Assessment of Reynolds stress components and turbulent pressure loss using 4D flow MRI with extended motion encoding

To measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps.

A method to assess both velocity and Reynolds stress using 4D flow MRI is presented and evaluated. The Reynolds stress is compared by cross-sectional integrals of the Reynolds stress invariants. Pressure maps are computed using the pressure Poisson equation-both including and neglecting the Reynolds stress.

Good agreement is seen for Reynolds stress between computational fluid dynamics, simulated MRI, and MRI experiment. The Reynolds stress can significantly influence the computed pressure loss for simulated (eg, -0.52% vs -15.34% error; P < 0.001) and experimental (eg, 306 ± 11 vs 203 ± 6 Pa; P < 0.001) data. A 54% greater pressure loss is seen at the highest experimental flow rate when accounting for Reynolds stress (P < 0.001).

4D flow MRI with extended motion-encoding enables quantification of both the velocity and the Reynolds stress tensor. The additional information provided by this method improves the assessment of pressure gradients across a stenosis in the presence of turbulence. Unlike conventional methods, which are only valid if the flow is laminar, the proposed method is valid for both laminar and disturbed flow, a common presentation in diseased vessels. Magn Reson Med 79:1962-1971, 2018. © 2017 International Society for Magnetic Resonance in Medicine.