Numerical analysis of flow through a severely stenotic carotid artery bifurcation

A turbulence model for pulsatile arterial flows

Difficulties in predicting the behavior of some high Reynolds number flows in the circulatory system stem in part from the severe requirements placed on the turbulence model chosen to close the time-averaged equations of fluid motion. In particular, the successful turbulence model is required to (a) correctly capture the "nonequilibrium" effects wrought by the interactions of the organized mean-flow unsteadiness with the random turbulence, (b) correctly reproduce the effects of the laminar-turbulent transitional behavior that occurs at various phases of the cardiac cycle, and (c) yield good predictions of the near-wall flow behavior in conditions where the universal logarithmic law of the wall is known to be not valid. These requirements are not immediately met by standard models of turbulence that have been developed largely with reference to data from steady, fully turbulent flows in approximate local equilibrium. The purpose of this paper is to report on the development of a turbulence model suited for use in arterial flows. The model is of the two-equation eddy-viscosity variety with dependent variables that are zero-valued at a solid wall and vary linearly with distance from it. The effects of transition are introduced by coupling this model to the local value of the intermittency and obtaining the latter from the solution of a modeled transport equation. Comparisons with measurements obtained in oscillatory transitional flows in circular tubes show that the model produces substantial improvements over existing closures. Further pulsatile-flow predictions, driven by a mean-flow wave form obtained in a diseased human carotid artery, indicate that the intermittency-modified model yields much reduced levels of wall shear stress compared to the original, unmodified model. This result, which is attributed to the rapid growth in the thickness of the viscous sublayer arising from the severe acceleration of systole, argues in favor of the use of the model for the prediction of arterial flows.

MRI and CFD studies of pulsatile flow in healthy and stenosed carotid bifurcation models

Pulsatile flow was studied in physiologically realistic models of a normal and a moderately stenosed (30% diameter reduction) human carotid bifurcation. Time-resolved velocity measurements were made using magnetic resonance imaging, from which wall shear stress (WSS) vectors were calculated. Velocity measurements in the inflow and outflow regions were also used as boundary conditions for a computational fluid dynamics (CFD) model. Experimental flow patterns and derived WSS vectors were compared qualitatively with the corresponding CFD predictions. In the stenosed phantom, flow in the bulb region of the "internal carotid artery" was concentrated along the outer wall, with a region of low and recirculating flow near the inner wall. In the normal phantom, the converse was found, with a low flow region near the outer wall of the bulb. Time-averaged WSS and oscillatory shear index were also markedly different for the two phantoms.

Lattice Boltzmann simulation on particle suspensions in a two-dimensional symmetric stenotic artery

The technique of lattice Boltzmann simulation has been applied to the study of two-dimensional particle suspensions through a modeled arterial stenosis. The stenosis model consists of two-side symmetric semicirculars in a planar channel with the width of the stenosis throat larger than d and less than 2d, where d is the diameter of the particles. When only one particle is positioned off-centerline initially, the particle migrates off-centerline after passing the stenosis and the velocity at the stenosis throat is much larger than that in a flat tube. Only when two particles are positioned symmetrically to the centerline to a very high accuracy can the flow be blocked by two particles completely. A very small asymmetry will be amplified proximal to the stenosis throat in that one of the particles goes back to leave space to let the other particle passing the stenosis first so that the particles cannot be blocked. An evidence of attractive interactions between the particles as well as a particle and a proximal protuberance is observed when the asymmetry is very small and the width at the stenosis throat is between two critical values. The hematocrit distribution of the particles is studied by simulating multiparticle suspensions. It is found that the width of the stenosis throat has a significant influence on the hematocrit distribution of the particles in the flat tubes far from the stenosis.

Site of carotid plaque ulceration in relation to direction of blood flow: an angiographic and pathological study

BACKGROUND

Rupture of atherosclerotic plaque is the main cause of acute coronary syndromes and carotid territory ischaemic stroke. Haemodynamic stress is important in early plaque formation and may affect the stability of mature plaques. There is some evidence that macrophage infiltration and plaque rupture tend to localise to the proximal (upstream) part of the plaque where shear stress is highest. However, previous studies have been too small to assess this reliably. We studied the site of ulceration in a large number of carotid plaques.

METHODS

We studied angiograms of 3007 symptomatic carotid stenoses, and the pathological appearance of 119 carotid plaques (77 asymptomatic), to identify the presence and position of plaque ulceration.

RESULTS

Angiographic ulceration, which was present in 421 patients (14%), was more likely to be PROXIMAL than DISTAL to the point of maximum stenosis (OR = 16.6, 95% CI = 11.6-26.9, p < 0.001). This trend increased with severity of stenosis (p = 0.002). Pathological examination of the 119 carotid plaques also showed that ulceration was more likely to occur proximal to the point of maximum stenosis (OR = 6.1, 95% CI = 2.8-13.6, p < 0.001).

CONCLUSIONS

Ulceration of carotid plaques, visible on angiography or on pathological examination, is seen most often in the proximal (upstream) part where shear stress is highest.

Experimental flow studies in exact-replica phantoms of atherosclerotic carotid bifurcations under steady input conditions

Extensive flow studies are conducted in two carotid bifurcation flow phantoms. These phantoms exactly replicate the lumen of the plaque excised intact from two patients with severe carotid atherosclerosis. The input flow into the phantom's common carotid artery is steady. Novel scanning techniques for flow visualization and particle image velocimetry are used. In addition, a novel boundary treatment technique is employed in velocimetry to extract first order accurate velocity gradients at walls. The data show that the flow fields are highly three-dimensional. Numerous separation and recirculation zones dominate the flow domain, except at the lowest Reynolds numbers. The separation regions are often so severe that highly directed internal jets form. At high Reynolds numbers, the flows become unsteady and chaotic, even though the input flow is steady. Flow fields have large regions of energetic flow and almost stagnant recirculation zones. These recirculation zones range in size from the full size of the arteries to zones within crevasses smaller than 1 mm. Velocity field and streamline patterns conform well to the lumen geometry. The streamlines are highly tortuous. Stagnation points correlate well with the topological features of the stenosis. Vorticity maps confirm the highly complex and three dimensional nature of the flow. Wall shear stresses at the stenoses are estimated to be on the order of 10 Pa. These studies conclusively show that the nature of the flow in the diseased bifurcation is primarily dictated by the lumen geometry.