On the flow separation in the wake of a fixed and a rotating cylinder.

The flow past a circular cylinder under diverse conditions is investigated to examine the nature of the different separation mechanisms that can develop. For a fixed cylinder in a uniform, steady, and horizontal stream, the alternating sheddings of vortices, characterizing the Kármán vortex street, occur from two separation points located in the rear cylinder wall. The prediction of the separation positions and profiles is examined in the light of the most recent theory of unsteady separation in two-dimensional flows. It is found that the separation points are fixed in space and located symmetrically about the horizontal axis passing through the center of the cylinder. The unsteady separation profiles are also well-predicted by the theory. If the cylinder rotates on its axis in the anti-clockwise direction, the upper and lower separation points are shifted in the upstream and the downstream direction, respectively, but are no longer attached to the wall and cannot be predicted by the theory. Instead, they are captured as saddle points in the interior of the flow without any connection to on-wall quantities, as suggested by the Moore-Rott-Sears (MRS) principle. The saddle points are detected through a Lagrangian approach as the location of maximum tangential rate of strain on Lagrangian coherent structures identified as the most attracting lines in the vicinity of the cylinder. If, in addition, the uniform stream is unsteady, the Eulerian saddle points, i.e., detected by streamlines, change position in time, but have no direct relation to the true separation points that are defined by Lagrangian saddle points, thus invalidating the MRS principle that is Eulerian by nature. Other separation mechanisms are also described and understood in view of Lagrangian identification tools.

New equations for the dose under pulsative/periodic conditions in the design of coated stents.

The notion of dose that comes from the biologists has been introduced by Delfour et al. (2005 SIAM J. Appl. Math. 65(3):858-881) in the context of coated stents to control restenosis. Assuming a stationary velocity profile of the blood flow in the lumen, it leads to a time-independent equation for the dose that considerably simplifies the analysis and the design problem. Under stable conditions the blood flow is pulsative, that is the velocity field can be assumed to be periodic. So it is necessary to justify the replacement of the periodic field by its time average over the pulsation period. In this paper, firstly we introduce the new unfolded dose and its equations without a priori constraint on the size of the period. So it can be used in biochemical problems where the period is large compared to the time constants of the system. Secondly, we show that, as the period goes to zero, the velocity field can be replaced by its average over the period. Numerical tests on a one-dimensional example are included to illustrate the theory.

Structure of large arteries: orientation of elastin in rabbit aortic internal elastic lamina and in the elastic lamellae of aortic media.

This study was designed to further our understanding of the elastic ultrastructure of vessels. Scanning electron microscopy and transmission electron microscopy were used to study the histomorphologic properties of the elastic fibers of rabbit aorta after purification of the elastin by means of hot alkaline treatments. The elastic fibers of whole rabbit aorta samples were also studied using confocal microscopy. Morphological assessment revealed that the elastin fibers contained in the elastic lamellae of media are perpendicular to the blood flow, and that the elastic fibers of the internal elastic lamina are parallel to the luminal flow. In conclusion, the structure of the elastin making up the elastic lamellae of the media is oriented in such a way as to sustain the circumferential mechanical stress of pulsation. By contrast, the structure of the elastin fibers that make up the internal elastic lamina provides little mechanical support for the circumferential tension, but can support longitudinal loading and act as a fenestrated membrane.

Mechanical hemolysis in blood flow: user-independent predictions with the solution of a partial differential equation.

This paper presents for the first time numerical predictions of mechanical blood hemolysis obtained by solving a hyperbolic partial differential equation (PDE) modelling the hemolysis in a Eulerian frame of reference. This provides hemolysis predictions over the entire computational domain as an alternative to the Lagrangian approach consisting in evaluating cell hemolysis along their trajectories. The solution of a PDE over a computational domain, such as in the approach presented herein, yields a unique solution. This is a clear advantage over the Lagrangian approach, which requires the human-made choice of a limited number of trajectories for integration and inevitably results in the incomplete coverage of the computational domain. The hyperbolic hemolysis model is solved with a Discontinuous Galerkin finite element method. The solution algorithm also includes adaptive remeshing to provide high accuracy simulations. Predictions of the modified index of hemolysis (MIH) are presented for flows in dialysis cannulae and sudden contractions. MIH predictions for cannulae differ significantly from those obtained by other authors using the Lagrangian approach. The predictions for flows in sudden contractions are used, along with our own experimental measurements, to assess the value of the threshold shear stress required for hemolysis that is included in the hemolysis model.

Asymptotically consistent numerical approximation of hemolysis.

In a previous communication, we have proposed a numerical framework for the prediction of in vitro hemolysis indices in the preselection and optimization of medical devices. This numerical methodology is based on a novel interpretation of Giersiepen-Wurzinger blood damage correlation as a volume integration of a damage function over the computational domain. We now propose an improvement of this approach based on a hyperbolic equation of blood damage that is asymptotically consistent. Consequently, while the proposed correction has yet to be proven experimentally, it has the potential to numerically predict more realistic red blood cell destruction in the case of in vitro experiments. We also investigate the appropriate computation of the shear stress scalar of the damage fraction model. Finally, we assess the validity of this consistent approach with an analytical example and with some 3D examples.

Hemodynamic characteristics of a mixed flow pump prototype: progress report of in vitro and acute animal experiments.

A new dual-inlet mixed-flow blood pump was designed and tested in our laboratory. The objective of the present study was to analyze hemodynamic characteristics of the pump prototype in vitro and during acute in vivo experiments. The mixed-flow pump was first tested in vitro and then implanted in 11 pigs and 3 calves. The left ventricular apex was cannulated with the pump and an outflow graft was anastomosed to the descending thoracic aorta. Flow and pressure probes were also implanted. Animals were killed 3 to 12 hours after surgery. In 11 pigs, pump outflow averaged 3.8 +/- 0.4, 4.5 +/- 0.4, 5.2 +/- 0.8, 5.9 +/- 0.3, and 6.5 l/min at 8,000, 9,000, 10,000, 11,000, and 12,000 pump speed in rpm. Differential pressure at the pump averaged 45 +/- 6, 54 +/- 8, 68 +/- 16, 70 +/- 12, and 85 +/- 7 mm Hg at 8,000, 9,000, 10,000, 11,000 and 12,000 rpm. Mean aortic pressure averaged 64 +/- 15 mm Hg throughout the procedures. In 3 calves, mean aortic pressure and left ventricular pressure remained stable during 4, 6, and 9 hours of support at 9,500, 10,000, 10,500, 11,000, and 11,500 rpm. The hemodynamic performance of our mixed-flow pump appears satisfactory during short-term support in animals. It supports similarly to axial-flow blood pumps in clinical trials. Based on these findings, an ameliorated design of this mixed-flow pump running at smaller rotational speed against a similar pressure head is under way.

Fast three-dimensional numerical hemolysis approximation.

The in vivo implantation of a mechanical device contributes to hemodynamic disturbances, which are responsible for damage to the membranes of red blood cells that in turn can lead to their rupture (hemolysis). It is important to ascertain at the design stage of such mechanical devices that they are innocuous to blood. Because there is no in vivo hemolysis index, we concentrated our efforts on the in vitro hemolysis index of the American Society for Testing and Material (ASTM) standard. We present in this work a framework for minimizing medical device-induced hemolysis by the development of a numerical method for predicting hemolysis similar to that used in in vitro experiments. The method is based on a novel interpretation of the Giersiepen-Wurzinger blood damage correlation that replaces the computation of blood damage along the streamline by a volume integration of a damage function over the computational domain. We assess the behavior and accuracy of this methodology with 3D examples.