Higher order weighted least-squares phase offset correction for improved accuracy in phase-contrast MRI

INTRODUCTION Phase-contrast magnetic resonance imaging has the ability to accurately measure blood flow and myocardial velocities in the human body. Unwanted spatially varying phase offsets are, however, always present and may deteriorate the measurements significantly. Some of these phase offsets can be estimated based on the pulse sequence (1), but effects caused by eddy currents are more difficult to predict. A linear fit of the phase values is often estimated from either a number of manually defined areas containing stationary tissue or by semi-automatic detection of stationary tissue using the temporal standard deviation in an image sequence (2). With the advent of shorter magnets and the usage of shorter echo times, a linear model is no longer sufficient to describe the phase offset variations. In many applications, e.g. particle trace visualization and assessment of myocardial deformation, it is critical to compensate for the phase offset variations over a large region. In this study we investigate the variation of the phase offset over the complete 3D volume of interest and propose a completely automated correction approach based on a weighed fit of a high order polynomial. METHODS The proposed approach corrects time-resolved 3D velocity fields for phase offset variations using a weighted least-squares fit to the measured velocity data. First, the temporal standard deviation of the velocity, SDv(x,y,z), is calculated for every voxel at location x,y,z. In order to include additional information about the certainty of the estimated phase values, the standard deviation map is combined with magnitude information m(x,y,z,t) as: ( ) ( ) ( ) v z y x SD t z y x m t z y x w , , , , , , , , = ,