Jun-Hyeong Kim^{1}, Jaewook Shin^{1}, Soo-Yeon Kim^{2}, and Dong-Hyun Kim^{1}

Phase-based EPT assumes the spatial homogeneity of both B1+ and B1- magnitude. However, when it comes to multi-receivers is used for improved SNR, the assumption becomes invalid especially for B1-. To overcome this problem, a subject-specific multi-Rx combination method was suggested [2]. However, this method can give a solution that is biased by the transmit field (B1+) when it is inhomogeneous. In this study, an alternative multi-Rx combination method is proposed. B1- is estimated from multi-receiver images by solving an inverse problem. Afterwards, optimal coil-coefficients for combination are calculated using the estimated B1- field. The method is applied to in-vivo breast conductivity imaging.

Figure 1 shows image combined using a simple ‘complex sum’ and the aforementioned subject-specific method(aka magnitude least squares(MLS) method)[2]. As in Fig.1a, the simple ‘complex-sum’ cannot flatten the image due to inhomogeneity of B1-. To overcome this problem, MLS-optimization was previously applied to multi-Rx combination [2]. (Fig.1b) However, when the magnitude of B1+ is inhomogeneous, even MLS-method can suffer from inhomogeneity. Specifically, magnitude of combined B1- would be inversely proportional to magnitude of B+ field over each homogeneous ROI.(Icommon=constant, Eq.1) $$ S_{comb} = I_{common}\cdot \mid B^+_1 \mid\mid B^-_{comb} \mid=1 \space\space\space\Rightarrow \space\mid B^-_{comb} \mid= \frac{1}{ I_{common}\cdot \mid B^+_1 \mid} (Eq.1) $$ To overcome the B1+ magnitude bias in MLS-method, MLS-optimization problem should be solved in B1-, not in received image. B1- field can be estimated by solving a log-linear inversion problem. Using Eq.2, log B1- field for each coil can be calculated. $$ log\mid S_{PD,j} \mid=log\mid PD_{w}\cdot B^+_1 \mid + log\mid B^-_{1,j} \mid , \space \space log\mid S_{T2,j} \mid=log\mid T2_{w}\cdot B^+_1 \mid + log\mid B^-_{1,j} \mid (Eq.2) $$ After B1- field was estimated, the coil-coefficients needed to yield a homogeneous B1- field is determined by Eq.3.

$$ \left\{c_j\right\}=argmin_{c_j}\left\{ \sum_{(x,y,z)\in ROI }\parallel \sum_{j }B^-_{1,j}(x,y,z)-1 \parallel ^2_2 +\lambda \sum_j \mid c_j \mid^2 \right\} (Eq.3) $$

1. Data Acquisition : In-vivo breast imaging experiments were conducted using a 3T clinical scanner (Skyra;Siemens,Erlangen,Germany), breast 18 channel-coil. TSE sequence was acquired : PDw 3.2-mm thickness, image size=384×260, FOV=320×320mm, TR=10800ms, TEeff=6ms, ETL=20, number of slice=45. In addition, a separate T2-weighted image (TE=101ms) was acquired. Total scan time ~5min. This study was approved by our Institutional Review Board (IRB).

2. Coil-combination using fat mask vs coil-combination with B1- estimation

Previous method(Homogenize magnitude of combined image over fat-masked region) :

a) Fat-mask was selected based on the intensity of T2-weighted image (12%thresholding).

b) The received image was implemented to MLS-optimization problem which yields the coil-coefficients: [2].

c) All coil images were complex-summed after multiplying with the acquired coil-coefficients.

Proposed Method(Homogenize magnitude of combined B1- over whole breast region) :

a) To estimate B1-, a log-linear inversion problem was solved. Using Eq.3, log B1- field for each coil was calculated.

b) The estimated B1- field was implemented into Eq.3 which yields the coil-coefficients:

c) All coil images were complex-summed after multiplying with the acquired coil-coefficients.

3. EPT reconstruction : A 3D-weighted polynomial fitting was performed[2].(maximum kernel size=1.75x2.5x3.2cm2) For magnitude weighting factor, both method using magnitude of combined image from MSL-method.

1. T. Voigt. et al., Quantitative conductivity and permittivity imaging of the human brain using electrical properties tomography. Mag. Reson. Med., Vol 66(2), August 2011, Pages 456-466.

2. Joonsung Lee, et al., MR_Based Conductivity Imaging Using Multiple Receiver Coils. Magn Reson Med. Volume 76, Issue 2, August 2016, Pages 530–539

3. W. T. Joines et al., The measured electrical properties of normal and malignant human tissues from 50 to 900 MHz. Medical Physics 21, 547 (1994)

Figure 1. (a) Complex sum of
received coil images. (b) Multi-receiver combined image using magnitude of fat
mask region.

Figure 2. Magnitude of estimated
B1- field.

Figure 3. (a) is magnitude of
combined image using previous method (b) is magnitude of combined image using
proposed method (c) is magnitude of B1- combined with coil-coefficient of
previous method. (d) is magnitude of B1- combined with coil-coefficient of
proposed method.

Figure
4.
first
column of (a), (b) is magnitude of combined signal. (a) is conductivity value
which is calculated from Previous method
1 (using fat mask ROI). (b) is conductivity value which is calculated from Proposed
method
2.
(c)
is fat mask for calculating mean and standard deviation of conductivity value
of fat region. (d) is line plot of mean conductivity and standard deviation of
fat