Quantifying errors in flow measurement using phase contrast magnetic resonance imaging: comparison of several boundary detection methods

Quantifying flow from phase-contrast MRI (PC-MRI) data requires that the vessels of interest be segmented. The estimate of the vessel area will dictate the type and magnitude of the error sources that affect the flow measurement. These sources of errors are well understood, and mathematical expressions have been derived for them in previous work. However, these expressions contain many parameters that render them difficult to use for making practical error estimates. In this work, some realistic assumptions were made that allow for the simplification of such expressions in order to make them more useful. These simplified expressions were then used to numerically simulate the effect of segmentation accuracy and provide some criteria that if met, would keep errors in flow quantification below 10% or 5%. Four different segmentation methods were used on simulated and phantom MRA data to verify the theoretical results. Numerical simulations showed that including partial volumed edge pixels in vessel segmentation provides less error than missing them. This was verified with MRA simulations, as the best performing segmentation method generally included such pixels. Further, it was found that to obtain a flow error of less than 10% (5%), the vessel should be at least 4 (5) pixels in diameter, have an SNR of at least 10:1 and have a peak velocity to saturation cut-off velocity ratio of at least 5:3.