Characterization of coherent structures in the cardiovascular system

Abstract

Recent advances in blood flow modeling have provided highly resolved, four-dimensional data of fluid mechanics in large vessels. The motivation for such modeling is often to better understand how flow conditions relate to health and disease, or to evaluate interventions that affect, or are affected by, blood flow mechanics. Vessel geometry and the pulsatile pumping of blood leads to complex flow, which is often difficult to characterize. This article discusses a computational method to better characterize blood flow kinematics. In particular, we compute Lagrangian coherent structures (LCS) to study flow in large vessels. We demonstrate that LCS can be used to characterize flow stagnation, flow separation, partitioning of fluid to downstream vasculature, and mechanisms governing stirring and mixing in vascular models. This perspective allows valuable understanding of flow features in large vessels beyond methods traditionally considered.

Figure 1

Evolution of attracting LCS in the carotid sinus over the cardiac cycle. This LCS captures the unsteady separation profile in the carotid sinus providing a clear, geometric representation of the separation.

Figure 2

Idealized AAA geometry and inflow waveform. The period of the cardiac cycle is 0.952 s.

Figure 3

Evolution of attracting LCS inside idealized AAA over the cardiac cycle.

Figure 4

Evolution of repelling LCS inside idealized AAA over the cardiac cycle.

Figure 5

Cross-sectional view of FTLE and residence time fields during mid-diastole.

Figure 6

Patient-specific AAA model and input supraceliac flow rate.

Figure 7

(Left) Cross-section of 3D FTLE field in the aneurysm. Cross-section taken at location of dotted-lines in Fig. 6. The integration time used to compute the FTLE was equal to one cardiac cycle. (Right) Residence time at planar section where FTLE is shown. Color map is specified in seconds.

Figure 8

(Left) Close up of FTLE field showing extracted LCS. (Right) Close up of residence time plot with extracted LCS. The LCS correspond closely to the boundaries between stagnant flow and flow that is quickly flushed from the AAA.

Figure 9

Model of total cavopulmonary connection. Plots shown in Fig. 10 correspond to location of shaded plane shown near the inlet of the IVC.

Figure 10

Cross-section of the FTLE field near the inlet of the IVC reveals an LCS that partition the IVC flow between the right pulmonary arteries (dashed region) and left pulmonary arteries (slanted lines) at two points in the respiratory cycle. Note, in this simulation IVC flow is periodic with the respiratory, not cardiac, cycle.