American Institute of Mathematical Sciences

2011, 8(3): 785-806. doi: 10.3934/mbe.2011.8.785

Numerical characterization of hemodynamics conditions near aortic valve after implantation of left ventricular assist device

 1 Department of Mathematics, University of Houston 4800 Calhoun Rd, Houston (TX) 77204, United States 2 Department of Mathematics, University of Houston, 4800 Calhoun Rd, Houston, TX 77204, United States 3 Department of Cardiology, Texas Heart Institute at St. Lukes Episcopal Hospital, and Mickael E Debakey VA Medical Center, 2002 Holcombe Boulevard, Houston, TX 77030, United States

Received  June 2010 Revised  September 2010 Published  June 2011

Left Ventricular Assist Devices (LVADs) are implantable mechanical pumps that temporarily aid the function of the left ventricle. The use of LVADs has been associated with thrombus formation next to the aortic valve and close to the anastomosis region, especially in patients in which the native cardiac function is negligible and the aortic valve remains closed. Stagnation points and recirculation zones have been implicated as the main fluid dynamics factors contributing to thrombus formation. The purpose of the present study was to develop and use computer simulations based on a fluid-structure interaction (FSI) solver to study flow conditions corresponding to different strategies in LVAD ascending aortic anastomosis providing a scenario with the lowest likelihood of thrombus formation. A novel FSI algorithm was developed to deal with the presence of multiple structures corresponding to different elastic properties of the native aorta and of the LVAD cannula. A sensitivity analysis of different variables was performed to assess their impact of flow conditions potentially leading to thrombus formation. It was found that the location of the anastomosis closest to the aortic valve (within 4 cm away from the valve) and at the angle of 30$^\circ$ minimizes the likelihood of thrombus formation. Furthermore, it was shown that the rigidity of the dacron anastomosis cannula plays almost no role in generating pathological conditions downstream from the anastomosis. Additionally, the flow analysis presented in this manuscript indicates that compliance of the cardiovascular tissue acts as a natural inhibitor of pathological flow conditions conducive to thrombus formation and should not be neglected in computer simulations.
Citation: Annalisa Quaini, Sunčica Čanić, David Paniagua. Numerical characterization of hemodynamics conditions near aortic valve after implantation of left ventricular assist device. Mathematical Biosciences & Engineering, 2011, 8 (3) : 785-806. doi: 10.3934/mbe.2011.8.785
References:

show all references

References:
 [1] Qiang Du, M. D. Gunzburger, L. S. Hou, J. Lee. Analysis of a linear fluid-structure interaction problem. Discrete & Continuous Dynamical Systems - A, 2003, 9 (3) : 633-650. doi: 10.3934/dcds.2003.9.633 [2] Grégoire Allaire, Alessandro Ferriero. Homogenization and long time asymptotic of a fluid-structure interaction problem. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 199-220. doi: 10.3934/dcdsb.2008.9.199 [3] Serge Nicaise, Cristina Pignotti. Asymptotic analysis of a simple model of fluid-structure interaction. Networks & Heterogeneous Media, 2008, 3 (4) : 787-813. doi: 10.3934/nhm.2008.3.787 [4] Igor Kukavica, Amjad Tuffaha. Solutions to a fluid-structure interaction free boundary problem. Discrete & Continuous Dynamical Systems - A, 2012, 32 (4) : 1355-1389. doi: 10.3934/dcds.2012.32.1355 [5] George Avalos, Roberto Triggiani. Fluid-structure interaction with and without internal dissipation of the structure: A contrast study in stability. Evolution Equations & Control Theory, 2013, 2 (4) : 563-598. doi: 10.3934/eect.2013.2.563 [6] Oualid Kafi, Nader El Khatib, Jorge Tiago, Adélia Sequeira. Numerical simulations of a 3D fluid-structure interaction model for blood flow in an atherosclerotic artery. Mathematical Biosciences & Engineering, 2017, 14 (1) : 179-193. doi: 10.3934/mbe.2017012 [7] Andro Mikelić, Giovanna Guidoboni, Sunčica Čanić. Fluid-structure interaction in a pre-stressed tube with thick elastic walls I: the stationary Stokes problem. Networks & Heterogeneous Media, 2007, 2 (3) : 397-423. doi: 10.3934/nhm.2007.2.397 [8] George Avalos, Roberto Triggiani. Uniform stabilization of a coupled PDE system arising in fluid-structure interaction with boundary dissipation at the interface. Discrete & Continuous Dynamical Systems - A, 2008, 22 (4) : 817-833. doi: 10.3934/dcds.2008.22.817 [9] Salim Meddahi, David Mora. Nonconforming mixed finite element approximation of a fluid-structure interaction spectral problem. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 269-287. doi: 10.3934/dcdss.2016.9.269 [10] Martina Bukač, Sunčica Čanić. Longitudinal displacement in viscoelastic arteries: A novel fluid-structure interaction computational model, and experimental validation. Mathematical Biosciences & Engineering, 2013, 10 (2) : 295-318. doi: 10.3934/mbe.2013.10.295 [11] Mehdi Badra, Takéo Takahashi. Feedback boundary stabilization of 2d fluid-structure interaction systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (5) : 2315-2373. doi: 10.3934/dcds.2017102 [12] George Avalos, Thomas J. Clark. A mixed variational formulation for the wellposedness and numerical approximation of a PDE model arising in a 3-D fluid-structure interaction. Evolution Equations & Control Theory, 2014, 3 (4) : 557-578. doi: 10.3934/eect.2014.3.557 [13] Henry Jacobs, Joris Vankerschaver. Fluid-structure interaction in the Lagrange-Poincaré formalism: The Navier-Stokes and inviscid regimes. Journal of Geometric Mechanics, 2014, 6 (1) : 39-66. doi: 10.3934/jgm.2014.6.39 [14] George Avalos, Roberto Triggiani. Semigroup well-posedness in the energy space of a parabolic-hyperbolic coupled Stokes-Lamé PDE system of fluid-structure interaction. Discrete & Continuous Dynamical Systems - S, 2009, 2 (3) : 417-447. doi: 10.3934/dcdss.2009.2.417 [15] Eugenio Aulisa, Akif Ibragimov, Emine Yasemen Kaya-Cekin. Fluid structure interaction problem with changing thickness beam and slightly compressible fluid. Discrete & Continuous Dynamical Systems - S, 2014, 7 (6) : 1133-1148. doi: 10.3934/dcdss.2014.7.1133 [16] Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424 [17] Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. FLUID STRUCTURE INTERACTION PROBLEM WITH CHANGING THICKNESS NON-LINEAR BEAM Fluid structure interaction problem with changing thickness non-linear beam. Conference Publications, 2011, 2011 (Special) : 813-823. doi: 10.3934/proc.2011.2011.813 [18] Daniele Boffi, Lucia Gastaldi. Discrete models for fluid-structure interactions: The finite element Immersed Boundary Method. Discrete & Continuous Dynamical Systems - S, 2016, 9 (1) : 89-107. doi: 10.3934/dcdss.2016.9.89 [19] Philipp Fuchs, Ansgar Jüngel, Max von Renesse. On the Lagrangian structure of quantum fluid models. Discrete & Continuous Dynamical Systems - A, 2014, 34 (4) : 1375-1396. doi: 10.3934/dcds.2014.34.1375 [20] Robert H. Dillon, Jingxuan Zhuo. Using the immersed boundary method to model complex fluids-structure interaction in sperm motility. Discrete & Continuous Dynamical Systems - B, 2011, 15 (2) : 343-355. doi: 10.3934/dcdsb.2011.15.343

2018 Impact Factor: 1.313