Fast Padé transform for increasing the signal to noise ratio of spectra provided by STEAM pulse sequence

Abstract

BACKGROUND/OBJECTIVE:

There are two routine pulse-sequences for single voxel spectroscopy (SVS), point resolved spectroscopy (PRESS) and stimulated echo acquisition mode (STEAM). Although STEAM has several advantages in comparison to PRESS, signal/noise ratio (SNR) superiority of PRESS makes it the first choice for SVS. Application of fast Padé transform (FPT) instead of Fast Furrier transform (FFT) might increase the SNR of the signal produced by STEAM pulse-sequence and therefore allows the benefits of its advantages. We aimed to evaluate and compare the noise root mean square (RMS) and SNR provided by STEAM pulse-sequence using both FPT and FFT.

MATERIALS AND METHOD:

A gelatin-based phantom was constructed in a 19-cm acrylic cylinder. The phantom had two normal/tumoral parts. The SVS was performed using a 3T MRI scanner. STEAM pulse-sequence were used with the following parameters: TR $=$ 2000 ms, TM $=$ 10 ms, and three TEs of 20, 135 and 270 ms with two data-points of 1024 and 512 and voxel-size of 1 cm ${}^{3}$ . The raw data were extracted and processed using both FFT and FPT estimators to produce the spectrum. The noise RMS and SNR of Cho and Cr metabolites were assessed.

RESULTS:

According to the results, noise RMS of spectra provided by FPT were decreased between 3619.01–14252.94% in comparison to FFT ( $p<$ 0.00001). The SNR of Cr1 and Cho peaks of the spectra provided by FPT were increased more than 96.80 and 97.18, respectively (0.00006 $<p<$ 0.02).

DISCUSSION:

The difference of noise RMS’s provided by FPT are thousands percent less than FFT. This enormous decrease in noise provides a good increase of SNR. While the range of Cr1 and Cho SNR by FFT are between 41.55–120.32 the range of SNRs of these peaks provided by FPT are between 1719.99–9744.79, which implies a significant difference between the efficiency of FPT and FFT.

CONCLUSION:

This study showed that application of FPT in comparison to FFT can increase the spectra SNR and so that its usage can be helpful during the application of STEAM pulse-sequence which results in lower SNR in comparison to PRESS pulse-sequence. Thus, we should make use of the advantages of STEAM pulse-sequence.

Keywords

Magnetic resonance spectroscopy fast Padé transform Fast Furrier Transform STEAM pulse sequence signal to noise ratio

1. Introduction

Magnetic resonance spectroscopy (MRS) is used to detect the metabolic changes of the tissues for different diseases. When a malignancy happens before the morphological changes can be detected, the functional modifications can be distinguished by observing the metabolic alterations. MRS can be performed as single voxel (SVS) or multivoxel spectroscopy (MRSI) [1, 2, 3].

There are two routine pulse sequences for SVS, point resolved spectroscopy (PRESS) and stimulated echo acquisition mode (STEAM). These sequences are different in terms of the angle of radiofrequency and arrangement of gradient pulses for localization. PRESS applies a 90 ${}^{\circ}$ followed by two 180 ${}^{\circ}$ slice selective pulses, however, STEAM utilizes three 90 ${}^{\circ}$ slice selective pulses. Thus, PRESS, by applying two 180 ${}^{\circ}$ pulses, can recover the full possible signal and therefore produce a higher signal to noise ratio (SNR). Applying three 90 ${}^{\circ}$ pulses, STEAM produces partially compensating signals with lower SNR, however, it permits the utilization of shorter echo times. STEAM is the sequence of choice because it has a short echo time ( $\sim$ 7 ms), has the least chemical shift artifacts and has a better voxel edge definition, which is important since the RF bandwidth of 90 ${}^{\circ}$ pulses is higher than 180 ${}^{\circ}$ pulses, and 90 ${}^{\circ}$ pulses produce a sharper slice profile. Although STEAM pulse sequence has several advantages in comparison to PRESS, SNR superiority of PRESS makes it the first choice for MRS since SNR is always important in this imaging modality [2, 4, 5].

