Sequence optimization for MRI acoustic noise reduction

The large acoustic noise of 80-110 dB during magnetic resonance imaging (MRI) scanning harms patients’ comfort and health. The noise can be reduced by hardware modification or active noise control, but these methods are expensive, difficult, or not very effective. In this study, a sequence optimization method is used to mitigate the acoustic noise problem while maintaining image quality. The 4th order polynomial function is applied to design the new quiet pulse sequences, decreasing the gradient slew rate and higher time derivatives of the original trapezoidal lobes. A sound pressure level (SPL) estimation method is proposed to predict the acoustic noise loudness from the gradient and is used for genetic algorithm sequence optimization. The original and quiet gradient recalled echo (GRE) sequences are applied on a 1.5 T MRI scanner. The average SPL is reduced by 18.6 dBA, and the images show small differences and have similar SNR values. This method is also applied for the scouting and shimming GRE sequences in common clinical applications with significant noise reduction.


Introduction
Magnetic Resonance Imaging (MRI) is a widely applied medical modality to reveal internal structures in the human body non-invasively.However, patients who are exposed to large acoustic noise during scanning might experience discomfort and face health risks.A common 1.5 T MRI examination can have an SPL of 80-110 dB [1].Large noise can cause anxiety and even hearing loss, sleep disturbance, neurological growth hindrance, etc. [2][3][4] Therefore, it is important to develop an approach to reduce the MRI scanning sound.
In previous research, the noise reduction method can be categorized into three types.Firstly, sound transmission can be impeded, like hardware reconstruction or wearing noise-proof equipment.In 2003, Roozen, et al implemented a supporting system with a piezo actuator of soft suspension to effectively prevent the vibration of the scanner frame shell [5].William, et al. in 2005 proposed to add passive copper shielding layer wrapping the gradient assembly to decrease warm bore sound creation [6].However, it might be expensive and difficult for machine rebuilding, and most passive noise reduction methods only effectively reduce high-frequency noises [1,7,8].As for noise-proof equipment, it can commonly reduce sound by 10 to 30 dB [9].The challenge is that the sound absorbers or headset occupy large space and the interspace of head coils is usually not enough [10].Most commercial headsets are also not suitable for the newborns who might feel uncomfortable with the size and material of the adult ear covers [2].The second approach is to use active noise control.The feedforward, feedback, and hybrid control design with different algorithms like filtered x least mean square (FXLMS) are studied.Mingfeng, et al. applied this method on a 4 T MRI scanner and achieves 21 dB noise reduction.A deep convolutional neuro network is also proposed to recognize advanced sounds and decreased the mean sound power by around 10 to 15 dB [11].However, it has high device requirements like wide bandwidth, high output, and limitation of ferromagnetic components [12].The third way is to redesign the pulse sequence.Baker demonstrates the influence of sequence parameters on the produced sound pressure and decreased sound by adjusting TR and TE in 2013 [13].Research by modification of gradient switching frequencies can also mitigate sound by 12 dB.
In this paper, we proposed a sequence optimization-based sound reduction method which is costeffective and avoids hardware construction.Here we provide a simple approach to optimize the sequence based on the prediction of its scanning SPL value with 4 th order polynomial function to modify the pulse shape and genetic algorithm to determine the best pulse duration combination of a sequence with given parameter requirements.We also compare the original trapezoidal and optimized pulses and present examples of acoustic noise-reduced GRE scouting and shimming MRI clinical applications.

MRI acoustic noise source
The acoustic noise of MR machines is mainly resulted from gradient coil vibration caused by the Lorentz forces.The scanner contains Golay coil sets for x and y axes gradients and Maxwell coil pairs of z axis gradient embedded on the cylindrical surfaces.The radial Lorentz forces on coils equal the cross-product of the axial external magnetic field and the tangential flowing current as shown in Figure 1.The gradient coils provide three spatially orthogonal gradient fields, , and [14].Since the gradient is proportional to its driving current, the primary force can be estimated as shown in Equation (1) [15].
(1) There are also Lorentz forces caused by eddy currents due to the changing magnetic field, which are proportional to the time derivative of gradients.It can be similarly calculated using Equation (2). (2) The and are coefficients depending on the gradient coil characteristics.The sound pressure is in proportion to the time derivative of the Lorentz forces [1].Thus, the basic silent sequence design objective is to decrease the gradient's slew rate and 2 nd order derivatives.

MRI acoustic noise estimation
Since the gradient to acoustic noise of MRI scanner is linear a system [16], the instantaneous sound pressure can be assumed as Equation ( 3), where , and are unknown weighting coefficients, represents gradient amplitude , represents the 1 st order gradient derivative and is the 2 nd order derivative .c (3) Since the gradient-sound pressure response of the three gradients is not the same, the effective sound pressure, the root-mean-square of , from 3-axis digitized gradients is assumed to be as Equation ( 4), where is the point index of the sampled gradient and its derivatives, is the total gradient sample number, , and are the weighting coefficients of the sound pressure caused by , and respectively.The SPL of MRI acoustic noise is calculated by the logarithmic ratio of the squared sequence sound pressure and squared reference of 1000 Hz, 2 10 Pa sound.

