Accuracy of phase-contrast velocimetry in systems with skewed intravoxel velocity distributions

Abstract

Phase contrast velocimetry (PCV) has been widely used to investigate flow properties in numerous systems. Several authors have reported errors in velocity measurements and have speculated on the sources, which have ranged from eddy current effects to acceleration artefacts. An often overlooked assumption in the theory of PCV, which may not be met in complex or unsteady flows, is that the intravoxel displacement distributions (propagators) are symmetric. Here, the effect of the higher moments of the displacement distribution (variance, skewness and kurtosis) on the accuracy of PCV is investigated experimentally and theoretically. Phase and propagator measurements are performed on tailored intravoxel distributions, achieved using a simple phantom combined with a single large voxel. Asymmetric distributions (Skewness ≠ 0) are shown to generate important phase measurement errors that lead to significant velocimetry errors. Simulations of the phase of the spin vector sum, based on experimentally measured propagators, are shown to quantitatively reproduce the relationship between measured phase and experimental parameters. These allow relating the observed velocimetry errors to a discrepancy between the average phase of intravoxel spins considered in PCV theory and the vector phase actually measured by a PFG experiment. A theoretical expression is derived for PCV velocimetry errors as a function of the moments of the displacement distribution. Positively skewed distributions result in an underestimation of the true mean velocity, while negatively skewed distributions result in an overestimation. The magnitude of these errors is shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution.

Impact of turbulence-induced asymmetric propagators on the accuracy of phase-contrast velocimetry

“…These experimental results are consistent with our recent theoretical analysis (27), where we derived an analytic expression for PC-MRI errors that resulted from the higher order moments of the displacement.…”

“…In a previous work (27), we showed analytically how the error in PC-MRI measurements depends upon the higher order moments of the intravoxel displacement distribution. Taking the intravoxel velocity measured by the PC-MRI sequence as…”

“…This assumption is generally valid for simple laminar flows, but is not necessarily valid for complex flows, such as flow through porous media (26). In a recent work, we described theoretically how the higher order moments (variance, skewness, kurtosis, see Figure 1b,c) of the displacement distribution can severely affect the accuracy of PC-MRI (27), causing both under-estimation (positive skewness cases) and over-estimation (negative skewness cases) of the true mean velocity. This type of error depends critically on non-zero skewness, with the magnitude of the error increasing with the both the skewness and variance of the distribution.…”

Segmental differences of cervical spinal cord motion: advancing from confounders to a diagnostic tool

“…Additionally, PC MRI readouts are influenced by a varying, so called “phase drift” 10 , ending in false velocity values, caused by a baseline offset error. Several reasons have been proposed for the observed errors including acceleration artefacts and phase contributions 11 , flow related eddy current effects 12,13 , maxwell gradient effects 14 , voxel size related partial-volume effects 15 , relaxation effects 16 , phase errors during the time between velocity encoding and echo, intravoxel velocity distribution 17 and other non-identified effects 13 . Standardized correction for phase drift is needed as it varies between scanners and different timepoints of measurement 10 and was proposed in diverse ways (phantom measurements 2,5,18 , measurements of static tissue 18 ).…”

Limits to flow detection in phase contrast MRI

“…The limit to flow detection with Eq. (5) is equivalent to the limit associated with taking the mean of the propagator in the case that the propagator is symmetric about the mean displacement [38,62]. Well-known detection limits for phase contrast velocimetry in the fast-flow regime are also provided [19].…”