Analysis of encoding efficiency in MR imaging of velocity magnitude and direction

The efficiency of balanced versus unbalanced techniques for phase-angle-based velocity magnitude and direction imaging is investigated. Methods having balanced flow-encoding gradients (gradients in positive and negative directions with a zero center of gravity) are compared with unbalanced methods. For three-dimensional imaging, a currently used balanced method is the six-point technique having opposed gradients pairs for each orthogonal direction. A currently used unbalanced method is a four-point null technique which has three orthogonal gradients and an additional acquisition having no specific flow encoding to correct the baseline (null) phase. In the gradient-limited case of slow flow and perfusion, the balanced method is predicted to have higher velocity magnitude-to-noise ratio per time (SNRV) by a factor of 1.63, with similar results for velocity direction. In the wraparound-limited case of faster flows and motions, similar results are found when a null acquisition is added to the balanced method. This results in a seven-point balanced method having an SNRV 1.51 times that of the four-point unbalanced method. If null phases are within the [-pi/2,pi/2] interval, this additional null acquisition is unnecessary. Other four-point methods are also considered. These results indicate that, in general, balanced methods have advantages over unbalanced methods for velocity imaging.