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Effect of Intense Utilization of Gradients in Magnetic Resonance Current Density Imaging and its Removal
Mehdi Sadighi1, Hasan Hüseyin Eroğlu2, and B. Murat Eyüboğlu1

1Electrical and Electronics Engineering Dept., METU, Ankara, Turkey, 2Electrical and Electronics Engineering Dept., Bartın University, Bartın, Turkey

Synopsis

Intense utilization of gradients causes spatial and temporal variations of the main magnetic field which are consistent with resistive heating of the magnet structures. Since MR phase measurements are sensitive to the errors related to the B0 inhomogeneities correction strategies are required. Here, it is shown that field variations due to the temperature change of MR equipment in Magnetic Resonance Current Density Imaging (MRCDI) using Induced Current Nonlinear Encoding-Spoiled Multi Gradient Echo (ICNE-SPMGE) pulse sequence introduces a bias to noise distribution of magnetic flux density (Bz) measurements. Removing this bias reduces the measured noise standard deviation of the Bz measurements.

Introduction

In phase-sensitive MR protocols, the homogeneity and stability of the magnetic field are important for measurement accuracy 1. In gradient echo based Magnetic Resonance Current Density Imaging 2 (MRCDI) and Magnetic Resonance Electrical Impedance Tomography (MREIT) pulse sequences such as Induced Current Nonlinear Encoding-Spoiled Multi Gradient Echo 3 (ICNE-SPMGE), intense gradient utilization causes main magnetic field variation (B0) 1. Therefore, to obtain true values of noise standard deviation and SNR level for the current-induced magnetic field, Bz, measurements, B0 shifts must be removed by post-processing.

Methods

To investigate the effect of main magnetic field variation on the measured Bz a set of N=50 measurements (magnitude and phase) are acquired using the ICNE-SPMGE sequence with the parameters given in Fig. 1(b). In order to remove systematic phase components from MR phase measurements, a single measurement is acquired without current injection.

Therefore, the obtained phase measurement related to jth echo (˜ϕj(x,y)) of ICNE-SPMGE sequence can be given as:

˜ϕj(x,y)=ζϕj(x,y)+ϕj(x,y)j=1...NE(1)

where ζϕj(x,y) is the noise component in the phase image introduced by current injection, ϕj(x,y) is the current induced phase, and NE is the number of echoes. By scaling ˜ϕj(x,y) with the gyromagnetic constant of the proton (γ=267.513×106rads1T1) and the current injection duration, Tc, Bz distributions can be obtained.

It is assumed that the noise distribution (ζBzj(x,y)) of Bz measurements is independent and identically distributed (i.i.d) complex Gaussian random noise with zero mean. Therefore, to estimate the distribution, Dij(x,y) and the variance ˆσ2ζBzj of noise for each echo, the sample mean, ˆμj(x,y), of N=50 Bz measurements is calculated as:

ˆμj(x,y)=1NNi=1˜Bizj(x,y)j=1...NEN=50(2)

where ˜Bizj(x,y) is the noisy magnetic flux density distribution of the ith measurement of the jth echo. Therefore, N=50 noise distributions (Dij(x,y)) of each echo can be obtained as:

Dij(x,y)=Ni=1(˜Bizj(x,y)ˆμj(x,y))j=1...NEN=50(3)

Then, the noise variance of each echo can be calculated as:

1MNMm=1Ni=1(˜Bizj(x,y)ˆμj(x,y))2=ˆσ2ζBzjj=1...NEN=50(4)

where M is the total number of pixels.

Experimental Setup and Sequence Parameters

A 3T clinical MRI scanner (MAGNETOM TRIO, SIEMENS) with 70cm bore diameter and 45mTm1 maximum gradient strength is used. Data acquisition is performed using a single channel body coil. Current pulses with 2mA amplitude are injected to the imaging phantom in synchrony with SPMGE pulse sequence Fig.1(a), with the parameters given in Fig. 1(b). Current injection is performed by a programmable current source 4 via shielded cables and recessed cupper sheet electrodes. A single current injection (horizontal) profile is used. The experimental phantom in Fig. 1(c) is made of Plexiglas filled with a saline solution. Properties of the saline solution are given in Fig. 1(d).

