# US 9,519,040 B2 · Methods and apparatus for phase correction in magnetic resonance imaging

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- Number: US 9,519,040 B2
- Document ID: US9519040B2
- Status: Granted
- Kind: B2
- Application number: 14/677,156
- Filed: 2015-04-02
- Published: 2015-11-05
- Granted: 2016-12-13
- Earliest claimed: 2014-04-04
- Assignees: Board of Regents, The University of Texas System
- Applicants: Board of Regents, The University of Texas System
- Inventors: Jingfei Ma; John Hazle; Jong Bum Son
- Web page: https://patentgrep.com/patent/US9519040B2

## CPC

- G01R 33/565: Correction of image distortions, e.g. due to magnetic field inhomogeneities
- G01R 33/4828: {Resolving the MR signals of different chemical species, e.g. water-fat imaging}
- G01R 33/5602: {by filtering or weighting based on different relaxation times within the sample, e.g. T1 weighting using an inversion pulse}
- G01R 33/5611: {Parallel magnetic resonance imaging, e.g. sensitivity encoding [SENSE], simultaneous acquisition of spatial harmonics [SMASH], unaliasing by Fourier encoding of the overlaps using the temporal dimension [UNFOLD], k-t-broad-use linear acquisition speed-up technique [k-t-BLAST], k-t-SENSE (structural details of arrays of sub-coils G01R33/3415)}
- G01R 33/56527: {due to chemical shift effects}
- G01R: MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES (indicating correct tuning of resonant circuits H03J3/12)

## Abstract

Methods, apparatuses, systems, and software for extended phase correction in phase sensitive magnetic resonance imaging utilizing an optimized region-growing based phase correction algorithm. Phase correction is formulated as selecting a vector for each pixel of an image from two input candidate vectors so that the orientation of the output vector is spatially smooth. In certain embodiments, the optimized region growing algorithm uses automated quality guidance for determining the sequence of region growing and jointly considers the two input candidate vectors during region growing. Further, the algorithm tracks the quality and the mode at each step of the processing. Spatially isolated tissue regions are automatically segmented and processed with different threads of region growing and the correct vector is reliably identified as the output vector for each thread of region growing. Final phase correction was performed by pixel level optimization.

## Claims

### Claim 1

A computerized method for generating a phase corrected magnetic resonance image comprising:
(a) acquiring a first magnetic resonance image containing error and intrinsic phase information;
(b) calculating two or more candidate input vector images from the acquired image; and
(c) performing an optimized region growing based phase correction algorithm to determine an output vector image that is spatially smooth in orientation and is substantially represented at each pixel by one of the calculated vector images at the same pixel, wherein phase correction is performed by:
selecting an initial seed pixel for a new thread of region growing and placing the initial seed pixel onto a highest priority pixel stack;
selecting a pixel that is placed on a pixel stack with a highest priority order from a list of pixel stacks that hold unprocessed pixels;
determining an updated vector pair for the selected pixel by jointly considering its input vector pair (A and B) with a reference vector pair (Ar and Br);
placing each of neighboring pixels of the selected pixel onto one of pixel stacks according to a quality metric by jointly comparing an input vector pair of a neighbor pixel with a reference vector pair;
recording and monitoring the priority and the mode of region growing for the selected pixel;
using the recorded mode of region growing to determine which vector pairs need to be considered and which vector of the updated vector pair is a correct vector; and
performing a final pixel-level optimization in which a vector O of a pixel is assigned as its original input vector A or B depending on if A or B has a smaller angular difference with the locally average O of the pixel over a selected boxcar.

