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A New Phase-based Algorithm for Fast and Accurate Motion Extraction from Navigator Echoes in Magnetic Resonance Angiography

Introduction Navigator echo is an effective technique to suppress respiratory and cardiac motion in MR angiography. Ahn and Cho's (AC) algorithm extracts the displacement from the navigator phase. Although computationally efficient, it is susceptible to noise, particularly contributions from points at the edges of k-space. We proposed a kspace weighted least-squares (KWLS) algorithm that is as efficient as AC algorithm but more robust against noise Methods The new algorithm is based on linear regression of the k-space navigator phase data. The noise in the MR phase varies according to the inverse of k-space signal-to-noise ratio (SNR). Consequently, the contribution to the linear fit of phase shift is weighted by the SNR of each point, which is high at the k-space center and low at the edges of k-space. Pencil-beam navigator data acquired on a computer-controlled motion phantom (sinusoidal motion with peak-to-peak amplitude of 4cm and period of 4sec) was used to evaluate the accuracy and computational efficiency of the proposed technique against the AC algorithm. The same algorithms were then applied to data from the diaphragm of a human volunteer to detect respiratory motion. In this case true motion is unknown, so an accurate but less efficient imagespace least-squares fitting algorithm was used to provide the standard for comparison. Finally, displacement information obtained with AC and KWLS algorithms were used to correct motion effects on the motion phantom. Results Fig.1 shows the navigator records acquired on the motion phantom (left) and the diaphragm of a volunteer (right). The corresponding displacements obtained using AC and KWLS algorithms are illustrated in Fig.2. The average CPU times to process a 256-point phantom navigator echo on a Sun Ultra2 computer were 0.53msec for AC and 0.57msec for KWLS (similar time). The absolute errors averaged over 256 echoes were 2mm for AC and 0.5mm for KWLS (4 times error reduction, Fig.2)). The errors in peak-to-peak motion amplitudes averaged over 10 cycles of the sinusoid were 5.5mm for AC and 1.3mm for KWLS (4 times reduction, Fig.2). Motion waveform extracted from diaphragm navigator data by KWLS was also more accurate than that obtained by AC: the average absolute errors were 2 mm for AC and 0.8 mm for KWLS (2.5 times reduction, Fig.3). The effectiveness of motion correction using displacement data obtained with AC and KWLS algorithms is demonstrated in Fig.3. Without motion correction, the image shows a substantial amount of ghosting and blurring (Fig.4, left). These artifacts are suppressed considerably with motion correction: the KWLS algorithm (Fig.4, right) provides a better motion suppression compared to the AC algorithm (Fig.4, middle). Discussion The proposed k-space weighted least-squares motion extraction algorithm is as fast as but more accurate than AC algorithm. This KWLS is also advantageous over image-space magnitude-based algorithms in terms of computational speed. Phase-based motion extraction methods are based on the assumption that a rigid motion is encompassed by the FOV (Fig.1, left, phantom). In practice, only part of the FOV undergoes motion (Fig.1, right, diaphragm). Even in this case, KWLS algorithm provides more accurate motion estimates than AC algorithm. References 1. Ahn CB, Cho ZH. IEEE TMI 6:32, 1987. Fig.1. Navigator records acquired from the motion phantom (left) and the diaphragm of a human volunteer (right).