▪ Abstract The relationship between flow in the arteries, particularly the wall shear stresses, and the sites where atherosclerosis develops has motivated much of the research on arterial flow in recent decades. It is now well accepted that it is sites where shear stresses are low, or change rapidly in time or space, that are most vulnerable. These conditions are likely to prevail at places where the vessel is curved; bifurcates; has a junction, a side branch, or other sudden change in flow geometry; and when the flow is unsteady. These flows, often but not always involving flow separation or secondary motions, are also the most difficult ones in fluid mechanics to analyze or compute. In this article we review the modeling studies and experiments on steady and unsteady, two-and three-dimensional flows in arteries, and in arterial geometries most relevant in the context of atherosclerosis. These include studies of normal vessels—to identify, on the basis of the fluid mechanics, lesion foci—and stenotic ves...

Flows in Stenotic Vessels

The mechanics of blood flow in arteries plays a key role in the health of individuals. In this framework, the role played by the presence of helical flow in the human aorta is still not clear in its relation to physiology and pathology. We report here a method for quantifying helical flow in vivo employing time-resolved cine phase contrast magnetic resonance imaging to obtain the complete spatio-temporal description of the three-dimensional pulsatile blood flow patterns in aorta. The method is applied to data of one healthy volunteer. Particle traces were calculated from velocity data: to them we applied a Lagrangian-based method for helical flow quantification, the Helical Flow Index, which has been developed and evaluated in silico in order to reveal global organization of blood flow. Our results: (i) put in evidence that the systolic hemodynamics in aorta is characterized by an evolving helical flow (we quantified a 24% difference in terms of the content of helicity in the streaming blood, between mid and early systole); (ii) indicate that in the first part of the systole helicity is ascrivable mainly to the asymmetry of blood flow in the left ventricle, joined with the laterality of the aorta. In conclusion, this study shows that the quantification of helical blood flow in vivo is feasible, and it might allow detection of anomalies in the expected physiological development of helical flow in aorta and accordingly, could be used in a diagnostic/prognostic index for clinical practice.

In Vivo Quantification of Helical Blood Flow in Human Aorta by Time-Resolved Three-Dimensional Cine Phase Contrast Magnetic Resonance Imaging

Mapping of blood velocities across the lumen of the ascending aorta was performed in eight patients during open-heart surgery. A Doppler ultrasound probe was constructed to measure velocities in 2 mm steps from the maximum convexity to the maximum concavity of aorta, 6 to 7 cm above the aortic valve. In five patients with angina and normal aortic valves, velocity profiles were very similar and showed the following main features: a skewed peak systolic velocity profile with the highest velocity along the left posterior wall, a bidirectional velocity profile in late systole and early diastole with retrograde velocities along the left posterior wall, and a sustained antegrade flow along the convexity well into diastole. The resultant mean velocity profile had the highest velocity at the convex side and a central minimum velocity. In patients with Medtronic-Hall tilting disc prostheses, where the larger opening was oriented backwards and to the right, mean flow velocity profile was skewed in the opposite direction of normal. Moreover, instant systolic velocity profiles were much more irregular and dependent on the exact orientation of the prosthesis. In one patient with aortic valvular disease, very irregular and different velocity profiles were found. Based on a symmetry assumption, overall mean velocity for the total cross section was computed, and the magnitude of error in estimation of total flow from measurement of velocities at different depths was calculated. To measure total flow in the aorta, i.e., cardiac output, by single-gated Doppler technique, the most representative sampling site was about one-third of the diameter from the convex wall.

Blood velocity distribution in the human ascending aorta.

In this paper, an experimental determination of the three-dimensional velocity distribution due to the physiological pulsatile flow of a Newtonian, incompressible fluid at various locations in a curved tube of circular cross-section is presented. Our results show four interesting features of the pulsatile flow development in the curved tube. First is the presence of a reversed flow along the inner wall of the tube during the diastolic (deceleration) phase of the pulsatile flow cycle. Second is that the flow does not appear to be fully developed in the curved tube through the cross-section whose L/a ratio is equal to 16·9, the final location at which measurements were made in this study, where L is the axial length and a is the radius of the curved tube. A third feature observed is the vacillation of the peak axial velocity across the horizontal diameter of the tube from the upstream to the downstream region in the curved tube. In the upstream region (L/a = 3·4), the maximum axial velocity measured occurred nearest to the outer wall. The maximum axial velocity shifted towards the inner wall in the middle of the tube (L/a = 10·2), while in the downstream region (L/a = 16·9), the maximum axial velocity measured was again near the outer wall. Finally, trapped vortical motions are observed to occur at the inner wall of the tube in the downstream region.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112081002292

K.B. Chandran

Papers

An experimental study of pulsatile flow in a curved tube