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Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents
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 
References:
[1] 
F. Autieri, N. Parolini and L. Quartapelle, Numerical investigation on the stability of singular driven cavity flow,, J. Comput Phys, 183 (2002), 1. doi: 10.1006/jcph.2002.7145. 
[2] 
S. Badia, A. Quaini and A. Quarteroni, Modular vs. nonmodular preconditioners for fluidstructure systems with large addedmass effect,, Comput. Methods Appl. Mech. Engrg., 197 (2008), 4216. doi: 10.1016/j.cma.2008.04.018. 
[3] 
S. Badia, A. Quaini and A. Quarteroni, Splitting methods based on algebraic factorization for fluidstructure interaction,, SIAM J. Sci. Comput., 30 (2008), 1778. doi: 10.1137/070680497. 
[4] 
S. Badia, A. Quaini and A. Quarteroni, Coupling Biot and NavierStokes equations for modelling fluidporoelstic media interaction,, J. Comput. Phys., 228 (2009), 7986. doi: 10.1016/j.jcp.2009.07.019. 
[5] 
M. Behr, D. Arora, Y. Nosé and T. Motomura, Performance analysis of ventricular assist devices using finite element flow simulation,, Int. J. Numer. Meth. Fluids, 46 (2004), 1201. doi: 10.1002/fld.796. 
[6] 
F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods,", Springer Series in Computational Mathematics, 15 (1991). 
[7] 
J. Coats, "A Manual Of Pathology,", Longmans, (1999). 
[8] 
R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales,, Comput. Methods Appl. Mech. Engrg., 191 (2002), 4295. doi: 10.1016/S00457825(02)003377. 
[9] 
A. Cordero, S. Castaño and G. Rábago, Prosthetic aortic valve thrombosis after Left Ventricular Assist Device implantation,, Rev. Esp. Cardiol., 58 (2005). 
[10] 
J. A. Crestanelloa, D. A. Orsinellib, M. S. Firstenberga and C. SaiSudhakar, Aortic valve thrombosis after implantation of temporary Left Ventricular Assist Device,, Interactive Cardiovascular and Thoracic Surgery, 8 (2009), 661. doi: 10.1510/icvts.2009.202242. 
[11] 
L. Formaggia and F. Nobile, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements,, EastWest J. Num. Math., 7 (1999), 105. 
[12] 
K. Fraser, T. Zhang, M. Ertan Taskin, B. P. Griffith, Z. J. Wu, F. Alamanni, E. G. Caiani and A. Redaelli, Computational fluid dynamics analysis of thrombosis potential in Left Ventricular Assist Device drainage cannulae,, ASAIO J., (2010). doi: 10.1097/MAT.0b013e3181d861f1. 
[13] 
M. A. Gimbrone, Endothelial disfunction, hemodynamic forces, and atherosclerosis (pubmed abstract),, Thrombos Haemost, 82 (1999), 722. 
[14] 
B. Ker, R. M. Delgado III, O. H. Frazier, I. D. Gregoric, M. T. Harting, Y. Wadia, T. J. Myers, R. D. Moser and J. Freund, The effect of LVAD aortic outflowgraft placement on hemodynamics and flow: Implantation technique and computer flow modeling,, Texas Heart Institute Journal, 32 (2005), 294. 
[15] 
K. D. MayNewman, B. K. Hillen, C. S. Sironda and W. Dembitsky, Effect of LVAD outflow conduit insertion angle on flow through the native aorta,, J. of Medical Engineering and Technology, 28 (2004), 105. doi: 10.1080/0309190042000193865. 
[16] 
A. L. Meyer, C. K. Kuehn, J. W. Weidemann, D. Malehsa, C. Bara, S. Fischer, A. Haverich and M. Strüber, Thrombus formation in a HeartMate II Left Ventricular Assist Device,, Thoracic and Cardiovascular Surgery, 135 (2000), 203. 
[17] 
F. Nobile, "Numerical Approximation of FluidStructure Interaction Problems with Application to Haemodynamics,", Ph.D thesis, (2001). 
[18] 
A. Quaini, S. Canic, R. Glowinski, S. Little and W. Zoghbi, The influence of the Coanda effect on the assessment of mitral valve regurgitation: A numerical investigation,, in preparation, (2010). 
[19] 
A. Quarteroni and A. Valli, "Numerical Approximation of Partial Differential Equations,", Springer Series in Computational Mathematics, 23 (1994). 
[20] 
A. G. Rose, J. H. Connelly, S. J. Park, O. H. Frazier, L. W. Miller and S. Ormaza, Total left ventricular outflow tract obstruction due to Left Ventricular Assist Device induced subaortic thrombosis in 2 patients with aortic valve bioprosthesis,, Journal of Heart and Lung Transplantation, 22 (2003), 594. doi: 10.1016/S10532498(02)011804. 
[21] 
Y. Saad, "Iterative Methods for Sparse Linear Systems,", 2^{nd} edition, (2003). 
[22] 
D. Seiffge, Thrombotic reactions of vascular anastomoses: Comparison of model studies with experimental findings,, Vasa Suppl., 32 (1991), 54. 
