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

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

Phase-contrast magnetic resonance velocimetry (PC-MRI) has been widely used to investigate flow properties in numerous systems. In a horizontal cylindrical pipe (3 mm diameter), we investigated the accuracy of PC-MRI as the flow transitioned from laminar to turbulent flow (Reynolds number 352-2708). We focus primarily on velocimetry errors introduced by skewed intra-voxel displacement distributions, a consequence of PC-MRI theory assuming symmetric distributions. We demonstrated how rapid fluctuations in the velocity field, can produce broad asymmetric intravoxel displacement distributions near the wall. Depending on the shape of the distribution, this resulted in PC-MRI measurements under-estimating (positive skewness) or over-estimating (negative skewness) the true mean intravoxel velocity, which could have particular importance to clinical wall shear stress measurements. The magnitude of these velocity errors was shown to increase with the variance and decrease with the kurtosis of the intravoxel displacement distribution. These experimental results confirm our previous theoretical analysis, which gives a relationship for PC-MRI velocimetry errors, as a function of the higher moments of the intravoxel displacement distribution (skewness, variance, and kurtosis) and the experimental parameters q and Δ. This suggests that PC-MRI errors in such unsteady/turbulent flow conditions can potentially be reduced by employing lower q values or shorter observation times Δ.

Limits to flow detection in phase contrast MRI

Pulsed gradient spin echo (PGSE) complex signal behavior becomes dominated by attenuation rather than oscillation when displacements due to flow are similar or less than diffusive displacements. In this "slow-flow" regime, the optimal displacement encoding parameter q for phase contrast velocimetry depends on the diffusive length scale q s l o w = 1 / l D = 1 / 2 D Δ rather than the velocity encoding parameter v _enc = π/(qΔ). The minimum detectable mean velocity using the difference between the phase at +q _slow and -q _slow is 〈 v m i n 〉 = 1 / SNR D / Δ . These theories are then validated and applied to MRI by performing PGSE echo planar imaging experiments on water flowing through a column with a bulk region and a beadpack region at controlled flow rates. Velocities as slow as 6 μm/s are detected with velocimetry. Theories, MRI experimental protocols, and validation on a controlled phantom help to bridge the gap between porous media NMR and pre-clinical phase contrast and diffusion MRI.

MR-based wall shear stress measurements in fully developed turbulent flow using the Clauser plot method

In arterial blood flow wall shear stress (WSS) quantifies the frictional force that flowing blood exerts on a vessel wall. WSS can be directly estimated from phase-contrast (PC) MR velocity measurements and has been suggested as a biomarker in cardio-vascular diseases. We present and investigate the application of the Clauser plot method for estimating WSS in fully developed turbulent stationary flow using PC velocity measurements. The Clauser plot method estimates WSS from the logarithmic region of boundary layer in fully developed turbulent stationary flow. The Clauser plot method was evaluated using 2D PC-MR phantom measurements at 3 T for different in-plane resolutions at various Reynolds numbers. WSS values derived from the Clauser plot were compared to results from Laser Doppler Velocimetry (LDV) measurements and theoretical results calculated using the friction factor formula for smooth pipe flow. For all Reynolds numbers, WSS values derived from the Clauser plot were in good agreement with results from LDV measurements and values using the friction factor formula (relative deviations ∼5%). Furthermore, Clauser plot derived results were almost independent of spatial resolution, in contrast to WSS results obtained with our in-house software tool for MR-based WSS quantification showing relative deviations of more than 100%. In fully developed turbulent flow, the Clauser plot method provides highly consistent WSS independent of the underlying spatial resolution. Therefore, it renders a valuable approach for MR-based WSS estimates in controllable flow settings. Although its direct in vivo applicability is severely limited because of the different flow character, it may serve as helpful approach for validation of MR-based WSS quantification algorithms prior to their clinical application.

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

Increased cranio-caudal spinal cord motion is associated with clinical impairment in degenerative cervical myelopathy. However, whether spinal cord motion holds potential as a neuroimaging biomarker requires further validation. Different confounders (i.e. subject characteristics, methodological problems such as phase drift, etc.) on spinal cord motion readouts have to be considered. Twenty-two healthy subjects underwent phase contrast MRI, a subset of subjects (N = 9) had repeated scans. Parameters of interest included amplitude of velocity signal, maximum cranial respectively maximum caudal velocity, displacement (=area under curve of the velocity signal). The cervical spinal cord showed pulse synchronic oscillatory motions with significant differences in all readouts across cervical segments, with a maximum at C5. The Inter-rater reliability was excellent for all readouts. The test-retest reliability was excellent for all parameters at C2 to C6, but not for maximum cranial velocity at C6 and all readouts at C7. Spinal cord motion was correlated with spinal canal size, heart rate and body size. This is the first study to propose a standardized MRI measurement of spinal cord motion for further clinical implementation based on satisfactory phase drift correction and excellent reliability. Understanding the influence of confounders (e.g. structural conditions of the spine) is essential for introducing cord motion into the diagnostic work up.