Characterization of Coherent Structures in the Cardiovascular System
- 583 Downloads
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.
KeywordsHemodynamics Computational fluid dynamics Biofluid mechanics Finite-time Lyapunov exponents Lagrangian coherent structures
The authors would like to sincerely thank Alison Marsden and Adam Bernstein for the TCPC velocity data and Andrea Les for the patient-specific AAA velocity data. The authors gratefully acknowledge the use of the AcuSolve linear algebra package (http://www.acusim.com) and the MeshSim automatic mesh generator (http://www.simmetrix.com). S. Shadden was supported by an NSF Mathematical Sciences Postdoctoral Research Fellowship. This work was also supported by the National Institutes of Health (P50 HL083800, U54 GM072970) and the National Science Foundation under Grant No. 0205741.
- 1.R. J. Adrian. Particle imaging techniques for experimental fluid mechanics. Annual Review of Fluid Mechanics, 23:261–304, 1991.Google Scholar
- 5.Fehlberg, E. Low-order classical Runge-Kutta formulas with step size control and their application to some heat transfer problems. NASA Technical Report, 315, 1969.Google Scholar
- 13.S. Laurent, J. Cockcroft, L. Van Bortel, P. Boutouyrie, C. Giannattasio, D. Hayoz, B. Pannier, C. Vlachopoulos, I. Wilkinson, and H. Struijker-Boudier. Expert consensus document on arterial stiffness: Methodological issues and clinical applications. European Heart Journal, 27(21):2588–2605, 2006.PubMedCrossRefGoogle Scholar
- 16.Marsden, A. L., A. Bernstein, V. M. Reddy, S. C. Shadden, R. L. Spilker, F. P. Chan, C. A. Taylor, and J. A. Feinstein. Evaluation of a novel Y-shaped extracardiac Fontan baffle using computational fluid dynamics. J. Thorac. Cardiovasc. Surg. (submitted)Google Scholar
- 20.J. M. Ottino. The kinematics of mixing: Stretching, chaos, and transport. Cambridge University Press, New York, 1989.Google Scholar
- 23.Sahni, O., J. Muller, K. E. Jansen, M. S. Shephard, and C. A. Taylor. Efficient anisotropic adaptive discretization of the cardiovascular system. Comput. Methods Appl. Mech. Eng. 195(41–43):5634–5655, 2006.Google Scholar
- 25.Shadden, S. C. A dynamical systems approach to unsteady systems. PhD thesis, California Institute of Technology, 2006.Google Scholar
- 36.Wang, K. C. On the current controversy about unsteady separation. In: Numerical and Physical Aspects of Aerodynamic Flows, edited by T. Cebeci. Springer, 1982.Google Scholar
- 40.N. Wilson, F. R. Arko, and C. A. Taylor. Patient-specific operative planning for aorto-femoral reconstruction procedures. Lecture Notes in Computer Science, 3217:422–429, 2004.Google Scholar