The highly efficient balanced Steady-State Free Precession (bSSFP) sequence has many research and clinical applications. However, it has a peculiar sensitivity to magnetic field inhomogeneity, often resulting in artifacts seen as dark bands. Phase-cycling can generate multiple acquisitions in which the banding is spatially shifted, and subsequently reduced by various algorithms. With 4 acquisitions and an elliptical signal model, it is possible to eliminate the banding by solving the system geometrically, algebraically, or in a combined manner for improved SNR. This work reports a Fourier approach that can effectively reduce the banding using only 3 acquisitions.
The bSSFP signal can be described with the following parametric equation of an ellipse,
I=M1−aeiθ1−bcosθ(1)
It can be seen from Eqn.(1) that the signal contains a parallel component P=M/(1−bcosθ) and a rotational component R=−Maeiθ/(1−bcosθ). For 3 acquisitions with 120∘ phase-cycling, the signals can be written as,
I1=P1+R1(2)
I2=P2+R2E(3)
I3=P3+R3E2(4)
where (P1,P2,P3) and (R1,R2,R3) are two groups of 3 complex numbers with the same phase or vectors along the same direction, and E=ei2π/3 is a phase factor due to phase-cycling. A 3-point Fourier transform can be performed on (I1,I2,I3) to obtain (S1,S2,S3) as defined below,
S1≡I1+I2+I3=(P1+P2+P3)+(R1+R2E+R3E2)(5)
S2≡I1+I2E+I3E2=(P1+P2E+P3E2)+(R1+P2E2+R3E4)(6)
S3≡I1+I2E2+I3E4=(P1+P2E2+P3E4)+(R1+R2+R3)(7)
In S1, the 3 vectors (P1,P2,P3) are all in-phase but the (R1,R2,R3) are dephased. This S1 is in fact the familiar “complex sum”[1,3] with reduced but still remaining banding; Conversely, in S3, the 3 vectors (R1,R2,R3) are refocused but the (P1,P2,P3) are dephased; In S2, both the (P1,P2,P3) and (R1,R2,R3) are dephased, in opposite directions. As a result, (S1,S2,S3) form 3 images containing spatially aligned banding with different amplitudes. A weighted summation can be performed to produce an image with minimized banding due to destructive interference. An algorithm based upon regional Gradient Energy Minimization (GEM) [6] was developed to find the appropriate weighting factors automatically.Three sets of bSSFP data with evenly spaced 120∘ phase-cycling were acquired from a phantom containing metal implant on a 1.5T scanner (Siemens Magneton Avanto, Erlangen, Germany). They were processed off line with codes written in C programing language.
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[5] Hoff MN, Andre JB, Xiang QS. Combined Geometric and Algebraic Solutions for Removal of bSSFP Banding Artifacts with Performance Comparisons, Magn Reson Med, First published online : 23 March 2016, DOI: 10.1002/mrm.26150
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