### Claim 2 (depends on 1)

The computerized method of claim 1 wherein performing an optimized region growing based phase correction algorithm comprises:
calculating a first candidate input vector map A and a second candidate input vector map B from the first magnetic resonance image;
generating an updated vector pair (A and B) for a given pixel jointly by comparing the angular differences of A and B, B and Ã, {tilde over (B)} and A, of a given pixel with a reference vector pair (Ar and Br) for the same pixel;
deciding the order by which a pixel is visited by the region growing using a quality metric based on the angular differences of A and B, B and Ã, {tilde over (B)} and A, of the pixel with a reference vector pair (Ar and Br) for the same pixel;
calculating the reference vector pair (Ar and Br) for a given pixel as the updated vector pair A and B averaged over all the pixels that have been previously processed by the region growing and are located within a boxcar neighborhood of the given pixel;
determining the mode of region growing by recording and monitoring the number of pixels selecting each of the three possible vector pairs (A and B, {tilde over (B)} and A, B and Ã) as their updated vector pair A and B, wherein à is the mirror vector of A with respect to B and {tilde over (B)} is the mirror vector of B with respect to A;
using the mode of region growing to select the correct vector O from the updated vector pair A and B; and
detecting spatially isolated tissue regions and starting new threads of region growing by recording and monitoring the quality of region growing.

### Claim 3 (depends on 1)

The method of claim 1 further comprising:
(e) generating the phase corrected magnetic resonance image or images from the acquired magnetic resonance image or images using a final output vector O to remove the error phase; and
(f) displaying or archiving the phase corrected magnetic resonance image or images.

### Claim 4 (depends on 1)

The method of claim 1 further comprising:
(g) selecting a seed pixel or pixels and assigning A and B of the seed pixel or pixels as the updated vector pair A and B for the seed pixel or pixels;
(h) selecting a second seed pixel from a pixel stack and determining its updated vector pair A and B jointly as its A and B, or B and Ã, or {tilde over (B)} and A, wherein à is the mirror vector of A with respect to B, and {tilde over (B)} is the minor vector of B with respect to A, depending on which of the three vector pairs has the smallest angular difference with a reference vector pair for the updated vector pair A and B of the second seed pixel;
(i) determining for the second seed pixel a local quality metric for each of nearest neighbor pixels of the second seed pixel for which the updated vector pair A and B have not been determined and assigning a priority to each of the nearest neighbor pixels using the local quality metric in order to determine the sequence by which each of the nearest neighbor pixels is to be selected as a further seed pixel; and
(j) repeating the steps of (h) and (i) to complete optimized region growing with respect to further seed pixels and to construct the updated vector image pair A and B for all pixels that are processed by the optimized region growing, wherein:
an initial seed pixel or pixels are placed onto a high priority pixel stack or stacks among a series of pixel stacks that are initially empty and which facilitate a sequencing of the optimized region growing;
a pixel is selected as a seed pixel if it has not been processed previously as a seed pixel and it is on a pixel stack that has a highest priority among pixel stacks that contain at least one pixel that has not been processed as a seed pixel; and
the local quality metric of a pixel is calculated as the smallest of the angular differences of A and B, B and Ã, {tilde over (B)} and A, of the pixel with an estimated reference vector pair Ar and Br for the same pixel.

### Claim 5 (depends on 4)

The method of claim 4, wherein the values of the vector A and vector B for an initial seed pixel are assigned as the updated vector pair A and B for the initial seed pixel, and an optimized region growing is performed to jointly construct an updated vector pairs A and B for all the pixels processed by the region growing, wherein a final correct vector O is selected by recording and monitoring the mode of region growing of the processed pixels.

### Claim 6 (depends on 4)

The method of claim 4 wherein acquiring the magnetic resonance image comprises acquiring two-point Dixon water and fat images, wherein a first image S1 is acquired at a first echo time TE1 and a second image S2 is acquired at a second echo time TE2.

