2$$$ or (4) $$$\|W_A(f)H(f)G(f)\|_2$$$, where is the standard A-weighting curve used in audio processing to account for the frequency dependent response of human perception to noise. (3) aims to use just A-weighting for minimization, which would not require measuring the acoustic response, while (4) uses the measured response functions (H_x,y,z) for each axis. The optimized sequences maintained the same gradient moments as the conventional sequences for all segments and gradient waveform timings matched to (2), the “slow” sequence.
Fig 2 shows gradient waveforms and parameters for the different sequences. Other parameters are: flip=10°, thickness=8mm, FOV=320x320, matrix=256x256. Sequences were all implemented in Pulseq [7].

Phantom Experiments and Analysis
The sequences were each run on a 3T Siemens Skyra scanner with a resolution phantom in a 32-channel chest coil. The audio was recorded during acquisition and the RMS average of the audio signal was reported after A-weighting in the frequency domain.

Results

Figure 1 shows the measured audio transfer functions (H_x,y,z). Figure 3 shows the gradient waveforms of the four different gradient configurations, along with the two frequency domain functions being minimized and their respective RMS norms. Figure 4 shows the images acquired with each of the GRE sequences, where little difference was seen in image quality. Figure 5 shows the recorded audio from each sequence in the frequency domain after A-weighting. The RMS average of each audio signal (arbitrarily scaled relative to the “slow” sequence) was: (1) 1.23, (2) 1.0, (3) 0.92, and (4) 0.84. For the full acoustic minimization sequence (fourth waveform), this represents a 31% decrease in acoustic noise compared to the fast scan, at the expense of a 17% increase in scan time, and a 16% reduction when compared to the conventional sequence with matched timings (“slow” waveforms).

Discussion

This work showed that gradient waveform optimization can be used to control and minimize the frequency content of gradient waveforms and the predicted acoustic output of the scanner. By maintaining constraints on the required gradient moments and hardware limits of the system, there was no significant change in image quality. The gradient waveforms were in general more rounded, but with some high frequency components to give more time efficient encoding. When run on the scanner, the RMS power of the recorded audio was reduced by up to 16% with the optimized waveform, but not to the degree predicted analytically (50%). The discrepancy between analytical and experimental results may be attributed to a suboptimal measurement of the frequency response function (i.e. quality of the recording equipment used and selected calibration gradient waveforms). Future work will address this with improved microphone quality, and a longer and more robust calibration scan. Additionally, the optimization framework only optimizes individual TRs, without considering the inter-TR contributions to acoustic noise, which can be readily addressed with the same framework. The measured frequency response spectra were different for each gradient coil axes, which means that the acoustically minimized solution is rotationally variant. Another future area of interest for this work is in determining the ideal measure of acoustic loudness to optimize against [8].

Acknowledgements

NIH Grant U01EB029427