MRI acoustic noise reduction
The gradient pulses should be kept constant during the RF transmission and signal acquisition, but the rest parts can be changed in shape and duration to have more gentle slopes.This modification needs to observe the following rules.Firstly, the start and end points, and , of a new quiet pulse should be of the same value as before, and the time derivatives of these two points are set to zero for smoothness.
In addition, the integral of the new pulse between and , should not change so that the spin phase variation during this time interval can be maintained.The new pulse can be set to a quartic polynomial function in Equation ( 5) since the polynomial function is commonly used for curve fitting and convenient for expression, where represents the original gradient pulse amplitude and means the new quiet one.
(5) The five unknown coefficients can be solved from the five boundary conditions in Equation (6).

MRI acoustic noise optimization
The new gradient lobes can be prolonged to occupy the originally empty durations that have no gradients.Since the durations of some lobes in a sequence affect and restrict each other, the time extension of each lobe should be found respectively.To avoid using the traversing method which will be time-consuming and computationally intensive, the genetic algorithm can be applied to obtain an optimized parameter combination.The new lobe durations can be set as genes to select the one that provides the lowest estimated SPL.

MRI acoustic noise estimation
To find the weighting coefficients , , and for SPL estimation, the actual SPL is measured by an A-weighted sound level meter UT353BT (UNI-T) placed on the axle line of the XGY Magicscan-1.5TMR scanner (Xingaoyi Medical Equipment Company, Inc.) and is 1.4 m away from the bore center as illustrated in Figure 2 to avoid the strong magnetic field and detect SPL values properly.The same gradient waveform is applied to the three axes separately, which is a trapezoidal lobe with 300 us ramp, and 1ms plateau duration repeated every 30 ms.The noise amplitude is recorded by the microphone and their average values are calculated to find the , and .The background noise including the cold head condenser and ventilating system is pre-measured and removed, so the rest SPL value is assumed purely from the sequence scanning.After calculating the , and of three axes from the pulse sequence with the acquired , , , the relative A-weighted SPL can be estimated, by comparing it with the measured SPL, the coefficients , and can be estimated using the curve fitting tool in Matlab R2018a (MathWorks).

MRI acoustic noise reduction
The gradient pulse simulation is conducted using Matlab.For a commonly used trapezoidal pulse lobe, the rising and falling edges produce large first and second order time derivative values as the solid lines shown in Figure 3 and Figure 4.If this trapezoidal pulse is optimized as the dashed arcs, its derivatives are significantly reduced.The sound spectrum amplitude reduction is also shown in the frequency domain.

MRI acoustic noise optimization
In this study, the GRE sequence is optimized as an example.A typical GRE sequence is illustrated in Figure 5.The silent version of this sequence can be modified using the 4 th order polynomial function to convert the original pulses to smooth curves except those during RF transmission and signal acquisition.The waveform in solid lines shows the original one and the dashed one is divided into several changeable segments with their duration to be optimized.
If the gradient and timing of the original pulse sequence are known and the new pulse repetition time and echo time are specified, the duration of the new pulses has limited ranges.There are 8 changeable parts of the sequence that can be optimized as denoted in the sequence diagram.Their minimum and maximum duration values are listed in Table 1.The values of and can be directly set to their maximums to achieve minimum sound.The rest and can be set as genes and the then becomes the maximum possible value based on the former two parameters.
The population size is set to 10, the chromosome kind is 2, the gene length is 3, and the generation is 50.The crossover probability is assumed to be 0.8 and the mutation probability is 0.3.One GRE pulse sequence designed with a matrix size of 256, field of view (FOV) of 25 mm, slice thickness of 5 mm, TR of 15 ms, TE of 7 ms and sampling frequency of 40k Hz is optimized using the genetic algorithm and tested on the 1.5 T MRI scanner.The sequences are tested on the water phantom and 25-year-old female with an 8-channel head coil.Two variants of the previous GRE sequence, the object scouting and field shimming sequences, are frequently used to pre-locate the object and calculate the magnetic field inhomogeneity.The former is a 2D GRE sequence on transverse, sagittal, and coronal planes and the latter is a 3D GRE sequence with two alternating TEs.With the practical requirement for a total scanning time of around 12 seconds, the clinical routine scouting sequence can prolong 26 ms TR to maximum 32 ms for further noise reduction, TEs are 7 and 6 ms for quiet and original ones, flip angle (FA) is 25 degrees, FOV is 280 mm, slices number is 2, matrix is 256×128, and slice thickness is 9.68 mm.The shimming sequence has TR of 26.1 and 23.1 ms for quiet and original ones, two TE of 4.6/9.2ms, 90 degrees FA, 64×20 matrix, and 250 mm FOV.

