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-
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=267.513×106rads−1T−1) 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)=1N∑Ni=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)=N∑i=1(˜Bizj(x,y)−ˆμj(x,y))j=1...NEN=50(3)
Then, the noise variance of each echo can be calculated as:
1MNM∑m=1N∑i=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 45mTm−1 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,t2−t1,TEj)=△ϕ(→r,t2−t1,TEj)γTEjj=1...NE(5)
where TEj is the echo time of the jth echo, △ϕ(→r,t2−t1,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.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.