### Claim 7 (depends on 6)

The method of claim 6, wherein the images S1 and S2 are expressed according to the following equations:
S1=(W+δ1Feiθ1)P1
S2=(W+δ2Feiθ2)P1P
where W and F are amplitudes for water and fat respectively, P1 is a phase factor of image S1, P is an additional phase factor of image S2 relative to image S1 and is determined by a background or error phase, and the method further comprises determining an amplitude attenuation factor (δ1, δ2) and phase (θ1, θ2) as a function of two echo times (TE1, TE2) using a known or pre-calibrated fat signal model.

### Claim 8 (depends on 6)

The method of claim 6, wherein the images S1 and S2 are used to generate two vector images A and B as expressed according to the following equations:
A=S*1S2[QA+δ1(1−QA)eiθ1][QA+δ2(1−QA)e−iθ2]
B=S*1S2[QB+δ1(1−QB)eiθ1][QB+δ2(1−QB)e−iθ2]
where QA and QB are the two mathematically possible solutions of the following quadratic equation of Q, which is defined as
Q
=
W
W
+
F
(the water fraction for a given pixel):
[(1+δ22−2δ2 cos θ2)M1−(1+δ122δ1 cos θ1)M2]Q2−2[(δ22−δ2 cos θ2)M1−(δ12−δ1 cos θ1)M2]Q+[(M1δ22−M2δ12)]=0
where M1 and M2 are the square of the amplitudes of the images S1 and S2, respectively (M1=|S1|2 and M2=|S2|2).

### Claim 9 (depends on 8)

The method of claim 8, wherein the vector images are further normalized and weighted by a signal amplitude:
A
′
=
A

A

⁢
M
1
+
M
2
B
′
=
B

B

⁢
M
1
+
M
2
where M1=|S1|2 and M2=|S2|2.

### Claim 10 (depends on 9)

The method of claim 9, wherein an optimized region growing algorithm is used to jointly construct an updated vector image pair A and B from the two input vector images A and B and a final vector image O is selected for phase correction, wherein:
final vector image O is selected based on the region growing mode and used to phase correct and remove the phase factor P from the image S2, the phase corrected S2 is combined with S1 to solve for WP1 and FP1, and then to generate a water-only image and a fat-only image according to the following equations:
W=Real{(WP1)WP1*/|WP1|}
F=Real{(FP1)FP1*/|FP1|}
where Real{ . . . } is to take the real component of its complex argument, * is to take the complex conjugate of its argument, and WP1 and FP1 represent low-pass filtering of WP1 and FP1, respectively.

### Claim 11 (depends on 6)

The method of claim 6, wherein one of the images is acquired at an echo time when water and fat are substantially in-phase, such as in a spin echo or fast spin echo pulse sequence.

### Claim 12 (depends on 11)

The method of claim 11, wherein images S1 and S2 are expressed according to the following equations:
S1=(W+F)P1
S2=(W+δFeiθ)P1P
where W and F are amplitudes for water and fat respectively, P1 is a phase factor of image S1, P is an additional phase factor of image S2 relative to image S1 and is determined by a background or error phase, and the method further comprises determining an amplitude attenuation factor δ and phase θ as a function of the echo time TE2 relative to the echo time TE1 using a known or pre-calibrated fat signal.

### Claim 13 (depends on 6)

The method of claim 6, wherein the images S1 and S2 are used to generate two vector images A and B as expressed according to the following equations:
A′=S*1S2(W1+δF1e−iθ)
B′=S*1S2(W2+δF2e−iθ)
where W1, F1 and W2, F2 are the two sets of algebraic solutions to the following equations:
I1=W+F
I22=W2+δ2F2+2δWF cos θ
where I1=|S1| and I2=|S2|.

### Claim 14 (depends on 1)

The method of claim 1 wherein acquiring a magnetic resonance image or images comprises acquiring a single-point Dixon water and fat image wherein a flexible echo time TE is used and the acquired magnetic resonance image is expressed as: S=(W+Feiθ)P, where θ is dependent on TE and the dependence is determined a known or pre-calibrated fat signal model, and P (≡eiφ) is a phase factor for the image S.

