Synopsis

Purpose: To propose a transition region extraction algorithm for two point fat-water separation.

Methods:In the proposed method, fat-water transition region is first extracted as initial information. Remaining pixels are determined based on transition region in units of sub-region instead of pixels to improve calculation efficiency and avoid the vulnerability to the growing path.

Results:Fat-water separation were successfully achieved by the proposed method in the datasets tested.

Conclusion: A method based on fat-water transition region extraction is proposed for two point fat-water separation.

Introduction

Theory

The analytical phasor solutions could be obtained in two point fat-water imaging [1]. Fat-water separation problem can be then translated into a binary choice problem between the two candidate solutions [2]. Resolving the ambiguity is possible when the fat ratio in a pixel approximates 50% as long as the echo time difference (ΔTE) induced fat-water phase difference is not kπ [3]. Traditional region growing methods usually starts from identifying these “seed pixels”, and solves the rest pixels by region-growing method [3] [4].

In our implementation, we made two major modifications to the traditional region-growing methods. First, the algorithm starts with a fat-water transition region extraction instead of seed pixels. Fat-water transition region is defined as where the water-dominant and fat-dominant pixels are neighbors. The extraction procedure is explained as follows:

The two candidate phasor solutions for each pixel are categorized into two groups: $P_w$ and $P_f$ . The solution corresponding to water-dominant result are grouped in $P_w$ , while fat-dominant in $P_f$ . Supposing water-dominant pixel 1 and fat-dominant pixel 2 are neighbors with the identical phasor $P_t$ . For pixel 1, the aliased phasor solution $P_a=P_t v^{*}$ , while for pixel 2 $P_a=P_t v$ , where $v =e^{i 2\pi f_{F}\Delta TE}$ . Once the angle of $v$ is unequal to $k \pi$ ( $k$ is an arbitrary integer), the true solution pair is the smoothest among all four possible combinations (Figure 1). For this kind of pixel pair, there exists a sudden phasor change ( $\angle v$ ) in both $P_w$ and $P_f$ . In order to identify these pixels, the local phasor change for pixel r is defined as:

$D_{i}(r)=\max_k{|angle[P_{i}(r)\cdot P_i^*(r_k)]|}$ $i = w,f$ (1)

where K denotes the index of 8-neighborhood in 2D image, $(.)^{*}$ is the conjugate operator. As long as $D_w$ or $D_f$ is larger than $\alpha*\angle v$, this pixel would be identified as transition region pixel.

Second, the remaining pixels are determined in units of sub-regions after the extraction of these transition regions. Solutions of pixel in one sub-region are either all from $P_w$ or all from $P_f$. The determination is based on the cost function defined as:

$c_{i}=\sum_J{|\angle(P_{i}(s_j)\cdot P_i^*(t_j))|}$ $i = w,f$ (2)

where $J$ denotes all neighboring pixel pairs between current sub-region $S$ and the neighboring solved transition region $T$ . $s_j\in S$ and $t_j\in T$ . The solution resulting in smaller cost function is considered as true solution for the sub-region.

Methods

Flowchart of proposed method is illustrated in Fig.2. $P_w$ and $P_f$ (Fig.2B) are calculated using the equations given in ref.[1]. The fat-water transition region (Fig.2C) is extracted from the image and the rest pixels (Fig.2D) are divided into several sub-regions. The cost function of each sub-regions are calculated according to Eq.(2). Having determined the phasor solutions of all sub-regions (Fig.2E), the transition region pixels, along with other undermined pixels, are updated with region growing schemes[5] (Fig.2F). Once the phasor solutions of the whole image are decided, fat and water component could be determined accordingly (Fig.2G).

Proposed method is tested on datasets acquired from a 3T system (uMR 770, Shanghai United Imaging Healthcare, Shanghai, China) in various anatomies. Acquisition parameters are as following: flip angle $10^{。}$, slice thickness 3 mm, bandwidth 1100 Hz/pixel, TE = 2.3/3.16 ms corresponding to 0 and $3\pi/4$ fat-water phase difference at 3T, TR = 9.35 ms.

Results

Discussion and Conclusions

Acknowledgements

References

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2. Peng, H., C. Zou, W. Liu, C. Cheng, Y. Qiao, Q. Wan, C. Tie, X. Liu, and H. Zheng, Robust Fat-water Separation using Binary Decision Tree Algorithm. ISMRM, 2018.

3. Xiang, Q.S., Two-point water-fat imaging with partially-opposed-phase (POP) acquisition: an asymmetric Dixon method. Magn Reson Med, 2006. 56(3): p. 572-84.

4. Ma, J., J.B. Son, and J.D. Hazle, An improved region growing algorithm for phase correction in MRI. Magn Reson Med, 2016. 76(2): p. 519-529.

5. Cheng, C., C. Zou, C. Liang, X. Liu, and H. Zheng, Fat-water separation using a region-growing algorithm with self-feeding phasor estimation. Magn Reson Med, 2017. 77(6): p. 2390-2401.