Result
The corresponding , , are found to be 0.35, 0.45 and 0.20 based on the recorded sound amplitude.By fitting the measured SPL values of different echo train pulses with the related gradient amplitudes and derivatives according to Equation (4), , and are found to be 0, 0.45 and 0.37 respectively.As expected from Equations ( 1) and ( 2), the sound pressure caused by the sequence scanning is in proportion with gradient 1 st and 2 nd derivatives.As shown in Figure 6, SPL in about 70 to 100 dBA range of different sequences can be successfully estimated from the pulse gradient with a mean and a maximum relative error of 1.55% and 4.84%.The optimized GRE SPL value with the defined parameters calculated from the genetic algorithm is decreased from 88.1494 dBA to 70.9517 dBA by 17.1977 dBA through 8 generations.The original and optimized GRE sequences are scanned, and their measured SPL values are plotted in Figure 7.The mean measured SPL after modification is reduced from 91.9 dBA to 73.3 dBA by 18.6 dBA.The original GRE water phantom and the noise-reduced one are similar as demonstrated in Figure 8, and the mean relative error is 9.498% whereas the within-sequence difference is around 3%.Their SNR is 23.803 and 21.501, respectively.The difference between the original and quiet GRE images might be due to the less eddy current of the latter since the gradients are smoothed.For the scouting sequence, the average SPL during scanning is decreased by 14 dBA from 100.6 dBA to 86.6 dBA. Figure 9 shows the reconstructed images of the original and optimized sequences on transverse, coronal and sagittal planes.The deviation between the two sequences is around 8.354%.
As for the shimming sequence, mean SPL decreased by 7.2 dBA from 101.8 dBA to 94.6 dBA.The phase deviation differences of the reconstructed 3D images' middle slices between the original and optimized sequences are also negligible (see Figure 10).Figure 10.The water phantom phase deviations (in radians) between two echoes using the original shimming sequence and optimized one of three planes.

Discussions
Smoothing the trapezoidal gradient pulses by using the quartic polynomial function shows the feasibility of reducing the acoustic noise during MRI scanning in this study.We also provide a way to calculate SPL of the pulse sequence from the gradient.The unknown coefficients of the proposed effective sound pressure calculation model are obtained from practical experiment data and show good consistency with expectations.In accordance with previous studies' assumption of the MRI acoustic noise source, the results proved that the SPL value is mainly positively related to the gradient slew rate and has positive relationship with the 2 nd order gradient derivative.Minimizing the sequence time derivatives can be the guiding principle in noise-reduction design.One limitation of the implementation is that more general study is not conducted on other MRI scanners of different vendors and magnetic strengths, but it offers a potential approach for SPL estimation.In the future study, the coefficients a, b, and c of different gradient axis will be further specified separately using the similar method.
The SPL estimation is applied for the fitness function calculation to determine the best combination of the pulse durations under flexible user requirements.This approach avoids hardware reconstruction, which is convenient to be applied on existing scanners and is very cost-effective.Compared with previous methods, the sequence is optimized more automatically without much artificial calculation.This study improved previous research of single gradient lobe improvement to a whole sequence sound optimization by taking all changeable parameters into consideration, further decreasing SPL.With the specified sequence parameters, this method provides an approach to find the optimized lobe duration combinations within the constraints and does not require extra time extension.No large SNR decrease, or image variation of the tested phantom is observed in the example GRE sequence scan.The SPL value drops substantially by 18.6 dBA, which is a decrease of 88.25% of the original sound with no protocol change, higher than the previously reported of around 12 dBA of the sequence-based method without optimization.This method is also successfully applied to clinical scouting and shimming sequences and achieves a significant noise reduction.The method can be applied to more kinds of sequences in the future studies.With the optimized sequences, patients can be more comfortable during MRI scanning and the negative influences of large acoustic noise can be mitigated.

Conclusions
The Lorentz force-induced gradient coil vibration produces loud noise during MRI scanning.In this study, the changeable segments of the original trapezoidal GRE sequence are identified and converted to quieter ones by applying the quartic polynomial function to smooth and prolong them.The lobe duration combinations are optimized using genetic algorithm by predicting the SPL value of the whole sequence.The example of optimized GRE sequence successfully reduces the SPL by 18.6 dBA on a 1.5 T MRI scanner, and scanned images have negligible differences.This method is also applied to clinical scouting and shimming pre-scans for MRI acoustic noise reduction and patient discomfort mitigation.

Figure 1 .
Figure 1.Lorentz forces on gradient coils.Figure 2. The sound measurement point.

Figure 2 .
Figure 1.Lorentz forces on gradient coils.Figure 2. The sound measurement point.

Figure 3 .
Figure 3.The simulated and and their 1 st and 2 nd order time derivatives in the time domain.

Figure 4 .
Figure 4.The simulated and and their 1 st and 2 nd order time derivatives in the frequency domain.

Figure 5 .
Figure 5.The GRE sequence diagram for optimization.

Figure 6 .
Figure 6.The estimated SPL against measured SPL and their linear fitting function.

Figure 7 .
Figure 7.The measured SPL values of the original and optimized GRE sequences.

Figure 8 .
Figure 8.The reconstructed water phantom and brain images of original and optimized GRE sequences.

Figure 9 .
Figure 9.The water phantom absolute images using original and optimized scouting sequences, and their differences of three planes.

Table 1 .
The duration ranges of the quiet GRE pulse.