Chaotic advection in blood flow

In this paper we argue that the effects of irregular chaotic motion of particles transported by blood can play a major role in the development of serious circulatory diseases. Vessel wall irregularities modify the flow field, changing in a nontrivial way the transport and activation of biochemically active particles. We argue that blood particle transport is often chaotic in realistic physiological conditions. We also argue that this chaotic behavior of the flow has crucial consequences for the dynamics of important processes in the blood, such as the activation of platelets which are involved in the thrombus formation.

Figure 1

Model of the inflow velocity in case of (a) coronary artery and (b) abdominal aorta during one heartbeat cycle. The arrows point to time instances when the streamlines are shown in Figs. 2, 3.

Figure 2

Snapshots of the streamlines of the blood flow in the 2D model of an obstructed coronary artery. The narrowed wall segment is of sinusoidal shape in the model. The time instances of snapshots are shown with arrows in Fig. 1a. The Reynolds number is 100, with peak value 200 during the cardiac cycle.

Figure 3

Snapshots of the streamlines of the blood flow in the 2D model of an aorta with aneurysm. The bulge has a sinusoidal shape in the model. The time instances of snapshots are shown with arrows in Fig. 1b. The Reynolds number is 1600, with peak value 2200 (close to turbulent threshold of around 2300) during the cardiac cycle.

Figure 4

Snapshots of the unstable foliation of blood flow in the stenosed coronary artery.

Figure 5

Snapshots of the unstable foliation of blood flow in the aorta with aneurysm.

Figure 6

(Color online) Time spent in the region of observation as a function of the initial position. Lighter colors indicate long residence time, up to 100 heartbeat cycles.

Figure 7

Residence time of particles started from the $x=9\text{cm}$ line in the region of observation before reaching the $x=13\text{cm}$ line as a function of the initial position in exercise conditions. Residence time is measured in heartbeats as time units.