The spectroscopic information is produced from an oscillating time signal called free induction decay (FID). There are some estimators that transform the time signal to frequency domain such as Fast Fourier transform (FFT). FFT is the routine transformation method in MR scanners. This is a nonparametric and low SNR estimator since it is a linear transform and it can transfer the noise from the time to frequency domain. Moreover, when FFT is applied, to improve the spectrum resolution, the acquisition time should be increased which results in a decreased SNR [6].

To transform the time signal to frequency domain, there are other methods such as fast Padé transform (FPT). FPT is a parametric high SNR estimator since it is a nonlinear mapping method that allows noise suppression [6, 7].

Application of FPT instead of FFT might increase the SNR of the signal produced by STEAM pulse sequence and therefore allows you to take benefits of its advantages. The objective of this study was to evaluate and compare the noise root mean square (RMS) and SNR provided by STEAM pulse sequence using both FPT and FFT.

2. Materials and methods

A gelatin-based phantom was constructed in a 19-cm acrylic cylinder. The phantom had two normal and tumoral parts. The phantom contained deionized water, 1 cc/L Magnevist and 5% weight fraction porcine gelatin. The metabolites of Choline and Creatine were used in the construction of the phantom. The concentration of Cr was 10 mM in both the normal and tumoral region and the concentration of Cho was 3 and 10 mM in the normal and tumoral areas. The previous studies have shown that the concentration of Cho, and as a result of that the Cho/Cr ratio, increases [8, 9].

Table 1
Noise RMS, SNR of Cr1 and Cho peaks of both normal and tumoral parts of the phantom in three TEs of 20, 135 and 270 ms and data points of 1024 which were provided by FPT and FFT and their $p$ -values

TE (ms)	Normal (1024)						Tumoral (1024)
	RMS	RMS	SNR Cr1	SNR Cr1	SNR Cho	SNR Cho	RMS	RMS	SNR Cr1	SNR Cr1	SNR Cho	SNR Cho
	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT
20	0.87	81.90	6610.97	85.90	5329.60	57.65	1.68	83.70	2963.67	63.79	5993.03	102.03
135	0.92	90.75	8015.35	72.41	5010.67	51.23	0.84	94.35	5789.99	53.55	9744.79	84.91
270	0.60	86.01	8371.41	57.24	6123.53	41.55	0.91	90.86	4862.18	46.03	8043.87	80.60
$p$ -value	$<$ 0.00001		0.000146		0.00008		$<$ 0.00001		0.005727		0.001945

Table 2

Noise RMS, SNR of Cr1 and Cho peaks of both normal and tumoral parts of the phantom in three TEs of 20, 135 and 270 ms and data points of 512 which were provided by FPT and FFT and their $p$ -values

TE (ms)	Normal (512)						Tumoral (512)
	RMS	RMS	SNR Cr1	SNR Cr1	SNR Cho	SNR Cho	RMS	RMS	SNR Cr1	SNR Cr1	SNR Cho	SNR Cho
	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT	FPT	FFT
20	1.48	60.32	2724.79	83.01	5104.12	82.23	1.62	70.56	2214.73	54.52	4617.97	114.86
135	1.05	71.36	3757.94	54.65	4714.30	63.95	1.82	70.19	1719.99	55.04	4764.56	120.32
270	1.25	60.56	4028.62	79.73	2491.17	62.46	1.78	66.33	4039.14	66.67	3150.10	88.85
$p$ -value	0.000066		0.000989		0.007727		$<$ 0.00001		0.021098		0.001393

Figure 1.

Spectra provided by FPT (A and C) and FFT (B and D) estimators from normal (A and B) and Tumoral (C and D) regions of the phantom, in three TEs of 20, 135 and 270 ms and data points of 1024.

The SVS was performed using a 3T Siemens Magnetom Prisma MRI scanner. STEAM pulse sequence was used with the following parameters: TR of 2000 ms, TM of 10 ms, and three TEs of 20, 135 and 270 ms with two data points of 1024 and 512 and a voxel size of 1 cm ${}^{3}$ . The FID of each imaging, which contains the raw data, was extracted and processed using both FFT and FPT estimator to produce the spectrum. The noise RMS and SNR of Cho and Cr metabolites were assessed. To evaluate the statistical significance between the FPT and FFT calculations, a T-test was performed using MedCalc V17.9.2. A $p$ -value of 0.05 was considered signifcant.

