On Coupling a Lumped Parameter Heart Model and a Three-Dimensional Finite Element Aorta Model
- 2.1k Downloads
Aortic flow and pressure result from the interactions between the heart and arterial system. In this work, we considered these interactions by utilizing a lumped parameter heart model as an inflow boundary condition for three-dimensional finite element simulations of aortic blood flow and vessel wall dynamics. The ventricular pressure–volume behavior of the lumped parameter heart model is approximated using a time varying elastance function scaled from a normalized elastance function. When the aortic valve is open, the coupled multidomain method is used to strongly couple the lumped parameter heart model and three-dimensional arterial models and compute ventricular volume, ventricular pressure, aortic flow, and aortic pressure. The shape of the velocity profiles of the inlet boundary and the outlet boundaries that experience retrograde flow are constrained to achieve a robust algorithm. When the aortic valve is closed, the inflow boundary condition is switched to a zero velocity Dirichlet condition. With this method, we obtain physiologically realistic aortic flow and pressure waveforms. We demonstrate this method in a patient-specific model of a normal human thoracic aorta under rest and exercise conditions and an aortic coarctation model under pre- and post-interventions.
KeywordsBlood flow Time varying elastance function Coupled multidomain method
Hyun Jin Kim was supported by a Stanford Graduate Fellowship. This material is based upon work supported by the National Science Foundation under Grant No. 0205741. The authors gratefully acknowledge Dr. Nathan M. Wilson for assistance with software development. The authors gratefully acknowledge Dr. Farzin Shakib for the use of his linear algebra package AcuSolveTM (http://www.acusim.com) and the support of Simmetrix, Inc for the use of the MeshSimTM (http://www.simmetrix.com) mesh generator.
- 11.Kerckhoffs, R. C. P., M. L. Neal, Q. Gu, J. B. Bassingthwaighte, J. H. Omens, and A. D. McCulloch. Coupling of a 3D finite element model of cardiac ventricular mechanics to lumped systems models of the systemic and pulmonic circulation. Ann. Biomed. Eng. 35(1):1–18, 2007.PubMedCrossRefGoogle Scholar
- 12.Kim, H. J., C. A. Figueroa, T. J. R. Hughes, K. E. Jansen, and C. A. Taylor. Augmented lagrangian method for constraining the shape of velocity profiles at outlet boundaries for three-dimensional finite element simulations of blood flow. Comput. Methods Appl. Mech. Eng. (in press). doi: 10.1016/j.cma.2009.02.012
- 13.Kirklin, J. W., and B. G. Barratt-Boyes. Cardiac Surgery: Morphology, Diagnostic Criteria, Natural History, Techniques, Results, and Indications, 2nd edition. New York: W.B. Saunders, 1993.Google Scholar
- 17.Ottesen, J. T., M. S. Olufsen, and J. K. Larsen. Applied Mathematical Models in Human Physiology. SIAM Monographs on Mathematical Modeling and Computation. Philadelphia: SIAM, 2004.Google Scholar
- 27.Stergiopulos, N., P. Segers, and N. Westerhof. Use of pulse pressure method for estimating total arterial compliance in vivo. Am. J. Physiol. Heart Circ. Physiol. 276(2):H424–H428, 1999.Google Scholar
- 30.Tang, B. T., C. P. Cheng, M. T. Draney, N. M. Wilson, P. S. Tsao, R. J. Herfkens, and C. A. Taylor. Abdominal aortic hemodynamics in young healthy adults at rest and during lower limb exercise: quantification using image-based computer modeling. Am. J. Physiol. Heart Circ. Physiol. 291(2):H668–H676, 2006.PubMedCrossRefGoogle Scholar