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

PurposeTo measure the Reynolds stress tensor using 4D flow MRI, and to evaluate its contribution to computed pressure maps. MethodsA 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 equationboth including and neglecting the Reynolds stress. ResultGood 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; Pamp;lt;0.001) and experimental (eg, 30611 vs 203 +/- 6 Pa; Pamp;lt;0.001) data. A 54% greater pressure loss is seen at the highest experimental flow rate when accounting for Reynolds stress (Pamp;lt;0.001). Conclusion4D 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. (c) 2017 International Society for Magnetic Resonance in Medicine. Funding Agencies|European Union [310612]; National Institutes of Health [HL114118, NS059944]