Results and Discussions

Noise distributions of Bz images for N=50 measurements of the 9th (last) echo are shown in Fig. 2

The noise means for N=50 measurements of entire 9 echoes is shown in Fig. 3(a).

The effect of intense gradient utilization on main magnetic field variation (B0) can be calculated as 1:

B0(r,t2t1,TEj)=ϕ(r,t2t1,TEj)γTEjj=1...NE(5)

where TEj is the echo time of the jth echo, ϕ(r,t2t1,TEj) is difference between the two phase images acquired with the same TE at different time instants ( t1 and t2). The results for B0 calculations is shown in Fig. 3(b).

To calculate B0 values as given in Eq. (5), the difference of phase images that are acquired with the same TE at different time instances is calculated. As, the temperature of the scanner increases during successive measurements, B0 values become positive whereas, the Bz noise means moves from negative through positive values. Therefore, there is a “DC offset” between the two measurements while the amount of total shift is the same.

B0 shift (bias level) can be removed from the Bz images by subtracting the bias level or mean value of each Bz measurement from the corresponding Bz image.

Therefore, the B0 shift (bias level) can be removed from the Bz images successfully. After B0 shift cancellation, the sample mean is recalculated and the noise distributions and the standard deviations are obtained as shown in Fig. 4-5.

Conclusion

The intensive utilization of MRI scanner gradients causes a shift in the main magnetic field (B0) which can be calculated using the method in 1. Here, it is observed that the B0 shift is introduced to Bz measurements of ICNE-SPMGE sequence as the mean of noise distribution (bias value). Therefore, to obtain true values for the noise standard deviation and SNR level of Bz measurements bias values are removed using two methods. After bias cancellation the noise standard deviation decreases which result in SNR enhancement.

Acknowledgements

This work is supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under Research Grant 116E157.

References

1. El-Sharkawy A M, Schär M, Bottomley P A, Atalar E. Monitoring and correcting spatio-temporal variations of the MR. MAGMA. 2006;19(5):223-236.

2. Scott G C, Joy M L G, Armstrong R L, Henkelman R M. Sensitivity of Magnetic-Resonance Current-Density Imaging. Journal of magnetic resonance. 1992;97:235-254.

3. Oh T I, Jeong W C, Kim J E, et al. Noise analysis in fast magnetic resonance electrical impedance tomography (MREIT) based on spoiled multi gradient echo (SPMGE) pulse sequence. Physics in Medicine and Biology. 2014;59(16):4723-4738.

4. Eroğlu H H, Eyüboğlu B M. Design and implementation of a bipolar current source for MR-EIT applications. MEDICON. 2013;41:161-164.

Figures

Fig.1 Experimental setup. (a) ICNE-SPMGE pulse sequence. Tc is the duration of current injection, Gz,Gx,Gy are the slice selection, frequency encoding and phase encoding gradients, respectively, (b) sequence parameters, (c) imaging phantom, (d) phantom dimensions and composition of saline solution.

Fig. 2 Noise distribution of N=50 measurements of the 9th (last) echo. The unit of the noise (x-axis) is nT. The noise distributions are Gaussian but their mean is not zero. The noise mean moves from the negative values of the first measurements to the positive values of the last. This behavior is observed for the other 8 echoes either.

Fig. 3 (a) The measured noise means (i.e. bias levels) and (b) the calculated B0 for N=50 measurements of 9 echoes. The noise bias of Bz measurements and B0 are too similar structurally. The amount of B0 shift is about 12nT during N=50 measurements of the 9 echoes which is similar to the total amount of bias level change from the first through the last echo. The only difference between the two plots is a “DC offset”.

Fig. 4 Noise distribution of N=50 measurements of the 9th (last) echo. The unit of the noise (x-axis) is nT. The noise distribution is Gaussian and zero mean for all measurements of 9 echoes after B0 shift (bias level) cancellation.

Fig. 5 The estimated noise standard deviation of Bz images for 9 echoes before and after B0 shift (bias level) cancellation.

Proc. Intl. Soc. Mag. Reson. Med. 27 (2019)
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