### Claim 15 (depends on 14)

The method of claim 14, wherein the vector image A is set to S and the vector image B is set to Se−iθ.

### Claim 16 (depends on 15)

The method of claim 15, wherein an optimized region growing algorithm is used to jointly construct an updated vector pair A and B from the two input vector images A and B, and a final vector image O is selected to phase correct or remove P from S to form S′, and a water-only image and a fat-only image are generated according to:
F=Imag{S′}/sin θ
W=Real{S′−F cos θ}
where Real{ . . . } and Imag{ . . . } are to take the real and imaginary components of their component, respectively.

### Claim 17 (depends on 1)

The method of claim 1, wherein acquiring a magnetic resonance image or images comprises acquiring a single-point silicone specific image wherein an echo time TE when water and fat signals are substantially in-phase is used, and the acquired magnetic resonance image is expressed according to the following equation:
S=(W+F+Ieiθ)P
where θ is determined with an image-based pre-calibration for the echo time TE as a phase discontinuity of a known silicone-only image region and a neighboring known water or fat only image region, and P (≡eiφ) is a phase factor for the image S.

### Claim 18 (depends on 17)

The method of claim 17, wherein vector image A is set to S and vector image B is set to Se−iθ.

### Claim 19 (depends on 18)

The method of claim 18, wherein an optimized region growing algorithm is used to jointly construct an updated vector pair A and B from the two input vector images A and B, and a final vector image O is selected and used to phase correct or remove P from S to form S′, and a silicone-only image and a silicone-suppressed image are generated according to:
I=Imag{S′}/sin θ
W+F=Real{S′−I cos θ}
where Real{ . . . } and Imag{ . . . } are to take the real and imaginary components of their component, respectively.

### Claim 20

A system for generating a phase corrected magnetic resonance image or images comprising:
(a) a magnetic resonance imaging controller;
(b) a processor coupled to the controller and configured to execute phase correction instructions applicable to a magnetic resonance image or images, wherein the instructions comprise:
(i) calculating a first input vector map A and a second input vector map B from the first magnetic resonance image;
(ii) determining an updated vector pair for a selected pixel by jointly considering its input vector pair (A and B) with a reference vector pair (Ar and Br);
(iii) placing each of neighboring pixels of the selected pixel onto one of pixel stacks according to a quality metric by jointly comparing an input vector pair of a neighbor pixel with a reference vector pair;
(iv) performing a final pixel-level optimization in which a vector O of a pixel is assigned as its original input vector A or B depending on if A or B has a smaller angular difference with the locally average O of the pixel over a selected boxcar;
(v) generating a phase corrected magnetic resonance image or images from the acquired magnetic resonance image or images using the final output vector O; and
(vi) displaying or archiving the phase corrected magnetic resonance image or images; and
(c) an output or storage device configured to display or store the phase corrected magnetic resonance image or images.

### Claim 21

A non-transitory computer readable storage medium with an executable program stored thereon, wherein the program instructs a microprocessor to perform steps comprising:
(a) calculating a first input vector map A and a second input vector map B from a first magnetic resonance image;
(b) determining an updated vector pair for a selected pixel by jointly considering its input vector pair (A and B) with a reference vector pair (Ar and Br);
(c) placing each of neighboring pixels of the selected pixel onto one of pixel stacks according to a quality metric by jointly comparing an input vector pair of a neighbor pixel with a reference vector pair;
(d) performing a final pixel-level optimization in which a vector O of a pixel is assigned as its original input vector A or B depending on if A or B has a smaller angular difference with the locally average O of the pixel over a selected boxcar;
(e) selecting a final output vector O to be used for phase correction for each pixel, wherein the final output vector O is selected by using a recorded region growing mode;
(f) generating a phase corrected magnetic resonance image or images from an acquired magnetic resonance image or images using the final output vector O; and
(g) displaying or archiving the phase corrected magnetic resonance image or images.