[23] 
N. G. Smedira, Invited commentary: Valve disease and LVAD,, Annals of Thoracic Surgery, 71 (2001). doi: 10.1016/S00034975(01)025772. 
show all references
References:
[1] 
F. Autieri, N. Parolini and L. Quartapelle, Numerical investigation on the stability of singular driven cavity flow,, J. Comput Phys, 183 (2002), 1. doi: 10.1006/jcph.2002.7145. 
[2] 
S. Badia, A. Quaini and A. Quarteroni, Modular vs. nonmodular preconditioners for fluidstructure systems with large addedmass effect,, Comput. Methods Appl. Mech. Engrg., 197 (2008), 4216. doi: 10.1016/j.cma.2008.04.018. 
[3] 
S. Badia, A. Quaini and A. Quarteroni, Splitting methods based on algebraic factorization for fluidstructure interaction,, SIAM J. Sci. Comput., 30 (2008), 1778. doi: 10.1137/070680497. 
[4] 
S. Badia, A. Quaini and A. Quarteroni, Coupling Biot and NavierStokes equations for modelling fluidporoelstic media interaction,, J. Comput. Phys., 228 (2009), 7986. doi: 10.1016/j.jcp.2009.07.019. 
[5] 
M. Behr, D. Arora, Y. Nosé and T. Motomura, Performance analysis of ventricular assist devices using finite element flow simulation,, Int. J. Numer. Meth. Fluids, 46 (2004), 1201. doi: 10.1002/fld.796. 
[6] 
F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods,", Springer Series in Computational Mathematics, 15 (1991). 
[7] 
J. Coats, "A Manual Of Pathology,", Longmans, (1999). 
[8] 
R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales,, Comput. Methods Appl. Mech. Engrg., 191 (2002), 4295. doi: 10.1016/S00457825(02)003377. 
[9] 
A. Cordero, S. Castaño and G. Rábago, Prosthetic aortic valve thrombosis after Left Ventricular Assist Device implantation,, Rev. Esp. Cardiol., 58 (2005). 
[10] 
J. A. Crestanelloa, D. A. Orsinellib, M. S. Firstenberga and C. SaiSudhakar, Aortic valve thrombosis after implantation of temporary Left Ventricular Assist Device,, Interactive Cardiovascular and Thoracic Surgery, 8 (2009), 661. doi: 10.1510/icvts.2009.202242. 
[11] 
L. Formaggia and F. Nobile, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements,, EastWest J. Num. Math., 7 (1999), 105. 
[12] 
K. Fraser, T. Zhang, M. Ertan Taskin, B. P. Griffith, Z. J. Wu, F. Alamanni, E. G. Caiani and A. Redaelli, Computational fluid dynamics analysis of thrombosis potential in Left Ventricular Assist Device drainage cannulae,, ASAIO J., (2010). doi: 10.1097/MAT.0b013e3181d861f1. 
[13] 
M. A. Gimbrone, Endothelial disfunction, hemodynamic forces, and atherosclerosis (pubmed abstract),, Thrombos Haemost, 82 (1999), 722. 
[14] 
B. Ker, R. M. Delgado III, O. H. Frazier, I. D. Gregoric, M. T. Harting, Y. Wadia, T. J. Myers, R. D. Moser and J. Freund, The effect of LVAD aortic outflowgraft placement on hemodynamics and flow: Implantation technique and computer flow modeling,, Texas Heart Institute Journal, 32 (2005), 294. 
[15] 
K. D. MayNewman, B. K. Hillen, C. S. Sironda and W. Dembitsky, Effect of LVAD outflow conduit insertion angle on flow through the native aorta,, J. of Medical Engineering and Technology, 28 (2004), 105. doi: 10.1080/0309190042000193865. 
[16] 
A. L. Meyer, C. K. Kuehn, J. W. Weidemann, D. Malehsa, C. Bara, S. Fischer, A. Haverich and M. Strüber, Thrombus formation in a HeartMate II Left Ventricular Assist Device,, Thoracic and Cardiovascular Surgery, 135 (2000), 203. 
[17] 
F. Nobile, "Numerical Approximation of FluidStructure Interaction Problems with Application to Haemodynamics,", Ph.D thesis, (2001). 
[18] 
A. Quaini, S. Canic, R. Glowinski, S. Little and W. Zoghbi, The influence of the Coanda effect on the assessment of mitral valve regurgitation: A numerical investigation,, in preparation, (2010). 
[19] 
A. Quarteroni and A. Valli, "Numerical Approximation of Partial Differential Equations,", Springer Series in Computational Mathematics, 23 (1994). 
[20] 
A. G. Rose, J. H. Connelly, S. J. Park, O. H. Frazier, L. W. Miller and S. Ormaza, Total left ventricular outflow tract obstruction due to Left Ventricular Assist Device induced subaortic thrombosis in 2 patients with aortic valve bioprosthesis,, Journal of Heart and Lung Transplantation, 22 (2003), 594. doi: 10.1016/S10532498(02)011804. 
[21] 
Y. Saad, "Iterative Methods for Sparse Linear Systems,", 2^{nd} edition, (2003). 
[22] 
D. Seiffge, Thrombotic reactions of vascular anastomoses: Comparison of model studies with experimental findings,, Vasa Suppl., 32 (1991), 54. 
[23] 
N. G. Smedira, Invited commentary: Valve disease and LVAD,, Annals of Thoracic Surgery, 71 (2001). doi: 10.1016/S00034975(01)025772. 
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