3. Results

SVS from both normal and tumoral areas of the phantom were performed using STEAM pulse sequence in three TEs of 20, 135 and 270 ms and two data points of 1024 and 512. The raw data were transformed from time to frequency domain by both FFT and FPT estimators. The resulted spectra are shown in Figs 1 and 2.

The noise RMS and SNR of the Cr1 and Cho were calculated and are shown in Tables 1 and 2. According to the results in Tables 1 and 2, the noise RMS of spectra provided by FPT were decreased between 3619.01 to 14252.94% in comparison to FFT ( $p<$ 0.00001). The SNR of Cr1 and Cho peaks of the spectra provided by FPT were increased more than 96.80 and 97.18, respectively (0.00006 $<p<$ 0.02).

Figure 2.

Spectra provided by FPT (A and C) and FFT (B and D) estimators from normal (A and B) and Tumoral (C and D) regions of the phantom, in three TEs of 20, 135 and 270 ms and data points of 512.

4. Discussion

SNR in MRS is a very important issue since the concentration of metabolites are several thousand times less than water and fat. Thus, any method that can improve the SNR is the method of choice. The application of 180 ${}^{\circ}$ pulses in PRESS pulse sequence allows the full recovery of signal and increases the signal amplitude which in turn leads to higher SNR in comparison to STEAM pulse sequence which uses 90 ${}^{\circ}$ pulses [2].

However, STEAM pulse sequence can reduce the chemical shift artifacts and permits application of shorter echo times. In this study, to be able to use the benefits of the STEAM pulse sequence, FPT transformation method was suggested as an alternative to the FFT method.

In previous studies, it was proven that FPT can increase the SNR of spectra especially when the signal length is short and FFT cannot produce a high resolution and high SNR signals [7, 10, 11, 12, 13, 14, 15, 16, 17]. However, to the best of our knowledge, there was no exclusive study that compared the SNR of peaks provided by FPT and FFT estimators when STEAM pulse sequence was used. In this study, the RMS of noise and SNR of Cho and Cr were compared when the spectra provided by FPT and FFT and STEAM pulse sequence was used.

According to Figs 1 and 2, the baseline noise of the spectra provided by FPT are less than the spectra provided by FFT in both data points of 1024 and 512 and in both normal and tumoral spectra. The smaller baseline noise results in an increase of SNR since the SNR is the proportion of signal amplitude to noise RMS.

From Tables 1 and 2 it can be calculated that the difference of noise RMS’s provided by FPT are thousands percent less than FFT and these differences are statistically significant ( $p<$ 0.00001). This enormous decrease in noise provides a good increase of SNR. While the range of Cr1 and Cho SNR by FFT are between 41.55 to 120.32, the range of SNRs of these peaks provided by FPT are between 1719.99 to 9744.79, which implies a significant difference between the efficiency of FPT and FFT.

5. Conclusion

This study showed that application of FPT in comparison to FFT can increase the spectra SNR so that its usage can be helpful during the application of STEAM pulse sequence, which results in lower SNR in comparison to PRESS pulse sequence. Thus, we can take advantage of STEAM pulse sequence.

Footnotes

Conflict of interest

None to report.

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Fast Padé transform for increasing the signal to noise ratio of spectra provided by STEAM pulse sequence

Abstract

BACKGROUND/OBJECTIVE:

MATERIALS AND METHOD:

RESULTS:

DISCUSSION:

CONCLUSION:

Keywords

1. Introduction

2. Materials and methods

Table 1 Noise RMS, SNR of Cr1 and Cho peaks of both normal and tumoral parts of the phantom in three TEs of 20, 135 and 270 ms and data points of 1024 which were provided by FPT and FFT and their p -values

5. Conclusion

Footnotes

Conflict of interest

References

Table 1
Noise RMS, SNR of Cr1 and Cho peaks of both normal and tumoral parts of the phantom in three TEs of 20, 135 and 270 ms and data points of 1024 which were provided by FPT and FFT and their $p$ -values