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

Abstract

Purpose: To measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps. Methods: 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. Result: 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). Conclusion: 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.